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U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

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Physical Properties Data

for Rock Salt
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Physical Properties Data for Rocit Salt

National Bureau of Slanjaids

Library, E-Ol Admin. BIdg.

MAR X 6 1981

L. H. Gevantman, Editor

National Bureau of Standards

Washington, D.C. 20234

no.

J. Lorenz, J. L. Haas, Jr., M. A. Clynne, R. W. Potter, II, and C. M. Schafer

National Center for the Thermodynamic Data of Minerals

U.S. Department of the Interior, Geological Survey

Reston, Virginia 22092

J. L. Haas, Jr., Director

R. P. T. Tomkins

New Jersey Institute of Technology

Newark, New Jersey 07102

in association with

Molten Salts Data Center

Rensselaer Polytechnic Institute

Troy, New York 12181

G. J. Janz, Director

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Luther H. Hodges, Jr., Deputy Secretary

Jordan J. Baruch, Assistant Secretary for Productivity, Technology, and Innovation

S. NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

A. Shakoor, H. R. Hume, J. M. Yang, H. H. Li, and R. A. Matula

Center for Information and Numerical Data Analysis and Synthesis

Purdue University

West Lafayette, Indiana 47906

Y. S. Touloukian, Director

Issued January 1981
Library of Congress Cataloging in Publication Data Main entry under title:

Physical properties data for rock salt.

(National Bureau of Standards monograpli; 167)

Supt. of Docs, no.: C 13.44:167

1. Rock-salt—Handbooks, manuals, etc.

2. Radioactive waste disposal in the ground—Handbooks, manuals,

etc. I. Gevantman, L. H. II. Series: United States. National Bureau of Standards

Monograph: 167 QC100.U556 no. 167 [TN900] 602M8s [620.r98]

80-607096

National Bureau of Standards Monograph 167

Nat. Bur. Stand. (U.S.), Mono. 167, 288 pages (Jan. 1981)

CODEN: NBSMA6

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WASHINGTON: 1981

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(Add 25 percent for other than U.S. mailing)
Preface

The Office of Standard Reference Data of the National Bureau of Standards is responsible for a broad-based program

to provide reliable physical and chemical reference data to the U.S. technical community. Under this program a number of data evaluation centers both at NBS and at universities and other private institutions are supported and

coordinated; these activities are collectively known as the National Standard Reference Data System (NSRDS).

Important areas of the physical sciences are covered systematically by NSRDS data centers, and data bases with broad

utility are prepared and disseminated. These centers can also take on special compilations of data addressing specific

applications such as those frequently required by other Federal Agencies in carrying out their mission responsibilities.

The existence of an ongoing program permits the collection of data for these special compilations to be carried out in an efficient and timely manner.

This Monograph on Properties of Rock Salt was prepared by the Office of Standard Reference Data in response to needs of the Department of Energy for reliable data in connection with nuclear waste disposal. The resources and

experience of several NSRDS data centers were enlisted to produce a compilation of the various relevant properties of

rock salt. We hope that the Monograph will be a useful source of reference data and serve as a model for other

compilations of data required by Government agencies and private institutions.

David R. Lide, Jr., Chief

Office of Standard Reference Data

iii
Acknowledgement

I wish to acknowledge the sponsorship and financial support of the Office of Nuclear Waste Isolation and to thank

Dr. G. Raines for his sound advice and support. I also appreciate the individual efforts of Drs. W. C. McClain and J. E. Russell, formerly of that office, for their encouragement and support during the execution of this project. I also wish

to thank the individual authors for their technical contributions and Drs. Y. S. Touloukian, G. J. Janz, and J. L. Haas,

Jr., for their aid and cooperation in making available the facilities of their individual data centers to the authors. The

efforts of Dr. D. Isherwood and her colleagues who served as technical reviewers are gratefully acknowledged. Finally,

I deeply appreciate the assistance of Mrs. M. E. Schlager, of the Office of Standard Reference Data, who helped me

with all of the many tasks leading to the publication of this Monograph.

L. H. Gevantman

IV
Contents

Page

Preface iii D. R. Lide, Jr., Office of Standard Reference Data, National Bureau of Standards,

Washington, DC 20234

Acknowledgement iv

Introduction 1

L. H. Gevantman, Office of Standard Reference Data, National Bureau of Standards,

Washington, DC 20234

Chapter 1. Geology, Mineralogy, and Some Geophysical and Geochemical Properties of Salt Deposits ... 3

J. L. Haas, Jr., J. Lorenz, M. A. Clynne, R. W. Potter, II, and C. M. Schafer.

United States Department of the Interior Geological Survey, Reston, VA 22092

General Introduction 4

Bedded Deposits 4

Salt Domes 11

Mineralogy and Petrology 14

Fluid Inclusions 22

Porosity and Permeability 29

Pore Fluids 32

References 40

Symbols and Units 43

Conversion Factors 43

Chapter 2. Physical and Chemical Properties of Components in Salt Deposits 45

R. P. T. Tomkins. New Jersey Institute of Technology, Newark, NJ 07102

Introduction 46

Experimental Techniques : 46

Physical Properties: Halite 49

Physical Properties of Major Impurities in Halite 51

Anhydrite 51

Gypsum 56

Calcite 57

Polyhalite 60

Clays 60

Chemical Properties Among Components in Salt Deposits 66

References 100

Symbols and Units 101

Conversion Factors 101

Chapter 3. Mechanical Properties 103

A. Shakoor and H. R. Hume. Center for Information and Numerical Data Analysis and

Synthesis, Purdue University, West Lafayette, IN 47906

Introduction 104

Review of Measurement Methods 104

Elastic Properties—Static and Dynamic 107

Strength and Creep 107

Hardness 164

Surface Effects 186

Effect of Nuclear Irradiation on Mechanical Properties of Rock Salt 189

References 203

Symbols and Units 203

Conversion Factors 203

V
Page

Chapter 4. Thermophysical Properties 205

J. M. Yang. Center for Information and Numerical Data Analysis and Synthesis,

Purdue University, West Lafayette, IN 47906

Introduction 206

Review of Measurement Methods for Thermophysical Properties 206

Thermal Conductivity 209

Thermal Diffusivity 211

Thermal Linear Expansion 211

Effect of Nuclear Irradiation on Thermophysical Properties 212

References 217

Symbols and Units 221

Conversion Factors 221

Chapter 5. Optical Properties 223

H. H. Li. Center for Information and Numerical Data Analysis and Synthesis,

Purdue University, West Lafayette, IN 47906

Introduction 224

Measurement Methods for Optical Properties 224

Refractive Index and Absorption Coefficient 226

Effect of Nuclear Irradiation on the Optical Properties 232

References 238

Symbols and Units 240

Conversion Factors 240

Chapter 6. Electrical and Magnetic Properties 241

R. A. Matula. Center for Information and Numerical Data Analysis and Synthesis,

Purdue University, West Lafayette, IN 47906

Introduction 242

Methods of Measuring Electrical and Magnetic Properties 242

Electrical Conductivity 243

Dielectric Constant 254

Dielectric Strength 261

Magnetic Susceptibility 276

Effect of Nuclear Irradiation on Electrical and Magnetic Properties 276

References 278

Symbols and Units 282

Conversion Factors 282

vi
Physical Properties Data for Rock Salt

L. H. Gevantman, Editor

Office of Standard Reference Data, National Bureau of Standards, Washington, D.C. 20234

Rock salt and pure sodium chloride properties data are assembled into a single source. The properties covered include geological, mechanical, optical, thermal, radiation

damage, electrical, magnetic, chemical, and physical. A concerted attempt has been made

to present the best data consistent with their availability in the literature. Recommended

values for data are given where possible. A brief discussion of measurement techniques is included for each property.

Key words: Chemical; electrical; geological; monograph; magnetic; mechanical; optical; physical; properties

data; radiation damage; rock salt; sodium chloride.

Introduction

This effort was begun at the direction of the Office of

Waste Isolation (OWI), Oak Ridge National Laboratory,

Department of Energy,* to answer a pressing need for a

single source of data on rock salt properties. This need

arose from the possibility that rock salt deposits provide an acceptable medium for the permanent storage of high

level radioactive wastes. While a considerable body of

data exists in the literature [references 1, 2, 3, and 4] on

the physical properties of rock salt, it is not readily

available in a single, easily identified source. Nor are the

data in a form that permits designers of waste burial

facilities to extract the variety of numerical values for use with any degree of confidence in these values. As a consequence, the Office of Standard Reference Data

(OSRD ) was asked to undertake a data evaluation proj ect which would produce a data book on rock salt properties.

These data also were to be evaluated, wherever possible,

for reliability consistent with the measurement state-ofthe-art. While the principal reasons for assembling this

Monograph are nuclear-waste-storage inspired, the data

for most of the properties cited would also apply to the

burial of other types of waste where long-term stable

facilities are required. It is intended that the data will serve as a source of generalized information to the salt industry. No attempt is made to argue the advantages or disadvantages for burial of nuclear wastes in rock salt formations. Such discussions are available elsewhere

[references 5, 6, and 7].

*This project was funded in part by the Office of Waste Isolation,

Oak Ridge National Laboratory, Department of Energy.

Now the Office of Nuclear Waste Isolation, Battelle Memorial

Institute, 505 King Avenue, Columbus, Ohio 43201.

History of the Project

In organizing and defining the scope of this project the

Office of Standard Reference Data recognized the need

for two types of input. One was the viewpoints and

criteria for information as represented by the sponsor.

The second was the need for expertise in data assembly

and evaluation, particularly the specific properties of

interest. It was therefore the Office's role to bring these

functions together to implement the project. In the first instance, the OSRD was fortunate in having excellent

representation and advice from the Office of Nuclear

Waste Isolation, which furnished an outline of the

properties desired. After some consultation the OSRD

was able to identify and designate three data centers

the Center for Information and Numerical Data Analysis

and Synthesis (CINDAS), the Molten Salts Data Center,

and the National Center for Thermodynamic Data of

Minerals—to evaluate the data. An ad hoc committee,

consisting of representatives from the Office of Standard

Reference Data, the Office of Nuclear Waste Isolation,

and each of the data center designates, met and reviewed

the outline of the physical properties data to be

contained in the Monograph. After some minor changes,

work assignments based on the final version of the

outline were distributed, and the work got under way.

The OSRD assumed full responsibility for coordinating

the efforts and for assembling and publishing the final

product.

Monograph Organization

The Monograph is in six chapters covering the

geological, mechnical, optical, thermal, radiation damage, electrical, magnetic, chemical, and physical properties of rock salt and pure NaCl. Each chapter has been

written by a different author, or authors, consistent with

1
his field of expertise. Some attempt at uniformity of

presentation has been made not only in the order of

presentation of the data but also in content. In some

instances exchanges of data among data centers have

taken place so that the data given in one chapter also

represent the efforts of other center contributors.

In general, each chapter attempts to present the best

data available on the subject property in both tabular and

graphic form. Wherever possible, recommended values

and error limits are given. If this is not possible because

the data are in disarray or are insufficient for subject

judgment, a full review of the useful data and a rationale

for working with the data are presented. Experimental

methods for data measurement are given in brief form

with precision limits on the measurement capability

where possible. Brief reviews of error analysis are also

included where applicable. In sum, every aspect of the

particular property has been compiled, evaluated, and

recorded when the data are available from the literature.

The lack of a recommended value means the data are

either lacking or too imprecise to permit evaluation.

Nevertheless it is felt that a useful attempt has been made

to present the better data now available in a single source.

As in all publications of this type, errors and omissions

j of one kind or another are bound to occur. Corrections

[ and additions to the data by readers are solicited.

References i

[1] Kaufman, D.W., Ed., "Sodium Chloride, the Properties of Salt and Brine," ACS Monograph Series, Reinhold Publishing

Corporation, New York (1960).

[2] "The Sterling Brine Handbook," International Salt Company,

(1972).

[3] Potter, K. W., II, Babcock, R.S., and Brown, D.L., J. Res., U.S.

Geological Survey, 5, 389, 1977.

[4] Stull, D.R. and Prophet, H., Ed., JANAF Thermochemical

Tables, 2nd Edition, NSRDS-NBS 37, June, 1971.

[5] Bradeholft,J.D., England, A.W., Stewart, D.B.,Trask, N.J. , and

Winograd, I.J., "Geologic Disposal of High Level Radioactive Waste—Earth Science Perspective," U.S. Geological Survey

Circular 779, 1978.

[6] "Subgroup Report on Alternative Technology Strategies for the

Isolation of Nuclear Waste," Interagency Review Group, TID

28818 (Draft), October 1978.

[7] "State of Geological Knowledge Regarding Potential Transport

of High Level Radioactive Waste from Deep Continental Repositories," The Ad-Hoc Panel of Earth Sciences,

EPA/520/4-78-004, June 1978.

2
Chapter 1

Geology, Mineralogy, and Some Geophysical and Geochemical Properties

of Salt Deposits

John Lorenz*, John L. Haas, Jr.*, Michael A. Clynne**, Robert W. Potter, II**, and Constance M. Schafer*

Contents

Page

1.1. General Introduction 4

1.2. Bedded Deposits 4

1.2.1. Introduction 4

1.2.2. Depositional Models 6

1.2.3. The Precipitation Sequence Predicted from Sea Water 6

1.2.4. Cyclic Sedimentation 6

1.2.5. Diagenesis and Metamorphism 7

1.2.5.1. Introduction 7

1.2.5.2. Dynamic metamorphism 8

1.2.5.3. Thermal metamorphism 9

1.2.5.4. Solution metamorphism 9

1.2.6. Regional Rock-Salt Geology 9

1.2.7. The variability within Salt Beds 10

1.3. Salt Domes 11

1.3.1. Introduction 11

1.3.2. Formation 11

1.3.3. Associated Structures 12

1.3.3.1. Internal structures 12

1.3.3.2. External structures 13

1.3.3.3. Caprock 13

1.3.4. Mineralogy 14

1.4. Mineralogy and Petrology 14

1.4.1. Introduction 14

1.4.2. Impurities 14

1.4.3. Grain Size and Orientation 16

1.4.3.1. Bedded deposits 16

1.4.3.2. Salt domes 16

1.4.3.3. Pseudomorphism 22

1.4.4. Density of Rock Salt Deposits 22

1.5 Fluid Inclusions 22

1.5.1. Formation 22

1.5.2. Composition 26

1.5.3. Pressured Gas Inclusions 28

1.5.4. Brine Pockets and Seeps 29

1.6. Porosity and Permeability 29

1.6.1 Porosity 29

1.6.2. Permeability 30

1.6.3. Permeability in LPG Storage Caverns 32

*U.S. Geological Survey, Reston, VA 22092. **Occidental Research Corporation, Irvine, CA 92713.

3
1.7. Pore Fluids 32

1.7.1. Composition 32

1.7.2. Vapor Pressure 32

1.7.3. Density 40

References 40

Symbols and Units 43

Conversion Factors 43

1.1. General Introduction

Rock salt is a coarsely crystalline, sedimentary rock

containing massive, fibrous, or granular aggregates.

Rock salt occurs in extensive beds, or in domes and

plugs. Rock salt is the result of evaporation of saline

water and is a member of a suite of related rocks, the

evaporite series. Rock salt is dominantly halite, but other

minerals are present such as calcite, dolomite, anhydrite,

gypsum, and potash minerals. (Potash is an industrial

term for the complex potassium and magnesium

evaporites. A more complete list of minerals commonly

found in evaporite deposits is given in chapter 2.) These

minerals may be deposited contemporaneously in

adjacent parts of a basin. The mineralogy is dependent on

variations in topography, water depth, salinity, and other

factors. Because these factors can change during

geologically short periods of time, beds of different

evaporite minerals overlie and overlap each other in

sequences reflecting the changes in equilibrium that occur locally during the subsidence and sedimentary

filling of basins.

Given the right conditions, halite can be the dominant

mineral that accumulates. Halite, the chloride of sodium

(NaCl), can form rare, pure beds as much as 80 meters

thick. Once deposited and buried by succeeding layers of

sediments, halite and associated minerals are susceptible

to a variety of changes brought about by the effects of the

elevated temperatures and pressures that are found at depths. Beside actual changes in mineralogy of the

accessory minerals, the most dramatic changes are due to the lowered viscosity of halite and the increased contrast

between its density and that of the surrounding

sediments. Deeply buried salt commonly forms diapirs

(domes or anticlinal folds, the overlying rocks of which

have been bent or ruptured by the squeezing out of the

plastic core) 1-6 kilometers in diameter by flowing

plastically from original bedding horizons up thousands

of meters through the sediments and sometimes to the

surface.

Some of the characteristics of rock salt deposits

change when the rock salt flows into domes. Domes

contain generally purer halite, and rock salts in domes

lose most of their primary sedimentary structures. Fluid

inclusions in domed rock salt are more apt to contain

foreign substances, such as oil. Other characteristics of

rock salt, specifically porosity and permeability, do not

necessarily change on intrusion. Both porosity and

permeability are minimal in bedded and diapiric rock salt deposits. Salt domes are discussed morelRriry in section

1.3 below.

Thick halite and associated evaporite deposits are found in four large sedimentary basins in the United

States (figure 1.1). Several smaller deposits exist, and

the major deposits themselves can be subdivided by age

and stratigraphy. Primary sedimentary thickness of the

deposits ranges from some 1300 to 1400 m in the Ochoan

evaporite sequence of Permian age (see Appendix 1.1 for

geologic time scale) [1] in the Delaware basin of Texas

and New Mexico [2] to surficial veneers now being

deposited in the playa lakes of the western States. Diapiric rock salt is found only in the Gulf Coast area, though secondary thickening at the crests of anticlines

has been described in the Paradox basin in Utah.

1.2. Bedded Deposits

1.2.1. Introducti^

Ionic ratios suggest that most salt deposits were

originally derived from evaporated sea water. Average

sea water contains 38,450 ppm (parts per million)

dissolved solids, of which about three quarters will

precipitate as halite on evaporation. The evaporation

rate of water is a function of the temperature of both the

air and the water and of such things as the turbulence of

the water surface. The rate of evaporation decreases as

salinity of the remaining brine increases. In addition,

Kinsman [3] has indicated that, for the precipitation of

halite, the relative humidity must be less than 76 percent

and, for the potash minerals, less than 67 percent. Most

ancient evaporite deposits are formed in warm and arid

climates. Another common feature of rock salt deposits

is that they contain very little silt, sand, or other coarse, granular sediment; apparently only small amounts of

these sediments were supplied to the basin during the

evaporation of the brine. Such impurities as are found

4
5
are usually clay sized and are rarely larger than silt. The

rate of supply of the fine-grained debris relative to the

rate of accumulation of the chemical precipitates is also

low for the beds of rock salt.

1.2.2. Depositional Models

Probably the most widely accepted ttieory to explain

formations of bedded rock salt has been the "bar theory"

originally proposed by Ochsenius [4] . This model in its simplest form hypothesizes an arm of the sea in which

circulation is restricted (by a bar, ridge, or reef across the

mouth) ; water in the arm is concurrently evaporated and

replenished, and its dissolved salt is precipitated into

basin-wide beds (figure 1.2). A large number of observed

primary sedimentary structures in evaporites may be

explained by this model: clay-filled desiccation cracks,

ripple marks, and crossbedding in halite [5] ; the

presence of preferentially oriented hopper crystals [6]

;

dissolution horizons, unconformities, and halite con- glomerates [7] ; and cyclic deposition.

A variation on this model that has gained many

adherents is Scruton's hypothesis [8] of constant water

volume in a basin and reflux of final-stage brines to the

sea (figure 1.3). This theory, which may have a modern

analog in the Gulf of Kara Bogaz off the Caspian Sea,

involves a subsea-level restriction that allows partial

circulation in and out of the basin. The sea adds water

over the restriction as it is evaporated from the basin.

This restricted addition of sea water creates a salinity

gradient; the water in the basin becomes progressively

concentrated away from the sea and precipitates its various components in a lateral continuum of minerals.

The final-stage brines either precipitate their contents

at the far end of the basin or are cycled back out of the

basin along the sea floor. This theory accounts for the

large-scale lateral facies variations seen in many

evaporite deposits.

Other theories have been formulated in attempts to explain characteristics of one or more salt deposits

[9,10] . A model of separate basins attempted to account

for some observed monomineralic accumulations of

limestone, gypsum, and halite. Various theories about

nonmarine or semimarine desert basins attempted to explain the lack of fossils in some salt deposits; at the

other extreme, theories of subaqueous deposition from

dense, deep-sea brines [11,12] were suggested to explain

the apparent correlations between unfossiliferous

deposits and their topographically low setting. The

uniform and laterally extensive character of some

bedding in salt deposits might also be explained by

variations of these models of subaqueous deposition.

The most recently proposed theory is based on the

discovery of salt deposits flooring the Mediterranean

Sea. Labeled "the theory of desiccating deep basins" by

Hsu [9] , it involves episodic cutoff and desiccation of

large bodies of water such as the Mediterranean Sea or the Gulf of Mexico and evaporite deposition in the

remnant salt lakes. Kirkland and Evans [13] assembled a

collection of papers dealing with the origin of marine

evaporites.

1.2.3. The Precipitation Sequence Predicted from

Sea Water

Usiglio [14] in 1849 studied the precipitation se- quence from evaporating sea water experimentally. His

and other experimentally determined proportions of

minerals from a fixed volume of sea water do not

correspond well with those found in typical rock salt deposits (figure 1.4 and table 1.1), but several theories

account for the discrepancies. If Scruton's reflux model

is accepted, then the sea water need not be evaporated

completely and the components of certain minerals may

be retained in solution even though the preceding

mineral in the series is extensively precipitated. The

more soluble a mineral is, the less likely it is to be

precipitated and preserved. The abundance of an

individual evaporite mineral in the entire sedimentary

rock record is inversely proportional to its solubility.

Another reason for the difference between observed

sequences and the ideal sequence described by Borchert

and Muir [15] is that the ideal sequence was precipitated

at a constant temperature.

A discrepancy present in actual deposits that have

reached the potash phase of deposition is the deficiency

of sulfate minerals with respect to the ideal sequence.

This deficiency is most often said to result from the

destruction of sulfate minerals by sulfate-reducing

anaerobic bacteria that derive their oxygen from the

SO^^- ion [16].

The mineral bischofite, which composes a sizeable part

of the ideal precipitation sequence, is rarely found in the

geologic record. The end brines containing this mineral

are hydroscopic; that is, they are stable, resist evaporation, and usually find their way back to the sea.

1.2.4. Cyclic Sedimentation

Jones [17] described bedded-sediment cycles in the

Salado Formation of New Mexico that approximate

Usiglio's predicted sequence [14]. The cycles are represented by beds 0.7 to 10 m thick; basal "clastic

stratum" (green, brown clays) grades up into a "sulfate"

(usually anhydrite) then to a "halite," and finally to a mixed "halite-clastic stratum." Similar cycles described

6
Evaporation

Coast Ope nMarine

Figure 1.2. Ochsenius' bar theory [4] of rock-salt deposition as illustrated by Hsu [142].

To Shore To Open Sea

Evaporation

t t t M t t M t t t t t t

Figure 1.3. Scruton's reflux hypothesis [l43] —restricted marine basin showing stratigraphic sequence

precipitated during lateral increase of brine salinity. Final stage brines may precipitate their contents at the shore end of the basin or may flow back to the sea along the basin floor. Modified

from [143].

for the Hutchinson Salt Member of the WelHngton

Formation in Kansas [18] contain very thin carbonate

beds above the basal shales. The basal clays in such

cycles are often interpreted as resulting from solution

lags caused by new influxes of fresh water that redissolve some of the clay-rich rock salt and set the precipitation

sequence back to the anhydrite/gypsum phase.

Cyclic layering is common in Gulf Coast salt domes,

where 2.4 to 25 cm-thick layers of anhydritic halite

alternate with layers of pure halite, but these layers are not necessarily of depositional origin. The Castile

Formation of southeast New Mexico also contains cyclic

banding of calcite rich in organic matter alternating with

pure anhydrite layers on a very small scale. These layers can be correlated for many kilometers across the

Delaware basin [19] and may represent seasonal variations in climate during the Permian age.

1.2.5. Diagenesis and Metamorphistn

1.2.5.1. Introduction

In this book, no distinction is made between

"diagenesis" and "metamorphism." The Glossary of

Geology [20, p. 192, 446] defines the terms as follows:

"diagenesis [sedimentary] All the chemical, physical, and biologic changes, modifications, or transformations undergone by a sediment after its initial deposition

(i.e., after it has reached its final resting place in the

current cycle of erosion, transportation, and deposition), and during and after its lithification, exclusive of

surficial alteration (weathering) and metamorphism.***"

" metamorphism The mineralogical and structural

adjustment of solid rocks to physical and chemical

conditions which have been imposed at depth below the

7
Sea Water German Zechstein Other Oceonic Salt Deposits

Figure 1.4. Proportions of minerals experimentally precipitated from sea water compared with those found in natural rock-salt deposits. Modified from [144).

Table 1.1

Minerals that Precipitate from Increasing Brine

Concentrations at Constant Temperature.

Modified from [123]

Dominant mineral

precipitating

at concentration

Limestone/ do lomite

Gypsum

Halite

Mg and K salts (potash

minerals)

Bischof ite

Brine concentration

(multiples of

sea-water

concentration)

1-4

4-12

12-64

64-120

120-240

surface zones of weathering and cementation, and which

differ from the conditions under which the rocks in

question originated***."

In an evaporite deposit, the distinction between

diagenesis and metamorphism would be arbitrary at best

because the contained minerals are responsive to small

changes in temperature and pressure above the ambient

conditions for deposition. Some changes that are considered metamorphic take place before others that are considered diagenetic.

The minerals most susceptible to change are those

precipitated from the most concentrated brines. Gypsum

is the dihydrate of calcium sulfate that usually forms as a primary precipitate, but anhydrite, its dewatered

equivalent, is the mineral most common in the rock

record. Minerals of the potash phase are rarely found in

their primary states. Some potash minerals do not form

except after burial. Evidences for changes in evaporite

deposits are the presence of minerals that do not form at normal surface temperature, abrupt lateral mineralogy

changes, and irregular trace-element profiles (especially

the profile for bromine). Braitsch [21] listed three types

of change—dynamic, thermal, and solution—and classified them as metamorphic processes.

1.2.5.2. Dynamic Metamorphism

Dynamic metamorphism is the simplest type of

metamorphism and the one that most readily affects the

mineral halite. Braitsch [21] described it as the

mechanical plastic deformation of salts under low stress and the associated isochemical and isophase recrystallization. Kupfer [22] indicated that the segregation of

anhydrite from halite in salt domes probably took place

during this type of deformation. Effects of dynamic

metamorphism include (1) textures characterized by

large, uniformly oriented crystals and (2) the folding of

original bedding. It is caused by overburden pressures

and tectonic stresses that produce movement of the rock

salt.

8
1.2.5.3. Thermal Metamorphism (Including Load

Metamorphism)

As sediments subside with a basin, they are subjected

to the elevated temperatures and pressures associated

with the temperature gradient of the earth's crust and

the increased pressure of the overlying sediments. These

temperatures and pressures dewater the loosely hydrated

minerals in the early stages of burial. Dehydration of

most evaporite minerals is easily accomplished and

usually takes place at temperatures below 100° C [23].

The most important of these reactions isCaS04 • 2H2O = CaS04 + 2H2O, which occurs at depths of 100-175 m

[24] . Carnallite (KCl • MgClz • 6H2O) is often dewatered to produce sylvite KCl and a MgCl2 brine. The

brine liberated from these reactions is important in so- lution metamorphism as described below.

Thermal metamorphism also causes extensive recrystallization in monomineralic beds, specifically halite

beds, though the resulting textures are not oriented as in

dynamic recrystallization. In beds containing more than one primary mineral, the ionic components of minerals

are mobile and new minerals are often formed at the

expense of primary ones. This complex process is described by Braitsch [21].

1.2.5.4. Solution Metamorphism

The dehydration of a cubic meter of gypsum produces

slightly less than V2 cubic meter of water. During

dehydration, a 10 m-thick bed of gypsum will decrease

in thickness to a 6.2 m-thick bed of anhydrite [25].

Because gypsum is one of the first minerals to precipitate

in the evaporation of sea water, most evaporite deposits

include a thick basal anhydrite sequence that provided

brines for solution metamorphism during the formation

of the anhydrite. In certain other deposits, brines may

have originated as magmatic or artesian ground waters

[26].

The brines created by these processes flow through

"tectonically created permeability" [27], dissolving the more soluble minerals and depositing less soluble

minerals from solution. (Some of the mobility of the

fluid may be due to this differential solubility of the host

rock rather than to its actual permeability.) Dissolution

and redeposition of the components available in the rock

result in a continuously changing composition in the

brines; the changes are directed towards the same end

composition as that of end brines in an evaporation

sequence [28].

The complex changes in mineralogy due to solution

metamorphism are most important in potash deposits,

where the secondary minerals are often more abundant

than the primary precipitates. Variations in metamorphic mineralogy are due to changes in temperature and

composition of the intruding fluids and intruded rocks.

Brines can cause temporary cavities, brecciation, and

collapse structures, as well as mineral changes. However,

the brines quickly become saturated with respect to

halite and anhydrite, and "further migration . . . can

usually produce no further effects within a pure rock salt deposit" [29].

1.2.6. Regional Rock Salt Geology

Summary discussions 01 me rock sah deposits in the

United States are given by Pierce and Rich [2] and by

Johnson and Gonzales [30] . The reader is referred there

for both further information and bibliographies on the

stratigraphy of individual deposits. The variability of salt deposits is exemplified by the differences in the data

supplied by Pierce and Rich for many of the basins;

presumably the data are derived from different authors

or different parts of a basin. However, much of the

variability may be real. Variability in salt depositis can be

a response to the shape of the basin, the topography

within the basin, the rate of subsidence of the various

parts of the basin, the location of freshwater or unsaturated marine water input, and the different rates of evaporation within the basin. Because rock salt has

been significantly changed by various chemical and

physical stresses after burial, studies of modern surficial

evaporite deposits are not as applicable to an understanding of rock salt as studies of subsurface deposits that only can be obtained in situ from well logs and mines. We

often only have a limited and localized knowledge of

subsurface deposits.

Rock salt deposits range greatly in size. The most

widespread deposits in the United States, excluding the

probable extension of the Louann Salt of Jurassic age

under the Gulf of Mexico, are the Permian evaporite

sequences of Texas, New Mexico, Colorado, Oklahoma,

and Kansas. Table 1.2 shows the correlation between

geologic ages and time before the present. These deposits

(figure 1.1) cover an area about 1000 km long, north to south, and about 240 to 320 km wide. They are subdivided by age and stratigraphy into at least five local

basins [31]. In New Mexico and Texas, the salt-bearing

Castile and Salado Formations, approximately 600 and

70 meters thick, respectively, are Late Permian in age

and are found in the Delaware basin. The Salado

Formation extends into the Midland basin. The

approximately 250 m-thick Wellington Formation, best

known in the Wellington basin of Kansas, is of early

Permian age. These salt deposits are part of the same

general depositional and tectonic province, called the

Permian basin, but are loosely related products of

9
Table 1 .2

GEOLOGIC TIME SCALE

Modified Subdivision in Use by the U.S. Geological Survey [1

,

p. 150J

Era or System or Age Estimates Commonly Used for

E rathem Period Boundaries (millions of years)

Quaternary

Cenozoi c 1.8 Tert i a ry

- - - - - 65

Cretaceous

136

M e s 0 z 0 i c Jurassic

190-195

T r 1 a s s 1 c 225

P erm i a n 280

Pennsylvanian

320

M i s s i s s i p p i a n 345

Paleozoic Devonian

395

Silurian

430-440

0 rdov i c 1 a n 500

Cambrian

- - - - - 570

P roterozoi c 2,500

A rc hea n

different localities in it and thin or wedge out between

subdivisions of the basin.

The Silurian salt-bearing Salina Formation of Michigan, northern Ohio, Ontario, New York, Pennsylvania,

and West Virginia covers a maximum linear distance of

880 km. The formation is a thin (0-100 m) blanket across most of Ohio, Pennsylvania, and West Virginia but

thickens to 300 m in parts of New York and to 600 m in

Michigan where the subsidence of the Appalachian and

Michigan basins allowed thicker accumulations.

The Williston basin in North Dakota, Montana, and

Saskatchewan is unique in that it had four episodes of

rock-salt accumulation in the same geographic location

(during Devonian, Mississippian, Permian, andTriassic

time) . In an area about 500 km long and 500 km wide, the

salt-bearing formations range from 30 to 50 m in

thickness, though they are buried deeply and are poorly

known.

The Louann Salt and the associated formations of the

United States Gulf Coast are also poorly known. Most oil- well drilling is terminated when the salt beds are reached

so that estimates of thickness are highly speculative,

ranging from 170 to 1700 m. The Louann Salt extends

well into the Gulf of Mexico to the Sigsbee knolls, which

are considered to be salt domes. Thus, it has great areal

extent, despite an area in central Louisiana that may be

salt free.

1.2.7. The Variability within Salt Beds

The percentage of a given formation that is bedded

rock salt ranges from 0 to 100 percent, though most

deposits shown in figure 1.1 are less than 50 percent

other minerals. The distribution of other minerals within

a formation is irregular, reflecting depositional changes,

subsequent metamorphism, and ground-water leaching.

The thickest individual monomineralic halite beds

that might exist in a formation cannot be identified from

the literature. Deciding the thickness and number of clay or anhydrite partings that must be in a rock salt bed

before it is no longer considered to be halite is a subjecttive process. Pierce and Rich [32] stated:

10
The normal bedded rock salt deposit is composed of a number of separate beds that have slight to large

variations in composition. A forty-foot vertical section,

selected at random in a salt sequence, might consist of:

Feet Inches

Salt 9 0

Anhydrite 2

O 1 . Salt 7 O

Shale 2

Salt 6

Shale 2 0

Salt 12 0

Shale and anhydrite 8

Salt _8 0

Total 40 0

Some authors would tend to call the above section a pure halite bed if the 2 foot (0.6 m) shale break were

thinner. Impurities m bedded rock salt may also be

present as finely disseminated intracrystalline particles

and blebs, especially of clay or anhydrite.

Gleaned from Pierce and Rich [2] , the following are estimates of the maximum thicknesses of "pure"

individual halite beds in some formations.

Thickness,

Formation in meters

Salina (Michigan) 80

Salina (Ohio) 20

Salina (Pennsylvania) 70

Lucas (Michigan) 30

Castile (New Mexico) 210

Salado (New Mexico) 20

Rustler (New Mexico) 70

Wellington (Kansas) 10

Supai (Arizona) 70

Charles (South Dakota) 50

Opeche (South Dakota) 50

Average bed thickness ranges are well below 50

percent of the above-given maximum thicknesses. The

Louann Salt of southern Louisian is perhaps one of the

purer rock salt deposits, but it is poorly known. Andrews

[33] described it as very white to grey, clear, coarsely

crystalline and containing anhydrite streaks, and very

pure without clastic material. The Hermosa Formation of

Utah, on the other hand, is described by Pierce and Rich

[34] as containing "many shale and anhydrite beds,"

despite its flowage into great accumulated thicknesses at anticline crests.

Gross-scale composite sections of some salt-bearing

formations in the United States are given by Lefond [35]

and can be found in the Northern Ohio Geological

Society Salt Symposia volumes.

1.3. Salt Domes

1.3.1. Introduction

Only the rock salt deposits of the Gulf Coast

embayment have produced salt domes in the United

States, though incipient doming is present in the

Paradox basin salt deposits. More than 300 salt domes

have been recognized, onshore and offshore, in Texas,

Louisiana, and Mississippi.

These domes have risen from great depths. Their

source, the bedded Louann Salt, is approximately 5000 m

deep north of the area in central Louisiana that may be

salt free. South of the area, the depth estimates range

from 11,700 m to as much as 20,000 m, though the

generally accepted figures are from 13,000 to 15,000 m. The domes rise above the source bed from local

thickenings of the bed all the way up to present-day land

surfaces. In the United States, the salt beds are not

exposed at the surface; however, the locations of many

domes are marked by solution and collapse that produced

lakes. Some of the lakes contain central islands that may

be the result of continued doming.

Domes may be circular to broadly elliptical, and their

diameter may either increase or decrease downwards.

Some domes may even have detached from their source

bed. Domes commonly have a mushroom shape near the

top, on any or all sides, termed "overhang" (figure 5).

The average diameter at the top of Gulf Coast domes is about 3.2 km, though they range from 1 to 6 km in

diameter [36a and b] . The upper surfaces may be flat, convex upward, or irregular and are usually but not

always covered by "caprock."

1.3.2. Formation

Salt-dome formation is related to the incompressible

and plastic characteristics of salt. As shown by figure 1.6,

halite has a greater density than clastic sediments at surface conditions. Pore spaces in forming rock salt are quickly filled by halite on recrystallization. In clastic

sedimentary rocks, pore space is filled by water; only

gradually is the water forced out and the pore space

reduced by the increasing pressure of thickening

overburden. The result is that the density of clastic

rocks, usually sandstone and shale, increases as depth of

burial increases whereas that of halite remains constant.

At a depth from 130 m [37] to 700 m [38] , the density of

11
Figure 1.5. Idealized stratigraphic cross section of upper part of an intermediate depth Gulf

Coast salt dome.

salt equals that of average sedimentary rocks; below that, an unstable density inversion is present because denser

clastic sediments overlie lighter rock salt. (The incipiently domed rock salt of the Paradox basin is covered by

about 700 m of overburden, but the deep salts of the

Williston basin are undomed.)

Added to this density inversion is the plasticity of

halite, which increases as temperature and pressure

increase. "At depths of between 2500 and 3000 meters,

the temperature is about 100°C and the pressure over 600 kg/cm^ 158.84 MPa]. Under these conditions, salt

is very plastic; it is in fact about as soft as butter on a hot

summer's day" [39]. While this is an overstatement, it must be recognized that rock salt, alone among the

common rock types, flows readily in response to small

gradients in pressure and temperature.

Salt flows toward sedimentary and tectonic irregularities in the overburden. Folded strata are especially

conducive to rock salt flowage because of the differential

stresses. Salt accumulates at the crests of folds. The

greater the depth of burial, the larger the local

accumulation of rock salt, and the greater the tendency

towards penetration of the overlying sediments. The

mobility of rock salt is such that its original site of

deposition may be as far as 25 km from the dome where it

is presently found [41].

Salt flows to and within domes in pulses, not I continuously. This pulsing flow is indicated by the

different episodes of folding (refolded folds) found

within domes and the irregular effects the rising dome

has had on the adjacent stratigraphy (described below).

Estimates of the actual rates of flow are on the order of a few millimeters per year [42] . In contrast with the

Persian domes that are pushed up to some 1300 m above

the surrounding plain and are still rising [43] , most of

the Gulf Coast domes seem currently to be in a state of

equilibrium. Sediment deposition on top of them would

probably remobilize them. BorchertandMuir [44] stated

"salt will normally continue to flow into the dome until

the supply from the surrounding area is exhausted. So

the height of the dome is largely governed by the

thickness .^f the original bed of salt."

1.3.3. Associated Structures

1.3.3.1. Internal Structures

The internal structure of salt domes is visible in the

contortions of the ubiquitous banding of pure halite and

12
anhydritic halite. This layering is usually 0.025 to 0.25 m

thick and is tacitly assumed to be the original

sedimentary layering. The anhydrite rarely makes up

more than 5 percent of the impure layers but gives them a

distinctively darker coloration.

Folding of the bands in domes of northern Louisiana is relatively simple because of the short distance that they

have risen, but the folding in southern Louisiana is complex. The overall pattern of folding is one of radially

distributed vertical folds. Because the major vector of

flow in domes is vertical, vertical cross-sections within

the domes rarely show more than parallel near-vertical

lineations. A horizontal section, however, shows

complex ellipses and concentric and ptygmatic (disharmonic) folding. Shearing and attenuation of folds, in

many places to elimination, are also common. Rare but

more competent anhydrite bands may show boudinage,

a set of regular extensional partings. All these folds have

axes that are near vertical and are continuous vertically

for as far as the exposure (usually a mining face) is available. Kupfer [45] stated "folding in domes is due to minor lateral drift of adjacent elements during vertical

motion." As such, it is secondary in importance as a record of movement to the vertical lineations. The

multiple episodes of refolding were probably caused by

varying components of this lateral drift. Generally, the

bedding is parallel to the side of the dome near the edges

and becomes more complex inward.

Differential vertical movement within the dome

produces "spines" of salt that rise higher than adjacent

parts of the dome. Spines are usually cited as the cause of

shear zones noted within salt domes. The structure in

shear zones has been homogenized and looks deceptively

simple, though pieces of the rock surrounding the dome

are sometimes incorporated into these zones. Rare highangle and more common bedding-slip faulting may also

be produced by spine movement [46]

.

1.3.3.2. External Structures

The rock salt of the Louisiana domes is rimmed by an

external shear zone called the "shale sheath." In the

Weeks Mine, Louisiana, this sheath is a chaotic

shale/salt mixture, 130-330 m thick. Sedimentary lay- ers pierced by salt domes may be abruptly truncated

against a dome-margin shear zone, but more commonly

they are upturned or even overturned against the shale

sheath.

Other adjacent sedimentary layers were directly

created by the doming action. As rock salt was withdrawn

from the beds peripheral to the dome, the overlying

sediments subsided into a "rim syncline," while the

central rocks were pushed upward by the dome.

Sediments eroded from the central high were redeposited

in the rim syncline, creating both a local unconformity

over the top of the dome and adjacent sedimentary strata that dip away from the dome and pinch out against it. In

other circumstances, a bed that was being deposited

regionally concurrent with doming would be thinner over the dome. The local stratigraphy records the

relationship between episodic growth of the dome and

the regional deposition.

Two sets of faults in the overlying sediments are usually associated with domes: 1) tear faults radial to the

dome and 2) tension faults tangential to the dome (figure

1.7). The latter often create a "central graben" over the

center of the dome.

1.3.3.3. Caprock

Some salt domes are covered by "caprock," a sequence

of a basal, granular anhydrite, an intermediate layer of

gypsum, and a covering of calcite (which in many places

contains minable quantities of native sulfur). Hawkins

andjirik [118] noted that 181 of the some 330 known salt

13
Figure 1.7. Example of the fault pattern in sediments overlying a salt dome near Galveston County, Texas. Modified from

[146]. domes along the Gulf Coast are known to have caprock

and that it is usually thicker on domes that are closer to the surface. Uncapped domes are also known. The

thickness of caprock ranges from less than 3 m to greater

than 500 m and averages 130 m [47]

.

The origin of caprock is probably a combination of a solution lag of anhydrite, as the anhydrite-bearing rock

salt of the dome intruded into the freshwater horizon

[48] , and an in-place alteration of the upper zones of that

anhydrite to gypsum and calcite. Given the low

percentage of anhydrite in dome rock salt, a large volume

of the rock salt must have been dissolved in order to leave

some of the thicker layers of caprock.

Arguments for the in-place origin of caprock are

largely based on the presence of authigenic minerals not

found within the dome rock salt and isotopic ratios

indicating organic activity. The S^VS^^ ratios of the

sulfur pockets found in the calcite are reflections of the

preference of certain anaerobic bacteria for one of those

isotopes [49] in their conversion of CaS04 to H2S and

ultimately to S in order to obtain oxygen. These bacteria

feed on the hydrocarbons associated with domes. The

remaining Ca combines with CO2, also bacterially

produced, to produce the top layer of calcite (which is enriched in C^^, also indicative of an organic origin).

The general sequence of events in the formation of

caprock is:

1. Solution lag of anhydrite (CaS04).

2. Hydration of anhydrite to gypsum

(CaS04 + 2H2O = CaS04 • 2H2O).

3. Bacterial reduction of gypsum and methane (CH4)

to produce H2S, CO2, and Ca^*.

4. Inorganic oxidation of H2S to S, and combination

of Ca^* and CO2 to form calcite (CaCOs).

1.3.4. Mineralogy

Gulf Coast salt dome deposits are generally more than

97 percent halite. The major impurity is anhydrite,

which makes up from 1 to 10 percent of the darker beds

[50, 51]. The bedding style is termed "graded" in that,

above a sharp basal contact, the impure bed gradually

grades to pure halite. More precise rock salt analyses and

descriptions of crystal habit are given in section 1.4. The mineralogy can change during diapirism (saltdome formation). Some evidence indicates that "differential purification may occur during diapirism" [52]

.

Halite-rich layers respond to stress and flow more readily

than the less plastic impurities such as the anhydrite or

clay layers. Though the Louann Salt is reported to be a

relatively pure halite deposit, the domes formed from it probably contain even fewer impurities.

The rock salt in some domes in Louisiana is incompetent. Hand specimens tend to fall apart readily

along crystal boundaries [53]. An inverse relationship

between competency and the vertical distance of

piercement may be present.

1.4. IVIineralogy and Petrology

1.4.1. Introduction

Halite has a cubic crystal shape, but it may also be

found in a massive, granular, or fibrous habit. It may

break with perfect right-angle cleavage or, to a lesser

extent, it may fracture conchoidally. Its hue, dependent on the amount and type of impurities, may be colorless,

grey, white, or red. In certain instances, it is a deep blue.

Summaries of the optical and physical properties of

halite and other evaporite minerals have been published

by Borchert and Muir [54] and by Braitsch [55]. They

are also discussed in other chapters of this book.

1.4.2. Impurities

Rock salt contains a variety of accessory or minor

minerals. The accessory minerals in salt domes (the type

of deposit that is most pure) are summarized in table 1.3. These minerals are also found in bedded deposits, where

14
XXX XX

Other

inclusions

SEX9X 'punoM sui>isoH XX XXX X X

SBxaj, 'Xa"[>[OOH XXXXXX X

VT 'PI3TJUUTM XXXXXX X X X

xxxxx

(U X

4-1

•VI 'puBisi s^aaM XXXXXXX X X X X X

•VI 'a3iu9A XX X X X X

!-. 4->

•VI 'Jniidxns X X X X XX X X

•VI 'S3>ITS XXX X

"Vl 'uoaSuTi{SBM a3[Bq XXXXXXXX X X XX

•VI '3SBq.imjaH s>tBT XXX X X X

• VI ' sSuiuuaf XX XX

•VI

' -pi uosjajjaf XXXXXXXXX XXX X X X X

•VI '^BH -pi uapjB3 XX XX X

•VI 'X^Jtaq^iOEH ^ISBg xxxxx X

•VI 'mojjbq XXX X

(D

rt X

)-l 4-)

•VI 'MBaooqo XXXXXXXXX X X X X X

•VI 'naxa noXBg xxxxx X

•VI 'puBXSi XjaAV XXXXXXXXX X X X X X

•VI 'a:;q.na Bq asuv XXXXXXX trace YA

Common

Minerals

(in

order

of

abundance)

0) 0) <U OJ PQJ <U<L) aj4-l4-)+J

•H 4-J 0) +J +J ^, 4_) -H -H -H

!-l -H P 0) N -H -H 3 -H P 0) Ul C

>,OU-HS-,0<UPHn)CD-HOr-l

q;oa3>s3-Hn3D(D<Urta3aj < Q u o. cy-j n: w X u pq s fc'S

Potash

salts

Oil Gas

Quartz

sand

15
their volume and distribution range from 0 to 100

percent of a formation or sample and from thick

intercalated beds to disseminated intercrystalline grains.

Jones [18, p. Al] summarized the small-scale occurrence

of impurities in rock salt beds of the Wellington

Formation in Kansas as follows:

"Anhydrite and detrital argillaceous clay materials

are the main accessory constituents of the rock and

commonly form angular interstitial patches and irregular

veinlike masses. Other minor constituents—such as polyhalite, dolomite, magnesite, hematite, celestite,

marcasite, and pyrite—occur as single crystals or as groups of crystals that project into halite from the edges

of argillaceous patches and from small lensic or veinlike masses of anhydrite. Small pseudomorphs after gypsum,

outlined by crystals and fine-grained masses of anhydrite, are scattered irregularly through the rock."

Representative analyses of hand samples from United

States salt domes are given in table 1.4. To illustrate the typical composition of rock salt containing more impurities, Jones [18] gave the

following breakdown for the entire Salado Formation of

New Mexico: rock salt, 38.6 percent; clay-rich rock salt,

45.0 percent; sulfate rocks, 12.5 percent; and clastic

rocks, 3.9 percent. These percentages vary across the

basin, and the formation becomes principally anhydrite

and dolomite on the southern edges. To the north, the

percentage of clay, sand, and silt in the Salado Formation

increases to dominance. Salt-percentage maps show that

rock salt composes the greatest percentage of most salt- bearing formations near the center of a basin.

Impurities in the Gulf Coast salt domes are very

irregularly distributed, and the composition and grade of

rock salt are often different in adjacent spines of a dome.

The overall impurity percentage estimates vary between

1 and 2 percent for domes in southern Louisiana [56] and

up to 15 percent for northern Louisiana and Texas [57]

.

The percentage of impurities also varies across the

complete spectrum at the intermediate scale of the 30

cm- to 8-m-thick beds that make up bedded formations.

As a rule, rock salt is purer in the upper parts of beds,

especially the thicker ones. In the Salina Formation in

New York, "halite makes up 85 to 95 percent of the

laminated salt by weight" [58, p. 41]; in the same

formation in northeastern Ohio, impurities (mostly

dolomite and anhydrite) range from 0 to 30 percent, the

percentage being greatest near contacts with beds of

anhydrite [59] . In the Salado Formation of New Mexico,

most salt beds contain from 1 to 10 percent impurities

including anhydrite, polyhalite, and clay [60] as disseminated intercrystalline blebs. A composite sample

of the Hutchinson Salt Member of the Wellington from

Kansas yielded 5.7 percent insoluble material, mostly

anhydrite [61].

1.4.3. Grain Size and Orientation

1.4.3.1. Bedded Deposits

The crystal size of halite in bedded deposits varies

from a few millimeters to more than 0. 1 m on a side. Most

often the crystals of a bed are of roughly the same size,

though gradations from a zone of one size to a zone of

another size are common. Larger crystals tend to be

found where fewer impurities are present to inhibit their

growth during recrystallization.

Where rock salt has not been extensively recrystallized, hopper crystals may be preserved in bedded salt. These pyramidal, originally open-ended crystals, 0.005

to 0.01 m on a side, grow point down at the evaporation

surface of a brine until their weight overcomes surface

tension and they settle to the bottom [62] . In some

instances, sheets of uniformly oriented hopper crystals are found in rock salt beds, indicating that they grew

together at the surface and settled as a unit. These

crystals often serve as nucleation sites for cubic crystals,

which grow in crystallographic continuity during

recrystallization or periods of supersaturation of brines

at the bottom of the basin or both. Hopper crystals can be

recognized by the abundant, minute fluid inclusions that

outline successive growth planes of the crystal and show

characteristic "chevron" patterns in thin section.

Another of the few remnant primary crystalline

textures in salt deposits is that displayed by gypsum.

Gypsum commonly grows as crystals attached to the

basin floor, in a distinctive "swallow-tail" configuration,

centimeters in length. This texture is commonly

preserved even though the gypsum may be changed to anhydrite or replaced by other minerals (usually halite).

The texture may be used to tell the "up" direction of a piece of core.

1.4.3.2. Salt Domes

The size of halite crystals in salt domes usually ranges

from 0.005 to 0.01 meters on a side, though some domes

contain rare zones of finer grained crystals. More

common "pods" of coarse grained crystals 0.025 to 0.05

meters on a side commonly cut across bedding and may

be the result of resolution and deposition caused by

ground-water intrusion [64] . These coarsely crystalline

pods are often associated with water seepages, oil inclusions, and shear zones between spines.

Halite crystals elongated preferentially in the vertical

direction, that is, parallel to the direction of flow, have

been reported [41, 42, 51, 65]. The length ratios of

vertical to horizontal axes are commonly about 1.5 and,

in some crystals, are as much as 6.0. The elongation is thought to be caused by a combination of mechanical

16
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21
rotation of the entire crystal and translation gliding

within it during flow. The rotation and translation are counteracted by the effects of recrystallization during

periods of quiescence or contemporaneously with flow.

In the deeper parts of domes, higher temperatures

increase diffusion rates, and recrystallization processes

keep pace with those causing crystal elongation.

Anhydrite stringers are commonly vertically aligned

in domes, where linear concentrations of small aligned

crystals form "pencil anhydrite." This alignment is well

shown in the Grand Saline Dome in Texas [65].

1.4.3.3. Pseudomorphism

Minerals may be entirely replaced several times by

other minerals more stable at varying temperature and

pressure conditions because the salts deposited from the

brines are only stable at low temperatures or because the

phases precipitated are metastable and increased

temperature permits the recombination of the chemical

components. Schaller and Henderson [63] cited many

examples of such pseudomorphism, which is the

replacement of the mineral but the retention of its crystal form. Among the more common, besides the

above-mentioned halite-for-gypsum replacement, are

polyhalite replacing anhydrite, kainite replacing langbeinite, and sylvite replacing carnallite. In some crystals,

where the physical properties of the replacement mineral

are similar to those of the original, x-ray diffraction tests are necessary to determine which mineral is present,

though the crystal form is distinctive of only the original

mineral.

1.4.4. Density of Rock Salt Deposits

At 15°C, the average density of pure NaCl is 2.165

g/cm^ [66] . The density of the rock salt in most natural

deposits is close to this. But, as the percentage of dense

anhydrite impurity increases, so does the density of the

sample. A rock that is 20 percent anhydrite and 80

percent halite rock would have a density of 2.32 g/cm^

and a specific volume of 0.431 cm^/g. Od6 [67, p. 685]

stated "the density of rock salt aggregates varies roughly

between 2. 16 and 2.25. The variations are usually caused

by anhydrite." Compaction is a negligible variable in

changing the density of salt, even to depths of 18,300

meters [68]. Tables 1.5b and 1.5a list published densities

and specific volumes of rock salt and other evaporites

from some United States deposits and of individual

constituent minerals in their pure form.

In the few cases where the type of density (table 1.5b) was indicated by the primary source, the bulk density was measured. This includes the volume of the pore

space in the rock. The bulk density is relevant to

geophysical measurements of the rock in place, whereas

the grain densities as listed in table 1.5a are useful for

laboratory work on individual crystals. In most salt deposits, the pore space is minimal, and only a slight

difference exists between bulk and grain densities of rock

salt. Guido and Warner [69] gave the following

comparison of density values for one sample from the

Winnfield Dome of Louisiana:

Bulk 2.163 + 0.018 g/cm3 (7 tests)

Grain 2.191 + 0.010 g/cm3 (4 tests)

The procedures used in the measurement of the densities were as follows:

Grain Density

a. Specimens powdered, dried, and weighed.

b. Specimen volumes determined by kerosene dis- placement.

c. Specimen densities averaged.

Bulk Density

a. Specimen stripped clean and weighed to 0.1 gram.

b. Specimen volume determined to 0.1 cm^ by Hg

displacement.

The more variable the mineralogy of a salt deposit, the

more variable will be the bulk densities. Where potash

beds are present and where diagenetic or metamorphic

changes have occurred, abrupt changes in mineralogy

and, therefore, density are common. In the potash

deposits of New Mexico, horizontal sylvite and langbeinite beds commonly are abruptly truncated by zones of

massive halite that were deposited from secondary

migrating fluids. The replacement of sylvite (density

1.98 g/cm^) by halite (2.16 g/cm^) would produce an

anomalously dense zone, whereas the replacement of

langbeinite (2.83 g/ cm^) by halite would cause a minor

decrease in relative density.

1.5. Fluid Inclusions

1.5.1. Formation

Fluid inclusions in rock salt deposits range in volume

from fractions of microliters to centiliters. They are formed when fluid is trapped in irregularities of growing

crystals or in rehealed fractures. As such, they are records of the composition, temperature, and pressure of

the fluid medium that was present during crystal growth

or fracturing.

Ionic ratios in primary inclusions in bedded halite

have been used to document the unchanged composition

of sea water since Paleozoic time. Because neither

22
Table 1.5a

Reported Densities of Selected Pure Evaporite Minerals

Grain Density Specific Volume Source

3 3 Sample Formula g/cm cm /g of Data

Anhydrite CaSO^ 2.89-2. 98 0 346- 0.336 [127

2.90 0. 345 [ 57

2.963 0. 337 [128

2.9-3.0 0 34 5- 0.333 [129

Calcite CaCO^ 2.72 0. 368 [127

2 . 712 0. 369 [128

Carnallite KMgCl^- 1 . 6 0. 625 [127

1 . 60 0. 625 [ 57

1 . 598 0. 626 [128

1.6 0 . 625 [129

Dolomite CaMgCC02)2 2.85 0 . 351 [127

2.866 0. 389 [128

Gypsum CaS04'H20 2.32 0. 431 [127

2. 31 0. 433 [ 57

2.317 0. 432 [128

2.3-2.4 0 435- 0.417 [129

Halite NaCl 2.16 0. 463 [127

2.16 0. 463 [ 57

2.163 0. 462 [128

2.1-2.2 0 467- 0.455 [ 129

Langbeinite K2S04'MgSO^ 2.77 0. 361 [128

2.82-2.83 0 357 - 0 . 353 [129

Polyhalite K2Ca2Mg CSO^)^ •2H2O 2 .78 0. 360 [127

2 .78 0. 360 [128

2.78 0. 360 [129

Sylvite KCl 1 . 99 0. 503 [127

1 . 98 0. 505 [ 57

1 .987 0. 503 [128

1 . 98 0. 503 [129

23
Table 1.5b

Measured Densities of Natural Salt Deposits

Sample

Composition

Anhydrite

Caprock

Anhydrite

banded

with salt

"rock"

Anhydrite

Sample

Location

Grand Saline

Dome, Texas

Hockley Salt

Dome, Texas

Bulk Density Specific Volume Source of

g/cm cm /g data

average from

several

localities

.

2.37-2.64

2.35-2.89

2.89-2.91

2.84-2.97

2.60-2.90

2.9

0.422-0.379

0.426-0. 346

0.346-0.344

0.352-0.337

0.385-0.345

0.345

[13 0]

[131]

[131]

[131]

[131]

[132]

Gypsum

Weathered

gypsum

Gypsum

Gypsum

Grand Saline

Dome, Texas

Hockley Salt

Dome, Texas

average from

several

local ities .

2.26-2.36

2.07

2.2-2.6

0.442-0.424

0.483

0. 4 55- 0. 38 5

[13 0]

[131]

[13 2]

Rock salt - Isolated Measurements

"Clear salt" Grand Saline

Dome, Texas

"Dark salt" Grand Saline

Dome, Texas

Salt

Salt

Salt

Salt

Winnfield Salt

Dome, LA.

Hockley Salt

Dome, Texas

Hockley Salt

Dome, Texas

Hockley Salt

Dome, Texas

Bedded salt Eddy County,

New Mexico

2.13-2.16

2.22-2.25

2.17

2. 20-2. 21

2.19-2.20

2.15-2.18

2.16

0.469-0.463

0.450-0.444

0.461

0.455-0.452

0.457-0.455

0.456-0.459

0.463

[13 0]

[13 0]

[130]

[130]

[130]

[130]

[130]

Rock salt - Variation within Domes

"Rock salt" Hockley Dome,

Texas

"Rock salt' Hockley Dome,

Texas

"Rock salt" Hockley Dome,

Texas

2 . 38

1 .92

2.20

0.420

0. 521

0.455

[131]

[131]

[131]

24
"Rock salt"

"Rock salt"

"Rock salt"

"Rock salt"

"Rock salt"

"Rock salt"

"Rock salt"

"Rock salt"

96.1>% NaCl

97.7% NaCl

87.5% NaCl

93.4% NaCl

99.3% NaCl

95.0% NaCl

7 8.4% NaCl

99.1% NaCl

97.1% NaCl

Dome salt

Dome salt

Dome salt

Dome salt

Dome salt

Hockley Dome,

Texas

Hockley Dome,

Texas

Hockley Dome,

Texas

Hockley Dome,

Texas

Hockley Dome,

Texas

Hockley Dome,

Texas

Hockley Dome,

Texas

Hockley Dome,

Texas

Winnfield

Dome , LA

Winnfield

Dome, LA

Winnfield

Dome, LA

Winnfield

Dome, LA

Winnfield

Dome, LA

Winnfield

Dome, LA

Winnfield

Dome , LA

Winnfield

Dome, LA

Winnf iel

d

Dome, LA

Avery Island

Salt Dome, LA

Avery Island

Salt Dome, LA

Avery Island

Salt Dome, LA

Avery Island

Salt Dome, LA

Avery Island

Salt Dome, LA

Table 1 . 5b- -Continued

2 . 39

2. 23

2.18

2.18

2.19

2. 21

2.26

2 . 28

2 .14

2.15

2.16

2.23

2.15

2.12

2.19

2.14

2.16

2.14

2.11

2.12

2.14

2.10

0.418

0.448

0.457

0.457

0. 457

0.453

0. 442

0.439

0.467

0.465

0.463

0.448

0.465

0.472

0.457

0.467

0.463

0. 467

0.474

0.472

0.467

0.476

25
bromine nor magnesium is a significant constituent of

any of the minerals formed prior to the haUte phase in

the precipitation sequence, the Br/Mg ratios of primary

fluid inclusions are similar to those of the original brines.

Holser [70] stated that: "Most of the Br/Mg ratios in the brine inclusions from

Hutchinson are close to that of sea water and to modern

bitterns. This indicates both that the inclusions are

virtually unchanged samples of the bitterns left behind

in Permian time and that the Br/Mg ratio of the sea has

remained constant since the Permian. . . . Brine inclusions from the Silurian of Michigan have a similar

composition . . Ionic ratios in fluid inclusions also record the stage of

evaporation or concentration of the brine at the time of

halite crystallization. Kramer [71] indicated that the

brines that precipitated the salt of the Salina Formation

in Ohio and Michigan had concentrations 12 to 14 times

that of normal sea water. Holser [70] believed that the

brines that deposited the salt of the Hutchinson Salt

Member of the Wellington Formation in Kansas were

concentrated almost to the potash phase (a concentration factor of almost 64 times).

Because halite contains essentially zero magnesium

and very little bromine, secondary inclusions formed

during resolution, and precipitation of halite can be

distinguished from primary inclusions by low Br/Cl and

very low Mg/Cl ratios.

The temperature of formation of inclusions is also

considered to be recorded in the vapor bubble that is present in some fluid inclusions. Assuming that the

crystal formed at the earth's surface (at ambient

pressure) in a purely aqueous medium, the vapor bubble

must have formed in response to the vacuum created as the fluid enclosed within the crystal subsequently cooled

and contracted. Unless some fluid has leaked from the

inclusion, temperatures of formation can be experimentally determined by heating the inclusion to the point

where the fluid expands to eliminate the bubble [72].

Dreyer and others [73] determined these temperatures for halite to be between 70° and 100 °C and

concluded that these high temperatures were records of

the exothermic heat of crystallization localized at the

crystal surface and not the overall temperatures of the

precipitating brines. Peach [74], however, believed that

these temperatures recorded overall formation temperatures and pressures during secondary recrystallization at depth.

1.5.2. Composition

Data on the composition of fluid inclusions is minimal; many publications give only comparative ionion ratios rather than absolute parts per million. Tables

1.6a and 1.6b list some of the published data, many of

them coming from Roedder [75]. In general, fluid

inclusions are at saturation with respect to NaCl

because their host mineral is halite. Metamorphism and

recrystallization can cause the other ionic constituents

of inclusions to vary greatly, even in adjacent inclusions. The major cations are Na*, Ca^*, and Mg^*;

the dominant anion is CI" , and some 504^" is present.

Kramer [76] stated "obviously secondary inclusions

from Ontario (the Salina Formation) were almost pure

NaCl brine." Roedder [77] noted that other inclusions

from the same formation contain concentrated calcium

brines. He also stated that most of the fluid inclusions at one locality of the Hutchinson Salt Member in Kansas

are nearly pure NaCl brine.

Inclusions in domed rock salt have been subjected to recrystallization and, at least, mechanical deformation.

At best, these inclusions can be considered to be only

residues of the precipitating liquors or samples of

secondary metamorphic brines. The methane gas and

liquid oil inclusions in many of the Louisiana salt domes

are certainly of secondary origin, having been incorporated into the salt contemporaneously with the dome

formation.

Kramer [78] detailed a procedure for preparing and

analyzing fluid inclusions, a summary of which follows:

1. 30 mg samples of inclusion-rich salt were first examined for inclusion morphology.

2. A 30 mg sample of inclusion-free salt from the same

specimen was selected as a blank.

Table 1.6a

Published Compositions of Fluid Inclusions in United States Rock Salt. Modified from [135]

Parts per Million of Total Inclusion Fluid

Sample ^ Number Na Ca 2 + Mg 2 + CI SO 4 F Concentration Location of Sample

69,100 3,500 13,700 1,600 110,000 44,800 58

88,200 4,700 16,400 2.050 145,000 38,100 63

242 ,600

294,500

Salina salt beds (Silurian)

Goderich, Ontario

Salina salt beds (Silurian)

Cleveland, Ohio

26
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27
3. Samples were weighed to +2 micrograms.

4. Samples were dried to a constant weight at 125°C.

5. Samples were ground with mortar and pestle and

again dried to constant weight at 125 °C.

6. Loss of weight between steps 4 and 5 was taken as the loss of inclusion water.

7. Ground samples were dissolved in water, and the

solution was analyzed chemically. Ionic values greater

than those of the blank sample were considered to have

been derived from the inclusion fluids.

8. "The methods employed were flame emission for

Na and K, chloranilate calorimetry and thorin titration

for sulfate, potentiometric titration with AgNOs for CI,

alizarin calorimetry for F, fluorescence titration with

calcein and EDTA for Ca, and EBT titration with EDTA

for Ca and Mg" [78]

.

Fluid inclusions in halite are irregularly distributed

and in many places are abundant adjacent to other zones where they are absent. They may be spherical,

minimizing surface area, or cubic "negative" crystals,

minimizing surface potential. Shuman and Fiedelman

[79] found that, in artificially grown crystals, round

inclusions formed in highly agitated water whereas cubic

inclusions formed in quiet water. The number of

inclusions in a sample is a "function of crystal size,

concentration of solid particles in suspension in the

brine, and particle size of the inclusions" [79]. Their

irregular distribution is probably due to secondary

metamorphism or recrystallization.

Inclusion volumes in some laboratory-grown halite

crystals range from 0.23 to 0.45 percent of the total volume [79] . Roedder [80] stated that commercial

reagent-grade halite contains abundant fluid inclusions

that constitute about 0.5 percent of the total weight and

that the inclusions in the bedded rock salt investigated

constituted 0.44 weight percent of the rock.

The reported water content of rock salt is often well

below this 0.5-percent figure. Aufricht and Howard [81]

gave the following percentages of total volume occupied

by water in rock-salt samples: rock salt in central Kansas,

0.05-0.08 percent; salt mines in Detroit, 0.1-0.15

percent; Louisiana salt domes, 0.003-0.008 percent. Ode

[82] listed typical weight percentages of moisture from

Hutchinson and Lyons Mines, Kansas, as 0.127-0.293

percent and 0.090-0. 100 percent, respectively. Although

Odfi's analyzed samples were heated in excess of 250° C,

most moisture analysts do not heat their sampes above

125°C. All moisture analyses in which the sample was

heated above 125° C must be suspect. At 125° C, rock salt

will still contain a residual calcium-magnesium-chloride

brine from which the water will not be removed.

As indicated by figure 1.8, 100 percent of the moisture

is not released by salt during normal laboratory heating

times until the sample is heated in excess of 625°C.

Shuman and Fiedelman [83] stated that, in order to ' remove 100 percent of the moisture in brine inclusions I in salt within 1 hour, the sample must be heated to 801 °C '

(1474°F), close to its melting point. Aufricht and I Howard [84] also observed this. Roedder [85] found his I 0.44 percent weight loss (attributed to vaporized fluid , inclusions) on decrepitation of salt heated to incipient

fusion [86]

.

f

624°C

180°C____

Time, hours

Figure 1.8. Rate of moisture release from brine inclusions in halite heated to various temperatures. Modified from [147].

1.5.3. Pressure Gas Inclusions

Although the vapor bubbles associated with fluid in

primary inclusions are theoretically under a vacuum,

other inclusions of gas are under considerable pressures.

Baar [87] attributed some of these pressures to plastic

deformation of rock salt by thick overburden and the

resulting compression of the gas-filled cavities.

In East Germany, CO2 gas associated with Tertiary

volcanic activity was trapped under pressure when it was

magmatically injected into buried salt deposits, partially

melting them. Solidification and recrystallization en- closed the gas as inclusions and as microscopic flaws at

crystal boundaries [88] . A diabase dike [89] is known to cut through the New Mexico rock salt deposits, though no association has been made between it and pressured

gas inclusions.

.

Gas inclusions are often associated with potash beds

[90] , and suggestions have been made that they are accumulations of argon, derived from the radioactive

potassium isotope found in such minerals as sylvite

(KCl) and langbeinite (K2Mg2 (S04)2). Hoy and others

[91] have noted that carbon dioxide pockets and

blowouts in Texas and Louisiana salt domes usually are near the dome boundaries. The gas probably has organic

origins and may have been entrapped in processes related

to the shearing and disruption of the salt during doming.

Another possible source for CO2 gas [92] is the

28
breakdown of the unstable magnesium chlorocarbonate

(MgCl2 • MgCOs • 7H2O).

Pressures of gas inclusions are variable and difficult to measure. A common mining measurement is the weight

of the rock salt that was shattered by the violent degassing of numerous concentrated inclusions. This

weight often measures in the thousands of tons, and the

estimates of gas released can range in the hundreds of

thousands of cubic meters (at ambient surface pressures). Some rock salt deposits are capable of yielding 3

to 20 cubic meters of gas per ton [88] although the

volume of the gas as inclusions is small under pressure.

Other pressure measurements are rare and scattered.

Hoy and others [93] reported estimated pressures of 50

to 100 MPa in CO2 blowouts in the Winnfield salt dome

in Louisiana. McClain and others [94] noted that the

steady shut-in pressure after a blowout in the AEC

(Atomic Energy Commission) No. 7 well, drilling

through the Permian Salado and Castile Formations of

New Mexico, was 0.79 MPa, a measurement made after a considerable amount of uncontrolled gas venting.

Roedder [92] cited examples of gas inclusions in

Mexican and German salt that expanded their volumes

250 times after release from the confining pressures.

The most common gas inclusions in rock salt contain

methane (CH4), carbon dioxide (CO2), and nitrogen

(N2) [95] . Methane and nitrogen have been reported in

the potash mines of New Mexico [96,97] . The weight

percent of constituents of blowout gases in the AEC No.

7 well, where six samples were collected for anlyses

during a 1 month period [98], was given as: CO2 — 0 to 0.54 percent

O2 — 0 to 0.81 percent

CH4 — 0 to 2.14 percent

CO — 0 percent

C2H6 — 0.031 to 0.05 percent

N2 — 97.08 to 99.904 percent

Analyses have also been made on the gases associated

with the Winnfield Dome in Louisiana. Belchic [99]

reported the presence of H2S and CO2. Hoy and others

[100] reported:

CO 2 — 46.9 percent

H20 — 17.3 percent

N2 — 18.4 percent

CO — 4.8 percent

02 — 4.4 percent

S02 — 3.7 percent

H2 — 1.8 percent

CH4 — 1.5 percent

Ar — 0.4 percent

C2H2 — 0.4 percent

Other hydrocarbons

1.5.4. Brine Pockets and Seeps

Pockets and seeps of brine in rock salt deposits are commonly associated with pressured gas inclusions.

Some of these brines may be large-scale entrapments of

the original fluids that precipitated the deposits, but

many are of secondary origin, remnants of metamorphic

brines, or ground waters that became saturated with

respect to the adjacent minerals and lost the ability to migrate by solution. Large but rare pockets containing "a

few gallons" [85] of Ca-rich brines are found in the

Goderich, Ontario, salt mine and the potash mines of

Saskatchewan. Baar [101] has suggested that large

pockets of Ca-rich solutions result from reactions of

MgCl2 brines (the liquors left in the last stages of

precipitation) with Ca-bearing rocks, in the reaction:

MgClz (brine) + CaSO* (anhydrite) = CaCl2 (brine) +

(MgS04 or any number of magnesium sulfate minerals).

Brine seeps and associated gases (usually CO 2) are

often found in the salt domes of the Gulf Coast. Belchic

[102] , citing the facts that brine seeps come up from the

floor of mines more often than down from the roof and

that they never freshen, believe that their source is deep

within the dome rather than from ground water. The

seeps are usually associated with anhydrite bands and

tend to move vertically along the banding, perhaps at the

anhydrite-salt contacts. The salt mine in Winnfield D ome, Louisiana, contains

the best-known examples of brine seeps. Most of these

gas and brine seeps are found nearer the outer walls of

the dome, though they are irregular in distribution. Flow

rates are greatest just after exposure by excavation in the

mine and dwindle to cessation during a period of a few

years [ 103] either because of the sealing of the fractures

or the eventual draining of the pocket of brine. Small gas

and brine pockets are also found by horizontal drill holes

into mining faces, but the flow from them ceases after a few hours [104]. Exploratory wells in the Winnfield

Dome have penetrated pressured gas and brine pockets.

Taylor [105] reported brine and gas under a pressure of

1.55 MPa at a depth of 180 meters below the mine level,

and Belchic and others [99, p. 34] noted a pressure of

0.90 MPa in a cavity full of water at the anhydrite-salt

contact.

1.6. Porosity and Permeability

1.6.1. Porosity

Most of the porosity in rock salt is quickly filled in by

crystal growth and plastic flowage during deposition.

Baar [106] listed porosity as a function of depth as follows:

29
40 percent at the surface

30 percent under 0.15 meters of overburden

20 percent under 0.30 meters of overburden

15 to 20 percent under 0.60 meters of overburden

5 to 10 percent at depths of 6 to 12 meters

gradually approaches 0 percent below 12 meters

Guido and Warner [69] calculated porosity in rock salt from the Winnfield Dome at 1.28 percent by using the

formula

porosity (0) = 1 bulk density

grain density

Aufricht and Howard [107] measured porosity in

three salt domes and one deposit of bedded rock salt by

using both gas expansion and brine resaturation tests performed on 2.5 to 5 cm cubic samples as follows:

"For the gas-expansion determinations, the bulk

volume of the samples was determined in a mercury

pycnometer. Pore volumes then were measured directly.

In determining the resaturation porosities, the bulk

volumes were also determined in a mercury pycnometer.

The dry samples were weighed, evacuated, pressure

saturated with brine and reweighed. The pore volumes

were taken as the weight gains occurring upon saturation."

l able 1.7 gives Aufricht and Howard's porosity data.

The range of individual samples was from 0.62 to 7.17

percent porosity, that of the averages from the four

localities from 1.0 to 6.0 percent. Reynolds and Gloyna

[108] gives average porosity values of 1.71 percent and

0.59 percent for rock salt from Grand Saline Dome,

Texas, and the bedded salt of the Hutchinson Salt

Member of the Wellington Formation, Kansas. The

laboratory procedure used for measurement was not

detailed.

Stevens [109] measured porosities in Permian

anhydrite beds associated with salt deposits in the upper

Brazos region of Texas. In 14 anhydrite samples, porosity

varied from 0.3 to 4.4 percent, averaging 1.9 percent.

Using Guido and Warner's bulk-to-grain density

proportion method for calculating porosity [69] , the

volume of fluid inclusions as well as the intercrystalline

pore spaces would be measured as porosity. Using the

brine resaturation method, however, only the intercrystalline voids in communication with the surface of the

sample would contribute to the total porosity figure.

1.6.2. Permeability

Under low confining pressures, that is at shallow

depths, dry halite allows fluid flow along crystal

boundaries and cleavage planes. Laboratory tests on rock

salt cores have measured these permeabilities with

respect to various fluids and gases (table 1.8). Reynolds

and Gloyna's data [108] illustrate the direct correlation

between permeability of rock salt and the confining

pressure. Baar [110] stated that the presence of trapped

gases in salt deposits testifies to their absolute

impermeability at depth, though Aufricht and Howard

[111] noted significant permeability still present in rock

salt samples at confining pressures less than 55 MPa.

Aufricht and Howard detailed their permeability

measurement procedures which are summarized below:

1. Samples were cut into cores 7.5 cm in diameter and

about 20 cm long.

2. Cores were cast in plastic or in bismuth alloy metal

or were jacketed in copper to seal lateral surfaces.

3. Samples were placed in a pressure vessel, and

simulated overburden pressures were created by

injecting nitrogen gas into the vessel.

4. The sample was saturated with nitrogen or degassed

saturated brine or liquid hydrocarbon.

5. The fluid was passed through the sample, and the

flow was allowed to stabilize.

6. Pressure drops across the sample, flow rates, and

the core dimensions were measured and used to calculate

permeability by Darcy's law.

Table 1.7

Average Porosities o£ Salt Samples Modified From References [13S

Average porositypercent bulk volume

Mine

Grand Saline, Texas

Winnfield, LA

Hutchinson, Kansas

Weeks Island, LA

Number By gas By

of samples expansion resaturation

1.7

1.8

1.0

1.8

0.8

6.0

30
Table 1.8 Permeability of Rock Salt

Samples

Grand Saline^-'' Dome, Texas

Permeability (md)

initial/max minimum

Hutchinson Salt

Bed, Kansas

1.01-4.25 0.11-3.24

0.01-0.46

0.05-0.21

0.51

0.06

0

0-0.072

0

0.0015

0 .023

0-0.15

0-0.05

0.0005

0.0002

0

0

0

0

0.0005

Confining

pressure (MPa)

3.4

6.9

10.3

15.9

20.7

3.4

6.9

10.3

13.8

15.9

2/

2/

Fluid Used

Kerosene or brine

BrineKerosene or brine

Kerosene

Brine—

Helium or kerosene

Br ine-^

Helium

Brine-^

Kerosene

Source of Data

[108]

[108]

[108]

[108]

[108]

[108]

[108]

[108]

[108]

[108]

Grand Saline

Dome, Texas

Hutchinson Salt

Bed, Kansas

Winnfield Salt

Dome , LA

Weeks Island

Dome , LA

Average Permeability

1-9

5 . 7

43

631

< 0.7

< 0.7

< 0.7

< 0.7

Dry nitrogen

Dry nitrogen

Dry nitrogen

Dry nitrogen

[139]

[139]

[139]

[139]

Footnotes

Quoted permeability converted to millidarcies

Brines used were NaCl , NaCl + CaSO^ , or NaCl + AlfNOj),

The permeability of halite is effectively zero when the

pressure is sufficient to deform the halite plastically and

close off the passageways at crystal interfaces. Observed

permeability in rock salt samples at high confining

pressures then, must be due to the presence of

impurities or must be artifacts of laboratory techniques.

Baar [112] asserted that "standard permeability tests on

rock salt cores are usually of no use, for the cores are damaged when taken out of their tri-axial in-situ stress

field. Such damage may be caused by stress relief

deformation that results in intergranular loosening."

Another variable is the solution flowing through the

sample. Fluids "inert" with respect to halite, such as hydrocarbons, flow more quickly and for longer periods

of time than do saturated brines. (Fresh water would, of course, dissolve halite and enhance permeability until

the fluid reached saturation.) Permeability using

saturated brine decreases rapidly with time (figure 1.9a),

probably owing to recrystallization of halite in the

passageways and the enhanced plasticity of halite in the

presence of water. Aufricht and Howard [111] believed

that, after a certain time, however, stabilization may

TIME, HOURS

Figure 1.9a. Laboratory permeability of rock-salt samples to saturat- ed brine at one atmosphere. Modified from [148].

31
occur in the brine/rock salt system, would stabilize, and

would contain a small remnant permeability.

The presence of brine also inhibits permeability

through the shale partings and anhydrite lenses often

found in rock salt deposits. Water may hydrate anhydrite

stringers and the clays of shale partings and increase

their volume, squeezing off permeability. The resolution

and deposition of CaS04 caused by brine in anhydrite

also helps choke off the permeability.

Laboratory permeability of rock salt to nitrogen, oil,

and brine under a simulated overburden pressure of 5.51

MPa [149] is shown in figure 1.9b.

COo

<

100

10

CD<

llJ

tr. UJ

Q.

0.1 -

0.01

—i.....

1 1 1 1 1 NITROGEN

OIL

\ BRINE ^

.

. \ —••

TO ZERO AT

672 HOURS

\

\ TO ZERO AT

1

\l78 HOURS

1 1 1 1 20 40 60 80 100

TIME, HOURS

120 140

Figure 1.9b. Laboratory permeability of rock salt to nitrogen, oil, and

brine under simulated overburden pressure of 5.51 MPa.

Modified from [149].

In spite of these theoretical and laboratory results,

evidence for local movement of quantities of water

through rock salt deposits is not uncommon. Anhydrite

banding in salt domes is "variably porous and permeable,

and often partially saturated with brine and CO2 gas"

[113]. Seeps and drips are known in most salt and potash

mines, though those that come down from the roof may

be ground water that has found its way down manmade

passages.

The interfaces between halite and shale or halite and

anhydrite are often suspected of having greater

permeability than the beds themselves [114,115].

Permeability is greater parallel to bedding than it is perpendicular to it. The Winnfield Dome salt mine has

numerous seeps of brine and gas from the floor and

ceiling, yet "little or no brine or gas flow from the walls"

[104].

The sheared "shale sheath" zone that encircles Gulf

Coast salt domes is avoided by salt miners because of severe water leakage problems found there [116] . These

leakage problems imply abundant and mobile water and

1 high permeability. On the other hand, this zone is also

avoided by well drillers because of overpressured gas

pockets commonly associated with it, implying nonpermeable zones.

1.6.3. Permeability in LPG Storage Caverns

The fluid integrity of many rock salt deposits with

respect to hydrocarbons has been tested by oil companies

who store liquid petroleum gas (LPG) in cavities

artificially dissolved out of the rock salt. Beds of halite are rarely thick enough to enclose a full-scale storage cavern, but the associated anhydrite bands and other

impurities seem to be largely impermeable in these caverns [60] . Aufricht and Howard [117] , using gasoline

as a fluid, found a range of permeabilities through salt from 0 to 6 md, the average permeability was 0.3 md.

Table 1.9 gives estimated recovery percentages for

storage caverns in the Salado Formation in New Mexico

and several other locations.

Hawkins and Jirik [118, p. 17] stated "with some

exceptions, the recovery of stored LPG products (from

caverns in Louisiana salt domes) has been good,

generally above 90 percent." The 1956 Interstate Oil

Compact Commission [119] also puts the recovery figure

at generally greater than 90 percent, and some of the loss

is probably due to above-ground handling losses. The

lowest recovery percentage given was 57 percent, but the

circumstances for this low figure were not described.

Recovery percentages usually increase after the initial withdrawal from the cavern, prior losses being contributed to by infilling of cavern irregularities with nonrecoverable oil. Aufricht and Howard [120] , however, noted a

slight decrease in permeability of salt with respect to oil (and nitrogen) with time. Table 1.9 shows a fair inverse

correlation between storage pressure and percent recovery.

1.7. Pore Fluids

1.7.1. Composition

The character of pore fluids is a function of the

composition and history of the rock salt. The only

generalization that is possible is that the NaCl content of

the pore fluid is saturated or nearly saturated in the

mineral halite. Tables 1.10 through 1.19 give the

concentration of NaCl that is m tne aqueous solution

containing KCl, MgCl2, CaCl2, and combinations of

CaCl2 with KCl between 0 and 100°C [121]. Table 1.21

gives the solubility of NaCl in halite saturated water

above 100° C.

1.7.2. Vapor Pressure

Table 1.20 gives the experimentally measured vapor

pressures for various synthetic, halite-saturated brines

32
Table 1.9 Percent Recovery of Stored Liquid Petroleum Gas Stored in Solution Cavities

in Salt Deposits. Adopted from Reference [119], table 13

Location Formation

Capacity of Storage

Cavern (gallons) Pressure (MPa)

Estimated

Recovery h

New Mexico Salado 781,200 4 1 90

New Mexico Salado 1,500,000 2 1 90

New Mexico Salado 1 ,848 ,672 1 4 98.0

New Mexico Salado 1,000,000 1 5 97

New Mexico Salado 1 ,456 ,980 1 4 98

New Mexico Salado 2,000,000 2 1 90 .0

New Mexico Salado 2,005,580 3 6 9 5i/

New Mexico Salado 2,422,000 3 8 92.0

New Mexico Salado 2,216,000 4 1 90.0

New Mex ico Salado 1 ,000 ,000 1 6 97

New Mexico Salado 1,000,000 1 6 97

Louisiana

Kansas

Kansas

Kansas

Pine Prairie

Salt Dome

Permian salt

Permian salt

Permian salt

93.3

92.86

95

92.5

- Originally shown in Table 13 as 9.7 percent - personal communication

to Warren Petroleum Corp., Hobbs , N.M., indicated 95 percent as an approximate figure.

Table 1.10

Solubility of NaCl (weight percent) in KCl solutions as given. Data in parentheses, ( ), are extrapolated; the solution may be supersaturated

in one or more solid phases other than halite. Precision (3 sigma) is given in brackets, [ ], for the 0°, 50°, and 100°C isotherms.

Temperature

C°C)

KCl concentration in weight percent

2 4 6 8 10 12

0 (25.94) (24 . 84) (23.75) (22.65) (21 . 56) (20.46) (19.37)

[•13] [.13] [-14] [.14] [.15] [.15] [.16]

10 (26.07) (24.98) (23.88) (22.79) (21.69) (20.60) (19. 50)

20 (26 . 23) (25.13) (24.04) (22.94) (21 . 85) (20 . 75) (19.66)

30 26.39 25.30 24 . 20 23.11 22.01 20 .92 19.82

40 26.57 25.48 24 .38 23.29 22.10 21 . 10 20 .00 50 26.77 25.68 24.58 23 .49 22.39 21 . 30 20 . 20 [.05] [.04] [.04] [.05] [.06] [.07] [.09]

60 26.99 25.89 24.80 23. 70 22.61 21 .51 20.42

70 27.22 26.12 25.03 23.93 22.84 21 . 74 20.65

80 27.46 26.37 25.27 24 .18 23.08 21 .99 20 . 89 90 27 . 73 26.63 25.54 24.44 23.35 22.25 21.16

100 28.00 26.91 25.81 24.73 23.62 22 . 53 21.43

[.08] [.07] [.07] [.08] [.08] [.09] [.10]

33
Table 1.11

Solubility of NaCl (weight percent) in MgCl^ solutions as given. Data in parentheses, ( ), are extrapolated; the solution may be supersaturated in one or more solid phases other than

halite. Precision (3 sigma) is given in brackets, [ ], for the 0°, 50°, and lOO'C

isotherms

.

Temperature MgCl^ concentration in weight percent

0-2-4-6-8-

10—12—14—

16—18—

0 (25.94) (23.62) (21.37) (19.17) (17 .04) (14.96) (12.95) (10.99) (9.09) (7.26)

[.13] [.13] [.13] [.13] [.14] [.14] [.15] [.16] [ .17] [.19]

10 ( 26.0 7) (23. 77) (21.53) (19.34) (17 . 22) (15.15) (13.15) (11 . 20) (9.32) (7.49)

20 26. 23 23.93 21 . 70 19.53 17.41 15.36 13.37 11.43 9.56 7.75

30 26.39 24.11 21.89 19.73 17.63 15.58 13.60 11.68 9.82 8.01

40 26.57 24.30 22.09 19.94 17.85 15.82 13.85 11 .94 10 .09 8.30

50 26. 77 24. 51 22.32 20 .18 18.10 16.08 14.12 12.22 10.38 8.60

[.05] [.04] [.05] [.06] [.07] [.07] [.06] [.06] [.07] [.08]

60 26.99 24 . 74 22.55 20.43 18.36 16.35 14 .40 12.51 10 .69 8.92

70 27.22 24.98 22.81 20.69 18.63 16.64 14.70 12.82 11.01 9.25

80 27.46 25.24 23.07 20 .97 18.92 16.94 15.01 13.15 11 . 34 9.60

90 27.73 25.51 23.36 21.27 19.23 17. 26 15.34 13.49 11.70 9.96

100 28.00 25.80 23.66 21 .58 19.56 17 . 59 15 .69 13.85 12.06 10 . 34 [.08] [.07] [.08] [.09] [.10] [-11] [.12] [.13] [.15] [.17]

Table 1.12 Solubility of NaCl (weight percent) in CaCl2 solutions as given. Data in parentheses, ( ), are extrapolated; the solutions may be supersatured in one or more solid phases other than halite. Precision (3 sigma) is given

in brackets, [ ], for the 0°, 50°, and 100°C isotherms.

Temperature CaCl2 concentration in weight percent

(°C) 0 2 4 6 8 10 12 14

0 (25.94) (23.01) (21.91) (19.94) (18.01) (16.12) (14.26) (12.43)

[.13] [.13] [.13] [.14] [.14] [.14] [.14] [.15]

10 (26.07) (24.06) (22.07) (20.12) (18.21) (16.32) (14.48) (12.67)

20 (26.23) (24.22) (22.25) (20.31) (18.41) (16.55) (14.71) (12.92)

30 26.39 24.40 22.44 20.52 18.63 16.78 14.96 13.18

40 26.57 24.60 22.65 29.75 18.87 17.03 15.23 13.46

50 26.77 24.81 22.88 20.99 19.13 17.30 15.51 13.76

[.05] [.05] [.06] [.07] [.07] [.07] [.07] [.08]

60 26.99 25.04 23.12 21.24 19.40 17.59 15.81 14.07

70 27.22 25.28 23.38 21.52 19.68 17.89 16.12 14.40

80 27.46 25.54 23.66 21.80 19.99 18.20 16.45 14.74

90 27.73 25.82 23.95 22.11 20.30 18.53 16.80 15.10

100 28.00 26.11 24.25 22.43 20.64 18.88 17.16 15.48

[.08] [.08] [.08] [.09] [.09] [.09] [.10] [.12]

34
Table 1.13

Solubility of NaCl (weight percent) in a solution containing 2 weight

percent CaCl^ plus the KCl concentration as given. Data in

parentheses, ( ), are extrapolated; the solution may be supersaturated

in one or more solid phases other than halite. Precision (3 sigma) is given in brackets, [ ], for the 0°, 50°, and 100°C isotherms.

Temperature KCl concentration in weight percent

(°C) 0 2 4 6 8 10 12

0 (23.91) (22.88) (21.86) (20.83) (19.81) (18.78) (17.76)

r 1 1 L

• J- jj I• J- J J [ . li 1

r 1

f; 1 [ . lb J

10 (24.06) (23.03) (22.01) (20.98) (19.96) (18.93) (17.91)

20 (24.22) (23.20) (22.17) (21.15) (20.12) f 19 . 101 (18 . 07) 30 24.40 23.38 22.35 21.33 20.30 (19.29) (18.25)

40 24.60 23.57 22.55 21.52 20. 50 19.47 18.45

50 24.81 23.78 22 . 76 21.74 20 .71 19.69 18 .66 [.05] [.04] [.04] [.05] [.06] [.07] [.09]

60 25.04 24.01 22.99 21.96 20.94 19.91 18.89

70 25. 28 24.26 23.23 22.21 21. 18 20. 16 19.13

80 25. 54 24 .52 23.49 22.47 21.44 20.42 19.39

90 25.82 24.79 23.77 22 . 74 21.72 20.69 19.67

100 26 . 11 25.09 24.06 23. 04 22 . 01 20.99 19.96

[.08] [.07] [.07] [.08] [.09] [.10] [.11]

Table 1.14

Solubility of NaCl (weight percent) in a solution containing 4 weight

percent CaCl^ plus the KCl concentration as given. Data in parentheses, ( ), are extrapolated; the solution may be supersaturated

in one or more solid phases other than halite. Precision (3 sigma) is given in brackets, [ ], for the 0°, 50°, and 100°C isotherms.

Temperature KCl concentration in weight percent

(°C) 0 2 4 6 8 10^ 12^

0 (21.91) (20.89) (19.88) (18.87) (17.86) (16.84) (15.83)

[.13] [.13] [.13] [.13] [.13] [.14] [.14]

10 (22.07) (21.06) (20.04) (19.03) (18. 02) (17.01) (15.99)

20 (22.25) (21.24) (20.22) (19. 21) (18.20) (17.19) (16.17)

30 22.44 21.43 20.42 19.41 18.39 (17.38) (16.37)

40 22.65 21.64 20. 63 19.62 18.60 17. 59 16.58

50 22.88 21. 87 20. 86 19.84 18.83 17.82 16.80

[.OS] [.04] [.04] [.04] [•05] [.06] [.08]

60 23.12 22.11 21. 10 20.08 19. 07 18.06 17.05

70 23. 38 22.37 21.36 20. 34 19.33 18.32 17.30

80 23.66 22.64 21.63 20.62 19.60 18.59 17.58

90 23.95 22.93 21.92 20.91 19.89 18.88 17.87

100 24. 25 23.24 22.23 21.21 20.20 19.19 18.17

[.08] [.08] [.07] [.07] [.08] [.09] [.10]

35
Table 1.15

Solubility of NaCl (weight percent) in a solution containing 6 weight percent CaCl^ plus the KCl concentration as given. Data in parentheses, ( ), are extrapolated; the solution may

be supersaturated in one or more solid phases other than

halite. Precision (3 sigma) is given in brackets, [ ], for

the 0°, 30°, and 100°C isotherms.

Temperature KCl concentration in weight percent

C°c) 0 2 4 6 8 10

Q [18 9 5) 1,1 /. Jo J

f 1 c 0 ft ^

J. J . y 0 J [•13] [•13] [.13] [.13] [.13] [.14]

10 (20.12) (19.13) (18.13) (17.13) (16.14) (15.14)

20 (20. 31) (19. 32) (18.32) (17.33) (16. 33) (15.34)

30 20.52 10.53 18.53 17. 54 16 . 54 (15.54)

40 20.75 19.75 18.76 17. 76 16. 76 15.77

SO 20.99 19.99 19. 00 18.00 17.01 16.01

[.06] [.05] [.04] [.05] [.06] [.08]

60 21.24 20.25 19.25 18.26 17 . 26 16.27

70 21.52 20.52 19. 52 18. 53 17.53 16.54

80 21.80 20.81 19. 81 18.82 17.82 16. 83 90 22 . 11 21.11 20.13 19.12 18.13 17.13

100 22.43 21.43 20.44 19. 44 18.45 17.45

[.09] [.08] [.07] [.08] [.09] [.10]

Table 1.16 Solubility of NaCl (weight percent) in a solution containing 8 weight percent

CaCl^ plus the KCl concentration as given. Data in parentheses, ( ), are extrapolated; the solution may be supersaturated in one or more solid phases

other than halite. Precision (3 signa) is given in brackets, [ ], for the

0°, 50°, and 100°C isotherms.

Temperature KCl concentration in weight percent

(°C) 0.1134567^ 0 (18.01) (17.53) (17.05) (16.57) (16.08) (15.60) (15.12) (14.63)

[.14] [.14] [.13] [.13] [.13] [.13] [.13] [.13]

10 (18.21) (17.72) (17.24) (16.76) (16.27) (15.79) (15.31) (14.82)

20 (18.41) (17.93) (17.45) (16.96) (16.48) (16.00) (15.51) (15.03)

30 18.63 18.15 17.67 17.19 16.70 16.22 15.74 15.25

40 18.87 18.39 17.91 17.42 16.94 16.46 15.97 15.49

50 19.13 18.64 18.16 17.68 17.19 16. 71 16.23 15.74

[.07] [.06] [.06] [.05] [.05] [.05] [.05] [.06]

60 19.40 18.91 18.43 17.95 17.46 16. 98 16.50 16.02

70 19.68 19.20 18. 72 18.23 17.75 17.27 16. 78 16.30

80 19.99 19.50 19.02 IS. 54 18.05 17.57 17.09 16.60

90 20.30 19.82 19.34 18.85 18.37 17.89 17.40 16.92

100 20.64 20.15 19.67 19.19 18.70 18 .22 17 . 74 17.25

[.10] [•09] [.08] [.08] [.08] [.08] [.08] [.09]

36
Table 1.17

Solubility of NaCl (weigiit percent) in a solution containing 10 weight

percent CaCl^ plus the KCl concentration as given. Data in

parentheses, ( ), are extrapolated; the solution may be supersaturated

in one or more solid phases other than halite. Precision (3 sigma) is

given in brackets, [ ], for the 0°, 50°, and 100°C isotherms.

Temperature KCl concentration in weight percent

(°C)

0 (16.12) (15.66) (15.20) (14.73) (14.27) (13.81) (13.35)

[.14] [.14] [.13] [.13] [.13] [.13] [.14]

10 (16.32) (15.86) (15.40) (14.94) (14.48) (14.02) (13.55)

20 (16.55) (16.08) (15.52) (15.16) (14.70) (14.24) (13.77)

30 16.78 16.32 15. 86 15.40 14.93 14.47 14.01

40 17.03 16.57 16.11 15.65 15. 19 14. 73 14.26

50 17.30 16 . 84 16.38 15.92 15.46 14.99 14.53

[.07] [.06] [.05] [.05] [.05] [.05] [.06]

60 17.59 17.13 16.66 16.20 15. 74 15.28 14.82

70 17.89 17.43 16. 96 16 . 50 16. 04 15.58 15.12

80 18.20 17.74 17.28 16. 82 16.36 15.89 15.43

90 18 . 53 18.07 17.61 17 . 15 16.69 16.23 15. 76 100 18.88 18.42 17.96 17.50 17.04 16.57 16.11

[.09] [.09] [.OS] [.08] [.08] [.09] [.09]

Table 1.18

Solubility of NaCl (weight percent) in a solution containing

12 weight percent CaCl^ plus the KCl concentration as given.

Data in parentheses, ( ), are extrapolated; the solution may

be supersaturated in one or more solid phases other than

halite. Precision (3 sigma) is given in brackets, [ ], for

the 0°, 50°, and 100°C isotherms.

Temperature KCl concentration in weight percent

i°ci

0

10

2030

40

50

60

70

80

90 100

(14.26) (13.83) (13.39) (12.96) (12.55) (12.10)

[.14] [.14] [.13] [.13] [.13] [.14]

(14.48)

(14.71)

14. 96 15.23

15.51

[.07]

15.81

16. 12 16.45

16.80

17 . 16

(14. 05)

(14.28)

14. 53 14.80

15.08

[.06]

15.38

15 . 69

16. 02 15.37

16.73

(13.61)

(13.85)

14 .10 14.36

14.65

[.05]

14.95

15.26

15.59

15 . 94 16.30

(13.18)

(13.42)

13.67

13.93

14.21

[.04]

14.51

14. 83

15. 16

15 . 50 13 . 86

(12.75)

(12.98)

13.23

13. 50

13 . 78 [.05]

14 . 08

14. 39

14 . 72 15.07

15 . 43 [.10] [.09] [.09] [.09] [.09]

(12.32)

(12.55)

12.80

13.07

13.35

[.05]

13.65

13.96

14.29

14.64

15.00

[.09]

37
Table 1.19

Solubility of NaCl (weight percent) in a solution containing

14 weight percent CaCl^ plus the KCl concentration as given.

Data in parentheses, ( ), are extrapolated; the solution may

be supersaturated in one or more solid phases other than

halite. Precision (3 sigma) is given in brackets, [ ], for

the 0°. 50°, and 100°C isotherms.

Temperature KCl concentration in weight percent

(°C] 2. 1 ±. 3 4 5

0 (12.43) (12.04) (11.64) (11.25) (10.85) (10.46)

[.15] [.14] [.14] [.14] [.14] [.14]

10 (12.67) (12.27) (11.88) (11.48) (11.08) (10.69)

20 (12.92) (12.52) (12.12) (11.73) (11.33) (10.94)

30 13.18 12.78 12.39 11.99 11.60 11.20

40 13.46 13.07 12.67 12.27 11.88 11.48

50 13.76 13.36 12.97 12.57 12.17 11.78

[.08] [.07] [.05] [.05] [.05] [.06]

60 14.07 13.67 13.28 12.88 12.49 12.09

70 14.40 14.00 13.61 13.21 12.81 12.42

80 14.74 14.35 13.95 13.55 13.16 12.76

90 15.10 14.71 14.31 13.91 13.52 13.12

100 15.48 15.08 14.69 14.29 13.89 13.50

[.12] [.11] [.10] [.10] [.10] [.10]

38
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39
Table 1.21

Density of halite saturated solutions in the system H20-Nacl.

From reference [122]. System H20-NaCl. The densities above

160°C are extrapolated to the saturation curve from densities

measured at lower temperatures and at concentrations at and

below 30 wt . percent. The precision between 0° and 110°C is

0.5 kg/m^; above 110°C the precision is 6 kg/nc'

.

Temperature Concentration Dens ity

(°C) (wt . percent) (kg/m^)

0 25.99 1208.9

10. 26.11 1204.5

20. 26.24 1200.1

30. 26.40 1195 . 8 40. 26 .57 1191 . 5 50. 26. 76 1187.2

60. 26.97 1182 . 9 70. 27.19 1178 . 7 80. 27.44 1174 . 4 90. 27.70 1170 . 3 100. 27.99 1166 .

1

110. 28. 29 1162 . 0 120. 28.61 1158.

130. 28.95 1153.

140. 29.31 1148.

150. 29.69 1143.

160. 30.10 1138 . 170. 30.52 1132 . 180. 30.96 1127 . 190. 31.42 1122.

200. 31.90 1116.

210. 32.40 1111.

220 . 32.93 1106.

230. 33.47 1101

.

240. 34.04 1097.

250. 34.62 1092 . 260. 35. 23 1088 . 270 . 35.86 1084 . 280. 36.51 1080.

290. 37.18 1077 . 300. 37.87 1073.

between 100° and 400°C. The precision of the data is given at the bottom of each column. NBT3 is a synthetic

bittern having the following composition:

Component

KCl

MgCl2

CaCl2

Total dissolved solids

Concentration

0.200 wt. pet.

9.366

37.821

47.387 wt. pet.

1.7.3. Density

The data for the densities of pore fluids are unreliable

because the composition and the sampling temperature

vary widely. The concentrations are higher than those

usually used in research studies on solutions of inorganic

salts. Table 1.21 gives the density of halite-saturated

solutions as a function of temperature [122] . Pore fluids,

containing less dissolved NaCl but more of the other

components such as KCl, MgCl2, MgS04, or CaCl2,

would be denser than the fluids in the system H20-NaCl

for which data are tabulated.

[1] Bishop, E.E., Eckel, E.B., and others. Suggestions to Authors of

the Reports of the United States Geological Survey, 6th Edition, 273 pp.. United States Government Printing Office,

Washington, DC (1978).

[2] Pierce,W.G., and Rich, E.I., Summary of Rock Sah Deposits in the United States as Possible Storage Sites for Radioactive Waste Materials: United States Geological Survey Bulletin

1148, 91 pp. (1962).

[3] Kinsman, D.J.T., Evaporites: Relative Humidity Control of Primary Mineral Facies: Journal of Sedimentary Petrology

46, 273-279 (1976).

[4] Ochsenius, C, Die Bildung der Steinsalzlager und ihrer

Mutterlangensalze, 172 pp., C.E.M. Pfeffer, Halle (1877).

[5] Dellwig, L.F., "Primary Sedimentary Structures of Evaporites,"

in The Geology ofSaline Deposits, G. Richter-Bernberg, Editor,

pp. 53-60, UNESCO Symposium, Paris (1972).

[6] Dellwig, L.F., Origin of the Salina Salt of Michigan: Journal of Sedimentary Petrology 25, 83-110 (1955).

[7] Richter-Bernberg, G., "Sedimentological Problems of Saline Deposits," in The Geology of Saline Deposits, G. T ichter- Bernberg, Editor, pp. 33-37, UNESCO Symposium, Paris

(1972).

40
[8] Scruton,. P.C., Deposition of Evaporites: American Association

of Petroleum Geologists Bulletin 37, 2498-2512 (1953).

[9] Hsii, K.J., Origin of Saline Giants: A critical Review after the Discovery of the Mediterranean Evaporite: Earth Science

Reviews 8, 371-396 (1972).

[10] Stewart, F.H., Marine Evaporites: United States Geological

Survey Professional Paper 440-Y, 52 pp. (1963).

[11] Sloss, L.L., Evaporite Deposition from Layered Solutions: American Association of Petroleum Geologists Bulletin 53,

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[12] Schmalz, R.F., Deep-water Evaporite Deposition: A Genetic

Model: American Association of Petroleum Geologists

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[13] Kirkland, D.W., and Evans, Robert, Editors, Marine Evaporites:

Origin, Diagenesis, and Geochemistry, 426 pp., Dowden,

Hutchison, and Ross Inc., Stroudsberg, PA (1973).

[14] Usiglio, J., Analyse de I'eau de la Mediterranee sur les cotes de

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(1849).

[15] Borchert, Herman, and Muir, R.O., Salt Deposits: The Origin,

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[16] Borchert, Herman, Principles of Oceanic Salt Deposition and

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821-861 (1969).

[17] Jones, C.L., "The Occurence and Distribution of Potassium

Minerals in Southeastern New Mexico," in Guidebook of

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New Mexico Geological Society (1954).

[18] Jones, C.L., Petrology of the Evaporites from the Wellington

Formation near Hutchinson, Kansas, United States Geological Survey Bulletin 1201-A, 70 pp. (1964).

[19] Anderson, R.Y., and Kirkland, D.W., Intrabasin Varve

Correlation: Geological Society of America Bulletin 77,

241-255 (1966).

[20] Gary, Margaret, McAfee, Robert, Jr., and Wolf, C.L., Editors,

Glossary of Geology, 805 pp., American Geological Institute,

Washington, DC (1972).

[21] Braitsch, Otto, Salt Deposits, Their Origin and Composition, 297

pp., Springer-Verlag, New York (1971).

[22] Kupfer, D.H., "Mechanism of Intrusion of Gulf Coast Salt," in Symposium on the Geology and Technology of Gulf Coast Salt, Baton Rouge, LA 1967, Proceedings, D.H. Kupfer, Editor,

25-66, Louisiana State University School of Geoscience, Baton Rouge, LA (1970).

[23] Reference [21], p. 108.

[24] Lees, G.M., "Salt—Some Depositional and Deformational

Problems," in Symposium on Salt Domes, Vol. 17. 259-280, Journal of the Institute of Petroleum Technologists, London

(1931).

[25] Reference [15], p. 133.

[26] Reference [15], p. 108

[27] Baar, C.A., Applied Salt-rock Mechanics I,TheIn-situ Behavior

of Salt Rocks: Developments in Geotechnical Engineering

16A, Elsvier, Amsterdam, 294 pp. (1977).

[28] Reference [15], p. 294.

[29] Reference [15], p. 109.

[30] Johnson, K.S., and Gonzales, Serge, Salt Deposits in the United

States and Regional Geologic Characteristics Important for Storage of Radioactive Waste: Earth Resource Associates,

Inc., Athens, GA, 188pp. (March 1978) (Prepared underU.S.

Government contract W-7405-eng-26 with the Department

of Energy, The Office of Waste Isolation.)

[31] Reference [30], figure 7.

[32] Reference [2], p. 69.

[33] Andrews, D.I., The Louann Salt and Its Relationship to Gulf

Coast Salt Domes: Gulf Coast Association Geological

Societies Transactions 10.215-240 (1960).

[34] Reference [2], p. 71.

[35] Lefond, S.J., Handbook of World Salt Resources: 384 pp.. Plenum

Press, New York (1969).

[36a] Halbouty, M.T., Salt Domes, Gulf Coast Region, UnitedStates and

Mexico, 425 pp.. Gulf Publishing Co., Houston, TX (1967).

[36b] Hurlbut, C.S. Jr., Dana's Manual of Mineralogy, 17th Edition,

609 pp., John Wiley and Sons Inc., New York (1959).

{37] Ode, Helmer, Review of Mechanical Properties of Salt Relating

to Salt Dome Genesis: Geological Society of America Special

Paper 88, 544-595 (1968).

[38] Nettleton, L.L., Fluid Mechanics of Salt Domes: American

Association of Petroleum Geologists Bulletin 18, 1175-1204

(1934).

[39] Reference [ 15] , p. 243.

[40] Romanes, James, "Salt Domes of North Germany," in Symposium on Salt Domes, Vol 17, 252-258, Journal of the

Institute of Petroleum Technologists, London (1931).

[41] Kupfer, D.H., Louisiana Salt Domes and the Mississippi Deltaic

Plain: 60 pp.. New Orleans Geological Society Guidebook

(1972).

[42] Schwerdtner, W.M., "Preferred Orientation of Halite in a 'Salt Seismogram,' " in Second Symposium on Salt, Jon L. Rau,

Editor, Vol. 1, 70-84, Northern Ohio Geological Society, Inc., Cleveland, OH (1966).

[43] Reference [24] p. 276.

[44] Reference [15], p. 244.

[45] Reference [41], p. 20.

[46] Reference [41], p. 24.

[47] Walker, C.W., "Nature and Origin of Caprock Overlying Gulf

Coast Salt Domes," in Fourth Symposium on Salt, Alan H. Coogan, Editor, Vol. 1, 169-195, Northern Ohio Geological

Society, Inc., Cleveland, OH (1974).

[48] Taylor, R E., "Caprock Genesis and Occurrence of Sulfur

Deposits," in The Geology of Saline Deposits, G. Richter- Bernberg, Editor, 253-254, UNESCO Symposium, Paris

(1972).

[49] Jenson, M.L., Isotopic Geology and the Origin of Gulf Coast and

Sicilian Sulfur Deposits: Geological Society of America

Special Paper 88, 525-536 (1968).

[50] Reference [41], p. 9.

[51] Kupfer, D.H., "Structure of Salt in Gulf Coast Domes,"

Symposium on Salt, Cleveland, 1962, A.E. Bersticker, Editor,

104-123, Northern Ohio Geological Society, Inc., Cleveland, OH (1963).

[52] Reference [22], p. 55.

153] Reference [22], p. 45.

[54] Reference [15], pp. 4-7.

[55] Reference [21], pp. 8-15.

[56] Reference [22], p. 45.

[57] Reference [37], p. 550.

[58] Treesch, M.I., and Friedman, G.M., "Sabkha Deposition of the

Salina Group (Upper Silurian) of New York State," in Fourth Symposium on Salt, Alan H. Coogan, Editor, Vol. 1, 35-46,

Northern Ohio Geological Society, Inc., Cleveland, OH

(1974).

[59] Hall, J. F., "Distribution of Salt in Ohio," in Symposium on Salt, Cleveland, 1962, A.C. Bersticker, Editor, 27-30, Northern

Ohio Geological Society, Inc., Cleveland, OH (1963).

41
Reference [2], p. 70. Taylor, R.E., Water Insoluble Residues in Rock Salt of Louisiana Salt Plugs: American Association of Petroleum

Geologists Bulletin 21, 1268-1310 (1937).

Reference [6] , p. 89. Schaller, W.T., and Henderson, E.P., Mineralogy of drill cores from the Potash Field of New Mexico and Texas: United

States Geological Survey Bulletin 833, 124 pp. (1932).

Reference [41], p. 18. Balk, R., Structure of Grand Saline Salt Dome, Van Zandt

County, Texas: American Association of Petroleum Geologists Bulletin 33. 1791-1820 (1949). Reference [37] , p. 549. Ode, Helmer, "Physical Properties Work Sessions," led by

Helmer Ode, Geological Society of America Special Paper

88, 683-701 (1968). Reference [37], p. 551. Guido, R.S., and Warner, S.E., Project Cowboy, Physical

Properties of Salt Samples: University of California, Lawrence Radiation Laboratory, U.C.R.L. 6069, 14 pp. (1960).

Holser, W.T., Chemistry of Brine Inclusions in Permian Salt from Hutchinson, Kansas [abs.j. Geological Survey of America Special Paper 88, 537 (1968). Kramer, J.R., History of Sea Water, Constant Temperaturepressure Equilibrium Models Compared to Liquid Inclusion Analyses: Geochimica et Cosmochimica Acta 29, 921-945

(1965).

McCulloch, D.S., Vacuole Disappearance Temperatures of Laboratory-Grown Hopper Halite Crystals: Journal of Geophysics Research 64, 849-854 (1959).

Dreyer, R.M., Garrels, R.M., and Howland, A.L., Liquid

Inclusions in Halite as a Guide To Thermometry: American

Mineralogist 34, 26-34 (1949).

Peach, P. A., Liquid Inclusions in Geothermomelry: American

Mineralogist 34, 460-461 (1949).

Roedder, Edwin, Composition of Fluid Inclusions: United

States Geological Survey Professional Paper 440-JJ, 164 pp. (1972).

Reference [71], p. 940.

Roedder, Edwin, Studies of Fluid Inclusions II: Freezing Data

and Their Interpretation: Economic Geology 58, 167-211

(1963). Reference [71], pp. 938-940. Shuman, C.A., and Fiedelman, H.W., "Gross Imperfections and

Habit Modification in Salt Crystals," in Second Symposium on

Salt, Jon L. Rau, Editor, Vol. 2, 246-253, Nortnern Ohio

Geologic Society, Inc., Cleveland, OH (1966).

Reference [77] , p. 182.

Aufricht, W.F., and Howard, K.C., Salt Characteristics as They

Affect Storage of Hydrocarbons: Journal of Petroleum

Technology 13, 733-738(1961).

Reference [67], Table 1.

Reference [79], p. 249.

Reference [81], p. 733.

Reference [77] , p. 183. Roedder, Edwin, United Slates Geological Survey, Reston, VA,

personal communication (1978).

Reference [27], p. 168.

Giesel, W., "Outbursts of Carbon Dioxide in Potash Mines

Fundamentals and Possibilities of Forecast," in The Geology

of Saline Deposits, G. Richter-Bernberg, Editor, 235-239,

UNESCO Symposium, Paris (1972).

[89] Calzia, James, and Hiss, W.L., Igneous Rocks in the Northern

Delaware Basin: New Mexico Bureau of Mines and of Mineral Resources Circular 159 (1978, in press).

[90] Refernece [27], p. 34.

[91] Hoy, R.B., Foose, R.M., and O'Neil, B.J., Structure of the Winnfield Salt Dome, Winn Parish, Louisiana: American

Association of Petroleum Geologists Bulletin 46, 1444-1459

(1962).

[92] Reference [75], p. 43.

[93] Reference [91] , p. 1458

[94] McClain, W.C., Lomenick, T.F., and Lowrie, R.S., Geologic

Disposal Evaluation Program Semi-annual Report, United

States Atomic Energy Commission, Oak Ridge National Laboratory, ORNL 5052, 135 pp. (1975).

[95] Reference [27] , p. 35.

[96] Reference [91] , p. 1459.

[97] Reference [61], p. 1283.

[98] Reference [94] , Table 2.3.

[99] Belchic, H.C., "The Winnfield Salt Dome, Winn Parish,

Louisiana," in Interior Salt Domes and Tertiary Stratigraphy of North Louisiana, 29-47, Shreveport Geological Society

Guidebook (1960).

[100] Reference [91], p. 1458.

[101] Reference [27], p. 44.

[102] Reference [99], p. 38.

[103] Atwater, G.I., Gulf Coast Salt Dome Field Area: Geological

Society American Special Paper 88, 29-40 (1968).

[104] Reference [99], p. 39.

[105] Reference (61), p. 1278.

[106] Reference [27], p. 36.

[107] Reference [81], p. 735

[ 108] Reynolds, T.D., and Gloyna, E.F., Permeability of rock salt and

creep of underground cavities: United States Atomic Energy

Commission Report TD 12383, 121 pp, as cited in Robertson,

E.G., Physical Properties of EvapOrite Minerals: United

States Geological Survey Report TEI-821, 99 pp. (1962).

[109] Stevens, P.R., United States Geological Survey, Reston, VA,

personal communication (1978).

[110] Reference [27], p. 89.

[Ill] Reference [81], p. 736.

[ 1 12] Reference [27] , p. 88.

[113] Reference [99], p. 37.

[114] Reference [81], p. 734.

[115] Parker, F.L., Hemphill, L., and Crowell, J., Status Report on Waste Disposal in Natural Salt Formations: United States Atomic Energy Commission, Oak Ridge National Laboratory,

ORNL 2560, 58 pp. (1958).

[116] Reference [41], p. 41.

[117] Reference [81], p. 738.

[118] Hawkins. M.E., and Jirik,C.J., Salt Domes in Texas, Louisiana,

Mississippi, Alabama, and Offshore Tidelands, A Survey:

United States Department of the Interior, Bureau of Mines

Information Circular 8313, 78 pp. (1966).

[ 1 19) Interstate Oil Compact Commission, Research and Coordinating

Committee, Underground Storage of Liquid Petroleum

Hydrocarbons in the United States: Oklahoma City, OK

(April 1956).

[120] Reference [81], figure 12.

[121] Clynne, M.A. and Potter, R.W., United States Geological

Survey, Menio Park, CA, unpublished data (1978).

[122] Haas, J.L., Jr., Physical Properties of the Coexisting

Phases and the Thermochemical Properties of the H2O

Component in Boiling NaCl Solutions: United States

Geological Survey Bulletin 1421-A, 73 pp. (1976).

42
[123] Borchert, Herman, "Secondary Replacement Processes in Salt and Potash Deposits of Oceanic Origin," inThe Geology of

Saline Deposits, G. Richter-Bernberg, Editor, 61-67, UNESCO Symposium, Paris (1972).

[124] Reference [61], table V.

[125] Looker, CD., "Salt," in Encyclopedia of Chemical Technology,

R.E. Kirk and D.F. Othmer, Editors, Vol. 12, 67-82,

Interscience Encyclopedia, Inc., New York (1954).

[126] Reference [108], p. 12.

[127] Reference [36b], pp. 597-609.

[128] Reference [108], pp. 14-17.

[129] Reference [15], pp. 4-7.

[130] Peters, J.W., and Dugan, A.F., Gravity and Magnetic Investigation at the Grand Saline Salt Dome, Van Zandt Co., Texas: Geophysics 10, 376-393 (1945).

[131] Allen, W.E., Caillouet, H.J., and Stanley, L., Gravity Investigations in the Hockley Salt Dome, Harris County, Texas: Geophysics 20, 829-840 (1955).

[132] Jakosky, J.J., Exploration Geophysics, 1195 pp., Trija Publishing

Co., Los Angeles, CA (1950).

[133] Reference [69], p. 8.

[134] Moore, J.G., Thermal Conductivity Measurement and Develop- ment: United States Department of Energy, Office of Waste

Isolation, Progress Report Y/OWI/TM-43/6, 13-15 (1978).

[135] Reference [75], Table 6.

[136] Holser, W.T., "Chemistry of Brine Inclusions in Permian Salt from Hutchison, Kansas," in Symposium on Salt, Cleveland,

1962, A.C. Bersticker, Editor, 86-95, Northern Ohio Geologic Society, Inc., Cleveland, OH (1963).

[137] Reference [71], table 5 and [75], table 4.

['l38) Reference [81], table 1.

[139] Reference [81], table 2.

[140] Landes, K.K., "Origin of Salt Deposits," in Symposium on Salt, Cleveland, 1962, A.C. Bersticker, Editor, 3-9, Northern Ohio

Geological Society, Inc., Cleveland, OH (1963).

[141] Reference [30], p. 10, figure 1.

[142] Reference [9], figure 1.

[143] Reference [8], figure 4.

[144] Reference [14], figure 5.

[145] Reference [38], figure 1.

[146] Reference [36a], figure 6-3.

[147] Reference [79], figure 4.

[148] Reference [81], figure 11.

[149] Reference [81], figure 12.

Symbols and Units

Symbol Name Unit

P

tT

P

</> m

Density

Temperature, degrees Celsius Temperature, kelvins Pressure, pascals

Porosity

Permeability

kg/ m' °C

K

Fa

md

Conversion Factors

Length

To convert from

feet

tometers

Multiply by

3.048

Temperature

To convert from

°C

toK

Add

273.15

Density To convert from

kg/ m'

tog/cm'

Multiply by

1 X 10-3

Pressure To convert from

MPa

tobar

Multiply by

10-1

43

Chapter 2

Physical and Chemical Properties of Components in Salt Deposits

Reginald P. T. Tomkins*

Contents

Page

2. Physical and Chemical Properties of Components ifi Salt Deposits 46

2.1. Introduction 46

2.2. Experimental Techniques 46

2.2.1. Chemical Compositions 46

2.2.2. Density 46

2.2.3. Crystallography 47

2.2.4. Thermodynamic Properties 47

2.2.5. Solubility 47

2.2.6. Accuracy and Precision 48

2.3. Physical Properties: Halite 49

2.3.1. Chemical Variability 49

2.3.2. Density 49

2.3.3. Compressibility 50

2.3.4. Crystallography 50

2.3.5. Thermodynamic Properties 51

2.3.6. Equation of State 51

2.4. Physical Properties of Major Impurities in Halite 51

Anhydrite 51

2.4.1. Chemical Variability 51

2.4.2. Density 54

2.4.3. Crystallography 54

2.4.4. Thermodynamic Properties 55

2.4.5. Equation of State 55

Gypsum 56

2.4.6. Chemical Variability 56

2.4.7. Density 56

2.4.8. Crystallography 56

2.4.9. Thermodynamic Properties 56

2.4.10. Equation of State 56

Calcite 57

2.4.11. Chemical Variability 57

2.4.12. Density 57

2.4.13. Crystallography 57

2.4.14. Thermodynamic Properties 57

2A 15. Equation of State 59

Polyhalite 60

2.4.16. Chemical Variability 60

2.4.17. Density 60

2.4.18. Crystallography 60

* Department of Chemical Engineering and Chemistry, New Jersey Institute of Technology, Newark, New Jersey

45
2.4.19. Thermodynamic Properties 60

2.4.20. Equation of State 60

Clays 60

2.4.21. Chemical VariabiHty 60

2.4.22. Density 60

2.4.23. Crystallography 60

2.4.24. Thermodynamic Properties 64

2.4.25. Equation of State 64

2.5. Chemical Properties Among Components in Salt Deposits 66

2.5.1. The System NaCl-KCl-MgClz-HzO 66

2.5.2. The System Anhydrite-Water-NaCl 67

2.5.3. The System Gypsum-Water-NaCl 74

2.5.4. Comparison of the Systems Anhydrite-Water and Gypsum + Water 83

2.5.5. The System Calcite-Water + (NaCl, CaClj . . .) 83

2.5.6. Dehydration of Gypsum 83

2.5.7. Additional Information 98

References 100

Symbols and Units 101

Conversion Factors 101

2. Physical and Chemical Properties of

Components in Salt Deposits

2.1. Introduction

The physical and chemical properties of the components found in salt deposits are presented in this chapter.

The concern is largely with the principal constituent of

such deposits, namely halite and some of the more common impurities, particularly anhydrite, CaS04;

gypsum, CaS04 • 2H2O; calcite, CaCOs; polyhalite,

K2Ca2Mg(S04) 4

• 2H2O, and various types of clay

minerals.

The properties of chemical variability, density,

crystallography, and thermodynamic parameters (entropy, enthalpy of formation and free eneigy of

formation) have been evaluated and are reported

herewith. An equation of state has been included if available. An assessment of the chemistry among the

components H20-NaCl-CaS04-CaC03-KCl-MgCl2 was

also undertaken. The results for data on aqueous

solubility, dehydration reactions, formation of solid

solutions and phase diagrams for the systems indicated

above are also reported in this chapter. A brief discussion

of the techniques used for such measurements, together

with remarks on the experimental accuracy, and

precision is first given since an appreciation of this is basic to the data tabulations that follow.

2.2. Experimental Techniques

The experimental aspects for property measurements,

such as chemical compositions, density, crystallography.

thermodynamic properties, and solubility are considered in this section. References to recommended experimental investigations, in which the various techniques have been used, are included.

2.2. 1. Chemical Compositions

Most of the analyses of the components of salt deposits

have been performed using atomic absorption spectroscopy. The limits of detection for the analysis of rock salt varied from 0.0025-0.00005 ppm.

An example of the experimental approach is that by

Bloomberg [1]. The salt was dissolved in water and

allowed to stand overnight, then filtered. The residue was washed with several portions of distilled water and

the filter paper and insolubles were dried overnight at 383 K. The paper was separated and ashed, then the

residue was added to the ash and the total weighed as insolubles. This portion was ground in an agate mortar

and analyzed spectrographically.

The trace elements in the soluble fraction were

precipitated with H2S from slightly alkaline brine, using

high purity lead as a carrier. The precipitate was allowed

to settle overnight and was then separated from the

alkaline brine by centrifuging, and washed several times

with slightly alkaline H2S-saturated distilled water. The

washed precipitate was then transferred to a crucible,

dried at 383 K, and analyzed spectrographically.

2.2.2. Density

Methods available for the determination of the densities of solids are described in detail by Bauer and Lewin

[2] . Most of the commonly used methods depend on

immersing the solids in some inert fluid of known

46
density. The methods may be conveniently divided into

displacement methods (pycnometric, dilatometric) and

buoyancy methods (Archimedean principle).

A common displacement method uses a pycnometer

where the volume of a known mass of the solid is found

by determining the changes in weight when the

pycnometer is successively filled with a liquid of known

density, solid plus air, and solid plus liquid. With due

precautions an accuracy of about + 0.0005 or + 0.1% for

the density can be achieved.

Hydrostatic weighing appears to be the most

commonly employed buoyancy method, in which the

apparent loss of weight is obtained by weighing the solid

first in air and then immersed in the liquid. The

accuracy of this method is about + 0.001 or + 0.2%. The

main difficulty in these methods is that of completely

removing all the air trapped by the solid. Variations of

up to 5 percent have been obtained for individual

crystals taken from the same source.

2.2.3. Crystallography

X-ray diffraction techniques have been used to obtain

the crystallographic parameters. The various techniques

for determination of the structure of minerals are described by Gr mshaw [3] . Large crystals are examined

by means of a smgle crystal goniometer, with a GeigerMiiller counter attachment to accurately detect the

positions and relative intensities of the spots. Interlattice

spacings accurate to + lO'^'^m are attainable using x-ray

methods.

In cases where single crystal specimens are not

available a powder sample can be used successfully. Most

minerals lend themselves to the powder technique.

However, it should be noted that the information

obtained from a powder diffraction pattern is less complete compared to the single crystal pattern due to accidental overlap of powder lines with approximately

the same Bragg angle. Another problem that is encountered with powder diffraction patterns is the

existence of a stronger background leading to the

possiblity of some weaker reflections being overlooked.

For measurements at higher pressures Jamieson [4]

has described a new technique using "amorphous"

boron as a pressure vessel for studies up to Wpascal

pressure. The cell consists of a boron water sandwiched

between two carboloy platens. The x-rays are collimated

so that the beam traverses the wafer normal to its axis.

The use of a Bridgman-anvil high pressure apparatus has

been reported by Sato [5], which adapts the x-ray

Debye-Scherrer system using a high pressure cell of

boron, solidified with a polyester resin. Readings

accurate to +0.02° were attainable with this technique.

There are two important methods for measuring x-ray

intensities. In the photographic or densitometric method, lo is the intensity of the incident light scanning the

densitometer trace and consequently Iq > I. The geiger

method involves a direct measurement of x-ray

scattering and accomplishes a comparison of the incident and scattered x-ray beam intensities. It is always

advisable to check on the technique employed before

using the reported values of intensities.

2.2.4. Thermodynamic Properties

The thermodynamic properties have been measured

(or derived from) either low temperature adiabatic

calorimetry (heat capacities) or combustion bomb

calorimetry (heats of combustion) . A detailed discussion

of these methods is given by Sturtevant [6] . Additional

discussion of the precision and accuracy attainable with

adiabatic calorimeters is reported by Staveley [7].

Depending on the temperature range the precisions

expected for heat capacity data are as follows: 0.7%

(10-30 K), 0.2% (30-100 K), and 0.1% (100-300 K).

The expected accuracy is about 0.16%.

Heat capacities are obtained using theNernst method,

in which the material under investigation is contained in a metal calorimeter which is equipped with a heater and a temperature measuring device such as a resistance

thermometer, thermocouple, or thermistor. The calorimeter is supported inside a jacket of large heat capacity

and accurately measurable temperature. The jacket is contained within another vessel, such as a Dewar flask,

which is cooled by liquid air or liquid hydrogen. Several

adiabatic calorimeters exist in which the jacketcalorimeter temperature difference is kept so small that

thermal leakage is negligible.

The enthalpies and free energies of formation reported

in this chapter have been obtained from heats of

combustion data using bomb calorimetry. Data having an

accuracy of a few hundredths of a percent may be

obtained using the bomb calorimeter. A detailed

description of the bomb calorimeter is given by

Sturtevant [6].

The selection of the best values for the thermodynamic parameters has been based on four major critical

compilations, namely: The JANAF tables [31], the

tabulations 'of Barin and Knacke [53] , the NBS Circular

500 [55] , and the U.S. Geological Survey Bulletin [ 1 17]

.

2.2.5. Solubility

Methods for measuring solubilities and phase diagram

data have been described concisely by Potter et al. [8]

.

Three major categories of experimental techniques exist

for the determination of the solubility of a salt in an

47
aqueous solution as a function of temperature. These are quench methods, visual methods, and so-called indirect

methods. Quench methods involve separating a representative sample of the saturated solution from the salt crystals at a certain temperature, quickly cooling the

separated solution to room temperature, and finally

analyzing its salt content using atomic absorption

spectrophotometry or titration methods. Studies

employing the visual method involving viewing a mixture of solution plus salt crystals plus vapor of

known bulk composition as temperature is increased

slowly until the last salt crystal dissolves. Solubility is determined with the indirect methods by utilizing

changes in the intensive properties of a system of salt crystals plus saturated solution plus vapor of known

bulk composition to detect the dissolution of the last

salt crystal.

The quench method has been developed to obtain data

at higher temperatures than were possible in earlier

studies. Basically the modification consists of a "bomb in

bomb" method, in which an empty bomb is sealed in a bomb filled with salt crystals plus solution in such a way

that the inner bomb can be opened and closed. Some of

the difficulties that are encountered with the quench

method include density, stratification, super-saturation,

analytical problems, precipitation on quench, and the

criteria for establishing equilibrium. With the visual

method, limiting factors include visibility during heating, density stratification, and the effect of devitrification on the ultimate strength of the glass.

Most of the geological solubility data have been

obtained via indirect methods. An example of an indirect

method consists of measuring the pressure as a function

of volume of a known bulk composition at constant

temperature. The dissolution of the last salt crystal is detected by discontinuities in the pressure-volume

curves. Another indirect method used for solubility

measurements is to measure vapor pressure of the

solution as a function of the composition at constant

temperature. The composition at which the pressurecomposition curve becomes constant is taken as the

solubility of the salt at the temperature of the

measurement. A limiting factor (with respect to the

accuracy) is the spacing of the compositions; the more

closely spaced, the greater the accuracy.

Potter et al. [8] have recently devised a new method

for measuring the solubility of simple salts in water at elevated temperatures involving heating assemblages of

salt crystals plus solution vapor at a constant rate in a platinum-lined bomb. The dissolution of the last salt

crystal is evidenced by a distinct discontinuity in the

pressure-temperature curve. The uncertainty of the

solubility data ob+ainerl bv this method was estimated to be +0.1 weight percent of salt.

The preceding observations on accuracies and

precision of the various techniques are summarized in

table 2.1.

2.2.6. Accuracy and Precision

The accuracy estimates are based on experimental

details including method of measurement, techniques,

analytical characterization of materials and, wherever

possible, intercomparisons with results from different

investigators. Where precision estimates were advanced

by the investigators, these are reported accordingly;

where the data were subjected to further analyses, the

precisions advanced are based on the statistical analyses.

Temperature-dependent or pressure-dependent equations are reported wherever possible. The statistical analysis was performed on the computer facilities at Rensselaer Polytechnic Insititue. The criterion for

choosing the equation of best fit using a least-squares

one-dimensional analysis is the standard error of

estimate defined by

s = n - q

where ^ e ~ the experimental value at each temperature,

7c = the value calculated from the least squares equation

at the same temperature as 7e> ~ the number of

experimental data points, and q

= the number of

coefficients in the least squares equation (2 for linear, 3

for quadratic). Alternatively, in the case of a linear

regression analyses, the measure of the precision of the

data is r^, defined as:

^"[x,.-<M!][.,,.<£|)l]

where and jj are the data pairs and n the number of

data pairs. For an exponential curve fit, is given by:

The closer the value of H is to unity the more precise is the data.

48
Table 2.1. Summary of accuracies and precisions for physical

and chemical properties of components in salt deposits

Prope rty Technique Accuracy Limits of

Precision

Recommended

Studies

Chemical

composition

atomic

absorbtion

0.0025-

0 .OOOOSppm

[1]

pycnometric ±0.11 0.051

Dens i ty

Archimedean ±0.01% 0.05%

[2]

Crystal - lography

x-ray diffraction±0.0051 0.00 2% [3]

Thermodynamic

properties

combustion or adiabatic

calorimetry

±0 .2% 0.1-0.7% [6], [7]

quench methods ±0 .5% 0.8%

Solub i 1 i ty visual ±0 .51 0.8% [8]

indirect [e.g.

pressure - com- position

±0.1% 0.5%

2.3. Physical Properties: Halite

2.3.1. Chemical Variability

The most common insoluble impurities in halite [9] are anhydrite, gypsum, dolomite, calcite, pyrite, quartz,

and iron oxides. The most common soluble impurities

include the following ions: Ca^2^ Mg^^ K% CI , C0^2,

and SOj^; in addition, Ba+2, Sr+2, B^^ ^^d Br may be

present in minor amounts. In some deposits associated

minerals are present. These minerals include the

following:

Sylvite, KCl

Carnallite, KMgCls • 6H2O

Tachydrite, 2MgCl2 • I2H2O

Bischofite, MgClz • 6H2O

Kainite, MgS04 • KCl • 3H2O

Anhydrite, CaS04

Vanthoffite, MgSo4 • 3Na2S04

Glaserite, K3Na(S04)2

Langbeinite, 2MgS04 • K2SO4

Syngenite, CaS04 • K2SO4 • H2O

Leonite, MgS04 • K2SO4 • 4H2O

Picromerite, MgSO* • K2SO4 • 6H2O

Gypsum, CaS04 • 2H2O

Kieserite, MgS04 • H2O

Epsomite, MgS04 • THjO

Glauberite, CaS04 • Na2S04

Bloedite, MgSO* • Na2S04 • 4H2O

Loeweite, MgS04 • Na2S04

Polyhalite, 2CaS04 • MgS04 ' K2SO4 • 2H2O

Krugite, 4CaS04 • MgSO* • K2SO4 • 2H2O

In natural halite there does not appear to be much

replacement of Na by K, although sylvite (KCl) is isomorphous with halite. Moisture is normally present as saturated brine inclusions within the salt crystals. Gas

bubbles are sometimes found within the inclusions and

consist mainly of air, CO2 and hydrocarbons. Some

typical analyses of halite are listed in table 2.2. These

analyses [10] cover samples found in Michigan, New

York, Ohio, Louisiana and Kansas, which account for

the bulk of production of rock salt in the United States. Commercial rock salt (halite) varies in purity from about

97% (Kansas) to about 99% (Louisiana).

2.3.2. Density

The summary of density values advanced by Doelter

and Leitmeier in 1929 [11] still appears authoritative.

Later values are given for halite from several sources

[12-16] at one temperature with accuracies of about

+ 0.1%. The samples varied from recrystallized salt to halite samples from various sources.

49
Table 2.1. Chemical variability of rock salt

Source

Component

USA

Louisiana New York Michigan Ohio Kans as

Weight Percent (1)

NaCl 99.01 9 8 24 9 8.08 9 7.87 9 7.27

CaSO^ 0.84 \ 48 1.55 1 . 84 2.22

CaCOj 0.10 g 0 S 0.11 0.11

MgCOj 0.01 0 0 6 0.06 n Oft 0.19

SiO^ 0.02 0 11 0.03 0.04 0.23

Fe203 0 .00 0 04 0.01 0.01 0.01

H,0 0.02 0 02 0.16 0.07 0.08

Hunt [12] used the buoyancy method with oil of

turpentine, whereas Moseley [14] reported the density

of hahte as part of a caHbration experiment for the

determination of the x-ray spectra of some elements.

Retgers [13] used a carefully calibrated pycnometer for

the measurement of density, but no other information was provided. The publications by Spencer [15] and

Spannenberg [16] are both review articles. There have

been no more recently determined values for the density

of halite. In 1960 Kaufmann [17] undertook a further

critical assessment of the density data for halite using the

references cited in the 1929 compilauion. The results of

Kaufmann's assessment are recommended as the best

values for density of halite. The densities are in table 2.3.

2.3.3. Compressibility

The values of the compressibility of halite are in table

2.4. These are based on the work of Richards and Jones

[19] and Slater [20]. Some details of these studies

follow.

In the low pressure study by Richards and Jones [19] a

Cailletet compression pump was used to attain the

pressures and the apparatus was immersed in a constant

temperature bath which was maintained at ±0.005°C.

The essential feature of the method was the comparison

of the unknown compressibility with the known

compressibility of mercury, by first compressing

mercury in a given apparatus, measuring both pressure

and change of volume and then displacing most of the

mercury by the substance to be studied, and again

noting the relationship of pressure to volume. The

experiments were performed on both sodium chloride

precipitated from reagent grade salt and on two

specimens of clear, natural halite. The pressure gauge

used in the experiments was calibrated by using the

difference between the compressibility of water and

mercury at 293 K.

Slate [20] used sodium chloride samples grown from

the melt and reported that the error in the values of

compressibility at zero pressure was less than 1%. The

values obtained for variation with pressure and

temperature were stated to be of the order of 5% and 20%

respectively.

2.3.4. Crystallography

The crystal symmetry of halite is cubic hexoctahedral;

this symmetry class is represented as 4/m3 2/m

[Hermann-Mauguin (International) symbols]

.

X-ray crystallographic data for halite have been

reported by several investigators [22-30] . The radiation sources used in these investigations were either

molybdenum [22-24, 27] or copper [25, 28-30] . In view

of several discrepancies in the intensities published on

the ASTM cards, a critical analysis of existing data was

undertaken by Swanson [30] in 1953, together with a redetermination of the crystal parameters using sodium

chloride, twice recrystallized from hydrochloric acid.

The results are in table 2.5. These values are recom- mended as the best values.

50
Table 2.3. Halite: Density (kg/m )

T

(K)

p (±2)

273 2168

283 2165

293 2163

298 2161

303 2160

313 2158

323 2155

heat of solution AHZ, 298.15 - 3857.6 J/mol for NaCl.

The heat capacities were obtained by high temperature

precision calorimetry [32-42] . Temperature drift was

reduced to a value less than 0.1° /min during a temperature measurement. Pt/10% Rhodium thermocouples were calibrated against the melting points of

NBS samples of lead, tin and zinc. The sample container was fabricated from Pt/10% Rhodium and contained a thermocouple well. The results were estimated to be

accurate to + 0.3% with a standard deviation of 54 J/mol.

2.3.6. Equation of State No information on an equation of state is available for

halite.

Temperature- dependent equation, and precision

p = 2237.2057 - 0.254286 T; (r^ = 0.995)

2.3.5. Thermodynamic Properties

Table 2.6 reports the recommended values for the

entropies, standard enthalpies of formation, standard

Gibbs free energies of formation and standard heat

capacities as a function of temperature. These are the

values advanced by Stull, Prophet et al. [31] from the

JANAF thermochemical tables, and are recommended

as the best values. The heat of formation is based on

Ai/°, 298.15 = -240.12 and -167.15 kj/mol for Na^

("1120) and CI' (°°H20), respectively, and on the

2.4. Physical Properties of Major Impurities in

Halite

The major impurities in halite considered here are anhydrite, gypsum, calcite, polyhalite and clays. The

properties of chemical variability, density, crystallography, thermodynamic properties and equation of state have been evaluated and are reported herewith.

Anhydrite, CaSOa

2.4.1. Chemical Variability

Anhydrite occurs as a monomineralic rock in many

textural varieties and grain sizes [43]. It is found mixed

Table 2.4. Coefficient of compressibility, for halite

Low Pressures

Temp Pressure Range gxlO"'^

(K) Pa/m^(xlO- m2/Pa Ref

.

273 9.8-1471 . 0 4 . 13 [18]

293 980. 7-4903 .3 4.11 [19]

303 0 4.20 [20]

High Pressures [21]

Pressure Pressure

Pa(xl0-7) 6(293 K) Pa(xl0-7) 6(293 K)

50 0.0196 300 0.0932

100 0.0371 350 0 . 1043

150 0.0531 400 0.1145

200 0.0677 450 0 . 1239

250 0.0810 500 0.1325

Pressure -dependent equation, and precision

i = 5. 2008x10"^ + 3.9836x10"^ P -• 3. 4203x10"^ P^ + 1.4(i63xl0"-'-'' P^

51
Table 2.5. Crystal lographic parameters for halite

Cubic system

a = b = c = 5.6402xl0"^''m ± 0 . 000 1x1

0

" '''m

a = B = Y = 90°

hkl'^

3.258 13 111

2 . 821 100 200

1.994 55 220

1. 701 2 311

1.628 15 400

1.410 6 400

1 . 294 1 331

1.261 11 420

1.1515 7 422

1.0855 1 511

0.9969 2 440

0.9533 1 531

0.9401 3 600

0 . 8917 4 620

0 . 8601 1 533

0.8503 3 622

0. 8141 2 444

d is the interlattice spacing, in mxlO

^^listhe intensity scaled to the strongest line which was assigned a

value of 100

c1-'hkl are the Miller indices

52
Table 2.6. Thermodynamic parameters for halite

(a) Entropy, enthalpy of formation and free energy of formation

T(K) S°(J/mol K) AH°(kJ/mol) AG°(kJ/mol)

(±0.21) ^(±0.5) '^(±0.5]

298 72,.115 -411 .260 -384,.212

300 72,.429 -411,. 107 -384., 005

400 87,.228 -413,.461 -374..837

500 99 ,.081 -413. 024 -365..229

600 109 ,.052 -412,.352 -355..730

700 117 ,. 729 -411

,

.456 -346.,356

800 125..499 -410. 352 -337.,136

900 132..629 -409,.064 -328., 064

1000 139 ,. 298 -407 ,.593 -319.,133

Temperature-dependent equations, and precision

S° = 47.211 + 0.096428 T;(r^ = 0.982)

AG° = -411.863 + 0.093137 T; (r^ = 0.999)

(b) Heat capacity C°

T(K) C (J/mol K)

P(±0.2)

10 ,.0 0 .,000

15,.0 0 ,, 490

20..0 1

.

,224

25,.0 2 .,937

50,.0 15 ,,175

75,.0 25,,945

100 ,.0 33.,533

150 ,.0 41 .,855

200 . 0 46 .505

250 .0 48 .953

293 .0 50,.177

300 .0 50 .421

400 . 0 52,. 869

500 .0 54,. 827

600 .0 56,. 296

700,.0 57,. 520

800 .0 58,. 743

900 .0 59,.722

1000 .0 60,. 701

1074 .0 61

,

.436

Temperature - dependent equation, and precision

C° = 47.494881 + 0.013561 T (temp, range 300-1074 K)

;

(r^ = 0.973)

53
with calcite, dolomite, magnesite, clay and many other

minerals, including halite. Anhydrite frequently occurs

in bands alternating with massive fibrous gypsum. Table

2.7 gives the chemical analyses for several samples of

anhydrite. It is apparent that only minor variations occur in its composition. Small amounts of strontium

and barium sometimes occur replacing calcium; oxides

are probably present as impurities and H20'^, when

present, is mainly due to the presence of gypsum.

2.4.2. Density

Density data for anhydrite have been reported in two

investigations [44, 45]. Both sets of density data for

anhydrite are in table 2.8. There is insufficient

information for value judgements. No information on

the experimental technique or sample preparation was

given by Braitsch [44]. Ludwig and Muller [45] used a pycnometer, which was calibrated with n-heptane. Due

precautions were taken to eliminate air from the

apparatus. The pressure was normal atmospheric pres- sure.

2.4.3. Crystallography

The unit cell of anhydrite is orthorhombic. The

structure of anhydrite is very different from that of the

barytes group of sulfates and shows more similarity with

the zircon type of structure. Sulfur atoms, (which are at the centers of regular tetrahedra of oxygen) and calcium

atoms, lie on the lines of intersection of the two sets of

mirror planes. Planes containing evenly spaced Ca and

SO 4 ions lie parallel to (100) and (010), whereas layering

is not so well defined parallel to (001). X-ray crystallographic data for anhydrite have been reported by several

investigators [24, 46-52]. The radiation sources used in

these investigations were either molybdenum [24, 46,

51, 52] or copper [47, 50]. In view of several

discrepancies in the intensities published on the ASTM

cards, Swanson [50] undertook a critical analysis of

Table 1.1. Chemical variability of anhydrite

Source

Component

USA Japan Germany

Illinois^ Kano

ussr'^ Stassfurt Celle Australia

Weight Percent (%)

0.50 2 . 73 0.01

AI2O3I

0.10 0.06 1.06 0.04 0.03

MgO 0.60 0.17 0.03

CaO 40 . 86 41.13 39 . 12 41.22 41.08 40 .47

SrO 0.00 0.01 0 . 71

BaO 0.00 0.05

Na^O

K^O

jo. 02 0.07

SO3 57.10 58.37 56.63 58.95 58. 50 58.94

CO,

;> 0 .37 0.17

0.69 0 . 10 0.01 0.04

H^O- 0.01 0.68 0.40

Total 100.61 99 . 75 100.49 100 .25 99 . 76 100.57

K

1

Includes 0.38 NaCl; SiO^ figure includes insoluble residt

Includes FeS2 0.02.

''^Fibrous anhydrite, dolomite rock.

54
Table 2.8. Density of anhydrite

Density

(kfi/inS) (±2) T(K) Ref

.

Table 2.9. CrystalloBraphic parameters for anhydrite

Orthorhombic system

a = e-ZSexlO"-^"!!!; b = 6 . 99 IxlO' ^"m ; c = 6 . 996x10 " '"m

(to.oooixio"-'-'') 2960-2980

2920-2950

298

298

[44]

[45]

existing data and redetermined the crystal parameters

using calcium sulfate prepared from the reaction

between potassium sulfate and calcium chloride solutions, the product being heated at 973 K for 16 hours.

Spectrographic analysis showed the following impurities: 0.01 to 0.1% each of Bi, Sr and Ti; 0.001 to 0.01%

each of Ag, Al, Fe, Mg, Ni and Sn; 0.0001 to 0.001% each

of Ba, Cr, Cu and Pb, and less than 0.0001% of Mn. The

values reported by Swanson [50] are recommended as the best values; the results are in table 2.9.

2.4.4. Thermodynamic Properties

The critical assessment of Barin and Knacke [53] is regarded as the most reliable. The results are advanced

herewith as the recommended values in table 2.10 for

entropies, standard enthalpies of formation, standard

Gibbs free energies of formation and standard heat

capacities for anhydrite. Temperature dependent equations and precisions are also included in table 2.10. For

earlier studies, refer to references [54-57].

2.4.5. Equation of State MuUer and Siemes [114] carried out compression tests

to examine the dependence of strength, ductility, and

preferred orientation of polycrystalline anhydrite upon

confining pressure (up to 5 kbar), temperatures (up to 300 °C) and strain (up to 30%). It was observed that as the mantle pressure was increased at room temperature

the strength and the ductility increased. Anhydrite was

found to be brittle up to 1 kbar with failure occurring by

tension and shear fractures. Between 1 and 3 kbar

pressure homogeneous flow occurs, this being due to

intercrystalline slip which is sensitive to pressure.

Beyond the elastic limit it was found that the stress- strain curves were nearly horizontal, with no preferred

orientation developing. However, the intracrystalline

mechanisms become noticeable between 3 and 4 kbar.

Under these conditions the stress-strain curves show a weak strain hardening and the (210) planes exhibit a weak preferred orientation perpendicular to the axis of

compression.

As the temperature is increased the strength of

anhydrite decreases at low strains « 5%), and intracrystalline mechanisms become more dominant. At high

strains (> 15%) both strength and ductility increase at

a = B = Y

= 90°

3.873

3.498

3.118

2.849

2.797

2.473

2.328

2.208

2.183

2.086

1.993

1.938

1 . 869

1 . 852

1 . 749

1 . 748

1.648

1.594

1.564

1.525

1.515

1.490

1 .424

1 .418

1 . 398

1.396

1 . 365

1.319

1.296

1 . 277

1.237

1.216

1 . 1993

1.1781

1 . 1663

1 . 1651

1 . 1483

1 .1062

1 . 1044

1 .0785

1"

6

100

3

33

4

8

22

20

8

9

6

4

15

4

11

10

14

3

5

4

1

5

3

1

3

2

1

4

2

5

2

4

2

<1

4

1

1

5

4

2

111

002,020

200

210

121

022

202,220

212

103

113

301

222

230

123

004

040

232

133

024,042

204,240

313 , 331

214

402,420

323

242

412

143

422

430

234

044

432

252

135

006

060

414

026

424 ,442

216

a) d is the interlattice spacing, in mxlO 10

I is the intensity scaled to the strongest line which was assigned

a value of 100.

hkl are the Miller indices.

55
Table 2.10. Thermodynamic properties of anhydrite

T(K) S°(J/mol K)

(±0.2)

AH° (kj/mol)

^(±0.5)

AG° (kJ/mol)

"^(±0.5)

C (J/mol K)

P(±0.2)

298 106 692 -1434. 110 -1321 696 99 646

300 107 307 -1434. 418 -1320 803 99 830

400 137 382 -1436. 727 -1282 908 109 704

500 162 920 -1437. 948 -1244 262 119 579

600 185 594 -1438. 205 -1205 527 129 453

700 206 29 2 -1437. 601 -1166 775 1 39 327

800 225 543 149 201

900 243 685 159 076

1000 260 956 168 950

Temperature- dependent equations and precisions

S° = 46.736 346 + 0.2211239 T; (r^ = 0 992)

AG° = -1436.

f

!08 66 + 0.3 854957 T; (r^ = 0.999)

C° = P 70.206518 + 0.048 744 T; (r^ = 1 000)

higher temperatures. As the strain is increased further,

strain hardening ceases once again and the stress-strain curves become nearly horizontal.

Gypsum, CaS04 : 2H2O

2.4.6. Chemical Variability

Gypsum shows very little variation in chemical

composition. Table 2.11 gives the analyses of several

samples of gypsum [43]. Most gypsum deposits contain

clay minerals and fine sands as well as chemical

sediments such as limestones and dolomites.

2.4.7. Density

Density data for gypsum have been reported in two

studies [45, 58] . There is insufficient information for

value judgements. No information on the experimental

technique or sample preparation was given by Appleyard

[58]. Ludwig and MuUer [45] used a pycnometer, which

was calibrated with n-heptane. Due precautions were

taken to eliminate air from the apparatus. In both cases the measurements were at room temperature. The

pressure was normal atmospheric pressure. Both sets of

density data for gypsum are in table 2.12.

2.4.8. Crystallography

The crystal structure of gypsum was determined by

Wooster [59] from two dimensional x-ray diffraction

data with Fourier methods. It was further refined by

Atoji and Rundle [60] using neutron diffraction data.

Cillery [61] undertook a further refinement of the l crystallographic data, the details of which are in '

agreement with conclusions drawn by other workersjl

from spectroscopic data. The values advanced by Gilleryl

[61 ] are regarded as the best values and are given in table

'

2.13.

2.4.9. Thermodynamic Properties

The critical assessment of Barin and Knacke [53] is considered still to be valid. The results are advanced

herewith as the recommended values in table 2. 14 for the i entropies, standard enthalpies of formation, standard

Gibbs free energies of formation and standard heat

capacities for gypsum. Temperature dependent equations and precisions are also included in table 2.14. For

earlier studies refer to [62].

2.4. 10. Equation of State

Heard and Rubey [115] have examined the stressstrain behavior of gypsum. The effect of dehydration on

the strength of gypsum was investigated because of the

known occurence of evaporites along many thrust faults. A series of stress-strain curves were obtained at a 5 kbar

confining pressure and at different temperatures. The

resulting curves showed large reductions in strength over a relatively narrow temperature range

(100°-150°C), which was attributed to the transformation of gypsum to metastable hemihydrate (anhydrite

plus water). The stress-strain data at 2 kbar confining

pressure showed identical results but at slightly lower

56 I
Table 2.11. Chemical variability of gypsum

Source

Component U.S.A. Germany USSR

Illinois^ 1 1 linois'^ Neutershausen'' Zaleschiki*^ Zaleschiki^

Weight Percent (a)

SiO^ 1 46 0 68

AI2O3I

2 3J MgO

0

1

16

14

0

0

18

28

0

0

.11

. 09

CaO 33 64 32 76 32 .08 33 . 30 32 . 36

SO,"3 45 88 45 88 45 .37 45.30 46.00

CO^ ^^2 2 04 0 28 0 .95 1 .26 0.28

16 04 20 23 20 .10 19 . 74 20.82

0 01 0 01

Total 100 71 100 99 98.88 99 .69 99 .62

^•'st. Louis limestone. Coarse- grained gypsum, (Includes 0.09

^'st. Louis limestone. residue).

'^^ Includes SrO 0.08, (Na^O + K^O) 0.06, CI 0.04. Fine-grained gypsum, (Includes 0.16 residue) .

Table 2.12. Density of gypsum

Density

(kg/m3) T(K) Ref.

2320-2330 298 [45]

2200-2400 298 [58]

temperatures. In addition it was observed that with

increased preheating periods (80°-130°C) and a thousand-fold decrease in the strain rate (to 3 x 10"^ s~^) the

strength sensitive region was depressed further.

Calcite, CaCOs

2.4.11. Chemical Variability

Some analyses of calcite [43] to show compositional

variations are given in table 2.15. A common substitution is that of IVIg for Ca giving magnesian calcites.

Barium and strontium may also substitute for calcium in

calcite. Although many divalent cations may partially

replace Ca in calcite, most calcite is relatively free from

other ions and is fairly close in composition to pure

CaCOa.

2.4.12. Density

The value for the density of calcite reported by

Humbert and Plicque [63] was calculated from x-ray

diffraction data. There is insufficient information for a value judgement. No information was provided on

sample preparation. The value reported is given in table

2.16.

2.4.13. Crystallographic Properties

The crystallographic structure of calcite is analogous

to that of halite, where the Na and CI ions are replaced by

Ca and CO 3 ions, respectively, and the unit cell is distorted by compression along a triad axis to yield a facecentered rhomobohedral cell. X-ray crystallographic

data for calcite have been reported by several investigators [24, 25, 64-68] . The radiation sources used in these

investigations were either molybdenum [25, 64, 66] or copper [24, 68]. In view of several discrepancies in the

intensities published on the ASTIVI cards, a critical

analysis of existing data was undertaken by Swanson

[68] in 1953, together with a redetermination of the

crystal parameters of calcite. These values are recom- mended as the best values and the results are in table

2.17.

2.4.14. Thermodynamic Properties

The critical assessment of Barin and Knacke [53] is regarded as the most reliable. The results are advanced

herewith as the recommended values in table 2. 18 for the

entropies, standard enthalpies of formation, standard

Gibbs free energies of formation and standard heat
Table 2.15. Crystallographic parameters for gypsum

Monoclinic system

a = 5. 68x10" -^^m; b = 15 . 18x10' -^"ra; c = 6 . S 1x10 " -^"m

a = T

= 90° ; $ = 118°23'

lb hkl'^

7.56 100 020

4.27 51 121

3.79 21 031 ,040

3.163 3 112

3.059 57 141

2.867 27 002

2.786 5 211

2.679 28 022,051

2.591 4 150,202

2. 530 <1 060

2.495 6 200

2.450 4 222

2.400 4 141

2.216 6 152

2.139 1 242

2.080 10 123

2.073 8 112,251

1.990 4 170

1.953 2 211

1.898 16 080,062

1 . 879 10 143

1 . 864 4 312

1.843 1 231

1.812 10 262

1.796 4 321

1 .778 10 260

1. 711 1 253

1.684 1 323

1.664 4 341

1.645 2 163

1.621 6 204,181,053

1.599 <1 352,190

1 . 584 2 224

1.532 1 282

1 .522 1 222,134

d is the interlattice spacing, in mxlO^'^.

I is the intensity scaled to the strongest line which was assigned

a value of 100.

hkl are the Miller indices.

58
Table 2.14. Thermodynamic properties of gypsum

T(K) S° (J/mol K)

(±0.2)

AHUk J/mol)

(±0.5)

AG° (kJ/mol)

(.±1) . b J

C (J/mol K)

^ (. + U . ZJ

T n o 1 c Z y 0 . i 0 193 970 -2022 . 628 -i/y/,iy/ 17 0 7 10 7 Z bU , b Z

1

7 n n oU U 195 523 -2022 . 023 1 7 0 A 0 9^ z D u . / u b

Ann 4 U U 268 998 -2041 . 700 1 T /I A 7 C A -X/4D, /bo 9 A n con Z OU , b oU

c n n

D U U 328 206 -2068 . 548 1 n n o 0 o -ioyy. Zoo 9 7 n yi c /I Z / U , 4 b4

Ann OUU 378 384 -2088 .364 -lDbo.y4U o on 7 9 Q ^ oU

.

jZ o

7 r\ n 422 341 -2110 . 387 -loiU. boo

0 n n oUU 461 738

900 497 649 309.951

1000 C "Z Pi 816 319.825

s°

Temperature -dependent

= 68.397727 + 0.48417 T;

CQuations and

(r^ = 0.983)

prec 1 s 1 ons

= -1934 894425 + 0.46659241 T; (r^ = 0 . 999)

C° = 221.08187 + 0.098743 T ; (r^ = 1.000)

Table 2.15. Chemical variability of calcite

Component

Source

Aus tral ia

Mariatros t^

Poland,

Vistuj.a° Ruj evac*" Japan

^ Hokkaido

Weight Percent ( 0

MgO 0 . 04 1 13 0 32

FeO 0 . 00 0 29

MnO tr

.

3 19

CaO 55 . 92 54 56 54 43 52 83

NiO 0 65

CO2 43. 95 44 . 37 44 13 42 78

Total 99. 91 100. 08 100 58 99 91

-^Colorless or pale yellowish calcite.

^'calcite, occurring as "rock-milk" (lublinite) , (Includes Fe20T^ +

AI2O3 0.18, insol. 0.76, ign. loss 0.21).

^^Ni-Mg calcite, as yellowish or greenish rhombohedra associated

with altered serpentine and marble, (Includes AI2O2 0.11, insol.

0.13).

'^Vale pink manganoan calcite, (Includes insol. 0.50).

59
Table 2.16. Density of calcite

Density

(kg/m3) TCK) Ref

.

2712 299 [63]

capacities for calcite. Temperature-dependent equations

and precisions are also included in table 2.18. For

earlier studies, refer to [54-57].

2.4.15. Equation of State

Vaidya et al. [116] examined the compressibility of

calcite up to 45 kilobars pressure. The data were fitted to an equation of the form:

V/Vo = ao-\-aP+ bP' + cP' + dP*

where Vis the volume of the material at agiven pressure

and Vo the volume at normal atmospheric pressure.

The values of the coefficients obtained in this study

for the pressure range 0-15 kbar were oo = 0; a X 10'' =

7.906; -6X 105 = 14.58O; cX 10^ = 58.756; and for the

pressure range 20-45 kbar were qq - 0.02814; a X 10* =

28.653; -6X 10^ - 3.177; cX 10^ = 1.205.

Polyhalite, K2Ca2Mg(S04)4 2H2O

2.4.16. Chemical Variability

The main impurity in polyhalite is Kieserite (MgS04-

H2O). An analysis of a polyhalite-Kieserite rock [69] is given in table 2.19. When polyhalite is heated to 573 K

it loses its water of hydration and the residual salts form

a heterogeneous mixture comprising at least two phases.

2.4.17. Density

Density data for polyhalite have been reported in two

studies [44, 70]. There is insufficient information for

value judgements. No information on the experimental

technique, sample preparation or temperature range was

given in either study. Both sets of density data for

polyhalite are in table 2.20.

2.4.18. Crystallography

X-ray crystallographic data for polyhalite have been

reported by several investigators [71-73]. In view of the

discrepancies occurring in the earlier studies, a critical analysis of existing data was undertaken by Braitsch [71]

in 1961 together with a redetermination of the crystal

parameters of polyhalite using more carefully designed

optical orientation methods. These values are recom- mended as the best values. The results are in table 2.21.

2.4.19. Thermodynamic Properties

I No information is available on the thermodynamic i properties of polyhalite.

| 2.4.20. Equation of State '

No information is available on the equation of state for polyhalite. ^

Clays S

The main types of sheet silicates found in salt deposits '

are talc, Mg3Si4 0io (OH) 2; chlorites; amesite, (Mg2 Al) '

(Al,Si)2 05 (OH)4;daphnite, (Fe2Al) (Al,Si)205 (0H)4; ! penninite, (Mg, Fe, Al)3 (Al, Si) 2 O5 (OH) 4; corrensite \ (chlorite-vermiculite clay mineral); and muscovite,

KAl2(AlSi3)Oio(OH)2; and serpentines (antigorite,

Mg3Si205(OH)4; ferroantigorite,Fe3Si205(OH)4); chrys-

| otile, Mg3Si205(OH)4). The properties of chemical

variability, density, crystallographic parameters, ther- \ modynamic data, and equation of state are reported for

j the clay minerals given above.

2.4.21. Chemical Variability

} The principal impurities in talc are carbonates

(magnesite, breunnerite), chlorites, and quartz. An j analysis of a talc-carbonate rock [74] is given in table '

2.22. ! Chlorite is the predominant clay mineral of many salt i clays and many chloridic salt rocks. There are two '

varieties: normal chlorite (penninite-clinochlorite

group) and chlorite (amesite-berthierite group). Both j forms are normally found together. The chemical \ composition of dioctahedral chlorite [75] is given in '

table 2.23. '

Corrensite is the predominant clay mineral in rock }

salt. It is always associated with varying amounts of a I penninite-like chlorite.

j Muscovite strongly predominates in the carbonate 1

part of the salt clays, but in the noncarbonate salt clays d

its abundance relative to the other clay minerals fP

diminishes.

j

2.4.22. Density H

Grimshaw [3] has determined the density of severaB

clay minerals using a pycnometric technique. There \am

insufficient information provided for value judgmentsJ|

The density data are in Table 2.24. A

2.4.23. Crystallography H

Grimshaw [3] undertook a critical analysis of existing^

data in 1971 and the values advanced in that study ar«

still considered to be authoritative. The values reporte(M

by Grimshaw [3] include the three principal lines and ar«

60
Table 2.17. Crystallographic parameters for calcite

Rhoinbohedral axes and hexagonal axes

a

= 4.989x10"^%; c = 17 . 062x10"^% (±0.001x10"^°)

o = 3 = Y

= 90°

1^ hkl'^

3.86 12 102

3.035 100 104

2.845 3 006

2.495 14 110

2.285 18 113

2.095 18 202

1.927 5 204

1.913 17 108

1.875 17 116

1 .626 4 211

1.604 8 212

1 . 587 2 1.0.10

1 .525 5 214

1.518 4 208

1.510 3 119

1.473 2 215

1.440 5 300

1.422 3 0.0.12

1.356 1 217

1.339 2 2.0.10

1.297 2 218

1.284 1 30 6

1.247 1 220

1.235 2 1.1.12

1.1795 3 2.1.10

1.1538 3 314

1.1425 1 226

1.1244 <1 2. 1.11

1.0613 1 2.0.14

1.0473 3 404

1.0447 4 138

1.0352 2 0.1.16,1.1.15

1.0234 <1 1.2.13

1.0118 2 3.0.12

0.9895 <1 231

0.9846 1 322

0.9782 1 1.0.17

0.9767 3 2.1.14

0.9655 2 234

d is the interlatticc spacing, in mxlO

'l is the intensity scaled to the strongest line which was assigned

a value of 100.

'hkl are the Miller indices.

61
Table 2.18. Thermodynamic properties of calcite

T(K) S°(J/mol K)

(±0-2)

AH° (kJ/mol)

(±0-5)

AGj(kJ/mol)

(tO-5)

C°(J/mol K)

P(±0.2)

298. 15

300

323

400

500

600

700

800

900

1000

1100

1200

92.885

95.324

115.035

137.633

157.293

174.640

190 . 171

204. 246

217.145

229.074

240 . 191

-1207 . 370

-1206.871

-1206 . 301

-1204.822

-1203.276

-1201 .719

-1201.145

-119 9.789

-1198.689

1128.842

-1102

-1076.

-1050.

1025.

•1000 .

-975 .

-950.

.155

. 292

.723

.427

.238

. 195

299

86.734

97.073

105.102

110 .466

114.570

118.001

121.047

125.846

126.491

1?9.022

Temperature- dependent equations and precisions

2 S° = 51.38356 0.1652209 T;

AG| = -1203.759955 + 0.2541190 T

(r = 0.986)

2 0.999)

80.3668348 + 0.0436905; (r' = 0.925)

Table 2.19. Analysis of polyhal i te - Kieser i te rock Table 2.20. Density of polyhalite

Mineral

Polyhalite

Kieserite

Magnesite

Dolomite

Halite (from excess chlorine)

Siliceous material

% Composition

85.2

3.6

4 . 4

0. 2

1 . 3

5.3

Density

2780

2800

Ref

.

[44]

[70]

100 .00

62
Table 2.21. Crystallographic parameters of polyhalite

Triclinic system

a = 6.962x10"^%; b = 6 . 974x10' ; c = 8.967xl0"^°m (±0 . 00 1x1

0

" ^°

)

a = 104.5°; 3 = 101.5°; y = 113.9°

d

a

hkl'^

6 . 0 12 100

5. 95 8 oil

S . 82 6 110

4. 802 6 111

4. 15 4 012

4. 04 2 102

3. 48 6 210,121

3. 406 12 211

3

.

353 2

- 021,201

3. 175 70 211

2 . 97 6 102

2. 943 12 220

2. 912

100 012

2. 89

2 . 846 16 103

2. 766 4 111,113

2,,404 6 222,123

2,.350 6 i22

2 . 334 6 222,213

2 . 25 4 120,123

2 .213 4 130 , 103

2 . lo 4 014,013

2 .035 4 004

1 .948 214

1 .904 6 331,214

1 . 897 6 222

1 . 873 6 322,233

1 . 859 4 221

1 .810 6 232

1 . 806 6 323

d is the interlattice spacing, in mxlO

I is the intensity scaled to the strongest line which was assigned

a value of 100.

hkl are the Miller indices.

63
Table 2.22. Chemical analysis of talc

Component Weight

Percent {I)

Component Weight

Percent C^)

SiO^ 31 . 04 TiO^ 0.08

MgO 35.15 CaO 0.23

AI2O3 0. 54 K^O 0.01

Ff> CI 3.02 0.01

FeO 4.32 C^203 0.33

Table 2.23. Chemical analysis of chlorite

Component Weight

Percent (%) Component Weight

Percent (I}

Si02 35.63 CaO 1.13

TiO^ Na^O 0. 24

AI2O3 34.87 K^O 0.46

Fe^Oj 5.01 "2° 1 .91

FeO 0.43 Ign. loss. 12.24

MnO 0,05 S

MgO 8.63

Table 2.24. Density of clay minerals

Clay Density

kg/m5 (±2)

talc 2750

antigorite 2570

amesite 2800

daphnite 3000

f erro-antigorite 3200

penninite 2700

chrysotile 2550

muscovite 2900

recommended as the best values; the results are in table

2.25.

2.4.24. Thermodynamic Properties

Robie et al. [117] has tabulated the thermodynamic

parameters for Several sheet silicates. In addition Tardy

and Garrels [118] have discussed a method of estimating

the Gibbs energies of formation of layer silicates. The

thermodynamic parameters for a selection of sheet

silicates are given in table 2.25A.

2.4.25. Equation of State

No information on equation of state is available for the

clay minerals.

Table 2.25. Crystallographic parameters for clays

Clay \j L y ^ L. a. ± oyb LcJIl u. i

talc Q . J u c5 U

70

1 n . 1 u inn 1 U U

X . 0 J R n

antigorits riT'l'ViriTVinTTil'^n c 7 Q n

3 ±innu u

2 . 5 2 7 n

aiTiG sits IliUJlUV- J. JLilJ.L. 7 . nou u i.innu u

3 . 50 100

L A 7 Q n y u

daphnitG g . 9 0 u

3 ^1 1X nnu u

A

. 0 y n J u

illUllUL. 1 Xll 7 . 1 Z inn i U U antigorite

1.J n . J u ±innu u

2 A n

L/V'iiiiXJlJ. L.^ IllLIllUC-L J.J1J.L. . o u

fi n

11 1 7 • J. / 1± nnu u

4 . 78 X1 nnu u

chrysotile orthorhombic 7 .07 40

3,.59 100

2..45 60

muscovite monoclinic 9,.98 100

3.,33 90

2.,57 100

Table 2.25. Crystallographic parameters for clays

d is the interlattice spacing, in mxlO'''''

I is the intensity scaled to the strongest line

which was assigned a value of 100

64
Table 2.25A. Thermodynamic properties of sheet silicates

Substance T(K) S°CJ/mol K) AHJCkJ/mol) AG°(kJ/mol) CS(J/mol K)

Talc 298. 15 260 .83 -5915 . 900 - 5536 . 048 321

.

70

Mp,3Si40^g(OH)2 400 365 . 30 -5917 .050 - 5405 .971 386., 59

SOD 455 .61 -5914 .990 - 5278 .425 420.,63

600 534 .40 -5911 . 596 -5151 . 383 444,,26

700 604 . 91 -5906 . 844 - 5024 .997 475., 20

800 669 .80 - 5898 .951 -4898 .009 525,,95

' smperature-dependent equations and

S° = 36.46201 + 0.8101748 T (r^ = 0,

AG| =-5914.45145 + 1.27097788 T; (r^

223.666881 + 0.3736424 T; (r

precisions

992)

= 0.999)

0.977)

Chrysotile

MgjSi^OjCOH)^

298. 15 221., 30 -4361. 660 -4034.,024 273. 70

400 309. 13 -4362. 729 -3921.,820 323.,22

500 385. 05 -4360..883 -3811., 788 356.,33

600 4 52., 14 -4357., 294 -3702

,

, 258 378.,95

700 511,.78 -4352

,

,759 -3593,,454 394., 26

800 565,,13 -4347,, 832 -3485,,318 404.,32

900 613,. 14 -4342,.911 -3377,.752 410,,47

Temperature -dependent equations and

S° = 48.9012637 + 0.6467995 T; (r^ =

AG| =-4357.940316 1.09075860 T {r

C" = 232.449813 + 0.21773908 T; (r p

precisions

0.990)

= 0.999)

= 0.901)

Muscovite

KAl2[AlSijO^Q] (OH)^ 298.15 306.40

400 411.12

500

600

700

800

900

501.73

582.02

653. 74

718.32

776. 92

-5976.740

-5981.048

-5979. 503

-5975. 746

-5970.644

-5964.809

-5958.697

-5600.671

- 5471 . 333

-5344.043

-5217.261

-5091.248

-4965. 994

-4841.485

326.10

385. 54

425.67

454.42

475. 56

491 . 35

503. 24

Temperature-dependent equations and precisions

S° = 98.64806443 + 0.776464288 T; (r^ = 0.990)

AG° =-5975.82273 + 1.26215765 T; (r^ = 0.999)

C = 267.805767 + 0.28280067 T; (r^ = 0.929)

Pyrophyllite

Al2Si,Ojo(OH)2 298.15 239.40

400 334.16

500 416.33

600 489.17

700 554.32

800 613.17

- 5643 . 300

-5645.141

-5643.939

-5640. 906

-5636.692

-5631.707

-5269.384

-5141.250

-5015.389

-4889.921

-4765.087

-4640.892

293.70

349.62

386.06

412.41

432.59

448. 71

Temperature-dependent equations and precisions

S° = 33.39804167 + 0.741676925 T; (r^ = 0.993)

AG° =-5642 . 315477 + 1.25281441 T; (r^ = 0.999)

C° = 222.5551083 + 0.29948891 T; (r^ = 0.949)

65
2.5. Chemical Properties Among Components in

Salt Deposits

The chemistry among components in salt deposits

includes data on aqueous solubility, dehydration

reactions, formation of solid solutions and vapor phases

and includes phase diagrams.

2.5.1. The Systems NaCl-KCl-MgClz-HzO

The determination of the solubility of sodium chloride

in water has been the subject of several investigations [8,

76-80]. The earlier measurements were subject to an

error of + 0. 1 weight percent of salt below 373 K and + 0.3

weight percent salt above 373 K. Potter et al. [8]

undertook a redetermination of the solubility using a

specially designed bomb lined with platinum (see section

2.2.5) and attained a precision of + 0.01 or +0.1 weight

percent of salt over the entire temperature range. A

comparison of the solubilities obtained by various

investigators is shown in figure 2.1. The data reported by

Potter et al. [8] have been reanalyzed and values of the

solubility of sodium chloride at rounded temperatures

are advanced as recommended values in table 2.26,

together with a temperature-dependent equation.

A temperature-composition phase diagram for the

NaCl-H20 system is shown in figure 2.2. As indicated

three solid phases exist in this system namely: NaCl,

NaCl • 2H2O (hydrohalite) and ice. The solubility of

NaCl increases slightly with increasing pressure, 1 reaching a maximum at about 4053 X 10^ Pa and de- creases slowly until at around 1266562 Pa it has the same value as at atmospheric pressure. At 298 K between

^ 800467 and 1175370 pascals hydrohalite is the stable

form. A temperature-pressure-composition model for the NaCl-H20 system is presented in figure 2.3. This figure shows the compositions of gas in equilibrium with solid, the melting surface with

coexisting gases, liquids, and solids, the envelope of 1 curves relating the composition of the two fluid phases '

and the critical composition and pressure for each

temperature studied. The system was studied to . pressures of 1240 bars and through the temperature i interval 250-700 °C. ; The temperature coefficient for the solubility of KCl j in water is strongly positive and this effect is also found j for the NaCl-KCl-H20 system as shown in figure 2.4. ! The addition of similar ions reduces the actual solubility

but has no marked effect on the temperature coefficient.

The solubility of NaCl in the presence of KCl is similarly

reduced and in fact below 373 K the temperature

coefficient for the solubility of NaCl becomes negative.

Absolute solution concentrations can be gained using

figure 2.4 directly for this system. At any given

temperature the unsaturated solutions lie between the

70 —

60

IDO

oc

111 a

S

50

^ 40

• EARL OF BERKLEY (l904)

fSCHROEDER AND OTHERS

A BENRATH et al (1937^ KEEVIL fl942) LIU AND UNDSAY (l972) --POTTER eta! MEASURED (1977) — POTTER etal EXTRAPOLATED fl977)

30 —

100 200 300 400 500

TEMPERATURE, IN DEGREES CELSIUS

600

Figure 2.1. A comparison of the solubilities of sodium chloride in water.

66
different temperatures at either KCl+NaCl saturation or

as a function of MgCl2 concentration. It is observed that

the temperature coefficient of solubiHty is negative at low MgCl2 concentrations, while at medium and high

concentrations it is positive. Also from about 50 mol

MgCh/ 1000 mol H2O it remains approximately constant

and independent of temperature.

2.5.2. The System Anhydrile-Water-INaCI

Several studies have been undertaken on the solubility

of anhydrite in water [82-88] . With the exception of two

studies [85, 87] , all of the previous work was carried out

at atmospheric pressure at temperatures above 373 K or

at the vapor pressure of the system at temperatures

above 373 K.

Dickson, Blount and Tunell [82] used a special

hydrothermal solution apparatus to determine the

solubility of anhydrite in water from 373 K to 548 K and

from 10^ to 10^ pascals pressure. The equipment consisted of a deformable teflon sample cell held in a stainless

steel pressure vessel and sealed in such a way as to prevent interchange of material between the sample cell and the steel bomb. Liquid and solid phases were allowed

to attain equilibrium in the teflon cell at constant

Table 2.26.

Solubility of NaCl in water as a function of temperature

T( K) Wt. % (±0

NaCl

.05)

425 29 . 76

450 30 81

475 31 .99

500 33 31

525 34 75

550 36 34

575 38 05

600 39 90

625 41 87

650 43 98

675 46 23

700 48 60

Temperature-dependent equation and precision

weight percent salt in solution = 32.161 - 0.05071 T + 0.000106 T

s = +0.05 Wt. % NaCl

If zero point and the appropriate isotherm. At points P and

! N in figure 2.4, there are five phases: i.e., solid phases.

I P: halite, hydrohalite, sylvite

I N: hydrohalite, sylvite, ice and at both points also

liquid solution and vapor phases.

I When the solution is evaporated the composition

I changes linearly. For example sylvite precipitates first when at 20° C the point a is reached. On further

i evaporation point b is eventually attained. After this

I NaCl and KCl precipitate simultaneously and the

I composition of the solution remains constant. At

i 60° C, NaCl precipitates (point c) and the solution

I composition changes along the 60° isotherm in the

( direction of a lower NaCl concentration. After reaching

si the curve RP (at point d) the concentration remains

constant until completely evaporated.

! The four component system NaCl-KCl-MgCl2-H20 is

' characterized by the existence of a ternary compound,

carnallite, KCl • MgCla • 6H2O. In figure 2.5 are the

solubility isotherms for KCl at various temperatures and

the NaCl isotherm at 293 K. In this figure the carnallite

isotherms have been extrapolated using the saturation

concentrations at the boundaries between the sylvite and

j bischofite fields. Figures 2.6 and 2.7 present information on the temperature coefficients of solubility of NaCl at

67
Mol NaoClo/IOOO Mol H2O

Figure 2.2. Ref. [44]. A temperature-composition phase diagram

for the NaCl-H20 system. The metastable areas are indicated by broken hnes. Below K (=cryohydric point) 'all phases are solid with stable paragenesis (ice + hydrohalite), left of K with ice inclusions, right of K with

hydrohalite inclusions. SW refers to seawater.

68
Figure 2.3. Ref. [81] Pressure-temperature composition model for the system

NaCl-HzO.

69
Mol K2CI2/IOOO Mol H2O

Figure 2.4. Ref. [44]. Solubility isotherms in the system NaCl-KCl-H20 for the temperature

range 0-100 °C.

70
140r D

120

100

O

CM

oS

o

o

o

o

os

80

60 -

40 -

20 -

,Bischof ite (+Na CI)

\

\

^ \ -\

^ \ \ Carnallite

^ ^ '-NaCD

10 20 30

Mol K2CI2/IOOO Mol HgO

(Mol Na2Cl2/lOOO Mol H2O)

Figure 2.5. Ref [44]. Solubility isotherms in the system NaCl-KCl-MgClz-HjO,

saturated with respect to NaCl, for the temperature range 0-100°C.

E: at this point there is no joint precipitation of carnallite and sylvite. D: upon final evaporation at this point the residual solution can yield

bischofite, carnallite and halite.

71
+o,io

+0,08

-+ao4

Figure 2.6. Ref. [44]. Solubility isotherms in the system KCl-NaCl-MgCl2-H20 at KCl + NaCl saturation for the temperature range 0-70 °C. The MgClj content in mol/1000 mol H2O serves as a parameter.

72
0,14

O 20 40 60 80

Mol Mg Cl2y/1000 Mol H2O

Figure 2.7. Ref. [44] . Temperature coefficient of NaCl solubility at temperatures from

0-70°C and MgCb concentrations system NaCl-MgCl2-H20 saturated in NaCl; system NaCl-KCl-MgCb-HjO saturated in NaCl and KCi;

MgSOj free seawater, NaCl-saturated, KCl-unsaturated; the same, simultaneous precipitation of NaCl + KCI; following by simultaneous

precipitation of NaCl + carnallite.

73
temperature and pressure. This procedure minimized the

contamination of the solutions.

The solubility data obtained with the use of the

hydrothermal solution equipment at pressure slightly

above the vapor pressure of the system are in good

agreement with previous data as shown in figure 2.8. The

data reported by Dickson et al. [82] have been reanalyzed

and values of the solubility of anhydrite in water at various pressures and at rounded temperatures are advanced as recommended values in tables 2.27-2.30.

Temperature-dependent equations, together with standard errors of estimate are also given.

It is seen that the solubility of anhydrite decreases

with rising temperature.

Templeton and Rodgers [89] have determined the

solubility of anhydrite in a number of salt solutions at elevated temperatures and at pressures just above the

vapor pressure. The CaS04-NaCl-H20 system was

investigated at 523, 548, 573 and 598 K from essentially zero to about 6 molal NaCl. A high temperature flow

solubility apparatus was used in this study with the

temperature controlled to + 1 K. Reagent grade salts were

used for all the measurements and distilled water was

used to prepare solutions. Spectrophotometric or EDTA

methods were employed to measure either calcium or

sulfate. The precision of the data was reported to be + 2%

of the value of cm(^^s,Q^ • The data of Templeton and | Rodgers [89] have been reanalyzed and values of the | solubility of anhydrite at rounded concentrations of ' NaCl are advanced in tables 2.31 and 2.32. Equations

representing the solubility of anhydrite as a function of

sodium chloride concentration are also given. In

addition, Templeton and Rodgers [89] measured the

solubility of anhydrite in the systems CaS04-CaCl2-H20

and CaS04-MgCl2-H20. These data have been similarly

reanalyzed and values of the solubility of anhydrite at rounded concentrations of either CaCl2 or MgCl2 are given in tables 2.33 and 2.34, respectively. Finally the

quaternary systems CaS04-CaCl2NaCl-H20 and

CaS04-MgCl2-NaCl-H20 were also investigated and

values are advanced in table 2.35.

2.5.3. The System Gypsum-Water-NaCI

Blount and Dickson [90] used the hydrothermal

solution apparatus to measure the solubility of gypsum

in water at various pressures and temperatures. Reagent

grade material was used and the maximum estimated

uncertainty in the values was +2.5% for the solubility

and +4 bars (4 X lO^Pa) for the pressure. The data were

reanalyzed and values of solubility at rounded pressures

are advanced in table 2.36. The gypsum solubility in

water at one atmosphere pressure changes only slowly

Figure 2.8. Comparsion of the hydrothermal method for solubilities of anhydrite at 1 atmosphere below 100°C and at the vapor pressure of the system above

100° C. (The curve represents a fit to all of the data.)

74
Table 2.27.

Solubility of anhydrite in water as a function of

temperature at a pressure of 100x10^ pascals

T r K ") Wt . 1 anhydrite T( K ) Wt. % anhydrite

380 0 ..073 440 0 ..017

390 0 ,.058 450 0 ,.014

400 0 ,.046 460 0 ,.011

410 0,.036 470 0 .009

420 0,.028 480 0 .007

430 0 .022 490 0 .007

Temperature-dependent equation and precision

Wt % = 5.2255961 - 3.21053.10"^ T + 6.6167237.10"^ T'

precision s = 2.123%

Table 2.28.

0.4568792.10"'' T'^

Table 2.29.

Solubility of anhydrite in water as a function of

temperature at a pressure of 500x10^ pascals

Solubility of anhydrite in water as a function of

temperature at a pressure of 1000x10^ pascals

T( K) Wt. ^ anhydrite T( K ) Wt. 1 anhydrite

375 0 .119 465 0.016

385 0 .097 475 0.013

395 0 .079 485 0.011

405 0.063 495 0 .010

415 0.050 505 0 .008

425 0.039 515 0.007

435 0.031 525 0.005

445 0.024 535 0.003

455 0.019

T( K ) Wt . % anhydrite T( K ) Wt . % anhydrite

380 0,.176 470 0.,023

390 0,. 145 480 0..018

400 0..118 490 0 ,.015

410 0,.095 500 0 ,.013

420 0,.076 510 0..011

430 0..060 520 0,.009

440 0 .047 530 0,.007

450 0 .037 535 0,.006

460 0 .029

Temperature-dependent equation and precision

Wt % = 5.978863

Temperature-dependent equation and precision

Wt I =7.4676808- 0.4118806.10"^ T + 7.1843308.10"^ T^

- 3.0831114.10'^ T^ - 1.5485214.10"-'-^ t'^

precision s = 5.767%

- 3.5464.10'^ T + 7.04671.10"^ T^

- 0 . 4683758.10"'' T^

precision s = 3.550%

Table 2.30.

Solubility of anhydrite in water as a function of temperature at

pressures slightly greater than the vapor pressure of the system .

T( K ) P(xlO ) Pa Wt anhydrite

369

378

404

430

583

2

6

5

15

100

0.0781

0.0682

0.0357

0.0198

75
Table 2.31.

Solubility of anhydrite in NaCl-H20 solutions at

constant NaCl concentrations.

T [ K ) anhydrite

\aCl = 2.0 \^^^ = 4.0 = 6.0

375 0 ,,0261 0 ,,0280 0 ,.0255

395 0 ,,0207 0 ,,0240 0 ,0235

415 0 ,,0168 0 .,0210 0 ,0220

435 0 .,0139 0 .,0187 0,.0209

455 0 .0116 0 .,0168 0 ,.0201

475 0 ,,0098 0 ,,0154 0 ,.0196

495 0 ., 0083 0 .,0142 0 ,.0193

515 0 ,, 0070 0 .,0133 0 ,.0191

535 0 ,, 0059 0 .,0125 0 ,.0191

555 0 ., 0049 0 .,0118 0 ,.0191

0/0 nu . n n d 1, U u 4 1 n t nil? U 1 1 c. nu ,. U X J ^

595 0 ,,0033 0 ,.0107 0 ,.0193

615 0 .,0026 0 ,0102 0 ,.0194

635 0 ,,0020 0 ,0097 0 ,.0195

655 0 ,0015 0..0092 0,.0194

675 0 ,,0011 0 ,0087 0 ,.0193

695 0,,0008 0.,0082 0 ,.0190

715 0 .,0005 0 ,0076 0 ,.0185

Temperature-dependent equations

^"NaCl = 2-0

In m == 10.16 - 0. 07407T + 1. 329

.

- 4 7 10 T"^ - 8.95.10'^ T-^

""•"NaCl

'-= 4,.0

In m == 4.943 - 0 . 04246 T + 6.640

- 5 2 .10 ^ T •- 3.667.10'^ T-^

'''"NaCl

== 6.,0

In m == 3.2342 - 3 . 741.10'2 T + 6 .443.10'^ T^ - 3.670.10"

76
Table 2.32.

Solubilities of anhydrite in NaCl-H,0 solutions from 523 K to 598 K

NaCl

7 K OHO iV 7 ^ K J J O IV

0 . 00025 0 . 000176 0 .000078

0 .00050 0 .000177 0 .000079

0 .00075 0 .000178 0 . 000079

0 .00100 0,.000179 0 .000080

0,.00250 0,. 000185 0 .000084

0 .00500 0,.000194 0,. 000091

0,. 00750 0.,000203 0,. 000098 0 . 000026

0,. 01000 0.,000213 0 ,, 000105 0 . 000032

0..02500 0., 000269 0., 000146 0 .000065 0 . 000051

0,, 05000 0.,000362 0..000215 0,. 000119 0 .000072

0,,07500 0., 000455 0., 000284 0,. 000173 0,. 000094

0,,10000 0,,000548 0,,000353 0..000227 0 ,.000118

0,,25000 0., 001104 0.,000765 0,, 000537 0,. 000297

0,, 50000 0. 002024 0 ,,001453 0 ,,001042 0 ,,000705

0.,75000 0. 002933 0. 002143 0,, 001563 0,, 001210

1.,00000 0. 003832 0 . 002838 0,,002127 0.,001775

2 .,00000 0. 007329 0. 005699 0,, 004968 0,, 004325

3. 00000 0. 010665 0. 008796 0 .,008352 0 .,007373

4. 00000 0. 013841 0 . 012265 0 ., 011473 0 ., 011444

5. 00000 0. 016856 0 . 016242 0 . 014734 0.,016227

6. 00000 0. 019711 0. 020862 0. 021596 0. 018813

77
Table 2.32.

Solubilities of anhydrite in NaCl-H20 solutions

from 523 K to 598 K "--Continued"

Concentration-dependent equations and precision

'^m , J

- ^ = a + b M + c + d M'^ + e m'^ + f anhydrite

M = the molal concentration of sodium chloride

Temp (K) a. 10^ 7 b. IC^

A c. 10

523 1 . 7516 0 . 37371 -0 .80182

548 0 . 772789 0 .27549 -0 .17102

573 0 . 098800 0.22202 -6 .0258

598 0 .32922 0 . 069153 16 . 399

Temp d. 10-^ e. 10^ f . 10*

523

548 0.02248 0.00109

573 0 . 066368 -0 . 17952 0 .15337

598 -0 . 74941 0 .17449 -0 .13965

Temp (K) precision

(s)

523 2 ,.371

548 1

,

.0 81

573 3,.121

598 0 ,,531

78
Table 2.33.

Solubilities of anhydrite in the CaSO . -CaCl,-H^O system

CaCl2 CaCl2

^^m^ 523 K 575 K ^5^] 523 K 573 K

0 ,04 0,.134 0 ,045 0 .,17 0 ,. 249 0 .,131

0 ,05 0 .. 142 0 .052 0 .,18 0 ..258 0 ., 138

0 ,06 0..151 0 ,.059 0 ., 19 0..267 0 ., 144

0 ,.07 0 .. 160 0 ,.065 0 .,20 0..275 0 .,151

0 ,08 0 .. 169 0 .072 0 ,,21 0 .. 284 0 .,157

0 ,09 0..178 0 ,.078 0 .,22 0 ,. 293 0 ., 164

0., 10 0..187 0,,085 0 ., 23 0.. 302 0 .,170

U .. 1 1

n

U ., 1 y 0 u , 0 0 9 . u y i nu . 7 A u ., J 1 1 nU . 17 7

0,,12 0 .. 204 0 ,098 0,.25 0 ..320 0 ..184

0.,13 0 .. 213 0 ., 105 0 ,. 26 0 ..329 0 .. 190

0., 14 0 .. 222 0 .,111 0 ,.27 0 .. 337 0 .. 197

0.,15 0,. 231 0 ,, 118 0 .. 28 0 ..346 0 .. 203

0,.16 0.. 240 0 .124 0.. 29 0.. 355 0,. 210

Concentration-dependent equations and precision

'^"CaSO^

= 0.98183.10"^ + 0 . 88596 . 10"^

'^m^^^^ (523 K) ; s = 4.011

'^"'CaSO^

" 0.19131.10""^ + 0 . 60801 . 10 " '^m^^^,^ (573 K) ; s = 6.321

79
Table 2.34.

Solubilities of anhydrite in the CaSO . -MgCl^-H^O system

MgCl2 MgCl^

^Sn^ 523 K 573 K 523 K 573 K

0 ,.04 0.. 2125 0 ,. 1454 0..17 0.. 5852 0..4739

0,.05 0.. 2467 0 .. 1706 0..18 0..6100 0..4992

0 ,.06 0..2797 0 .. 1959 0 .. 19 0..6346 0,,5245

0..07 0..3116 0 .2212 0 ,. 20 0..6592 0.,5498

0..08 0.. 3423 0 ,. 2465 0 .,21 0 ..6839 0 .,5750

0..09 0..3721 0 .. 2717 0 ,.22 0.. 7087 0,,6003

0..10 0.. 4010 0 ,.2970 0 ,. 23 0.. 7337 0,,6256

0 .. 11 0 .. 4291 0 .. 3223 0 ,. 24 0 .. 7589 0 ,.6509

0., 12 0..4564 0 ,.3476 0 ,.25 0.. 7846 0,,6762

0., 13 0 .. 4831 0 .3728 0 ,. 26 0.. 8108 0,, 7014

0., 14 0.. 5093 0.. 3981 0 ,.27 0.. 8375 0 ,7267

0., 15 0..5349 0 .4234 0 ,.28 0.. 8648 0,, 7520

0..16 0.. 5602 0 ,.4487 0 .. 29 0,. 8929 0 ,, 7773

Concentration-dependent equations and precision

cr, = 0.61341.10"^ + 0.409.10''-'- Si., - 0 . 83632 . 10" Su, CaSO^ MgCl2 MgCl^

+ 0.14303 Sifj^gj,^ ( 523 K) ; s = 0.20^

f^nip = 0.44251.10"^ + 0 . 2 5276 . 10 " "''^m^^ [ 573 K) ; s = 0.27%

80
Table 2.35.

Solubilities of anhydrite in solutions of constant ionic

strength for some quaternary systems

Table 2.35.

Solubilities of anhydrite in solutions of constant ionic

strength for some quaternary systems "--Continued"

CaSO. -CaCl^-NaCl-HjO System

r CaCl2 ''>aCl

Cm

CaSO^

523 K I = 0 SO

0 . 492 0 00199

n n OR

n

U . U U o U 0. 4747 0 000496

0.0080 0. 4747 0 000517

0.0250 0. 4246 0 000263

0.0250 0. 4246 0 000262

0.0700 0. 2898 0 000236

0.0700 0. 2898 0 000244

0.1666 0 000237

O i? J V T -i — 0

0. 8868 0 00330

0 . 0040 0. 8763 0 00186

0.0100 0 8653 0 00109

0 . OlSO 0 8434 0 000746

0.0250 0

Q ? 1 1 u n n n c 7 U u u o J i

0 . 0400 0 7 788 0 000420

0.0800 0 6594 0 000372

0.0800 0 6594 0 000370

0.0800 0 6594 0 000364

0.100 0 5995 0 000360

0.200 0 2996 0 000366

0.200 0 2996 0 000385

0.300 0 000364

573 K, I = 0 J u

0. 496 nu U U 1 u u 0.0080 0. 4747 u \J \J V ± O H 0.0250 0. 4246 nu

n n n n Q Q u u u u y J y 0.0250 0. 4246 n

u nou u nu HQu y 7/ nu 0.0700 0. 2898 n

u u u u u 0 0 y 0.0700 0. 2898 Q u u u u y J. o 0.1666 n

u u U U J. J. u

573 K, I = 0 90

0. 892 0 00189

0.0040 0 8763 0 000802

0.0180 0 8434 0 000315

0.0400 0 7788 0 000210

0.0400 0. 7788 0 000217

0. 0800 0 6594 0 000166

0.200 0 2996 0 000208

0. 200 0 2996 0 000195

0.300 0 000223

CaSO^-MgCl2-NaCl-H20 System

MgClj "NaCl CaSO^

523 K 1 = 0 5 0

0 492 0 00199

0 .00295 0 48 53 0 00204

0 . 00811 0 4694 0 00218

0 . 00811 0 4694 0 00214

0 0204 0 4320 0 00262

0.0240 0 4320 0 00260

0.0608 0 3070 0 00358

0. 0608 0 3070 0 00360

0.1219 0 1240 0 00490

0.1219 0 1240 0 00492

0.1631 0 00568

573 L' h. T — n

A

U 4 y D

nU u u 1 u u

0 . 00295 0 4853 0 00107

0 . 00295 0 4853 0 00107

0 . 00811 0 4694 0 00131

0.0204 0 4320 0 00166

0.0608 0 3070 0 00251

0.0608 0 3070 0 00265

0.1219 0 1240 0 00378

0.1631 0 00456

0 . 1631 0 00455

81
Table 2 . 36.

The solubility of gypsum in water as a function

of temperature and pressure

PxlO'^ Pa (±4)

313 K 323 K 333K 540 K 352 K 356 K

CaSO^Cc^)

3 0,, 0138

5 0,, 0139

25 0,. 0155 0.,0147 0.,0140

50 0.,0159 0.,0151 0,,0143

75 0., 0162 0.,0155 0,,0146 100 0,.0166 0,,0159 0,,0149

125 0..0170 0,,0163 0,,0152

150 0,.0173 0,, 0167 0,, 0155

175 0..0177 0,,0171 0,,0158

200 0,.0181 0,,0174 0,, 0162

225 0,.0185 0,,0178 0,. 0165

250 0,.0189 0,,0182 0,.0168 275 0,.0193 0,,0186 0,. 0172

300 0 .. 0198 0,, 0190 0 .0175 325 0,.0202 0,,0195 0 .0179

350 0,, 0206 0,. 0199 0 .0182 375 0,.0211 0,,0203 0 . 0186

400 0,.0215 0,.0207 0 .0190 425 0,.0219 0,.0211 0 .0194 450 0.. 0224 0,.0215 0 .0198 475 0,,0229 0,.0219 0,.0202

500 0,. 0233 0,.0223 0,.0226 0,.0206

525 0,.0238 0,.0229 0 .0210

545 0,.0259

550 0 ,.0260 0,.0243 0,.0232 0 ,0214

555 0,.0262

560 0,.0263

565 0,, 0264

570 575 0..0248 0.,0235 0..0218 600 0..0253 0.,0219 0.,0222 625 0,.0258 0.,0242 0.,0227 650 0,.0263 0.,0247 0.,0231

675 0..0268 0.,0251 0.,0236 700 0,.0273 0.,0256 0,,0240

725 0..0278 0.,0261 0.,0245

750 0.,0284 0.,0266 0.,0250

77 5 0

,

,0289 0 .,0272 0 ,, 0255

800 0..0294 0.,0278 0.,0259 825 0..0300 0.,0284 0,,0264 850 0,,0305 0.,0290 0., 0269

875 0,,0311 0.,0297 0.,0274 900 0,,0317 0.,0304 0., 0279

925 0.,0323 0.,0312 0., 0285

950 0,.0328 0.,0319 0.,0290 975 0..0334 0.,0327 0.,0295 998 999 1000

1001

1002

1003

1004

0.0336 0.0301

0.0311

0.0311

0.0311

0.0311

0.0311

0.0310

0.0310

82
Table 2.36.

The solubility of gypsum in water as a function

o f temperature and pressure "--Continued"

Pressure-dependent equations and precision

'^"'r^Qn = a + bP + cP^ CaSO^

T( K) a. 10 b .10^ c . 10 precision

(s)

313 0.13106 U . 0 7 C T Q / J b Z 0

n n n 9- U . U U '0

323 0.15165 0. 13797 0 . 50605 0 . 7 z, 1

333 0 . 14332 0 . 1 c o n ri 1 bzy U U . 14 / b Z U , U U "6

340 0. 23529 -0. 13725 2.5769 1.501

352 0. 13747 0. 10966 0 . 53396 0.94%

356 0.51140 -0. 20040 1.05%

with temperature and passes through a very weak

maximum at about 313 K.

A study of the solubihty of gypsum in NaCl-H20

solutions from 273-383 K has been performed by

Marshall and Slusher [91]. A small high pressure

titanium alloy vessel incorporating a Teflon gasket was

used for the measurements, with the special feature of

the design being the containment of the Teflon above its transition temperature of 600 K. Selected mixtures of

solid and solution were sealed in the vessels. The solution phases were sampled by means of flexible capillary

tubing and valves. Since the liquid phase was sampled at

its equilibration temperature and subsequently analyzed, a correction for loss of water or other constituents

to the vapor was unnecessary. The temperature of equilibrium was approached from both lower and higher temperatures; agreement of analyses was used to show that

equilibrium had been attained. The data of Marshall and

Slusher [91] were reanalyzed and values of the solubility

of gypsum were generated at rounded concentrations of

sodium chloride over the temperature range from

273-383 K. The recommended values, compositiondependent equations and precisions are in tables

2.37-2.39.

2.5.4. Comparison of the Systems Anhydrite-Water and

Gypsum-Water

A comparison of the solubilities of anhydrite and

gypsum in water with added sodium chloride is shown in

figure 2.9. The solubility of gypsum and anhydrite is

in general influenced by the presence of additional ions,

increasing through the addition of foreign ions, and

conversely being reduced by the addition of the same

ions. These effects for both gypsum and anhydrite are shown in figure 2.10. Because of the different temperature coefficients, the point of intersection of the gypsum

and anhydrite solubility curves is displaced towards

lower temperatures as the NaCl content of the solution

increases. With an additional S04^ content the solubility of gypsum and anhydrite is reduced and the max- imum becomes broader.

2.5.5. The System Calcite-Water-|- (NaCi, CaCU . . .)

The solubility of calcite in water as a function of CO2

pressure and temperature is presented graphically in

figures 2.11-2.15. The curves in these figures represent

fits to all of the data.

Macdonald and North [97] investigated the effect of

pressure on the solubility of calcite in water between 273

and 308 K and for pressures up to 101325 Pa. The

distilled water used in the measurements was de-ionized

water which was boiled vigorously prior to use to expel

any dissolved CO2. The calcium carbonate was in the

form of small natural calcite crystals. An analysis of the

calcite showed that it contained less than 0.1% of

magnesium. In the determination of solubility the

solutions were saturated by allowing the water to percolate, at a known rate, through the reaction column

which was packed with the dissolving solid. The

particular method used in this study produces a large

surface area to liquid volume ratio and so allows a

relatively rapid attainment of equilibrium. The solutions were analyzed for calcium by atomic absorptiorb, and all determinations had an accuracy of at least + 2%. The data

of Macdonald and North [97] were reanalyzed and

values of both solubility and thermodynamic solubility

products were derived at rounded pressures and are advanced as recommended values in tables 2.40-2.43,

together with pressure dependent equations.

Akin and Lagerwerff [98] studied the effects of added

electrolytes on the solubility of calcite in water, using an

apparatus designed to minimize CO2 fluctuations.

Calcium was determined by EDTA titration, while

sodium was monitored with a flame photometer. The

values reported by Akin and Lagerwerff [98] were re- evaluated using statistical analysis and results are given

for the solubility of calcite at rounded concentrations of

sodium chloride in tables 2.44-2.48. Concentration-dependent equations and precisions are also reported.

2.5.6. Dehydration of Gypsum

The main point of interest in the chemistry of gypsum

concerns the products of its dehydration. Four principal

phases have been reported [99] in the system calcium
Table 2.37

The solubility of gypsum in NaCl-H20

solutions at 273-293 K

NaCl CaS0.-2H,0

273. 5 K 278 K 283 K 288 K 293 K

0 . 01 0 . 0148 0 . 01 54 0 . 0162 0 . 0168 0 . 0165

0 . 02 0 .,0152 0 .,0158 0 . 0166 0 . 0173 0 . 0170

0

,

, 03 0 .,0156 0 ., 0163 0 . 0171 0 . 0177 0 .,0175

0 ., 04 0 .,0160 0 .,0167 0 .,0175 0 ., 0182 0 .,0179

0 ., 05 0 ..0165 0 ,,0171 0 .,0179 0 ., 0186 0 ,, 0184

0 ., 06 0 .,0169 0 .,0175 0 ,,0184 0 ,,0190 0 .,0188

0 ., 07 0 .,0173 0 .,0180 0 .,0188 0 ..0195 0 ,.0193

0 ., 08 0 .,0177 0 ..0184 0 .,0192 0 ,,0199 0 ,.0197

0 ,, 09 0 .,0181 0 .,0188 0 ,.0196 0 .,0203 0 ,.0202

0 ., 10 0 ,.0185 0 ..0192 0 .,0200 0 ..0207 0 ..0206

0 ,, 20 0 ..0230 0 ,.0231 0 ..0239 0 ,.0247 0 ,.0248

0 ., 30 0 ..0258 0 ..0266 0 ., 0275 0 ..0283 0 ,.0286

0 .. 40 0 ,.0291 0 ..0298 0 ,. 0308 0 .. 0316 0 ..0320

0 ., 50 0 ..0320 0 ..0328 0 .. 0338 0 ,. 0347 0 ,.0352

0 ., 60 0 .. 0348 0 ,.0355 0 ,.0366 0 .. 0374 0 ,.0380

n

u

.

7 n u

.

n T 7 7 n n 7 Q n n Q n u ,, nU J QJ QJ n n 4 n

0,.80 0,. 0395 0 ,. 0401 0..0413 0,, 0421 0,. 0428

0 ,. 90 0,. 0416 0,. 0421 0.. 0433 0,. 0442 0,. 0448

1

,

.00 0,. 0435 0,.0439 0 ,, 0451 0,. 0460 0,.0465

2 ,.0 0,,0542 0,.0535 0..0547 0..0553 0 .0553

3,. 0 0,.0564 0 .0553 0 ,.0560 0,.0566 0,.0562

4 . 0 0 .0556 0 .0554 0,.0554 0,.0563 0 .0563

5 . 0 0 .0530 0 .0537 0,.0534 0,.0553 0,.0556

6 . 0 0 . 0451 0 . 0447 0 .0455 0 . 0489 0 .0473

Concentration-dependent equations and precisions

"^m = a + b M + c + d M-^ + e m'^ gypsum

M = molal concentration of sodium chloride

Temp

( K)

a. 10 b.lO c. 10 d.lO"- e. 10-" precision

(s)

273.5 0,. 1436225 0,.4279379 -0..1623401 0 ,.2766863 -0,.1845770 1 .67%

278 0.. 1496224 0,.4394013 -0 ..1815735 0,.3388285 -0,. 2408431 1 . 961

283 0,.1574711 0,.4445050 -0,.1814384 3.. 276261 -2,. 248609 1 . 97%

288 0., 163198 0..4512401 -0,.1873406 3 ..423325 -2., 339645 2 . 25%

293 0.,1605044 0..4775160 -0..2102661 0 ..4057587 -0.,2891751 2 .73%

84
Table 2.38.

The solubility o£ gypsum in NaCl-HoO solutions at 298-343

K

NaCl CaS0.-2HT0

29 8 K 30 3 K 313 K 343 K

0,. 01 0 . 0174 0 .0164 0 . 0169 0 . 0170

0,.02 0 . 0178 0 . 0171 0 .0175 0 .0174

0,. 03 0 .0182 0 . 0178 0 .0181 0 .0178

0,. 04 0 . 0187 0 .0184 0 . 0187 0 . 0182

0..05 0 . 0191 0 . 0191 0 . 0193 0 . 0186

0,. 06 0 . 0196 0 .0197 0 . 0198 0 . 0190

0,. 07 0 . 0200 0 .0203 0 .0204 0 .0194

0,, 08 0 .0204 0 .0209 0 .0210 0 . 0198

0,, 09 0 .0208 0 .0215 0 .0215 0 .0202

0,, 10 0 .0213 0 .0221 0 . 0220 0 . 0205

0., 20 0 . 0252 0 .0271 0 . 0268 0 . 0242

0,,30 0 . 0288 0 . 0311 0 . 0307 0 . 0277

0.,40 0 .0321 0 . 0342 0 .0339 0 .0308

0,, 50 0 .0351 0 . 0366 0 . 0366 0 .0338

0 ,,60 0 . 0377 0 . 0385 0 .0388 0 . 0365

0,,70 0 .0401 0 . 0402 0 . 0407 0 . 0390

0.,80 0 . 0423 0 . 0418 0 . 0424 0 . 0413

0., 90 0 . 0442 0 . 0436 0 . 0441 0 . 0434

1,, 00 0 .0459 0 . 0458 0 .0458 0 . 0453

2,,00 0 .0541 0 .0558

3., 00 0 .0553 0 . 0567

4., 00 0 .0561 0 . 0566

5., 00 0 .0569 0 . 0643

6.,00 0 .0511 0 . 0883

Concentration-dependent equations and precisions

2 3 4

'^m =a + bM+cM + dM + eM

gypsum

M = molal concentration of sodium chloride

Temp a. 10 b.lO c.lO d.lO^ e.lO^ precision

(K) (s)

298 0,, 1690221 0,,4549512 -0 ,,2017596 0 .3924890 -0.2891751 2 .16%

303 0,,1573776 0,,7053267 -0 ,,7498029 3 .449260 -0.2779556 1 . 34%

313 0., 1624119 0,,6350437 -0., 5876340 2 .798339 1 .40%

343 0,.1660804 0,,4073127 -0,,1344950 1 .446642 5 . 51%

85
Table 2.39.

The solubility of gypsum in NaCl-H,0 solutions at353-383K

NaCl CaSO^-2H20

353 K 368 K 383 K

0 . 01 0 .0176 0 . 0158 0 . 0119

0 . 02 0 .0178 0 .0161 0 . 0124

0 . 03 0 .0180 0 .0164 0 .0129

0 . 04 0 .018 2 0 .0166 0 .0135

0 . 0 5 0 .0184 0 .0169 0 . 0140

0 . 06 0 .0186 0 .0172 0 . 0145

0 . 07 0 .0188 0 .0174 0 .0150

0

,

. 08 0 .0190 0 ,.0177 0 .0155

0 ,. 09 0 ,.0192 0 ,.0180 0 . 0160

0

.

. 10 0 ,.0194 0

.

.0183 0 ,. 0165

0

.

. 20 0 ,.0214 0 ,,0209 0 ,.0213

0 ,, 30 0

,

.0234 0 ,,0236 0 ,.0257

0

.

. 40 0 ., 0254 0 ,,0261 0

.

. 0299

0

.

, 50 0 .,0273 0 .,0287 0 .. 0338

0

.

, 60 0

.

,0292 0 .,0312 0 ., 0374

0

.

, 70 0 .,0311 0 ., 0336 0 ,, 0408

0.,80 0 ., 0330 0. 0360 0.,0439

0. 90 0., 0349 0 . 0384 0 . 0468

1

.

00 0. 0367 0 . 0407 0 . 0494

2 . 00 0. 0538 0. 0612 0. 0647

3. 00 0 . 0688 0. 0771 0 . 0670

4. 00 0 . 0814 0 . 0883 0 . 0661

5. 00 0 . 0919 0. 0950 0. 0717

6. 00 0 . 1001 0. 0970 0. 0934

Concentration-dependent equations and precisions

'^m = a + b M + c + d

gypsum

M = molal concentration of sodium chloride

Temp precision (s)

(K )

353 0.1735577 0.2046287

368 0.1552855 0.2745152

383 0.1137741 0.525739

-0.1109989 6.3%

-0.2312935 6.71

-1.619548 0.1618607 5.8%

86
25 50 75 100 125 150 175 200

Temp.rC.)

Figure 2.9. Ref. [86] . Solubility of gypsum, hemihydrate, and anhydrite in water.

10 20 30 40

Mol Na2Cl2/ 1000 Mol H2O

50

Figure 2.10. Solubility of gypsum and anhydrite in saline solutions from 25-70°C. Solid phases; anhydrite = solid and broken

lines; gypsum-dotted lines (heavy and light). 1 [93] ; 2-4 [94] ; 5 [95] 6, extrapolated from 3 and 4; 7, seawater and its alterations in concentration.

87
zo

o

M

E

O) O

O

o

«o

uCB u

i

O)

o

<

1-60r

1-40

1-20

100 -

0-80

0-60 -

0-40 -/

020

^ Ref(96)

A Ref (108)

80 90 100

COj PRESSURE (atm.)

Figure 2.11. The solubility of calcite in water at 75 °C as a function of CO2 pressure.

1.60r10

Ref (96)

Ref (109)

Ref (108)

20 30 40 50 60 70 80

CO2 PRESSURE (atm.)

90 100

Figure 2.12. The solubility of calcite in water at 100°C as a function of CO2 pressure.

88
89
o.40rRef(96)

Ref (109)

40 50 60 70 80

CO2 PRESSURE (atm.)

KiicURE 2.14. The solubility of calcite in water at 150°C as a function of CO2 pressure

90 100

.80r

g 70

I-=)

.60-

40 50 60 70 80 90

CO? PRESSURE (atm.)

Figure 2.15. The solubility of calcite in water at 200°C as a function of CO2 pressure.

90

100
Table 2.40.

Effect of pressure on the solubility of calcite in water at 274 K and thermodynamic solubility products [CaCO^Cs) = Ca^* + CO^^"]

PxlO'^ Ca^* Kp

(p ascals) (ykg/kg) (xlD^)

Q t; A ft ? 7 ft C 1

> J 1

AH , R t: .ODDft 7 . XQ0 y

T "7 ^ ± / D

CJ , n R 7 oo , 9 7

cJ 1 9 Q 9 Q , U 4

cD . 9 Qy , Q 7 1 y /

9^ on7 u

c 7 7 Q 1 n 1 u , Q ft

. y u

J 0 u . nU J 4 1 9 J. c ,. U 0

J / u O , 9i!, Qy Qy J. J 1 9 1

*t i. u

ft 7 J. '+

.

9

J u 6 866 J- J . 9 8

4- J U 171 1 7 6 2

7 _,49 2 19 . 4 7 570 7 .. 831 21

,

. 53 610 8..189 23,.85 645 8., 519 26.,09

685 8.,918 28,.93 725 9., 340 32..08 765 9.,788 35..57 805 10.,262 39..42 845 10., 765 43..66

Pressure-dependent equations and precisions

[Ca^"^] = 4.084933 + 5 . 7517223x10"® P - 8 . 6390113x10 ^ P^

+ 4.039419x10"^'' P-'

standard error of estimate = 0.891

K = 4.26629 + 2.5 594 74 8x10"'' P - 2 . 6 2485 54x10 " '"^ P^ + 6 . 0507034x10

P precision s = 1.961

91
Table 2.41.

Effect of pressure on the solubility of calcite in water

at 281 K and thermodynamic solubility products

PxlO"^

Cp ascals)

Ca2^

(ykg/kg)

Kp

(xl59)

35 4 . 585 5 .48 75 4 . 824 6 . 32 120 5.095 7 . 24 160 5.337 8.06

200 5.583 8.88

240 5. 833 9 . 75 280 6. 088 10.67

320 6.350 11.67

360 6.620 12.77

400 6.899 13.98

440 7.188 15 . 34 480 7.488 16 . 85 520 7.800 18.55

560 8. 126 20 . 44 600 8 .466 22.56

640 8.823 24.91

680 9.196 27.53

725 9.638 30 . 82 765 10.051 34.06

805 10 .485 37.62

Pressure-dependent equations and precisions

[Ca^"^] = 4.374741 + 6.010 54 56x10"^ P - 4 . 4 7 76 2 31x10'"'^'' P^

+ 2.9932948x10"^^ P^

precision s = 0.761

-7 -1S7 -243

K = 4 . 702247 + 2 . 2867598x10 P - 2 . 0448748x10 P + 53 . 224503x10 P P precis ion s = 4.991

92
Table 2.42.

Effect of pressure on the solubility of calcite in water at 300 K

and thermodynamic solubility products

PxlO"^

[p ascals)

Ca2*

(pkg/kg) (xl09)

45 5.296 4.91

85 5.415 5.17

130 5. 576 5 .57

170 5. 743 6.03

210 5.929 6.57

250 6.133 7.21

290 6.355 7.95

330 6. S93 8. 77 370 6.845 9.69

410 7.110 10 . 71

450 7 . 386 11.81

490 7.673 13.01

530 7.969 14.30

570 8.272 15.68

615 8.620 17.35

655 8.934 18.93

695 9 . 252 20 .60

735 9. 571 22. 37

775 9.891 24. 23

815 10 . 210 26. 18

855 10 .526 28.22

Pres sure - dependent equations and precisions

[Ca^"^ ] = 5.190895 + 1.9 7 78 396x10"^ P + 8.0679045x10""'^^ P

- 3.6058291.10""'* P^

precision s = 1.05%

K = 4.731204 + 2.6838933x10"^ P + 2 . 899 8339x10 "" ^ P^

P precision s = 2.96%

93
Table 2.43.

Effect of pressure on the solubility of calcite in water at

298 K and thermodynamic solubility products

PxlO"^

(p ascals

)

Ca^-^ (ykg/kg) (xl69)

25 4.898 5.04

75 5.151 4.68

130 5.431 4.71

180 5.687 5.10

230 5.945 5.80

280 6. 205 6.76

330 6.468 7.95

380 6. 734 9.34

430 7.003 10.88

480 7. 276 12.55

530 7.553 14.31

580 7.834 16.11

630 8.121 17.93

685 8.442 19 .91 735 8 . 739 21.64

785 9.043 23.28

835 9.353 24.78

890 9. 702 26.23

940 10.027 27. 33

Pressure-dependent equations and precisions

[Ca^*] = 4.7712206 + 5.0521 587x10"^ P + 1.0647239x10'"^^ P^

+ 4.9697389x10"^^ P^

precision s = 3.41

K = 5.3800985 - 1.55 79606x10"'' P + 8.671274 5x10""^^ P^- 4.81845 8x10"^^ P"^ P precision s = 3.78%

94
Table 2.44.

The solubility of calcite in solutions containing NaCl and NaHCO

[concentration of NaHCO^ = 0.04 mol/m^) ; P = 26000 pascals,

T = 300 K]

NaCl CaCOj NaCl CaCO^

mol/ra^ mol/m3 mol/m3 mol/m3

4 .5175 32 .465

6 .5280 34 .436

8 . 5400 36 .408

10 . 5530 38 . 382

12 . 5640 40 .359

14 . 5730 42 . 343

16 . 5790 44 . 335

18 . 5805 46 . 338

20 .57 75 48 .356

22 . 5695 50 . 391

24 .5565 52 .447

26 . 5390 54 . 527

28 . 5175 56 .639

30 . 4930

Concentration-dependent equation and precision

= 0.511263 - 1.91324 x 10"^ M + 1.07952 x 10"^

CaCOj

- 5.3719 X 10"^ + 6.38586 x

10"''

M = molal concentration of sodium chloride

precision, s = 1.70%

95
Table 2.45.

The solubility of calcite in solutions containing NaCl

[P = 35700 pascals; T = 501 K]

NaCl

mol /m^.

CaC03

mo 1 /m-^ NaCl_

mo 1 / m-^ CaC03_mo 1 /m

8 .6050 36 . 7065

10 . 6085 38 . 7090

12 .6140 40 . 7105

14 . 6220 42 . 7115

16 .6305 44 . 7115

18 .6400 46 . 7115

20 . 6500 48 . 7120

22 .6600 50 . 7130

24 .6695 52 . 7150

26 .6780 54 . 7185

28 .6860 56 . 7240

30 . 6930 58 . 7330

32 .6985 60 . 7450

34 . 7030

Concentration-dependent equation and precision

; = 0.629765 - 0.0824625 M + 7.882835 x 10"^

""CaCOj

- 9.92469 X 10"^ + 1.488825 x 10"^

M = molal concentration of sodium chloride

precision, s = 0.001

96
Table 2.46.

The solubility of calcite in solutions containing CaCl2 and NaCl

[concentration of CaCl2 = 1.00 mol/m ;

P = 55000 pascals; T = 502 K]

NaCl

mo 1 /ni"^ CaC03

mo 1 /m^

NaCl

mol/iii-5 CaCO^mol/m3

0 . 353 55 . 502

5 . 374 60 . 520

10 .390 65 . 559

15 .402 70 .557

20 . 412 75 . 572

25 .422 80 . 584

50 .431 85 . 591

35 .442 90 . 590

40 .454 95 .579

45 .468 100 . 555

50 .484

Concentration-dependent equation and precision

= 0.3530265 + 4.8765 x lO'-^ M - 1 . 4755 x 10"*

+ 2.907575 X 10"^ - 1 . 717735 x 10"^ m'^

M = molal concentration of sodium chloride

precision, s = 0.89%

Table 2.47.

The solubility of calcite in solutions containing CaCl^ and NaCl

[concentration of CaCl2 = 2.47 mol/m'^;

P = 26000 pascals; T = 300 K]

NaCl

mol/m^

CaCOj

mol/m3

NaCl

mol/m^

CaC03

mol/m3

0 .250 55 .335

5 . 265 60 .339

10 .275 65 .343

15 . 285 70 . 347

20 . 294 75 .352

25 . 502 80 .357

30 . 509 85 .363

35 . 515 90 . 569

40 .521 95 .377

45 . 526 100 .385

50 . 550

Concentration-dependent equation and precision

c = 0.250000 + 2.78839 x

10"-^ M - 3.31517 x 10"^

"CaCOj

+ 1.87678 X 10"^

M = molal concentration of sodium chloride

precision, s = 0.00%

97
Table 2.48.

The solubility of calcite in solutions containing

NaCl , NaHCOj and CaClj

NaHC03 NaCl CaCl2 P T CaC03

mol/m-^ mol/m^ mol/m^ (PaxlO"^) (K) mol/m-^

19 . 3 0.53 0 0 .254 300 0.015

2.10 19. 79 0 0 .254 300 0.150

0 56.38 0 0.274 299 0 . 700

0 18.65 0.84 0 .254 300 0.400

sulfate-water: CaS04 • 2H2O (gypsum), CaS04 • 1/2H2O

(bassanite), 7-CaS04 (soluble anhydrite), and )8-CaS04

(anhydrite). A good deal of controversy exists as to the

actual existence of two distinct compounds other than

the dihydrate and anhydrite; however, both thermal

dehydration studies [99] and x-ray studies [100] provide

substantial evidence for the existence of the hemihydrate. On the dehydration of gypsum, water is removed zeolitically but with slight changes in cell parameter due to lack of collapse of the Ca-S04

framework until n = V2. Further heating expels the

remaining water molecules yielding7-CaS04, again with

a slight deformation of the structure and corresponding

change in cell parameters. The hemi-hydrate—»7-CaS04

may not be recognized.

Of the four principal phases in the system CaS04-

H2O, only two, the hemihydrate and 7-CaS04, exist

metastably. Thus under equilibrium conditions the

reaction

gypsum

^ anhydrite + water

occurs without the 'formation of intermediate compounds. The temperature of the transition of gypsum to anhydrite in pure water is 315 K. Gypsum persists

metastably above this temperature where it inverts to the

metastable hemi-hydrate at 370 K [92] . The solubilities

of gypsum and anhydrite in various saline solutions are shown in figure 2.10. This shows that at 303 K gypsum is the stable phase up to a concentration of 4.8 times the

normal salinity of sea water. The effects of pressure and of different concentrations

of NaCl on the gypsum-anhydrite equilibrium temperature have been calculated by Macdonald [101] and are

illustrated in figures 2.16 and 2.17. At 314 K dP/dT =

85.4 X 10^ Pa/K if the same pressure acts on all phases,

but dP/dT = -39.45 X 10^ Pa/K if the rock pressure is assumed to act on the solid and hydrostatic pressure on

the liquid phase.

Gypsum in contact with aqueous salt solutions is converted to natural anhydrite at 363.5 K. The

mechanism of the reaction is the conversion of gypsum

first to the hemi-hydrate and then to natural anhydrite.

The investigation shows that gypsum is the stable phase

of calcium sulfate precipitated from water solutions at temperatures as high as 370 K. The solid phases

occurring during the dehydration of gypsum [102] are summarized in table 2.49.

2.5.7. Additional Information

a. Thermodynamics of brine-salt equilibria.

Wood [103] has developed a thermodynamic model

for concentrated brines which is capable of predicting

the solubilities of many of the common evaporite

minerals in chloro-sulfate brines. Solubility curves and

solution compositions were predicted for the systems

NaCl-KCl-MgCl2-CaCl2-H20 and NaCl-MgS04-H20.

The model requires data on the constituent binary and

quaternary systems only. Data on the binary systems

must include measurements on the unsaturated

solutions but solubility data is all that is required for

the quaternary systems.

Pitzer et al. [110,111] have discussed several ap- proaches which use equations to provide a convenient

analytical representation of the thermodynamic properties of sodium chloride.

b. Models for calculating density and vapor pressure

of geothermal brines.

Potter and Haas [104] have developed a model for

estimating the density of a brine at a known temperature,

pressure and composition using the densities of the

component salt solutions in the complex brine. In

addition a model for estimating the vapor pressure is also

reported. The methods can be used to estimate the partial

molal volume and partial molal enthalpy of H2O in the

natural brine and the partial molal volume change and

partial molal heat change for the H2O component in the

vaporization process. Preliminary steam tables are

available [105,106] that give the thermodynamic data for

the coexisting liquid and gas phases for the NaCl-H20

system, for liquid concentrations between 0 mol

NaCl/kgH20 and halite saturation at temperatures

between 353 and 598 K. The densities of aqueous sodium

chloride solutions from 273 to 773 K at pressures up to 2

X 10^ Pa have also been reported using a regression

analysis of available data [107].

At a pressure of 10^ Pa and with 93 parts per thousand

of chlorine by weight, the transition of anhydrite to gypsum is predicted to occur at 303 K. The depth to which gypsum is found in nature will depend on the

temperature gradient, composition of groundwaters and

ratio of lithostatic to hydrostatic pressure acting on the

calcium sulfate deposit.

98
Figure 2.16. Pressure-temperature relations for the reaction gypsum anhydrite + water. A. Pure water; same pressure on all phases.

B. Pure water; rock pressure on solid phases, hydrostatic pressure on water.

C. Saturated NaCl solution; same pressure on all phases. D. Saturated NaCl solution; rock pressure on solid phases; hydrostatic pressure on NaCl

solution.

40

1 1 1 1 1 1

oo 30

« Gypsum Anhydrite 3O ZO

Tempei

10

0 1 1 1 I 1 1 1 1 I I I I I I I 0 10 20 30 40 50 60 70 80

Mols. NaCl /lOOOg H^O

34 64 91 115 137 157 176

Chlorinity, parts per thousand

Figure 2. 17. Ref. [101]. Dependence of the dehydration temperature of gypsum on concentration of NaCl in solution at 10^ pascal pressure.

Table 2.49. Dehydration of gypsum to anhydrite at 56 3 . 5 K

Time

(sec)

Initial

lost water Solid Phase

30 0 CaSO^ ZH^O

120 3. 7 CaSO^ 2H2O and CaSO^

240 6. 2 CaSO^ 2H2O and CaSO^

978 3 . 1 CaSO^ 2H2O and CaSO^

2508 14. 9 CaSO^ 2H^0 and CaSO^

2880 11. 7 CaSO^ 2H2O and CaSO^

5400 26. 8 CaSO^ 2H2O and CaSO^ ilH20

5700 31

.

5 CaSO^ 2H2O and CaSO^ !sH20

8178 68 . 8 CaS04-!sH20

11442 95. 2 Anhydrite

15342 95. 2 Anhydrite

99
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[74] Gad, G.M., Trans. Brit. Ceram. Soc, 51, 429 (1952).

[75] Sudo, T., and Sato, M., Int. Clay Conference, Jerusalem, Israel,

Israel Program for Scientific Translations, (1966).

[76] Berkley, Earl of; Royal Soc. London Philos. Trans., Ser A., 203,

189 (1904).

[77] Schroeder, W.C., Gabriel, A., and Partridge, E.P., J. Amer. Chem. Soc, 57, 1539 (1935).

[78] Benrath, A., Gjedebo, F., Schiffers, B., and Wunderlich, H., Z. Anorg. u. Allg. Chemie., 231, 285 (1937).

[79] Keevil, N.B., J., Amer. Chem. Soc, 64, 841 (1942).

[80] Liu, C, and Lindsay, W.T., Jr., Office of Saline Water, Research

and Devel. Prog. Rept. 722, 124 pp. (1972).

Sourirajan, S., and Kennedy, G.C., Am. J. Sci., 260, 137 (1962)

.

Dickson, F.W., Blount, C.W., and Tunell, G., Amer. J. Sci., 261, 61 (1963).

Booth, H.S., and Bidwell, R.M., J. Amer. Chem. Soc, 72, 2567

(1950).

Partridge, E.P., and White, A.A., J. Amer. Chem. Soc, 51, 360

(1929).

Hall, R.E., Robb, J. A . and Coleman, C.E., J. Amer. Chem. Soc,

48, 927 (1926).

Posniak, E., Am. J. Sci., 35A, 268 (1938).

Melcher, A.C., J. Amer. Chem. Soc, 32, 50 (1910).

Hill, A.E., J. Amer. Chem. Soc, 59, 2242 (1937).

[89] Templeton, C.C., andRodgers, J.C., J. Chem. Eng. Data, 12,536

(1967).

[90] Blount, C.W., and Dickson, F.W., Amer. Mineralogist, 58, 323

(1973) .

[91] Marshall, W.L., and Slusher, R., J. Phys. Chem., 70, 4015

(1966).

Posnjak, E., Amer. J. Sci., 35A, 247 (1938). D'Ans. J., Bretschneider, D., Eick, H., and Freund, H.E., Kali und Steinsalz; 9, 17 (1955).

[94] Madgian, W.M., and Swales, D.A., J. Appl. Chem. (London), 6,

482 (1956).

Posniak, E., Am. J. Sci., 238, 559 (1940).

[96] Segnit, E.R., Holland, H.D., and Biscardi, C.J., Geochimica et Cosmochimica Acta, 26, 1301 (1962).

[97] Macdonald, R.W., and North, N.A., Can. J. Chem., 52, 3181

(1974) .

[98| Akin, G.W. and Lagerwerff, J.V., Geochimica et Cosmochimica

Acta, 29, 343 (1965).

[99] Florke, O.W., Neues. Jahrb. Minn., Abh., 84, 189 (1952).

[100] Cano, R., and Chatelain, P., Bull. Soc. Franc. Min. Crist., 81, 10

(1958).

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[81]

(82]

[83]

[84]

[85]

[86]

[87]

[88]

[92]

[93]

[95]

[102] Ostroff, A.G., Geochimica et Cosmochimica Acta, 28, 1363

(1964).

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(1975).

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6, 247 (1978).

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Printing Office, Washington, D.C. (1976).

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Printing Office, Washington, D.C. (1976).

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1421-C; U.S. Govt. Printing Office, Washington, D.C.

(1977).

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[109] Ellis, A.J., Amer. J. Sci., 257, 354 (1959).

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(1977).

[Ill] Pitzer,K.S.,andMayorga,G.,J.Solution,Chem.,3,539(1974).

[112] Heard, H.C., Geophysical Monograph, 16, 191 (1972).

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[114] Mueller, P., and Siemes, S., Tectonophysics, 23, 105 (1974).

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(1966).

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[117] Robie, R.A., Hemingway, B.S., and Fisher, J.R., U.S. Geol. Survey, Bulletin 1452, U.S. Govt. Printing Office, (1978).

Symbols and Units

Symbol Physical Quantity Unit

P density kg m"^

s° entropy J

• mol-'K-'

Ah° standard enthalpy of formation kj mol-'

free energy of formation kj mol '

heat capacity J

• mol-'K-' P pressure N m-2

concentration mol dm ^

solubility product

Conversion Factors from Non-SI Units to SI Units

0°C

lA

1 bar

1 atm

1 cal

1 g cm"

273.15 K

lO-iOm

105 Pa

101325 Pa

4.184 J 1X10' Kg m-3

101

Chapter 3

Mechanical Properties

H. R. Hume and A. Shakoor*

Contents

Page

3.1. Introduction , 104

3.2. Review of Measurement Methods 104

3.2.1. Elastic Constants 104

3.2.2. Stress-Strain and Creep-Strain Data 105

3.2.3. Hardness 106

3.2.4. Joffe Effect 106

3.2.5. Radiation Effect Determinations 106

3.3. Elastic Properties—Static and Dynamic 107

3.3.1. Density 107

3.3.2. Compression 107

3.3.3. Young s Modulus 107

3.3.4. Shear Modulus Ill

3.3.5. Bulk Modulus 112

3.3.6. Poisson's Ratio 112

3.3.7. Wave Velocities 112

3.4. Strength and Creep 117

3.4.1. Stress-Strain Data ,. . 119

3.4.2. Creep Data 151

3.5. Hardness 164

3.6. Surface Effects 186

3.6.1. Joffe Effect 186

3.7. Effect of Nuclear Irradiation on Mechanical Properties of Rock Salt 189

3.7.1. Effect on Stress-Strain Behavior , 189

3.7.2. Effect on Young's Modulus 196

3.7.3. Effect on Creep 196

3.7.4. Effect on Hardness 196

3.7.5. Evaluation of Data 202

3.8. References 203

Symbols and Units 203

Conversion Factors 203

*Center for Information and Numerical Data Analysis and Synthesis, I'urdue L tiiver>ilv, Yeager Road, West Lafayette, Indiana 47906

103
3.1. Introduction

As a general introduction, some typical in situ values

of the elastic constants of rock salt are presented as well

as a brief introduction to the geological environment and

some of the factors affecting the mechanical behavior of

rock salt.i

3.2. Review of Measurement Methods

3.2.1. Elastic Constants

Compression: Data shown in figure 3.2 on compression were obtained by Voronov and Grigor'ev [2] and

by Heard et al. [7]. Voronov and Grigor'ev applied

Physical constants of rock salt obtained in situ

These resuhs (salt dome) were obtained in the Winnfield salt dome, Louisiana, using surface geophysical techniques; the bedded salt results are from the GNOME drift, New Mexico.

Salt Dome Deviation, % Bedded Salt Deviation, %

Longitudinal velocity 4370 m s-i + 0.7 4085 m S-' + 2.3 Shear velocity 2550 m s-i + 1.2 2150 m s-i + 2.6 Poisson's ratio 0.241 + 6.1 0.31 Modulus of elasticity 35.6 GPa + 4.5 24.5 GPa

Modulus of rigidity 14.4 GPa + 3.3 9.8 GPa

Lame's constant 13.4 GPa 16.1 GPa

Bulk modulus 23.0 GPa 21.7 GPa

Density 2160 kg m-3 2020 kg m-3

Mechanical properties of salt are strongly temperature

dependent since deformation and work hardening, due to a specific load, increase and decrease, respectively, with

a rise in temperature. Confining pressure (fig. 3.1) also exerts an influence on the mechanical behavior of salt; however, it is less significant than that exerted by

temperature. In addition there are several other factors

which influence the mechanical properties of in situ

rock salt: stress rate application, magnitude of stress difference, grain size, thickness of salt body or formation, and the amount and nature of the impurities

present.

Since the pertinent data available at present are inconclusive, and the composition of rock salt and the

location of defects strongly influence the mechanical

behavior, it has been decided not to present recom- mended values. It should be noted that there is some

doubt (Baar [17]) about the extrapolation of laboratory

obtained parameters for use as in situ parameters.

The data are presented as a series of figures and

corresponding combined specification and data tables. The curve numbers in circles shown in the figures

correspond to the data set numbers in the tables.

'A comprehensive report [28] was released as this manuscript was

completed, treating a number of physical aspects of in-situ rock salt masses. This work should be of value in engineering studies.

ultrasonic methods under hydrostatic conditions Oi =

02 using two high pressure chambers at 298 K. Heard

et al. tested four samples (50 X 32 mm) under hydrostatic conditions to 0.8 GPa, two samples (25 X22 mm)

under quasihydrostatic {o^ - a^) conditions from 0.8

to 3.2 GPa and applied uniaxial strain loading (£2 = ^3) on single sample with single strain gauge.

Elastic Moduli: Dynamic moduli of NaCl give more

consistent values than static moduli and, therefore, all modern investigators prefer to use ultrasonic techniques

for their measurement, i.e., to calculate them from a measurement of longitudinal and shear wave velocities.

Voronov and Grigor'ev measured acoustic velocities of

NaCl samples, 6-10 mm long and 15 mm in diameter,

using two high pressure chambers of 2.7 cm^. The time

taken by the ultrasonic wave to travel through the

investigated samples was measured with a two channel

ultrasonic system to an accuracy of +0.01 )us. The

experimentally determined pressure dependence of the

length of a sample and the change in the travel time of the

ultrasonic signal were used to calculate the velocitiei which were then used to determine Young's modulus,

shear modulus, bulk modulus, and Poisson ratio. Th

measurements were made up to a pressure range of O-lOj

GPa and at a temperature ot 300 K. It is noteworthy thai

at pressures less than 0.1 MPa dynamic methodi

probably give extrinsic values of constants due to ope

cracks in the samples. The results of these investigation are shown in figures 3.3, 3.4, 3.5, 3.6, 3.7, and 3.8.

104
Heard et al. [7] measured loading and unloading

moduli in uniaxial stress and strain at pressures to 0.7

GPa. They also measured ultrasonic velocities at pressures to 0.4 GPa to find the dynamic values of shear

modulus, bulk modulus, and Poisson's ratio. The

samples used for static tests were 19 mm in diameter and

38 mm in length, while those for dynamic tests measured

19 mm in diameter and 25 mm in length. The

temperature for all tests was 298 K. The range of

pressures used by Heard et al. was small—up to 3.2 GPa,

but the data obtained is useful in studying the variation

of static and dynamic moduli at low confining pressures.

The data from these studies are shown in figures 3.5,

3.6, 3.7, 3.8, and 3.9. In order to study the effect of very high confining

pressures on the elastic moduli, Frankel, Rich, and

Homan used a pressure range of 2.5-27.0 GPa to measure

the velocities. The highest range to which the acoustic

velocities had previously been measured was 10 GPa by

Voronov and Grigor'ev. To measure the acoustic

velocities at these very high pressures it was necessary

to use a solid pressure device with a large specimen.

Details of the apparatus can be found in Reference [16]

and the data have been plotted in figure 3.7. Morris, Jamieson, and Yarger [4] used the ratio of

longitudinal to shear wave velocity, measured up to a pressure of 9 GPa, to determine directly the Poisson's

ratio and used shock wave data to determine other

moduli. The Poisson ratio was derived from the equation

below:

a = 0.5 - 2)/(/?2 _ 1)

R being the ratio of the velocities. Before determining

the velocities, Morris, Jamieson, and Yarger used third

order elasticity theory to correct for a probable uniaxial

superimposed stress component. This was an improvement upon the previous methods. They also modified the

ultrasonic interferometer so that thicker samples with

higher and more uniform pressure distribution could be

used. The details of the apparatus can be found in

reference [4] and the data have been plotted in figure

3.7.

3.2.2. Stress-Strain and Creep-Strain Data

Data related to figures 3.10 and 3.11 were obtained on

samples of halitic rock with a mean grain diameter of 2

mm. Samples were cubical with an 0.106 m edge length.

Stresses up to 44.471 GPa were applied using a 444.8

MN triaxial testing machine with an 0.1 mX0.1 mXO.l

m loading platen.

Three experiments were conducted under triaxial

conditions and one test under multiaxial loading

conditions at 293 K. Sample No. 1 was loaded uniaxially,

3 and 4 were triaxially loaded at 4.447 GPa and 13.341

GPa, respectively. Sample No. 2 was multiaxially loaded

with lateral stresses of 2.223 GPa and 4.447 GPa.

The differential stress versus confining pressure data

shown in figure 3.13 were obtained using uniaxial strain

loading. A single sample utilizing a single strain gauge was used. Maximum confining pressure was 700 MPa

because of limitations in strain gauge accuracy.

Heard et al. [7] used a single cylinder of fine grained

NaCl with 1% porosity for the determination of data

shown in figure 3.14 (confining pressure = 100 MPa).

The cylinder dimensions were 19 mm diameter, 38 mm

length. Axial and circumferential strain gauges were

fitted to the sample which was subjected to uniaxial

stress loading and unloading. Several other similar tests were run using different confining pressures. Their

results followed the same trend as indicated by the data

given in figure 3.14.

Artificial rock salt samples were used by Dreyer [12]

,

to obtain the data in figure 3.36. Mean grain size diameter was 0. 1 to 0.6 mm. Time-strain tests were run on samples

at temperatures of 302 K, 377 K and 471 K and at pressures of 45.36 GPa, 9.07 GPa, and 0 GPa.

The creep behavior illustrated in figure 3.37 was

determined on square rock salt prisms (0.04m X 0.04 m

XO.l m) using a 44.48 MN constant load lever testing

apparatus. Deformation was accurate to 10~^% and

temperature could be controlled to within 0.5 K (Dreyer,

[ 12] 1972) . The untempered specimen was banded white

rock salt with a mean rock salt content of 98.64%, 1.05%

anhydrite, 0.29% Keserite, and 0.02% clay. The tempered sample had a different composition, having 7.56%

anhydrite, 1.03% keserite and 0.23% clay.

For details concerning test methods for data shown in

figure 3.12, the reader is referred to reference [5].

Nair and Deere [23] , Burke [ 19],Thompson [25] , Ode

[24] , and Baar [ 17] all presented various forms of straintime data for rock salt. These data are displayed in figures

3.23 to 3.35.

Burke [19] used a dead load compression creep unit

fitted with fine grained aluminum oxide platens. Sample

deflections were measured using a colinearly mounted

dial gauge. Commercially obtained high purity artificial

salt samples were used in all cases. Extruded single

crystals of 0.64 X 10"^ m diameter and 0.305 m long were used. These crystals were extruded at 573 to 623 K

an hour at extrusion rates of 0.254 m to 0.381 m per

hour. Certain samples were annealed and then slow

cooled. Test temperatures were kept constant at approximately 275 K.

The values produced by Thompson [25] were achieved

using a triaxial creep testing machine. The confining

pressure provided by oil was measured by a Bourdon gage

105
and kept constant by use of a hydraulic accumulator

filled with nitrogen. The axial load was read using a dynamometer between the hydraulic ram and the line

leading to the test chamber. The entire test chamber was

temperature controlled thermostatically by means of a heating tape wrapped around the chamber. The

specimens themselves were of various lengths between

0.203 m - 0.305 m with a diameter of 0. 102 m having been

drilled from blocks taken in situ from Grand Saline,

Texas and Hockley, Texas.

Heard [21] used artificial samples of reagent grade

NaCl compacted hydrostatically at 170 MPa for 2 h at 403

K. The apparatus used consisted of an externally heated

pressure vessel fitted with an internal force transducer to measure axial strain. Differential stress-strain behavior

of annealed jacketed samples of the above NaCl was then

determined in tension at a confining pressure of 2 kbar

and temperatures of 296 K to 673 K and strain rates ranging from 10"' to 10^ s ^ Creep data obtained by Le Comte [22] were achieved

using creep apparatus capable of achieving greater than

573 K, and a confining pressure of 100 MPa at a stress difference of 13.8 MPa. LeComte's results were obtained

in compression on artificially made specimens consisting

of chemically pure NaCl. Prior to testing these samples were annealed at 573 K and then slowly cooled. For

details of the apparatus used refer to reference [22]

.

Ode' [24] and Baar [17] present a synthesis of data

collected by other researchers and for identification of

the original data the user is referred to each of these

documents.

3.2.3. Hardness

The data shown in figure 3.38 were obtained by

Strelkov, Shpunt, and Nabutovskaya [15] by using

methods developed by them earlier and referred to in

Reference [ 15] . The vibration on the automatic indentor was only 0.3-0.4 yum causing the error due to this factor

to be negligible.

Ksishsh and Sharkezi [14] used NaCl crystals (2X2 X

6 mm) grown by the Kiropolous method and with cation

impurities introduced in them. High purity NaCl

crystals were developed by the Bridgeman method. All

samples were primarily annealed at 923 K and then

cooled at 2°/h. The microhardness was then determined on Model 32 of the Zeiss type instrument with an

indentor load of 4 g. The microhardness of each sample was estimated from 30-40 impressions. The results are

plotted in figures 3.39 and 3.40.

3.2.4. Joffe Effect

The method described below was used to obtain the

data shown in figure 3.41. Polishing of crystals was

achieved by submersing the crystal and agitating in water

for 30 seconds. Thereafter a 5-10 second methyl alcohol

bath and then a 5 second ether bath was given again using

agitation. The crystal was then dried in a hot air stream.

If the time in the methyl alcohol and ether was shortened

not all the water from the initial bath was removed. This

resulted in a small amount of sodium chloride being

precipitated on the surface of the crystal as a "stain" or

tarnish.

"Painting" of polished crystals was achieved using a drop of saturated sodium chloride solution or distilled water. This drop was "painted" on a specific area of a

crystal and then the crystal was air dried. This

"painting" produced a precipitate on the surface of the

crystal which seems to introduce microflaws in its immediate vicinity.

The crystals had a 1.27 cm gauge length and were

water polished, rinsed, and dried so that the cross section was 0.254 cm square. Each crystal was sealed in

aluminum grips with Duco cement and heated to 323 K

for 24 hours in order to dry the cement. The tests themselves were done on a conventional hard tensile

machine at a strain rate of 5 X 10"^ s

3.2.5. Radiation Effect Determinations

Bradshaw et al. [13] used two inch cubes prepared

from large blocks of bedded and dome salt to study the

effects of ionizing radiation on stress-strain and creep

behavior as shown in figures 3.42, 3.43 and 3.47. The test cubes were accurately machined to assure uniform

application of pressure and were subjected to irradiation

in a gamma field of 3.2 X 10^ R per hour with a temperature of 343 K inside the chamber. Radiation

doses of 0, 106 , 10M08 , and 5 X 108 R ^gre used first at room temperature and then at 473 K.

Most of the investigations done in connection with

radiation effects on NaCl were on macrocrystals.

Demidova and Gol'denberg [8] used NaCl whisker

crystals measuring 10- 100 yum in diameter and irradiated

them at room temperature with unfiltered x-radiation for

2-16 hours. This makes it possible to study the

difference between macro and whisker crystal behavior on irradiation. The data from these experiments are shown in figures 3.44 and 3.45.

In order to investigate the dislocation density and the

correlation existing between interstitials and dislocations which might explain why small irradiation doses

produce very little hardening compared to coloration,

Inabe and Takeuchi [9] used NaCl crystals grown by the

Kiropolous technique. Speciments measuring 7X7X3

mm^ were annealed in air at 923 K for 80 hours and

cooled at 20°/h to room temperature. Some of these

106
crystals were heated again and then querch; .! Tic-: dislocation density of a specimen was deiefra iii'-d l y

counting etch pits on a unit area. Each specirasr. v^s? irradiated with an exposure rate ( f 500 R/mtn usin? - rays from a tungsten target. Their results are pr.'s^-n' e !

in figure 3.4.7.

velocity to determine PoisFon'.s ratio and shock wave

data to obtain other elastic modiiii. They also corrected

their valuf-f for a probable - ipt^r.mposed uniaxial stress comp )i)en;. Frankel et si.

^ t] used ultrasonic interferometry to measure room aperature longitudinal and

shear acouoiic velocities hi j;,:.ilv crystalline NaCl at static

Dressures from 2.5 1.0 27.0 'IP a.

3.3. Elastic Properties-Sialic an i

Dynamic

Considerable interest has been thown i.i the ;n^ % ^ ; tions of elastic properties of rock salt in recent y is. Some of the researchers in thii. field are Vorono/,

Grigor'ev, Morris, Yarger, Frank ^1, Burke an 3 H.eard.

Although their work provides imoortant inform tion,

the data are not sufficient to geaerare reco: i e ided

values except in a few cases. A word of caution is sounded since sotr.-: .thors,

notably Baar [17] and Handin [2 i\ are criiica; of the

significance of elastic properties in the case of i ck salt,

Baar, in particular, regards elastic param 'ers as insignificant when regarded from i design vi.:wpoi)it,

given the extremely low limits of elastic behavir r of rock

salt.In general, dynamic elastic constants are les.' .ensitive to pore crush-up (closing of pore spaces v/ithiw the salt)

that occurs somewhere between 0.0;> GPa and 0,2 GPa

during the loading of salt specimens than are the static

constants. For example, Poisson's ratio, a. for the static case shows a marked variation at 'ow C')'ifinir,gpr€.?3ur!=!S

because of pore crush. The dynamical y obiained values on the other hand do not shovv su ;h a pronounced

variation. This applies also to bcth the shear modu'ris

and bulk modulus.

Voronov and Grigor'ev [2] mea'iut ed the velocitiefi of

longitudinal and transverse elastic waves on polycrystal

line NaCl samples under quasi-hydrostatic conditio

using ultrasonic methods at pressures froni 0-10 GPa at 298 K. These velocities were then used to caiculare

compression, Poisson ratio, bulk modulus, shear

modulus, and Young's modulus. Heard et al. [7]

investigated in detail the variation of these properties at a low range of pressure under different conditions. They

tested NaCl samples with 1.0% porosity to determine

loading and unloading moduli in uniaxial stress and

uniaxial strain at pressures up to 0.7 GPa, in hydrostatic

compression up to 0.8 GPa, and in (j\iasi-hydrostatio

compression up to 3.2 GPa. They also determined

ultrasonic velocities at pressures up to 0.4 GPa, iViorris,

Jamieson, and Yarger [4] measured Iransii times of longitudinal and transverse ultrasonic waves in Na( il as a function of quasi-hydrostatic pressure up to 9.0 GPa.

They utilized the ratio of the longiiudinal to shear wave

: gity

The average density of rc :' It measured in situ using

s ul') tieopbysi^- ->'tb is 2160 kg m~^. The

relafu 'ic:n;ip of iri! , -ii'h lining pressure has been

stud^ei! by Voron , ( . ev [2] up to 8.0 GPa and

by Heard .. ; t' ' 5Pa. The data from these

investigations are giv.sn in i.z:,l^ and plotted in figure

3.1. Densit ^ i

' confining pressure is nonlinear but : i[) \ :dmation linearity can be

assuro^id, at iea.sr 'o KM- i iPa. Hydrostatic, quasihydrostatic, anc' ' .'I' i;ading all yield fairly

consistiMit value?.

i •ession

F.)r a piaslic so; relationship is ol i various confining k tions, as calculatedCI, the pressure-volume

'alues of compression at ;nd/or hydrostatic condio ' '.ov and Grigor'ev [2] and

Heard et al. j7] are y

- h\ a in table 3.2 and shown in

figure 3.2. Voronov au.lGr; , r'ev's values are represented by curve 1 and - ' i(i o- by them to match closely

with the values ' tridgeman, Albuerne and

Drickamer, and De v. .S-^^ an, and Kabalkina. Curves

2 and 3 represent ; f,r<1 e! i! [7] values for hydrostatic

and uniaxial sir.-i. ioadr.'- conditions respectively.

Their vali.ies fcv lydrosta ic and quasi-hydrostatic

conditions fall cr he saim composite curve. For a pressure of 3*' '? th'; variation in compression

between curve.? i ;ad 2 a; compared with the total compression is i..^*^";;. Ths; r ;asons for this discrepancy

are not apparevit

Voronov ana Gr^-C'r ev s alues of compression, being

the average of Jdii.i v irvs'estif.ations, are recommended as the more dependabii-; vahits.

mg's Modulus

Ti:i;' '.''erage st.?.iic nr. dynamic values of Young's

luodulu-t can be, take i a .(Sand 36.9GPa, respectively.

\ oron.n andG- ;;;. ased pressure dependencies

of the velnc'lie ; y. v to 10.0 GPa to calculate

\ ;)Ui , '

'

' .-elationship of Young's

Tiodui;r- ' r f !» \ ; is shown in figure 3.3 and

i- conesporidii'^' i given in table 3.3. Burke

, the variation of Young's
TABLE 3.1. PRESSURE DEPENDENCE OF DENSITY OF ROCK SALT

[Confining Pressure, P, GPa; Density, p, kg m~']

Author (s), Year [Ref.] P p Remarks

Voronov , F .

F

and 0 Densities calculated from wave velocities at Grigor'ev, S B., 1976 1 2248 298 K.

[2] 2 2322

3 2388

4 2449

5 2506

6 2559

7 2610

8 2658

Heard, H.C., Abey

,

0 2140 Results obtained dynamically from tests on

A.E., Bonner B.P., 0 1 2151 polycrystalline halite at 298 K. and Duba, A. 1975 [7] 0 2 2164

0 3 2181

0 4 2192

108
TABLE 3.2. PRESSURE DEPENDENCE OF COMPRESSION OF ROCK SALT

[Confining Pressure, P, GPa; Compression, Pq/p]

°s'e' Author (s). Year [Ref.] P Loading' Unloading

Voronov, F.F. and

Grlgor'ev, S.B., 1975

[2]

0.97

1.00

1.03

1.95

2.0

2.2 2.62

2.67

3.00 3.03

3.03

3.9 4.0

4.05

4.10

5.0 5.18

5.30

5.70

5.85

6.0

7.0 7.03

7.95 8.00

8.36 8.70

8.87 9.23

9.60

9.70

9.90

10.05

10.10

0.965

0.963

0.963

0.931

0.932

0.925

0.919

0.917

0.906

0.907

0.904

0.885

0.884

0.885

0.887

0.863

0.862

0.858

0.852

0.847

0.846

0.829

0.832

0.817

0.814

0.809

0.803

0.803

0.798

0.793

0.790

0.789

0.788

0.792

Polycrystalline samples of sodium

chloride; quasihydrostatic conditions; two high-pressure chambers

used at 298 K; ultrasonic method

employed

.

Heard, H.C., Abey,

A.E., Bonner, B.P.,

and Duba, A. , 1975 [7]

0. 0001 1,.000 0,,9933

0. 01 0.,9991

0. 02 0.,9985

0. 03 0..9981

0. 09 0.,9976

0. 05 0,,9972

0. 06 0.,9967

0. 07 0.,9961

0. 08 0.,9957

0. 09 0.,9952

0. 10 0.,9947 0..9892

0. 20 0.,9893 0.,9852

0. 30 0.,9828 0..9814

0. 40 0.,9775 0..9769

0. 50 0.,9735 0..9727

0. 60 0.,9696 0..9688

0. 80 0.,9623 0..9613

1. 00 0.,9544 0..9613

1. 50 0.,9377 0,.9377

2. 00 0.,9225 0.,9225

2. 50 0.,9090 0,,9090

3. 00 0.,8969 0.,8969

3. 20 0. 8928 0.,8928

Six samples of polycrystalline NaCl

tested; four samples (50 mm x 32 mm

dia) tested hydrostatically to 0.8 GPa (0j-a3); two samples (25 mm x

22 mm dia) tested quasihydrostatically

from 0.8 to 3.2 nva at 298 K.

109
TABLE 3.2. PRESSURE DEPENDENCE OF COMPRESSION OF ROCK SALT (continued)

Author (s), Year [Ref.] P p^/p Remarks

3 Heard, H.C., Abey, 0 76 0 9656 Uniaxial strain loading, E2 = A. E. , Bonner , B .P .

,

0 Ik 0 9659 Ej = 0; single sample with

and Duba, A. , 1975 0 73 0 9662 single strain gauge; maximum

[ 7 ] 0 48 0 9749 confining pressure 689 KPa.

0 45 0 9758

0 43 0 9768

0 39 0 9782

0 37 0 9792

0 32 0 9816

0 27 0 9847

0 22 0 9881

0 20 0 9892

0 18 0 9908

0 15 0 9925

0 12 0 9946

0 10 0 9953

0 09 0 9959

0 08 0 9966

0 07 0 99 72

0 06 0 9975

0 05 0 9981

6.04 0 9984

0 03 0 9988

0 02 0 9992

0 01 0 9997

O Reference 2 % Reference 7 A Reference 7

CONFINING PRESSURE, P, GPa

Figure 3.2. Pressure dependence of the compression of rock salt (curve numbers

correspond to data set numbers in matching table).

110
modulus with temperature in figure 3.4 and the

corresponding table. The dynamic values of Young's modulus are more

consistent as compared with static values. This is a fortunate situation as the data on longitudinal and shear wave velocities in NaCl by various investigators agree

closely. Therefore, the corresponding values of Young's

modulus could be calculated with a reasonable degree of

accuracy using the data on velocities.

3.3.4. Shear Modulus

Table 3.5 shows the values of shear modulus

(dynamic) for various values of confining pressure as calculated by Voronov and Grigor'ev [2] while curve 3 in

figure 3.5 is a plot of the same values. Static and dynamic

values of shear modulus calculated by Heard et al. [7] are

also given. As can be seen from the figure, the dynamic

shear modulus increases continuously with pressure in

both cases, but the static modulus shows a marked

variation at low confining pressures (< 0.1 GPa). Heard

et al. related this variation to pore crush-up that occurs somewhere between 0.05 GPa to 0.2 GPa. According to them, static moduli at low pressures are sensitive to closing of pores while dynamic moduli are not. As the sonic velocities are generally consistent, they can be used to find the values of shear modulus. On this

basis, Voronov and Grigor'ev's values may be used as the

provisional values.

TABLE 3.3. PRESSURE DEPENDENCE OF YOUNG'S MODULUS OF ROCK SALT

[Confining Pressure, P, GPa; Young's Modulus, E^, GPa]

Author(s), Year [Ref.] P Eg Remarks

Voronov, F.F. and 0 36.91 Values calculated from pressure-velocity-density

Grigor'ev, S.B., 1976 1.0 40.72 relationship - sonic method; samples were com-

[2] 2.0 44.02 posed of compacted, fine, chemically pure NaCl

3.0 46.85 powder.

4.0 49.30

5.0 51.44

6.0 53.39

7.0 55.25

8.0 57.16

I 1 1 1 I I I I I 0 2 4 6 8 CONFINING PRESSURE, P, GPa

Figure 3.3. Relationship between Young's Modulus and confining pressure (curve numbers correspond to data set numbers in matching table).

Ill
TABLE 3.4. EFFECT OF TEMPERATURE ON DYNAMIC YOUNG'S MODULUS OF NaCl

[Temperature, T, K; Young's Modulus, E, MPa]

Data

Set Author (s)

,

[Ref.] Year

T E Remarks

1 Burke, P.M., 1968 290.,262 36..830 d = 2 mm.

[19] 337. 036 36..100 411. 993 34..750 456.,947 34.,240 484. 788 33.,740 506. 179 33..740 544. 738 JZ .. yuu

594. 027 31.,540 666. 880 29.,680 711. 874 28..580 797. 520 27.,320 881.,091 25..120

2 Burke, P.M., 1968 296.,400 36..010 d = 2 mm.

[19] 349.,950 34,,910

401.,332 1AJH ,. 9An ^tu

433.,440 33..900

491..257 32,,970

531..938 32,.380

613..313 31..030

643..305 30,,360

3 Burke, P.M.

,

1968 287,.804 36 ,600 d = 2 mm.

[19] 309,. 211 36,,350

317,. 796 35,,930

330,.613 Jo ,, loU

433,,412 34,,330

587,.639 31,,120

654,,074 29,,250

951,,895 21,,900

984,.015 21,,390

4 Burke, P.M.

,

1968 296,.303 37 ,450 d = 50 pm.

[19] 379 .856 35,,510

489,.135 32,,720 581 ,273 30,.350 630 ,556 29 ,080 684 ,175 26,,970 754 ,911 24 .760 844 ,978 21 .380 907 ,136 19 .520 941 .400 18 .920 990 .609 18 .760

3.3.5. Bulk Modulus

Voronov and Grigor'ev's [2] values of bulk modulus

have been plotted as curve 2 of figure 3.6 while curves

1, 3, and 4 represent bulk modulus data from Heard et

al. [7] under various conditions of testing. These data

are also tabulated in table 3.6. The minimum difference

between dynamic bulk modulus measured by Voronov

and Heard, respectively, is 2.4 GPa. The values for

other conditions also differ considerably. As a general

trend, both static and dynamic values of bulk modulus

increase with confining pressure at pressure values >

0.2 GPa. Recommended values cannot be generated at

this stage.

3.3.6. Poisson's Ratio

The relationship between Poisson's ratio and confining pressure is shown in figure 3.7 for dynamic and static cases and the corresponding values are tabulated in table

3.7. The dynamic values of Poisson's ratio calculated by

Voronov and Grigor'ev [2] agree closely with those

calculated by Morris et al. [4] . However, the corresponding values as determined by Heard et al. [7] differ from

other data by approximately 8.0%. Voronov's values of

Poisson's ratio may be used as provisional values because

of their close agreement with Morris' data.

3.3.7. Wave Velocities

Data on longitudinal and shear wave velocities from

Voronov and Grigor'ev [2], Heard et al. [7], Morris,

Jamieson, and Yarger [4] , and Frankel, Rich, and Homan

[16] have been plotted in figure 3.8 and also given in

table 3.8. These values are seen to agree within the

uncertainty of measurements. Frankel et al. [16] values

represent the largest range of pressure and may be used

as the recommended values. These longitudinal and

shear acoustic velocities in polycrystalline NaCl were measured at static pressures in the range of 2.5-27.0GPa

at 300 K. The measurements were made by ultrasonic

112
40 T

113
TABLE - . "

. T^.jrS"^E PEPENDENCF f SHFAi' -I'-riULb'S OF ROCK SALT

Data

Set

P a T* If c

-

J

:'>,£. , Ucnnei , B .

!

; , Pi

. \j -L J W •- - 7 3-' mm 1pT*o't"Vii" nniaviaT Tnan — J J. .vo '> J\j lUiu ) Li Lij. d 1^ X0 J. xvjau and Duba, A. .Iv7 :

' / U .

1 1 L 1

i 1 1 • "1 T TTtP a Gl tT"P iH TiTT t'rl aVTSlI flTln fTTfllTTl

J ' 5 -L^ C 1

(\

V' .1 uu 1 S OC

(

1

I DK.l X J 200 15 31

15 43

-il, u L ^ 1) J

"1 ? IS 69

-1 00 15 91

H&arcl. H . C , , ^ ! . , , CIO 13 SC .f.its: ur.iaxial strain loading

1 f\- z T '} ^

- ' \ ' 1 11 50

1 l3 ?o

l--'' 00

V (. '/i.-llOV ^ E , c . i-; b" '

' j "ipi Lt' valuss obta incd us ing ultrasonic

97 , , I \y yx 298 K

.

1 ? 03

1

1 7 0 7

"1 R 7

"

S f) 19 4i 20 06

1

'

20 77 21 39

0 2 4 6 8

CONFINING PRESSURE, P, GPa

FiGL'Rt, 3.5. \ ariation of shear modulus with confining pressure (curve numbers correspond to data set numbers in matching iable).

114
TABLE 3.6. PRESSURE DEPENDENCE OF BULK MODULUS OF ROCK SALT

[Confining Pressure, P, GPa; Bulk Modulus, K^ GPa]

Dat3 Author (s), Year [Ref.] P K Remarks

1 Heard, H.C., Abey, 0.00 11 15 Hydrostatic and quasi-hydrostatic loading;

A. E ., Bonner , B.P.

,

0.02 12 30 samples were dry, polycrystalline, fine grained

and Duba, A, , 1975 [7] 0.02 15 08 NaCl (99.4-99.9% pure); porosity 1.1%; samples

0.02 17 71 were partially work hardened; measurements

0.11 20 00 made at 296 K. 0.12 20 66 0.15 20 66 0.17 20 34 0.21 19 03 0.24 17 55 0.26 16 22 0.29 16 08 0.31 16 08 0.33 17 07 0.38 18 71 0.45 21 01 0.54 22 82 0.70 25 12 0.90 27 26 1.15 29 73 1.51 32 38 1.86 35 35 2.33 38 32 2.85 41 63 3.09 43 12 3.22 41 11

2 Voronov, F.F and 0.0 25 23 Dynamic test results; longitudinal and transGrigor'ev, S B., 1976 1.0 30 18 verse wave velocities are ultrasonic at pres-

[2] 2.0 35 07 sures 0-10 GPa; sample material pure, fine 3.0 39 79 nn T ur* T*\7 c f" a 1 1 inf^ Wj>r^T * mp^i QiiTAniPn 1" q m^inp f" 4.0 44 24 298 K. 5.0 48 36 6.0 52 08

7.0 55 34 8.0 58 10

3 Heard, H.C.

,

Abey, 0.0 18 98 Two different dynamic test technicjues were

A.E., Bonner B.P. , 0.1 22 63 used to obtain shear wave velocity and longiand Duba, A. 1975 [7] 0.2 23. 20 tudinal wave velocity; variability between two 0.3 24 27 methods greatest at ambient temperature - 11% 0.4 24 19 in V-|^Qj^g and 8% in ^gj^g^j.; sample composition

as for Data Set 1.

4 Heard, H.C, et al.

,

0.01 21. 3 Static uniaxial loading was used; sample compo1975 [7] 0.02 17. 3 sition as for Data Set 1; measurements made at 0.1 23.8 296 K. 0.4 22 0

115
CONFINING PRESSURE, P, GPa

Figure 3.6. Variation of bulk modulus with confining pressure (curve numbers correspond to data set numbers in matching table).

TABLE 3.7. PRESSURE DEPENDENCE OF POISSON'S RATIO OF ROCK SALT

[Confining Pressure, P, GPa; Poisson's Ratio, a]

Data

Set Author(s), Year [Ref.] P Remarks

1 Heard, H.C., Abey, 0.01 0 26 Static uniaxial loading test; ratio obtained

A.E., Bonner, B.P., 0.02 0 32 by using transverse and axial strain gauges;

and Duba, A. , 1975 [7] 0.1 0 24 measurements made at 298 K. 0.2 0 29

2 Voronov, F.F. and 0.0 0 256 Dynamic results calculated from sound velociGrigor'ev, S.B., 1976 1.0 0 275 ties; measurements made at 298 K.

[2] 2.0 0 291 3.0 0 304 4.0 0 314 5.0 0 323 6.0 0 329 7.0 0 334 8.0 0 336

3 Morris, C.E., Jamieson, 0.00 0 250 Dynamic results calculated from measurements

J.C., and Yarger, F.L.

,

1.50 0 280 obtained using a specially modified pressure

1976 [4] 3.06 0. 300 cell; samples composed .of reagent grade NaCl

4.50 0 315 (99.5% pure)

.

4 Heard, H.C., Abey, 0.0 0 230 Dynamic results calculated from ultrasonic

A.E., Bonner, B.P., 0.1 0 229 velocities for pressures between 0 and 0.4 and Duba, A. , 1975 [7] 0.2 0. 230 GPa and at a temperature of 298 K. 0.3 0. 236 0.4 0. 230

116
interferometry in a variable lateral support Bridgeman

anvil device. Th 5 previous measurements of velocities in

the range of 0- J ") GPa agree with these values. As can be

seen from the figure, at higher pressures the shear wave

velocity is almost constant or increases very gradually

with increasing pressure. Figure 3.9 (after Heard) also

indicates that at lower values of confining pressure the

velocity increases rapidly with increasing pressure, but

at higher values of confining pressure, the increase in

velocity is gradual and small.

3.4. Strength and Creep

Due to the low limit of elasticity of rock salt, it is hard

to divorce strength and creep. To quote Handin [20]

,

"Strength is a meaningless term unless all environmental conditions are specified". In tests of short duration,

the terms yield strength or ultimate strength or stress at a given strain are appropriate provided pressure, temperature, and chemical environment are specified. To quote

Handin [20] further, with reference to the term

strength, "It is better to avoid the term altogether for

tests of long duration since there is no obvious

connection between rigidity and creep". Ode [24] makes

the following statement: "It is not known yet whether

rock salt has a true yield limit, but, if it does the limit is low". From these quotes by both Handin and Ode, it is apparent that difficulties exist in the definition of

strength for an elasto-plastic material like rock salt.

Bearing such comments in mind, it is difficult to reconcile the claims and statements of various re- searchers. It is suggested that possibly the elastic-ductile

transition is perhaps a distinction criterion between

strength and creep provided all conditions are specified.

Baar [17] claims much of the technical and scientific

literature on salt rocks is misleading. The reason given is that laboratory testing gives different behavior than that

found in-situ. Laboratory strength testing causes "work

hardening" which does not occur in-situ. From an

engineering viewpoint it appears that laboratory

obtained parameters are possibly not valid. An example

occurs in underground excavations where most rocks

behave elastically; however, this does not occur in salt rocks because they display stress relief creep.

Generally, salt rocks are elasto-plastic and behavior

will be elastic unless the {01-O3) stress difference

exceeds the limit of elasticity. Such rocks reassume

elastic behavior once the stress difference has dropped

below a certain critical value. It should be noted that

stress difference initiates creep and not stress magnitude.

In particular, Baar [17] disagrees with the ideal creep curves obtained by many researchers. It is his contention

that the decreasing creep rates displayed by such curves

are a manifestation of work hardening, something not

often found in situ. Assuming a viscous analogue, salt may be assigned an

equivalent viscosity. This viscosity behavior is a

117
TABLE 3.8. PRESSURE DEPENDENCE OF LONGITUDINAL AND SHEAR WAVE VELOCITIES OF ROCK SALT

[Confining Pressure, P, GPa; Velocity, v, m s ^]

~r Author(s), Year [Ref.] P v Remarks

Set

1 Frankel, J., Rich, F.J. and Homan, C.G. , 1976

[16]

2.5

3.0

3.5 4.0

4.5 5.0

5.5 6.0

6.5

7.0

7.5 8.0

9.0 10.0 11.0

12.0

13.0 15.0

17.0

19.0 21.0

23.0

25.0

27.0

5007 5088

5165 5238

5307 5380

5450

5518

5585

5648

5710

5769

5877

5986 6092 6193

6290

6478

6647

6785

6915

7056 7188

7304

Longitudinal wave velocity; polycrystalline

NaCl; longitudinal wave velocity measured at static pressures from 2.5-27.0 GPa at 300 K; Bridgeman Anvil device used for velocity measurements

.

Frankel, J. , et al.

,

1976 [16]

2.5 3.0

3.5 4.0

4.5

5.0

5.5 6.0

6.5

7.0

7.5 8.0

9.0 10.0

11.0

12.0

13.0

15.0

17.0 19.0

21.0 23.0

25.0

27.0

2679

2696 2710

2722

2732 2750

2768

2785

2804

2820 2835

2849

2867 2894

2923

2950

2976

3033

3076

3083

3088

3123

3154

3169

Shear wave velocity; sample specifications and

testing conditions are the same as above.

Voronov, F.F. and Grigor'ev, S.B., 1975

[2]

4551

4785

4989

5166 5317

5445

Longitudinal wave velocity; ultrasonic method

used on polycrystalline NaCl samples under

quasi-hydrostatic conditions; measurements

made at 298 K.

118
TABLE 3.8. PRESSURE DEPENDENCE OF LONGITUDINAL AND SHEAR WAVE VELOCITIES OF ROCK SALT (continued)

Data

Set Author (s). Year [Ref.] P V Remarks

3 Voronov, F.F and 6 5551

'cont ) Grigor'ev, S B., 1975 7 5638

[2] 8 5708

4 Voronov, F.F and 0 2606 Shear wave velocity; conditions same as above. Grigor'ev, S B., 1975 1 2665

[2] 2 2709

3 2743

4 2767

5 2786

6 2802

7 2818

8 2837

5 Heard, H.C., Abey

,

0.000 4078 Longitudinal wave velocity; ultrasonic velociA.E. , Bonner, B.P.

,

0.010 4310 ties calculated on 4 small samples (19 mm

and Duba, A.

,

1975 [7] 0.020 4371 diameter x 25 mm length) and 2 slightly larger

0.050 4419 samples; transducers were polycrystalline

0.075 4430 ceramic Pb(Zn,Ti)03 polarized for transverse

0.100 4453 shear with dominant frequency of 1 MHz. 0.150 4463 0.200 4493 0.250 4509 0.300 4538

0.350 4530 0.400 4549

6 Heard, H.C., et al.

,

0.000 2419 Shear wave velocity; test conditions similar

1975 [7] 0.020 2509 to above

.

0.050 2591 0.070 2629 0.100 2636 0.150 2659 0.200 2657 0.250 2666 0.300 2668 0.350 2676 0.400 2685

O Reference 16 A Reference 2

0 8 16 24 32

CONFINING PRESSURE, P, GPa

Figure 3.8. Variation of longitudinal wave velocity and shear wave velocity with high confining pressures (curve numbers correspond to data set numbers in matching table).

119
0 100 200 300 400

CONFINING PRESSURE, P, MPa

500

Figure 3.9. Variation of longitudinal wave velocity and shear wave velocity with lower confining

pressures (curve numbers correspond to data set numbers in matching table).

function of temperature, confining pressure, differential

stress and time. Assuming that creep of salt takes place

by a steady state mode there are factors such as axial

stress, grain size, temperature and confining pressure

which affect its behavior.

Le Comte [22] investigated the above four factors and

drew the following conclusions. In the case of the axial

stress an increase in the stress produces an increase in

creep rate. An increase in grain size on the other hand

decreases that creep rate. Confining pressure tends to decrease the creep rate, whereas, an increase in pressure

increases the creep rate several fold. Of these factors the

temperature effect is by far the most significant and

exerts the greatest influence.

Due to the controversy surrounding the term

"strength" when applied to rock salt, it has been decided to drop this term and rather to designate data in a general way as "stress-strain" or as "creep" data. It is then left to the user as to which of the two groups best

satisfies his needs.

3.4.1. Stress-Strain Data

In the case of stress, the primary quantities are the

principal stresses ai, as, the differential stress (01-CT3),

and the shear stress, r. On occasions a relationship

between differential stress and the minor principal stress

(as) is also used.

Initially, in almost every case, the relationship at either low confining stress or strain displays behavior

with an elastic component. Beyond a certain stress {03) or strain, however, the salt shows more of a plastic

character. The former behavior may be regarded as

elastic, whereas the latter is plastic in nature. In the case of some relationships between shear stress and strain, the elastic-plastic transition is not pro- nounced and has arbitrarily been taken to occur at about

0.2% axial strain. The above transition is observed at 298

K; however, this transition changes and may even almost

disappear depending on the prevailing temperature.

Dreyer's [12] data on shear and normal stress and

their variation with test conditions are tabulated in

tables 3.9 and 3.10 and are shown in figures 3.10 and

3.11, respectively. In general, the relationship suggests

that the influence of strain hardening is small and, as expected, the shear stress bearing capacity is a minimum under uniaxial loading and increases as the

confining pressure increases.

The effect of temperature and confining pressure on

the deformation of halite single crystals has been studied

by Gera [5] and can be seen in Figure 3.12 with the

corresponding values in Table 3.11. From the figure it is observed that as temperature increases, creep also

increases, and that the effect of confining pressure is secondary. This latter observation is clear from the small

difference between the 100 MPa and 200 MPa curves.

120
TABLE 3.9. RELATIONSHIP BETWEEN SHEAR STRESS AND STRAIN FOR ROCK SALT UNDER VARYING TEST CONDITIONS

[Shear Stress, T, GPa: Strain, e , %]

Data

Set Author (s), Year [Ref.] Remarks

1 Dreyer, W. , 1972 [12]

2 Dreyer, W. , 1972 [12]

3 Dreyer, W. , 19 72 [12]

4 Dreyer, W. , 1972 [12]

2 .206 0 .15

3 .625 0 . 33

4 .650 0 .52 5.243 0 . 74

5 .639 0 .95

5 .887 1 .13

6 .037 1 .35

6 .119 1 .57

6 .239 1 . 74

6 . 320 1 .95

6 .362 2 .16

3 .309 0 .22

4 .649 0 .45

5 .399 0 .64

5 .795 0 .85

6,.034 1,.06

6,.312 1,.25

6,.472 1,.46

6,.671 1,.67

6,,791 1..84

6,.872 2..05

6

,

. 953 2..25

2..678 0,,13

5..081 0..34

5.,989 0.,55

6.,384 0.,74

6.,583 0.,93

6.,744 1.,18

6.,903 1.,37

7.,024 1. 56

7.,144 1. 76

7. 186 1. 98

7. 306 2. 16

7. 309 2. 39

2. 204 0. 07

3. 228 0. 10

5. 611 0. 34

6. 500 0. 51

6. 974 0. 72

7. 252 0. 95

7. 412 1. 14

7. 572 1. 35

7. 653 1. 56

7. 734 1. 75

7. 855 1. 98

7. 975 2. 17

8. 057 2. 39

8. 177 2. 58

Cubical samples of halite with 10.6 cm edge

length; grain size distribution homogeneous;

uniaxially loaded - 02=0

perature.

=0; room temSample similar to above; multiaxially loaded;

02^0^, 02=4.447 GPa,

perature

.

=2.223 GPa; room temSample similar to above; room temperature.

03=4.447 GPa;

Sample similar to above; room temperature.

121
10

Figure 3.10. Shear stress-strain behavior of rock salt for different

test conditions (curve numbers correspond to data set numbers in matching table).

122
TABLE 3.10. STRESS-STRAIN RELATIONSHIP FOR ROCK SALT UNDER VARYING TEST CONDITIONS

[Stress, 0j , GPa; Strain, e , %]

Data

Set Author (s), Year [Ref.] Remarks

1 Dreyer, W. , 1972 [12]

2 Dreyer, W. , 1972 [12]

3 Dreyer, W. , 1972 [12]

A Dreyer, W. , 1972 [12]

3 234 0 06

7 142 0 28

9 164 0 49 10 511 nu 0 O 11 185 0 90 11 724 1 10 11 994 1 32 12.129 1 51

12 263 1 73 12 533 1 92

12 802 2 11

3 234 0 03

8 760 0 19 11 455 0 39 13 072 0 58 13 341 0 71 U 015 Q Qn

U 419 1 10 14 959 1 32 15 363 1 52 15.632 1 73 15 767 1 95 16 037 2 14

16 037 2 33

9 703 0 08

14 419 0 28

16 576 0 49

17 115 0 69

17 249 nu oo

17 657 1 08

17 923 1 32 18 193 1 51

18 597 1 71 18 732 1 92 18.866 2 12

19 136 2 33

19 54 0 08

24 39 0 27 26 144 0 47

27 087 0 68

27 626 0 88

28 030 1 08

28 300 1 29 28 569 1 49

28 839 1 71 29 108 1 90

29 243 2 11

29 648 2 29

29 917 2 51

Cubical sample of halite with 10.6 cm edge

length; uniaxially loaded, 02= temperature.

03=0; room

Sample similar to above; 025*03, 02=4.447 GPa,

03=2.223 GPa; room temperature.

Sample similar to above; room temperature.

02=03, 03=4.447 GPa;

Sample similar to above; 02=03, 03=13.341 GPa; room temperature.

123
STRAIN, € , %

Figure 3.11. Normal stress-strain behavior of rock salt for different

test conditions (curve numbers correspond to data set numbers in matching table).

124
TABLE 3.11. RELATIONSHIP BETWEEN DIFFERENTIAL STRESS AND STRAIN FOR SINGLE HALITE CRYSTALS

AT VARYING CONFINING PRESSURE AND TEMPERATURE

[Differential Stress (Oi-Oj), MPa; Strain, e, %]

e Remarks

0.A2 0 .11 Halite single crystals; deformed dry in com- 9.30 0 .23 pression at 200 MPa; temperature 297 K; data

14.35 1 .64 obtained from smooth curves. 20.21 4 .12 27.75 7 .68

J4 . OD 1 1 XX . U J 41.97 14 .70 49.08 18 .26 54.09 21 .28 58.27 23 .44 59.94 24 .63

0.85 0 .00 Specimen similar to above; deformed dry in 9.29 0 77 compression at 100 MPa; temperature 297 K; 15.18 2 28 data obtained from smooth curves. 19.36 4 23 23.97 6 49 28.57 8 76

'^'^ JO t Xl1 7 24 39.01 14 80 44.86 18 15 50.11 20 63 52.36 21 81 54.86 23 76

1.27 0 11 Specimen similar to above; deformed dry in 10.11 1 74 compression at 2000 MPa; temperature 423 K; 13.02 4 11 data obtained from smooth curves.

7 34 20.46 11 76 24.18 15 86 26.65 18 98 28.69 21.99

30.76 24.26

4.22 0 33 Sample similar to above; deformed dry in corn- 10.11 1 95 pression at 100 MPa; temperature 423 K; data

14.25 5 73 obtained from smooth curves. 16.31 8. 31

18 . 36 11 33 21.25 14.67

22.87 17. 47 24.09 19. 84 25.32 21. 56 26.55 23. 50

1.27 0. 11 Sample similar to above; deformed dry in com8.02 0. 98 pression at 200 MPa; temperature 573 K; data

9.24 2. 81 obtained from smooth curves. 8.32 6. 04 8.29 7. 55 8.67 9. 38 9.49 10. 67 10.73 11. 96 11.12 13. 47 11.02 15. 62 11.02 18. 10 10.96 20. 36 10.07 22. 40

Data

Set

Gera, F. , 1972 [5]

Gera, F. , 1972 [5]

Gera, F. , 1972 [5]

Gera, F., 1972 [5]

Gera, F. , 1972 [5]

125
0 4 8 12 16 20 24

STRAIN, €, %

Figure 3.12. Differential stress-strain relationship at several temperatures and different confining pressures (curve numbers

correspond to data set numbers in matching table).

Another relationship of interest is that of differential

stress versus confining pressure which is shown in figure

3.13. The corresponding data are taken from ref. [7] and

reported in table 3.12. It can be observed that after a maximum differential stress of about 50 MPa has been

achieved, there is a decrease in differential stress {a\-

03) as 03 increases. This behavior has been attributed by

Heard et al. [7] to pore collapse in the rock salt and

continues until confining pressure has reached a value of

about 230 MPa after which differential stress increases

with confining pressure.

Axial and circumferential strain of rock salt samples as

a function of stress difference during triaxial loading and

unloading are presented in figure 3.14 with the

corresponding values in table 3.13. The data have been

taken from ref. [7] and indicate that for cylindrical

samples with an L/D ratio = 2, and loads>50MPa, there

is a marked change in the slope of both stress-strain curves. This implies two different modes of behavior

beyond this 50 MPa demarcation, i.e., elastic-plastic

transition.

Typical differential stress-strain curves for annealed

halite aggregates are illustrated in figures 3.15 to 3.19

and tables 3.14-3.18 for a broad range of strain rates at

273 K to 400 K (Heard [21]). It is noteworthy that strain

hardening is decreased by decreasing strain rate 0

increasing temperature. Steady-state flow is closel" approximated during most of the deformation at 10~^ s~^ and 373 K. The onset of steady-state flow occurs a' somewhat higher rates at intermediate temperature, and

at 673 K, strain hardening appears dominant only at th

highest rates investigated.

Figures 3.20 and 3.21 and tables 3.19-3.20 show

stress-strain results as a function of temperature at two

strain rates, 10~^ and lO"*" s~i at a confining pressure 0

200 MPa. In both of these cases, strain hardenin

disappears as the intermediate temperatures are reached.

A comparison of the behavior of annealed and

unannealed rock salt samples which are work hardened

to some degree can be observed in figure 3.22 and tabl 3.21 which represent data from Gera [5] . The anneale

sample shows lower shear stress resistance as evidence

by the greater amount of strain it undergoes for the sam

load compared to the unannealed sample. This lower

resistance of the annealed sample is thought to be caused

by recrystallization that occurs during annealin

allowing the rock salt to revert to its former state (i.e. work hardening effect is destroyed).

126
TABLE 3.12. VARIATION OF DIFFERENTIAL STRESS WITH CONFINING PRESSURE FOR UNIAXIAL STRAIN LOADING OF ROCK SALT

[Confining Pressure, a,, MPa; Differential Stress, (a-^-a^), MPa]

Data

Set Author (s), Year [Ref.] (01-03) Remarks

Heard, H.C. , Abey,

A.E., Bonner, B.P., and Duba, A., 1975 [7]

4 90 18 39

6 12 23 23 11 23 26 14 11 17 30 65

12 41 34 20

16 22 38 08

26 44 42 93

46 99 45 52 59 83 48 12 71 39 50 10 80 37 51 68

111 26 51 06

126 70 51 07

135 72 50 12 155 03 49 49 160 21 47 23 175 65 47 25 197 52 47 91

227 16 44 39 243 87 45 69 274 74 46 69 296 57 49 93 322 31 49 95 378 85 55 48 425 15 57 11 663 06 67 98 681 06 68 96 697 77 70 27 699 12 65. 43 641 62 35 38

600. 92 -0 136

Dry, fine grained, polycrystalline NaCl with

1% porosity; uniaxial strain loading (02=03=

0) ; maximum confining pressijre 100 MPa; tem- perature 296 K.
TABLE 3.13. AXIAL (Ei) AND CIRCUMFERENTIAL (E3) STRAINS AS A FUNCTION OF

STRESS DIFFERENCE ON UNIAXIAL STRESS LOADING AND UNLOADING

[Differential Stress, (Oj-aj), MPa; Strain, e]

Data

Set Author (s). Year [Ref.] (01-03) Remarks

Heard, H.C., Abey,

A.E., Bonner, B.P., and Duba, A. , 1975 [7]

Heard, H.C. , et al.

,

1975 [7]

3 89 0 000

9 93 0 000

26 70 -0 001

43 73 -0 002

55 51 -0 004

59 33 -0 006

66 41 -0 010

74 43 -0 023

80 75 -0 039

66 29 -0 048

41 05 -0 045

13 01 -0 045

3 89 0 000

9 67 0 000

26 44 0 000

55 32 0 001

66 37 0 004

71 08 0 007

78 06 0 012

82 02 n 019

65 82 0 020

12 48 0 020

Axial strain (Ej); dry, fine grained, polycrystalline NaCl with 1% porosity; uniaxial

stress loading and unloading; 03=100 MPa.

Circumferential strain (£3); sample and test conditions same as above.

100

-0.04 -0.02 -0.01 0.00 0.01

STRAIN, €

0.02 0.03

Figure 3.14. Axial (ej) and circumferential (ts) strain as a function of differential stress (curve numbers

correspond to data set numbers in matching table).

128
TABLE 3.14. DIFFERENTIAL STRESS-STRAIN CURVE^FOR POLYCRYSTALLINE HALITE

EXTENDED AT 200 MPa, 373 K, AND e = 1.5 x 10"^ TO

1.5 X 10~^ s

1

[Strain, e, %; Differential Stress, (a^-O^) MPa]

Data Author(s), Year ^ ^ t> ^ Set [Ref.] ! ^l:!!

^^"'^^^^

Heard, H.C., 1972 0.000 4.988 e = 1.5 x 10 ^ s

>

[21] 0.087 9.977

0.218 14.966

0.480 17.728

0.655 19.955

1.004 22.449

1.441 25.033

1.878 27.171

2.576 29.309

3.712 31.804

4.978 33.674

6.943 35.902

8.603 37.327

9.869 38.307

11.354 39.287

Heard, H.C., 1972 0.655 12.294 e = 1.5 x lO"** s"l

[21] 1.004 14.877

1.616 18.262

2.358 20.935

3.537 23.875

5.371 26.726

7.031 28.418

8.777 30.111

10.131 31.180

11.616 32.249

Heard, H.C., 1972 0.262 10.155 e = 1.5 x 10"^ s~l

[21] 0.742 15.055

1.354 18.351

2.052 20.222

2.314 20.935

3.362 22.539

5.066 24.409

6.376 25.389

7.904 26.369

9.127 26.993

10.611 27.616

11.528 27.884

129
TABLE 3.14. DIFFERENTIAL STRESS-STRAIN CURVE FOR POLYCRYSTALLINE HALITE

EXTENDED AT 200 MPa, 373 K, AND E = 1.5 x 10- 3 1.5 X 10 (Continued)

TO

Data Author(s), Year

Set [Ref . ] Remarks

Heard, H.C.

[21]

1972 0.087

0.175

0.262

0.437

0.611

1.004

1.703

2.402

3.712

5.066

6.201

7.991

9.389

10.699

11.310

2.405

4.988

6.770

9.977

11.492

13.363

15.055

16.302

17.995

19.420

20.311

21.469

22.093

22.717

22.806

e = 1.5 X 10"^ s

1

Heard, H.C, 1972

[21]

0.568

1.310

2.271

,450

.585

,201

,467

8.908

10.000

10.699

10.957

12.472

13.897

15.233

16.124

17.104

17.728

18.262

18.619

18.708

E = 1.5 X 10 ' s

7 e-1

Heard, H.C. , 1972

[21]

0.437

0.568

0.742

1.354

2.183

3.362

4.803

6.594

7.904

9.127

10.262

175

621

977

£ = 1.5 X 10 " s

8 o-l

10.423

10.779

11.135

11.403

11.581

11.670

11.581

11.581

130
STRAIN , € , %

Figure 3.15. Differential stress-strain curves for polycrystalline halite at 373 K.

131
TABLE 3.15. DIFFERENTIAL STRESS-STRAIN RELATIONSHIP FOR POLYCRYSTALLINE

HALITE AT 200 MPa, 473 K, AND e = 1.8 x

10~^ TO

1.2 X 10"^ s~l

[Strain, e, %; Differential Stress, (01-03) ffPa]

Data Author(s), Year

Set [Ref . ] O1-O3 Remarks

Heard, H.C., 1972

121]

0.050

0.145

0.280

0.547

1.034

1.785

2.842

3.811

4.823

5.880

7.904

9.883

11.686

4.955

9.999

12.299

15.041

17.516

19.990

22.020

23.254

24.310

25.366

26.949

28.000

28.610

e = 1.8 X 10"^ s

1

Heard, H.C., 1972

[21]

0.635

1.032

1.385

1.869

3.849

5.917

7.984

9.919

11.107

14.598

16.100

16.806

17.335

19.006

20.145

21.196

22.070

22.507

e = 1.5 X 10"

Heard, H.C., 1972

[21]

0.323

0.764

1.161

1.821

3.889

5.913

7.892

9.914

11.233

11.591

12.916

13.533

14.149

15.731

16.959

17.745

18.265

18.524

£ = 1.5 X

10"'' s

1

Heard, H.C. , 1972

[21]

0.051

0.141

0.495

0.760

1.290

1.906

2.787

3.887

4.987

5.911

7.934

9.913

11.232

5.044

6,901

9.023

9.907

11.232

12.290

13.525

14.492

15.283

15.720

16.594

17.292

17.727

1.2 X 10 * s

1

132
TABLE 3.15. DIFFERENTIAL STRESS-STRAIN RELATIONSHIP FOR POLYCRYSTALLINE

HALITE AT 200 MPa, 473 K, AND e = 1.8 x 10"^ TO

1.2 X 10"^ (Continued)

Data Author (s), Year

Set [Ref . ] Remarks

Heard, H.C., 1972

[21]

0.405

1.374

1.859

3.047

3.883

5.951

7.929

9.908

10.919

7.254

8.842

9.547

10.691

11.395

12.534

13.143

13.663

13.747

1.2 X 10" -,-1

Heard, H.C., 1972

[21]

0.140

0.624

1.900

3.923

5.945

7.924

9.946

11.397

6.194

6.722

7.335'

7.943

8.375

8.895

9.150

9.142

e = 1.2 X 10-6

Heard, H.C., 1972

[21]

Heard, H.C. , 1972

[21]

0.093

0.357

1.281

1.897

2.952

3.875

5.985

7.963

9.985

11.348

0.138

1.106

1.897

3.084

3.920

5.414

5.414

5.500

5.543

5.587

5.939

6.554

3.893

4.245

4.683

4.945

5.117

5.289

5.543

5.532

5.521

5.514

4.424

5.038

5.388

5.647

5.642

5.723

5.546

3.864

3.687

3.510

3.508

3.416

e = 1.2 X 10'

e = 1.2 X 10"^

Heard, H.C. , 1972

[21]

0.048

0.136

1.191

3.008

3.273

3.268'

1.2 X 10'

133
134
TABLE 3.16. DIFFERENTIAL STRESS-STRAIN CURVES FOR POLYCRYSTALLINE HALITE

EXTENDED AT 200 MPa, 521 K, AND C = 1.8 x 10~' TO

1.2 X 10"^

[Strain, e, %; Differential Stress, (01-O3) MPa]

Data Author(s), Year

Set [Ref . ] ai-as Remarks

Heard, H.C., 1972

[21]

1.631

1.733

2.643

3.702

5.714

7.623

9.630

10.282

15.457

15.761

17.633

19.300

21.571

23.285

24.745

25.147

e = 1.8 X 10" _-

1

Heard, H.C. , 1972

[21]

0.063

0.126

0.239

0.353

0.716

1.025

1.329

1.785

2.693

3.748

5.705

7.661

9.716

11.470

2.433

4.969

7.503

9.988

12.572

14.244

15.053

16.116

17.632

18.539

19.949

21.104

22.057

22.859

1.9 X 10"^ s

'

Heard, H.C, 1972

[21]

0.063

0.076

0.189

0.303

0.563

0.766

1.220

1.824

3.783

5.788

7.743

9.747

11.149

2.438

4.979

7.468

10.008

12.039

12.546

13.306

14.116

15.731

16.838

17.641

18.443

18.893

e = 1.5 X 10- 3

Heard, H.C, 1972

[21]

0.063

0.126

0.489

0.947

1.804

2.909

2.433

4.969

7.502

8.920

10.284

11.191

e = 1.2 X 10 s

^

135
TABLE 3.16. DIFFERENTIAL STRESS-STRAIN CURVES FOR POLYCRYSTALLINE HALITE

EXTENDED AT 200 MPa , 521 K, AND £ = 1.8 x 10"^ TO

1.2 X 10"^ s ^ (Continued)

Data Author(s), Year

Set [Ref . ] Remarks

4 Heard, H.C. , 1972

(cont.) [21]

Heard, H.C, 1972

[21]

Heard, H.C, 1972

[21]

3.812

5.816

7.819

9.822

10.672

0.283

1.887

3.941

5,844

7.846

9.848

10.998

0.321

1.876

3.929

5.930

7.931

9.931

10.431

11.795

12.595

13.193

13.588

13.735

6.235

7.089

7.838

8.386

8.730

9.023

9,169

4.004

4.858

5.506

5.748

5.890

5.930

5.927

1.2 10-5 -1

1.2 10

-6 -1

Heard, H.C. , 1972

[21]

0.167

0.718

1.870

4.021

5.972

7.923

9.973

11.023

3.295

3,495

3,742

4.035

4.126

4,267

4,307

4.250

1.2 10"

136
TEMPERATURE = 521 K

J

STRAIN , € , %

Figure 3.17. Differential stress-strain curves for polycrystalline halite at 521 K.

137
TABLE 3.17. DIFFERENTIAL STRESS-STRAIN CURVES FOR POLYCRYSTALLINE HALITE AT

200 MPa, 573 K AND £ = 1.8 x 10"' TO 1.2 x 10"^

[Strain, c, %; Differential Stress, (aj-as) MPa]

Data Author(s), Year

Set [Ref . ] Remarks

Heard, H.C. , 1972

[211

Heard, H.C. , 1972

[21]

Heard, H.C, 1972

[21]

Heard, H.C.

[21]

1972

0.957

I. 304

2.043

2.870

4.043

5.174

6.087

8.043

9.957

11.913

0.043

0.217

0.391

0.435

0.696

1.304

2.043

4.000

6.043

8.043

9.957

12.043

0.087

0.217

0.304

0.565

1.043

2.043

3.609

4.000

6.000

8.043

9.957

11.304

0.348

2.043

4.000

6.000

8.000

9.957

II. 043

7.556

8.933

10.933

12.533

14.044

15.066

15.600

16.711

17.466

18.044

0.044

2.533

5.066

5.866

6.533

7.422

8.266

10.133

11.733

13.066

14.133

14.933

0.044

2.488

3.466

4.533

5.777

7.022

8.088

8.444

9.644

10.533

11.066

11.155

2.311

4.266

5.644

6.444

6.^77

7.288

7.377

e = 1.6 X 10 ^ s

*

e = 1.8 X 10 ^ s

*

e = 1.2 X 10"^ s

^

e = 1.5 X

10"**

138
TABLE .3.17. DIFFERENTIAL STRESS-STRAIN CURVES FOR POLYCRYSTALLINE HALITE AT

200 MPa, 573 K AND e = 1.8 x 10"^ TO 1.2 x 10"® Continued)

Data Author (s), Year ^ _ , ^et [Ref.]

" ^i:^ ^^"'^^^^

5 Heard, H.C., 1972 0.304 2,044 e = 1.2 x 10"^ s~'

[21] 0.739 2.577

1.000 2.711

2.043 3.155

4.000 3.866

6.000 4.355

8.000 4.755

9.957 4.888

11.087 4.844

6 Heard, H.C., 1972 0.391 1.911 e = 1.2 x 10"^

[21] 0.652 2.177

0.826 2.222

2.043 2.444

4.000 2.666

6,000 2.844

8,043 2,800

10,000 2,844

11.435 2.844

7 Heard, H.C., 1972 0,304 1.600 e = 1.2 x 10"^ s~'

[21] 0.652 1.955

0,913 2,044

1,217 2.044

2.043 2.088

4.000 2.133

6.000 2.844

8.043 2.800

10.000 2,844

11,435 2,844

8 Heard, H,C,, 1972 0,261 1,422 e = 1,2 x 10"^

|-2il 1.174 1,555

2.000 1.600

3.913 1.600

139
STRAIN , € , %

Figure 3.18. Differential stress-strain curves for polycrystalline halite at 573 K.

140
TABLE 3.18. DIFFERENTIAL STRESS-STRAIN CURVES FOR POLYCRYSTALLINE HALITE

EXTENDED AT 200 MPa, 673 K, AND e = 1.9 x 10"' TO

1.2 X s 10"' -"1

[Strain, e, %; Differential Stress, (Oi-a^) MPa]

Data Author(s), Year

Set [Ref.J

Remarks

Heard, H.C. , 1972

[21]

0.137

1.175

1.996

3.940

5.970

7.999

9.985

11.237

2.894

3.549

3.897

4.462

4.851

5.065

5.191

5.275

1.9 X 10' ' s-l

Heard, H.C.

[21]

1972 0.135

0.221

1.993

3.980

5.966

7.952

10.024

11.060

1.929

1.973

2.669

3.146

3.448

3.530

3.524

3.521

1.4 X 10"^ s

^

Heard, H.C.

[21]

1972 0.134

0.350

0.523

1.991

3.977

5.963

8.035

10.020

11.316

1.578

1.753

1.884

2.012

2.138

2.176

2.170

2.208

2.248

1.2 X 10"% ^

Heard, H.C.

[21]

1972 0.263

1.429

1.990

4.019

5.961

8.033

10.019

10.407

1.402

1.574

1.573

1.611

1.606

1.600

1.594

1.637

e = 1.2 X

10""*

s

^

Heard, H.C. , 1972

[21]

0.573

0.791

1.616

2.093

3.305

4.300

5.857

8.019

9.359

10.526

4.340

4.997

6.793

7.581

9.025

9.900

10.992

12.258

12.868

13.347

e = 1.2 X 10"^ s

^

141
TABLE 3.18. DIFFERENTIAL STRESS-STRAIN CURVES FOR POLYCRYSTALLINE HALITE

EXTENDED AT 200 MPa, 673 K, AND t = 1.9 x 10"^ TO

1.2 X 10"^ s

^ (Continued)

Data Author(s), Year ^ , Set UefJ I ^11^3

R^ks

Heard, H.C., 1972 0.093 2.499 e = 1.2 x 10"^ s

^ [21] 0.182 3.376

0.270 4.078

0.618 5.042

1.052 5.918

1,615 6.706

1.962 7.143

3.000 7.974

3.952 8.629

5.940 9.764

7.971 10.547

9.958 10.980

11.253 11.021

Heard, H.C., 1972 0.049 1.973 £ = 1.2 x 10"' s"'

[21] 0.095 3.069

0.572 4.165

1.957 5.433

3.989 6.392

5.933 6.957

8.006 7.433

10.035 7.647

11.633 7.774

142
STRAIN , € , %

Figure 3.19. Differential stress-strain curves for polycfystalline halite at 673 K.

143
TABLE 3. 19. DIFFERENTIAL STRESS-STRAIN CURVES FOR POLYCRYSTALLINE HALITE

EXTENDED AT 200 MPa. TEMPERATURE FROM 300 TO 673 K AND

e = 1.2-1.5 X 10"^ s"^

[Strain, £, %; Differential Stress, MPa]

Data Author (s), Year

Set [Ref . ] Remarks

Heard, H.C. , 1972

[21]

0.183

0.189

0.252

0.583

0.802

1.236

1.831

2.694

3.771

4.846

5.759

6.833

7.746

8.874

9.679

10.269

11.731

15.130

20.173

25.105

27.296

30.253

33.099

36.272

39.115

41.080

42.608

44.025

45.114

46.421

47.401

47.835

Temperature = 300 K.

Heard, H.C, 1972

[21]

0.170

0.341

0.725

1.266

1.859

2.934

3.848

5.833

7.818

9.802

11.464

4.932

10.085

15.125

17.862

19.941

21.906

23.215

25.063

26.482

27.663

28.308

Temperature = 373 K.

Heard, H.C. , 1972

[21]

0.495

1.248

1.947

3.021

3.932

5.863

7.846

9.830

10.848

6.904

8.542

9.524

10.831

11.482

12.563

13.205

13.737

13.949

Temperature = 473 K.

Heard, H.C.

[21]

1972 0.332

0.333

0.440

1.996

3.926

5.808

6.028

6.246

7.111

7.973

Temperature = 521 K.

144
TABLE 3.19. DIFFERENTIAL STRESS-STRAIN CURVES FOR POLYCRYSTALLINE HALITE

EXTENDED AT 200 MPa. TEMPERATURE FROM 300 TO 673 K AND

e = 1.2-1.5 X 10"^ s"i (Continued)

Data Author(s), Year ^ , _Set FRef.]

^

"i-<^3 ^^^^^^^

4 Heard, H.C., 1972 5.909 8.505

(cont.) [21] 7.892 8.928

9.875 9.132

11.160 9.231

5 Heard, H.C., 1972 0.326 2.190 Temperature = 573 K

[211 1.988 3.273

3.972 3.915

5.901 4.448

7.938 4.871

9.867 5.075

10.671 5.178

6 Heard, H.C., 1972 0.325 2.080 Temperature = 673 K. [21] 1.934 2.616

3.970 3.148

5.899 3.462

7.989 3.664

9.918 3.759

11.471 3.637

145
STRAIN , € , %

Figure 3.20. Differential stress-strain curves for polycrystalline halite at temperatures from

300 to 673 K.

146
TABLE 3.20. DIFFERENTIAL STRESS-STRAIN CURVES FOR POLYCRYSTALLINE HALITE

EXTENDED AT 200 MPa, 300 TO 673 K, AND i = 1.2-1.5 x 10~'^s~l

[Strain, c, %; Differential Stress, (01-03) MPa]

Data Author(s), Year

Set [Ref . ] 01-03 Remarks

Heard, H.C., 1972

[21]

0.225

0.493

0.674

0.986

1.516

1.955

2.438

3.181

3.924

5.933

7.898

9.862

11.040

4.987

10.064

15.141

20.128

25.203

27.695

29.385

30.540

31.337

32.841

33.811

34.246

34.418

Temperature = 300 K.

Heard

,

[2]]

H.C. 1972 0.581

0.756

1.456

1.981

3.947

5.956

7.965

9.929

11.195

10.509

11.399

12.909

13.530

15.658

17.073

18.131

18.744

18.826

Temperature = 373 K.

Heard, H.C.

[21]

1972 0.311

0.748

1.184

1.970

4.021

5.985

7.993

10.000

11.178

4.007

4.450

4.715

4.978.

5.412

5.669

5.659'

5.648

5.642.

Temperature = 473 K.

Heard, H.C.

[21J

1972 0.310

0.397

1.969

4.020

6.027

7.991

9.998

10.958

3.294

3.472

3.820

4.076

4.333

4.233

4.312

4.306

Temperature = 521 K.

147
TABLE 3.20. DIFFERENTIAL STRESS-STRAIN CURVES FOR POLYCRYSTALLINE HALITE

EXTENDED AT 200 MPa, 300 TO 673 K, AND i = 1.2-1.5x10"'*' s~

(Continued)

Data Author(s), Year

Set [Ref . ] CJi-as Remarks

Heard, H.C., 1972 0.220 1.780 Temperature = 573 K. [21] 0.483 1.957

1.966 2.127

4.017 2.205

6.025 2.195

7.989 2.362

9.996 2.352

11.130 2.435

Heard, H.C., 1972 0.307 1.423 Temperature = 673 K.

[21] 2.009 1.682

4.017 1.671

6.024 1.749

7.988 1.739

9.951 1.817

10.693 1.813

148
0 4 8 12 STRAIN , € , %

Figure 3.21. Differential stress-strain curves for polycrystalline halite at temperatures from

300 to 673 K.

149
TABLE 3.21. EFFECT OF ANNEALING AT 873 K ON STRESS-STRAIN RELATIONSHIP OF ROCK SALT

[Stress, Oi, MPa; Strain, e , Z]

"^•^^ Author (s). Year [Ref.] Oj e Remarks

Set

Gera F. , 1972 [5] 0.15 0.00 Lower Stassfurt halite; unannealed; sample

1.29 0.02 taken from a mine.

1.9 0.02

2.66 0.03

3.42 0.04

3.80 0.04

4.48 0.04

5.32 0.05

5.93 0.06

6.92 0.07

7.60 0.08

8.36 0.09

8.97 0.10

9.65 0.10

10.57 0.11

11.63 0.13

12.85 0.14

13.45 0.16 14.14 0.17 14.75 0.19

15.28 0.22 15.97 0.26 16.42 0.29 16.88 0.33

17.26 0.36

17.57 0.39

17.95 0.41 18.26 0.45 18.71 0.48

19.02 0.52

19.32 0.552

19.71 0.581

19.78 0.596

Gera, F., 1972 [5] 0.00 0.00 After annealing; sample similar to above. 0.61 0.02

1.45 0.05

2.21 0.08

2.74 0.10

3.35 0.13

3.88 0.15

4.57 0.19

5.18 0.21

5.71 0.25

6.32 0.29 6.70 0.32

7.16 0.36

7.47 0.39

7.85 0.43

8.15 0.47

8.46 0.49

8.69 0.52

8.99 0.55 9.22 0.58

9.38 0.61

9.68 0.63

9.91 0.67

10.22 0.69 10.37 0.72 10.60 0.75

10.75 0.76

150
0.0 0.2 0.4

STRAIN, %

0.6 0.8

Figure 3.22. Effect of annealing on a stress-strain relationship (curve numbers

correspond to data set numbers in matching table).

3.4.2. Creep Data

Creep can be defined as slow deformation over a long

period of time at essentially constant load. At room

temperature and low stresses, rock salt will exhibit

considerably less creep deformation than at high

temperatures and pressures. In general, salt shows

marked plastic character, and even at relatively low

temperatures it will display a recognizable component of

creep. Creep data are generally presented as some type of

time relationship.

Thompson [25] investigated creep as a function of

differential stress on four rock salt specimens from

Hockly, Texas. The tests were conducted at 306 K and a confining pressure of 11.37 MPa. Various load stresses and strain rates were adopted. These data are tabulated in

table 3.22 and displayed in figure 3.23. Typical curves showing primary and steady-state creep were presented

by Burke [19]. This information was obtained using a

dead load compression unit and artificial salt samples and

is illustrated in figure 3.24 and table 3.23. Tensile tests using various Oi and 03 values were carried out by Nair

and Deere [23]. Data obtained from these triaxial

extension tests are displayed in table 3.24 and figure

3.25.

Two variations on basic creep relationships are given

by Ode [34] in which he shows nonuniform creep of

NaCl at different load stresses and the behavior of halite

single crystals compressed at different constant loads.

Data related to these two aspects are given in table 3.25

and figure 3.26 and table 3.26 and figure 3.27, respectiveThe effect of confining pressure and temperature on

the creep of rock salt has been investigated by several

researchers. LeComte [22] investigated the effects of

temperature to 573 K and confining pressure to 100

MPa. The results of this work are presented in table 3.27

151
TABLE 3.22. CREEP CURVES FOR HALITE

[Time, t, min; Strain, C, %]

Data

Set

Author (s), Year

[Ref .] t e Remarks

1 Thompson, E.G. , 1965 315.562 0.226 a = 16.54 MPa

[25] 906.262 0.357 e = 90 X 10"^ min~i.

1268.959 0.411 Temperature = 306 K

1788.877 0.473 and confining pres2466.337 0.540 sure = 11.37 MPa.

2960.531 0.596

3324.826 0.637

3952.755 0.677

4317.368 0.715

4761.392 0.750

5362.318 0.796

5831.427 0.842

U . obi

6746.797 0.904

7346.444 0.961

7764.744 0.990

8208.768 1.026

8702.323 1.087

2 Thompson, E.G., 1965 585.268 0.176 a = 13.78 MPa

[251 1395.184 0.238 i = 4.7 X 10"^ min"^

1811.885 0.281 Temperature = 306 K

2783.497 0.314 and confining pres3517.198 0.352 sure = 11.37 MPa.

4305 . 226 0.377

5642.729 0.437

6587.657 0.473

8138.625 0.512

9032.425 0.535

10267.990 0.565

3 Thompson, E.G., 1965 495.792 0.043 O = 9.65 MPa

[25] 1389.592 0.065 e = 53 X 10"^ min"^.

2153.491 0.071 Temperature = 306 K

2864.664 0.078 and confining pres3575.518 0.086 sure = 11.37 MPa.

4287.649 0.085

5763.362 0.092

6553.625 0.098

8609.012 0.108

11586.479 0.125

13114.600 0.135

14431.812 0.145

152
Figure 3.23. Creep curves for halite at various load stresses and strain rates.

153
TABLE 3.23. TYPICAL CREEP CURVES FOR POLYCRYSTALLINE NaCl SHOWING PRIMARY AND

STEADY STATE CREEP AT TEMPERATURE = 721 K AND GRAINIZE 370 ym

[Time, t, mln; Strain, e, %]

Data Author(s), Year

Set [Ref . ] Remarks

Burke, P.M. , 1968

[19]

3.120

7.430

11.653

15.875

17.319

21.476

24.276

27.077

29.885

32.670

35.456

38.957

5.137

6.272

6.994

7.716

8.129

8.540

8.953

9.365

9.812

10.155

10.498

11.014

a = 4.34 MPa

e = 2.3 X 10' ,-1

Burke, P.M., 1968

[191

1.582

3.070

7.227

12.084

17.612

26.560

35.465

45.726

69.618

96.201

113.923

144.569

184.702

224.858

248.706

319.470

328.310

1.068

1.688

2.100

2.614

3.094

3.710

4.119

4.527

5.238

5.844

6.249

6.818

7.348

7.981

8.485

9.516

9.614

0 = 3.03 MPa

e = 2.6 X 10 ^ -1

Burke, P.M., 1968

[19]

5.455

19.706

41.476

76.125

109.396

129.094

165.078

179.329

210.572

249.269

306.308

351.124

0.135

0.162

0.460

0.717

0.871

0.999

1.151

1.178

1.368

1.519

1.798

2.015

a = 2.17 MPa

£ = 6.8 X 10"' s

^

154
T IME , t , minutes

Figure 3.24. Typical creep curves for polycrystalline NaCl.

155
TABLE 3.24. CREEP STRAIN-TIME CURVES FOR SALT (TENSILE TEST)

[Time, t, hr; Strain, e, %]

Data Author(s), Year

Set [Ref.] Remarks

Nair, K. and Deere,

D.U. , 1970 [23]

0.250E+00

0.502E+00

0.125E+01

0.275E+01

0.464E+01

0.220E+02

0.482E+02

0.114E+03

0.369E+03

0.479E+03

G.991E+03

0.180E+00

0.215E+00

0.272E+00

0.344E+00

0.455E+00

0.698E+00

0.845E+00

0.113E+01

0.171E+01

0.199E+01

0.278E+01

a, = 20.7 MPa

3.4 MPa.

Nair, K. and Deere,

D.U., 1970 [23]

0.509E+00

0.994E+00

0.212E+01

0.204E+02

0.489E+02

0.982E+02

0.292E+03

0.719E+03

O.256E+00

0.297E+00

0.393E+00

0.845E+00

0.115E+01

0.154E+01

0.244E+01

0.362E+01

O3 = 17.9 MPa

a, = 0.7 MPa.

Nair, K. and Deere,

D.U., 1970 [23]

0.192E+00

0.334E+00

0.447E+00

0.135E+01

0.275E+01

0.620E+01

0.126E+02

0.448E+02

0.996E+02

0.189E+03

0.248E+00

0.292E+00

0.310E+00

0.422E+00

0.559E+00

0.697E+00

0.908E+00

0.143E+01

0.223E+01

0.357E+01

03 = 23.6 MPa

O, = 2.1 MPa.

Nair, K. and Deere,

D.U., 1970 [23]

0.985E-01

0.993E+00

0.183E+01

0.931E+01

0.198E+02

0.122E+03

0.224E+00

0.558E+00

0.676E+00

0.133E+01

0.195E+01

0,478E+01

^3 =

a, = 24.8 MPa3.4 MPa.

Nair, K. and Deere,

D.U., 1970 [23]

0.999E-01

0.509E+00

O.lOlE+01

0.197E+01

0.620E+01

0.207E+02

0.238E+00

0,461E+00

0.685E+00

0.893E+00

0.145E+01

0.254E+01

22 MPa

0.7 MPa.

156
TABLE 3.24. CREEP STRAIN-TIME CURVES FOR SALT (TENSILE TEST) (Continued)

Data Author(s), Year

Set [Ref . ] Remarks

Nair, K. and Deere,

D.U., 1970 [23]

0.164E+00

0.198E+00

0.253E+00

0.107E+01

0.205E+01

0.498E+01

0.144E+02

0.219E+02

0.269E+02

0.495E+02

0.397E+00

0.434E+00

0.488E+00

0.892E+00

O.lllE+01

0.161E+01

0.250E+01

0.294E+01

0 . 312E+01

0.470E+01

25.5 MPa

2.1 MPa.

Nair, K. and Deere,

D.U., 1970 [23]

0.301E+00

0.680E+00

0.165E+01

0.498E+01

0.865E+01

0.198E+02

0.541E+00

0.748E+00

0.113E+01

0.186E+01

0.243E+01

0.340E+01

26.5 MPa

0.7 MPa.

Nair, K. and Deere,

D.U., 1970 [23]

0.131E+00

0.200E+00

0.513E+00

O.lOOE+01

0.818E+01

0.670E+02

0.387E+03

0.394E+00

0.437E+00

0.612E+00

0.730E+00

0.144E+01

0.295E+01

0.720E+01

O3 = 22 MPa

Oj = 1.4 MPa.

Nair, K. and Deere,

D.U., 1970 [23]

0.121E+01

0.200E+01

0.499E+01

0,494E+02

0.196E+03

0.376E+03

0.129E+01

0.145E+01

0.186E+01

0.346E+01

0.492E+01

0.596E+01

a 3 = 24.1 MPa

Oj = 3.4 MPa.

10 Nair, K. and Deere,

D.U., 1970 [23]

O.lOlE+01

0.308E+00

0.512E+00

0.103E+01

0.191E+01

0.309E+01

0.505E+01

0.726E+00

0.121E+01

0.156E+01

0.203E+01

0.268E+01

0.333E+01

0.440E+01

03 = 31.7 MPa

a, = 3.4 MPa.

11 Nair, K. and Deere.

D.U., 1970 [23]

O.lOlE+00

0.148E+01

0.136E+02

0.193E+02

0.399E+00

0.587E+00

0.115E+01

0.134E+01

a, = 17.2 MPa

3.4 MPa.

12 Nair, K. and Deere,

D.U. , 1970 [23]

0.625E+01

0.980E+01

0.218E+02

0.520E+02

0.141E+03

0.545E+03

0.120E+00

0.135E+00

0.155E+00

0.187E+00

0.221E+00

0.319E+00

o, = 17.2 MPa6.9 MPa.

157
TIME , t, hours

Figure 3.25. Tensile creep-strain curves foi'salt (curve numbers correspond to data set numbers in matching

table).

158
TABLE 3.25. NONUNIFORM CREEP OF NaCl WITH VARYING LOADS

[Time, t, min; Strain, e, %]

Data Author (s). Year

Set [Ref . ] Remarks

Ode, H., 1968 [24]

Ode, H., 1968 [24]

0. 244E+00 0. 735E-02

0. 490E+00 0. 323E-01

0. 943E+00 0. 495E-01

0. 140E+01 0. 578E-01

0. 199E+01 0. 661E-01

0. 252E+01 0. 687E-01

0. 290E+01 0. 698E-01

0. 342E+01 0. 708E-01

0. 393E+01 0. 724E-01

0. 432E+01 0. 745E-01

0. 474E+01 0. 766E-01

0. 545E+01 0. 864E-01

0. 583E+01 0. 958E-01

0. 625E+01 0. lOlE+00

0. 702E+01 0. 104E+00

0. 736E+01 0. 107E+00

0. 808E+01 0. 109E+00

0. 908E+01 0. lllE+00

0

.

997E+01 0

.

112E+00

0. 197E+02 0. 116E+00

0. 249E+02 0. 117E+00

0. 408E+02 0. 120E+00

0. 503E+02 0. 121E+00

0. 622E+02 0. 123E+00

0. 120E+03 0. 125E+00

0. 232E+03 0. 126E+00

0. 244E+00 0. 166E-02

0. 331E+00 0. 946E-02

0. 492E+00 0. 178E-01

0. 651E+00 0. 240E-01

0. 786E+00 0. 267E-01

0. 993E+00 0. 303E-01

0. 144E+01 0. 381E-01

0.191E+01 0. 438E-01

0. 285E+01 0. 465E-01

0. 395E+01 0. 491E-01

0. 575E+01 0. 517E-01

0. 964E+01 0. 539E-01

0. 158E+02 0. 570E-01

0. 247E+02 0. 597E-01

0. 454E+02 0. 629E-01

0. 601E+02 0. 650E-01

0. 891E+02 0. 930E-01

0. 890E+02 0. 966E-01

0. 976E+02 0. lOlE+00

0. 112E+03 0. 106E+00

0. 118E+03 0. 108E+00

a = 44.5 MPa load

stress

.

a = 2.45 MPa load

stress

.

159
TABLE 3.25. NONUNIFORM CREEP OF NaCl WITH VARYING LOADS (Continued)

Data Author(s), Year

Set [Ref . ] Remarks

2 Ode, H. , 1968 [24]

(cont .

)

3 Ode, H., 1968 [24]

4 Ode, H., 1968 [24]

0. 145E+03 0. 112E+00

U . 1 / J h+U J) U . 115E+00

riV . z1dE+U3 r\ 117E+00

U . U . 121E+00

U . U . 124E+00

U .

/. n o T? 1 r\f\

(J . 795E- 02

u

.

O53E+00 0

.

121E- 01

u

.

O25E+00 0

.

142E- 01

0 . 996E+00 0

.

163E-01

U . 132E+01 0

.

200E-•01 0

.

148EH-01 0

.

221E-01

0

.

167E+01 0

.

236E- 01

0

.

201E+01 0

.

252E-01

0. 232E+01 0

.

273E-01

0

.

265E+01 0

.

289E-01

0

.

293E+01 0

.

304E-01

0

.

329E+01 0

.

315E-01

0

.

361E+01 0

.

325E-01

0

.

397E+01 0

.

341E-•01

/-V 0

.

490E+01 0

.

367E-01

0

.

605E+01 0

.

388E-01

0. 596E+01 0. 398E-01

0

.

801E+01 0. 430E-01

r\u

.

880E+01 0. 445E-01

0

.

lOlE+02 0. 466E-•01 U . 117E+02 0. 482E-01

U . l'*lE+(Jz 0. 508E-•01 U . o A (*i "c 1 no zU9E+(J/ 0.555E-•01 U . Z41E+U2 0. 571E-•01 n

0 . iz/E+Oz 0. 592E-•01 U . / n nT" 1 r\ o 499E+(jz 0. 618E-•01 0. 709E+02 0. 655E-•01

0. 103E+03 0. 686E-•01

0. 134E+03 0. 702E-01

181E+03 0. 718E-01

0. 246E+03 0. 719E-01

0

.

509E+03 0. 719E-01

0

.

999E+00 0. 389E-02

0

.

123E+01 0. 702E--02

0

.

142E+01 0. 911E--02

0

.

171E+01 0. 112E-01

0. 197E+01 0. 123E--01

0. 243E+01 0. 138E--01

0. 308E+01 0. 170E--01

0. 389E+01 0. 185E--01

0. 480E+01 0. 201E--01

0. 593E+01 0. 217E--01

o = 2.94 MPa load

stress

.

o = 3.43 MPa load

stress

.

160
TABLE 3,25. NONUNIFORM CREEP OF NaCl WITH VARYING LOADS (Continued)

Data Author (s), Year

Set [Ref . ] Remarks

k Ode, H,, 1968 [24]

(cont.

)

0. 805E+01 0. 228E- 01

0. 994E+01 0. 254E- 01

0. 138E+02 0. 301E- 01

0. 159E+02 0. 322E- 01

0. 201E+02 0. 363E- 01

0. 242E+02 0. 390E- 01

0. 344E+02 0.447E- 01

0. 524E+02 0. 484E- 01

0. 711E+02 0. 510E- 01

0.899E+02 0. 552E- 01

0. lOlE+03 0. 572E- 01

0. 186E+03 0. 625E- 01

0. 246E+03 0. 636E- 01

0. 297E+03 0. 636E- 01

0.487E+03 0. 642E- 01

K)-' I 10' 10^ TIME , f , minutes

Figure 3.26. Nonuniform creep of NaCl.

161
TABLE 3.26. CREEP CURVES FOR HALITE SINGLE CRYSTALS

AT DIFFERENT CONSTANT LOADS

[Time, t, min; Strain, e, %]

Data Author (s). Year

Set [Ref .

] Remarks

Ode, H. , 1968 [24] 83.952

146.852

204.529

403.971

603.509

808.323

1002.679

0.498

0.997

1.416

2.492

3.385

4.251

4.987

a = 25 MPa.

Ode, H. , 1968 [24] 120.767

204.787

404.433

604.161

803.929

1003.725

1203.561

1403.384

1597.971

1797.834

2002.947

0.551

0.919

1.602

2.128

2.576

2.971

3.288

3.631

3.921

4.185

4.476

a = 23 MPa.

Ode, H. , 1968 [24] 36.788

73.385

110.105

204.678

404.433

604.242

804.092

998.693

1203.847

1398.474

1598.378

1793.020

1998.200

0.105

0.577

0.813

,128

,602

.971

,262

,526

,738

.950

,136

,321

a = 17 MPa.

1.

1.1.

2.

2.2.

2.

3.

3.3.481

Ode, H. , 1968 [24; 78.838

199.796

399.686

604.854

804.758

1004.703

1199.371

1399.316

1604.524

1799.206

l':-99.151

0.210

0.395

0.607

0.793

0.979

1.086

1.220

1.327

1.434

1.541

1.649

22 MPa.

162
TABLE 3,26. CREEP CURVES FOR HALITE SINGLE CRYSTALS

AT DIFFERENT CONSTANT LOADS (Continued)

Data Author (s), Year

Set [Ref ] Remarks

Ode, H., 1968 [24] 10.445 0.157 a = 70 MPa.

89.297 0.341

126.098 0.420

205.032 0.448

404.963 0.581

604.935 0.636

810.143 0.743

1004.866 0.772

1204.824 0.853

1399.547 0.882

1599.533 0.911

1799.519 0.939

1999.518 0.942

Ode, H., 1968 [24] 10.526 0.000 O = 10.5 MPa.

205.235 0.055

405.207 0.110

605.180 0.165

805.179 0.167

1005.138 0.249

1205.110 0.303

1405.082 0.358

1599.791 0.413

1794.514 0.442

1999.749 0.497
and figure 3.28. Similar work on the effects of confining

pressure only was conducted by Thompson [25]

.

Differential stress was kept constant and a range of

confining pressures was used. The evidence is that the

effect of confining pressure is minimal. Data related to Thompson's work are supplied in table 3.28 and figure

3.29. Baar [17] gives field data indicating the acceleration of creep caused by heating of a salt mine pillar to peak temperatures of about 423 K. The data presented

in table 3.29 and figure 3.30 yield four data sets, each

set related to connected rooms in the salt mine in which

the experiment was performed. From the information

presented, it can be seen that creep is a thermally

activated process since if it were not, the creep rate at any temperature would depend on stress difference

only. LeComte also investigated the effect of axial stress on creep and the combined effects of grain size and axial

stress on creep of rock salt. These results can be found

in table 3.30 and figure 3.31, and table 3.31 and figure

3.32, respectively.

Steady-state creep rate as some function of stress has

been studied by Burke and is also reported by Ode'. Burke

[29] presents a relationship between steady-stat« creep

rate and stress for coarse-grained salt (1000-3000 fxm).

These values are given in table 3.32 and figure 3.33. The

same relationship for polycrystalline NaCl and single

crystal NaCl was also investigated by Burke at 1013 K

(see table 3.33 and figure 3.34). Steady-state creep rate of

NaCl at several stresses as a function of temperature are reported by Ode' [34] and is illustrated in figure 3.35 and

table 3.34.

Figure 3.36 shows the time-strain data at various

confining pressures and temperatures and table 3.35

tabulates the corresponding values. These values were

obtained by Dreyer [12] in 1972 from creep tests on

artificial rock salt samples. The lower three curves

indicate that confining pressure has only a small

influence on time dependent strain at room temperature.

The upper curves show that the effect of confining

pressure is greater at higher temperatures. In general,

temperature has a marked effect on the deformational

behavior of rock salt. Dreyer [12] has also studied the creep behavior of

untempered and tempered rock salt as a function of time

and the relevant data are presented in figure 3.37 and

table 3.36. Although these two rock salt samples have a

slightly different composition (see measurement methods), it is considered that they are representative of the

trend in creep behavior of tempered and untempered

rock salt. Generally, tempered samples show a much more

prolonged "creep life" than do untempered samples.

This is because untempered samples reach this maximum

creep strain in a short time whereas tempered samples

take longer to reach their maximum. In addition,

tempered rock salt exhibits a much higher maximum

creep strain (5 to 6 times greater). It is believed that the

behavior of the tempered salt is due to recrystallization

during tempering.

3.5. Hardness

The hardness of rock salt depends on atmospheric

humidity, previous plastic deformation, impurities in the

crystals, and quench temperatures. Large discrepancies

in hardness values of NaCl are found at small loads. The

various factors which influence the hardness number at small loads include microrelief of surface, roughness of

indentor, elastic recovery in indent, vibration, loading

rate, etc. Strelkov and Shpunt [15] have shown that the

published data on hardness may be represented by curves 1-3 of figure 3.38 which may be obtained on a single

specimen of NaCl by varying the atmospheric humidity B

and the previous plastic deformation e . Curve 1 is for an

unstressed (e ~ 0) specimen in dry air (B|<'30%) while curve 3 is for the same specimen in moist air. Curve 3 is

for a deformed specimen (e ^ 0.3-0.4%) in dry

atmosphere.

The values of hardness at low loads indicated by these curves and tabulated in table 3.37 have not been

corrected for the factors mentioned above. The absolute

values of hardness can be obtained onl^ if all factors have

been considered, which is difficult to accomplish.

However, as the above curves represent an average of a

large data set, they can be considered to represent the

recommended values of microhardness.

According to Strelkov and Shpunt [15] 1*^3

transition involves a delay (relative to the change in B)

of 15-20 minutes. Curve 2 differs from 1 for

e^O.3-0.4%. The 2*='3 transition is analogous to\l 3. A. 2 — 1 transition occurs on annealing even highly

deformed materials (e^2-3%). The maximum humidity

at which NaCl can be tested for microhardness is 75%;

for values higher than this water is deposited on the

crystals.

For values of load p > 20 g and indentation depth

h> 6-7/x, the microhardness is steady and independent

of load, humidity, and previous plastic deformation.

The values of steady microhardness have been found to

fall in the range of 19-23 kg/mm^ due to differences in

impurity content.

Kishsh and Sharkezi [14] have studied the microhardness of NaCl crystals containing cation and anion

impurities in relation to temperature and rate of

quenching. Their data are presented in figure 3.39 with

the corresponding values in table 3.38. The figure shows

164
TABLE 3.27. EFFECT OF TEMPERATURE AND CONFINING PRESSURE

ON THE CREEP OF ROCK SALT

[Time, t, hr; Strain, e, %]

Data Author(s), Year

Set [Ref . ] Remarks

LeComte, P. , 1965

LeComte, P., 1965

LeComte, P. , 1965

LeComte, P., 1965

[22] 2.328 1.199

6.003 1.719

9.693 2.141

19.558 3.085

24.520 3.346

33.191 3.900

43.116 4.422

52.426 4.879

67.948 5.597

79.749 6.120

90.924 6.643

94.650 6.806

[22] 1.759 0.810

5.416 1.460

1 1 540 ^- . -J JO

21.428 3.118

32.589 3.737

36.311 3.933

49.352 4.521

59.296 4.914

68.629 5.209

83.564 5.668

96.637 6.029

[22] 0.485 0.972

4.856 1.006

14.846 1.075

27.318 1.274

36.679 1.375

54.775 1.576

72.256 1.712

84.733 1.879

98.459 2.046

120.944 2.152

134.060 2.222

[221 10.592 0.231

35.578 0.338

55.568 0.410

72.433 0.481

86.178 0.519

96.803 0.523

108.677 0.528

131.167 0.601

153.042 0.610

173.037 0.650

Confining pressure = 100 MPa;

Temperature = 471 K; Axial stress = 6.9

MPa.

Confining pressure = 0.1 MPa;

Temperature = 377 K;

Axial stress = 6.9

MPa.

Confining pressure = 100 MPa;

Temperature = 377 K;

Axial stress = 6.9

MPa.

Confining pressure = 0.1 MPa;

Temperature = 302 K; Axial stress = 6.9

MPa.

165
TABLE 3.27. EFFECT OF TEMPERATURE AND CONFINING PRESSURE

ON THE CREEP OF ROCK SALT (Continued)

Data Author (s). Year

_Set [Ref . ]

5 LeComte, P., 1965

LeComte, P. , 1965 [22

[22] 8 097 0.197

15 592 U . Z J J 23 712 U . Z Do

49 327 n "iZi 69 327 n 99 n Q Q t; u . jy J 142

-L U 7

r ?p 1

1. ^ J 4

.

_J338J O 30. 578 0.336

58. 697 0.379

78. 692 0.419

94. 321 0.393

119. 316 0.435

126. 811 0.470

151. 185 0.479

179. 935 0.490

Remarks

Confining pressure = 100 MPa;

Temperature = 302 K; Axial stress = 6.9

MPa.

Confining pressure =

20 MPa;

Temperature = 302 K; Axial stress = 6.9

MPa.

166
TABLE 3.28. EFFECT OF CONFINING PRESSURE ON THE STEADY STATE

CREEP RATE OF HALITE

[Time, t, min; Strain, C, %]

Data Author(s), Year

Set [Ref . ] Remarks

Thompson, E.G.

[25]

1965 442.493

784.022

1441.997

1942.167

2311.024

2916.783

3443.446

4391.568

5103.045

5708.932

6420.281

7105.457

7922.395

8581.334

9872.526

10821.354

11348.339

12191.706

12956.042

13483.091

14379.317

0.236

0.287

0.335

0.367

0.378

0.405

0.431

0.474

0.490

0.512

0.533

0.547

0.563

0.571

0.600

0.614

0.627

0.641

0.652

0.662

0.671

Confining pressure

13.78 MPa.

Thompson, E.G. , 1965

[251

417.092

785.178

1442.832

2074.700

2785.406

3575.529

4260.448

4918.874

5656.651

6472.562

7210.276

8554.391

9318.791

9924.871

0.196

0.239

0.300

0.338

0.386

0.421

0.445

0.474

0.493

0.552

0.573

0.595

0.603

0.616

Confining pressure

10.33 MPa.

ThomDson, E.G.

[25]

' 1965 361.792

677.533

1125.100

1783.654

2152.575

2705.925

3311.876

4049.655

4734.895

5393.577

6078.753

6605.866

7528.137

8924.918

0.303

0.330

0.356

0.380

0.388

0.402

0.421

0.439

0.450

0.469

0.482

0.491

0.512

0.536

Confining pressure

3.44 MPa.

167
TABLE 3.28. EFFECT OF CONFINING PRESSURE ON THE STEADY STATE

CREEP RATE OF HALITE (Continued)

Data Author(s), Year

Set [Ref . ] Remarks

Thompson, E.G.

[25]

1965 466 .868 0. 319

1124 .008 0. 401

1544 .889 0. 441

1965 .834 0. 479

2465 .619 0. 527

3361 .010 0. 570

3887 .481 0. 604

4941 .192 0. 642

5441.554 0. 666

6126 .602 0. 685

7074 .916 0. 719

8287 .013 0. 749

8945 .695 0. 768

9683 .666 0. 779

10395 .079 0. 797

11106 .619 0. 811

12529 .509 0. 846

13056 .494 0. 859

13978 .958 0. 873

Confining pressure

0 MPa.

I

0 = 9.65 MPa

TIME , t , minutes

Figure 3.29. Effect of confining pressure on steady state flow of halite.

168
TABLE 3.29. ACCELERATED CREEP CAUSED BY HEATING A SALT MINE PILLAR TO

PEAK TEMPERATURE OF ±423 K

[Time, t, days; Vertical Deformation, AL, cms]

Data Author(s), Year

Set [Ref . ]

1 Baar, C.A., 1977 [17] 472.185 0.091

487.272 0.248

498.591 0,358

506.150 0.398

511.190 0.424

517.493 0.449

523.789 0.490

531.351 0.523

537.654 0.548

545.216 0.581

554.044 0.607

561.613 0.624

571.707 0.640

583.051 0.690

593.141 0.716

603.232 0.741

614.585 0.764

624.680 0.782

639.824 0.800

652.434 0.840

681.464 0.866

701.652 0.899

718.056 0.924

730.668 0.957

744.550 0.975

759.699 0.983

774.847 0.993

787.459 1.026

798.816 1.043

808.903 1.077

813.947 1.092

823.983 1.249

826.481 1.318

834.013 1.424

844.087 1.491

849.110 1.559

856.652 1.640

864.217 1.666

871.769 1.724

884.365 1.800

891.923 1.841

899.485 1.874

923.438 1.966

930.993 2.016

941.087 2.032

952.430 2.082

169
TABLE 3.29. ACCELERATED CREEP CAUSED BY HEATING A SALT MINE PILLAR TO

PEAK TEMPERATURE OF ±423 K (Continued)

Data Author (s). Year

Set [Ref . ]

1 Baar, C.A., 1977 [17] 968.831 2.115

(cont.) 981.447 2.141

990.272 2.174

997.837 2.199

1005.409 2.209

1012.982 2.217

1023.076 2.232

1038.210 2.275

2 Baar, C.A., 1977 [17] 463.384 0.000

472.147 0.182

485.941 0.414

499.758 0.589

507.303 0.662

511.091 0.665

516.108 0.746

523.667 0.789

529.963 0.830

537.518 0.881

545.073 0.929

553.898 0.962

562.723 0.998

571.544 1.038

582.891 1.079

594.244 1.104

606.853 1.148

640.903 1.247

653.519 1.272

667.394 1.305

680.010 1.331

702.717 1.381

714.071 1.407

731.734 1.440

744.350 1.465

756.962 1.498

773.376 1.498

787.255 1.524

799.871 1.549

808.689 1.600

811.187 1.666

823.711 1.915

827.448 2.039

836.232 2.171

846.282 2.296

848.759 2.413

858.854 2.430

866.382 2.547

875.189 2.621

170
TABLE 3.29. ACCELERATED CREEP CAUSED BY HEATING A SALT MINE PILLAR TO

PEAK. TEMPERATURE OF ±423 K (Continued)

Data Author(s), Year

Set [Ref . ] AL

Baar, C.A. , 1977 [17] 604.794 0.010

611.097 0.035

624.972 0.068

642.635 0.101

655.241 0.152

666.591 0.185

681.736 0.203

703.183 0.243

718.325 0.269

732.200 0.302

747.341 0.327

758.695 0.353

776.364 0.370

785.196 0.386

802.859 0.421

809.152 0.469

812.916 0.528

822.938 0.718

829.214 0.810

836.749 0.911

843.025 1.003

850.573 1.069

856.859 1.135

865.667 1.209

873.209 1.292

883.289 1.343

894.625 1.409

902.177 1.468

912.255 1.526

926.120 1.585

942.500 1.668

955.105 1.717

967.715 1.760

981.576 1.826

995.448 1.866

1004.273 1.902

1013.104 1.917

1025.717 1.950

1040.848 2.001

Baar, C.A. , 1977 [17] 613.639 0.000

624.989 0.027

627.508 0.043

642.652 0.061

655.265 0.094

667.898 0.078

680.504 0.127

700.692 0.160

718.352 0.203

171
TABLE 3.29. ACCELERATED CREEP CAUSED BY HEATING A SALT MINE PILLAR TO

PEAK TEMPERATURE OF ±423 K (Continued)

Data Author (s). Year

Set [Ref.]

^

4

(Cent.

)

Baar, C.A., 1977 [17] 732.234 0.221

744.850 0.243

759.991 0.269

773.877 0.279

785.230 0.304

801.634 0.330

809.196 0.363

814.206 0.462

822.959 0.670

829.231 0.769

836.763 0.876

843.042 0.960

850.590 1.026

858.139 1.094

865.677 1.186

873.229 1.244

884.538 1.376

893.346 1.450

902.157 1.518

912.234 1.577

926.092 1.651

931.129 1.684

942.476 1.727

953.822 1.767

966.418 1.841

980.286 1.892

994.151 1.950

1002.976 1.983

1014.329 2.009

1024.417 2.042

1039.551 2.085

172

TABLE 3.30. EFFECT OF AXIAL STRESS ON THE CREEP OF ROCK SALT

[Time, t, hr ; Strain, e, %]

Data Author(s), Year

Set [Ref ] Remarks

LeComte, P., 1965 [22]

LeComte, P., 1965 [22]

LeComte, P. , 1965 [22]

2. 548 0. 643

7. 755 0. 933

15. 585 1. 206

26. 033 1. 496

28. 640 1. 608

35. 176 1. 737

48. 247 1. 994

57. 401 2. 139

73. 095 2. 381

97

.

949 2. 703

124. 117 2. 992

143. 746 3. 186

158. 139 3. 347

168. 608 3. 443

194. 786 3. 653

240. 595 4. 023

265. 465 4. 217

292. 956 4. 394

311. 282 4. 523

336. 158 4. 652

362. 343 4. 797

371. 506 4. 862

6. 438 0. 997

27. 368 1. 271

37. 836 1. 383

60. 077 1. 641

71. 853 1. 770

83. 629 1. 899

108. 496 2. 108

133. 366 2. 301

141. 217 2. 382

155. 618 2. 462

5

.

150 0. 804

13. 008 0.,820

24. 797 0.,836

32. 655 0.,853

48.,376 0.,853

73.,265 0.,869

96. 842 0.,902

123. 043 0,,902

145. 313 0.,903

171. 511 0.,935

195.,090 0.,952

216. 050 0,,952

238. 321 0.,953

263.,208 0,,985

Confining pressure = 100 MPa;

Temperature = 302 K; Axial stress = 13.8

MPa.

Confining pressure = 100 MPa;

Temperature = 377 . 5 K

Axial stress = 6.9

MPa.

Confining pressure = 100 MPa;

Temperature = 377 . 5 K

Axial stress = 34.5

MPa.

174
TABLE 3.30. EFFECT OF AXIAL STRESS ON THE CREEP OF ROCK SALT (Continued)

Data Author(s), Year

Set [Ref .

] Remarks

3 LeComte, P., 1965

(cont.) I22J

293.337

311.676

336.567

364.074

391.583

1.002

1.018

1.019

1.051

1.068

LeComte, P. , 1965

122]

6.467

16.944

28.734

49.693

81.132

116.500

150.557

168.898

187.238

0.740

0.772

0.772

0.789

0.805

0.838

0.871

0.871

0.871

Confining pressure = 100 MPa;

Temperature = 377 K; Axial stress = 34.5

MPa.

LeComte, P., 1965

[22]

10.451

24.855

36.643

49.740

60.219

79.866

104.749

127.014

142.735

151.902

170.242

180.719

0.257

0.322

0.338

0.371

0.387

0.419

0.484

0.533

0.533

0.565

0.566

0.598

Confining pressure = 100 MPa;

Temperature = 302 K; Axial stress = 6.9

MPa.
TABLE 3.31. EFFECT OF GRAIN SIZE AND AXIAL STRESS

ON THE CREEP OF ROCK SALT

[Time, t, hr; Strain, e, %]

Data Author(s), Year

Set [Ref . ] Remarks

LeComte, P., 1965 [22] 3.560

8.382

11.603

13.212

26.063

29.263

33.285

36.498

39.715

49.358

51.771

58.209

61.418

73.478

77.504

86.356

110.515

122.597

128.231

135.478

143.526

156.425

0,941

1.000

1.026

043

212

279

321

363

397

515

1.541

1.600

650

786

819

904

099

192

242

302

378

454

Confining pressure = 100 MPa;

Temperature = 377 . 5 K.

LeComte, P., 1965 [22] 2,885

3.676

6.081

6.872

10.081

14.089

16.498

26.967

32.605

38.249

51,152

55.178

65.681

74.563

82.645

98.800

106.882

122.232

134.357

146.473

169.102

184.444

195.764

0,681

0,714

0,757

0,790

0,841

0.908

0.942

1.027

1.069

1.103

1.171

1.205

1,222

1.248

1.257

291

300

326

335

361

1,388

1,430

1,431

Confining pressure = 100 MPa;

Temperature = 377.5 K.

176
TABLE 3.31. EFFECT OF GRAIN SIZE AND AXIAL STRESS

ON THE CREEP OF ROCK SALT (Continued)

Data Author (s), Year

Set [Ref . ] Remarks

2 LeComte, P., 1965 [22] 217.588 1.449

(cont.) 246.681 1.484

265.279 1.485

288.716 1.512

311.357 1.513

333.986 1.540

359.053 1.541

LeComte, P. , 1965 [221 2.167

3.750

4.537

5.328

7.728

11.750

22.223

26.253

36.735

43.991

51.251

59.303

64.946

76.253

77.862

89.174

98.847

102.077

0.504

0.572

0.614

0.647

0.698

0.740

0.816

0.842

0.901

0.944

0.978

045

079

105

122

139

199

Confining pressure = 100 MPa;

Temperature = 377 . 5 K; Axial stress = 6.9

MPa.

1.207
TABLE 3.32. EFFECT OF STRESS AND TEMPERATURE ON THE STEADY STATE CREEP

RATE OF COARSE GRAIN S0DIU>1 CHLORIDE

[Stress, O, MPa; Log Steady State Creep Rate, log E s ^]

Data Author (s), Year

Set [Ref . ] log(c Remarks

Burke, P.M., 1968 4.327

[19] 8.612

-0.611E+01 Temperature = 638 K. -0.475E+01

Burke, P.M., 1968 3.066

[19] 5.932

-b.561E+01 Temperature

-0.351E+01

722 K.

Burke, P.M. , 1968 2.122

[19] 4.237

-0.530E+01 Temperature = 513 K. -0.356E+01

Burke, P.M., 1968 0.9439

[19] 1.860

-0.530E+01 Temperature = 876 K. -0.424E+01

5 Burke, P.M., 1968

[19]

0.276

0.406

0.477

0.550

0.806

0.930

0.896

-0.539E+01 Temperature = 1015 K.

-0.494E+01

-0.519E+01

-0.457E+01

-0.411E+01

-0.356E+01

-0.336E+01

"1 1 1—I I I "1—I—I

ry

o

iiJ

(£ -4

Q.UJ

UJ

aco

UJ

IV)>

Q<

UJ -6

o

COARSE GRAINED SALT GRAIN SIZE 1000-3000 um

1015 K

J L I I I J L I I I I

10 STRESS , cr , MPa

10'

Figure 3.33. Effect of stress and temperature on the steady state creep rate of coarse grained NaCl (curve numbers

correspond to data set numbers in matching table).

178
TABLE 3.33. STEADY-STATE CREEP RATE OF SINGLE CRYSTAL AND POLYCRYSTALLINE

SODIUM CHLORIDE AS A FUNCTION OF STRESS AT 1013 K

[Stress, o, MPa; Creep Rate, e,

Data Author(s), Year

Set [Ref . ]

Burke, P.M., 1968 0.688 0.662E-03

[19] 0.999 0.209E-02

Burke, P.M., 1968 0.499 0.928E-05

[19] 2.391 0.526E-02

Burke, P.M., 1968 0.606 0.313E-04

[19] 1.02 0.232E-03

Burke, P.M., 1968 0.599 0.396E-05

[19] 0.656 0.482E-05

0.717 0.515E-05

0.799 0.607E-05

0.841 0.627E-05

Burke, P.M., 1968 0.046 0.198E-07

[19] 0.104 0.363E-03

1.033 0.326E-03

Burke, P.M., 1968 0.104 0.363E-03

[19] 0.296 0.306E-05

179
STRESS, cr, MPa

Figure 3.34. Steady state creep rate single crystal and polycrystalline NaCl as a function

of stress at 1013 K (curve numbers correspond to data set numbers in matching table).

180
TABLE 3.3A. STEADY STATE CREEP RATE OF NaCl VERSUS

TE-ffERATURE AT VARIOUS STRESSES

[Temperature, T, K; Creep Rate, £, min ']

Data

Set

Author (s) , Year

[Ref .] T e Remarks

1 Ode, H. , 1968 [24] 900 0 163E-03 a = 0.59 MPa load

917 0 75AE-03 stress

.

999 0.1A2E-01

1004 0 183E-01

2 Ode, H. , 1968 [24J 907 0 178E-03 0 = 0.78 MPa load

937 0 637E-03 stress

.

1014 0 113E-01

1057 0 133E-01

3 Ode, H., 1968 [24] 937 0 19AE-03 a = 0.98 MPa load

943 0 344E-03 stress

.

984 0 113E-02

1024 0 608E-02

1032 0 873E-02

1029 0 970E-02

800 900 1000 1100 TEMPERATURE , T, K

Figure 3.35. Relationship of steady state creep rate of NaCl with temperature at various

stresses (curve numbers correspond to data set numbers in matching

table)

.

181
TABLE 3.35. TIME-STRAIN DATA OF HALITIC ROCK SALT AT VARIOUS CONFINING PRESSURES AND TEMPERATURES

[Time, t, hrs; Strain, e, %]

Author (s)

,

Year [Ref.] t e Remarks

1 Dreyer

,

w.

,

, 1972 [12] 1..83 13..34 Artificial rock sample; confining pressure

8..84 24..93 0 MPa; temperature 377.65 K. 19

.

74 33,.38

29..37 38,.67

66..67 53..84

84..70 58,.79

96..93 62,.33

2 Dreyer

,

w.

,

, 1972 r 1 ?i 9 ^. 48 24,.93

21..65 36,.19 1088 MPa; temperature 471.35 K.

40..28 46,.06

67.,93 58,.40

90..43 68,.28

3 Dreyer

,

w. , 1972 n ?i I -L*^ J 6

.

36 11,,59 At" t" "1 f "1 p "I a 1 iTf^r'^ canmTp* r* nnT i n n n o TiT'PQQnTP

25.,70 13,.74 1088 MPa; temperature 377.65 K.

54.,06 16,.62

83.,72 19,.49 121.,12 22.. 39

4 Dreyer

,

w.

,

, 1972 [12] 27.,71 3..57 Artificial rock salt sample; confining pres53

.

51 4,.69

81.,90 5.,45 105.,12 5.,86 123.,82 6.,25 150.,27 7.,00

5 Dreyer

,

w.,, 1972 [12] 6.,42 3.,52 Artificial rock salt sample; confining pres23.,85 2.,51 sure 212 MPa; temperature 302.15 K.

36.,10 2.,89 56.,75 2.,59

78. 69 2.,99 118.,68 4.,14 141..91 3.,84 166,,41 4.,95 183.,19 4..64

6 Dreyer

,

w.

,

, 1972 [12] 6.,42 3..52 Artificial rock salt sample; confining pres23.,21 2.,51 sure 1088 MPa; temperature 302.15 K.

36,,11 2.,89 56. 75 2..94

78,,69 2.,99 100.,62 3.,74 125. 13 3.,80 150. 29 4.,21 167. 07 3.,20 175. 46 3.,57 183. 20 3.,58

182
TIME, t, hrs

Figure 3.36. Time-strain relationship for halitic rock salt (curve numbers

correspond to data numbers in matching table ).

183
TABLE 3.36. TIME-STRAIN RELATIONSHIP OF TEMPERED AND UNTEMPERED ROCK SALT AT 106 MPa AND 298 K

[Time, t, days; Strain, E, %]

°f'^ Author(s), Year [Ref.] t e Remarks

Set

Dreyer, W. , 1972 [12] 0.25 86 Square prisms (4 x 4 x 10 cm) of white rock

salt containing alternating layers of fine

and coarse grained material separated by thin argillaceous bands of anhydrite; untempered; constant stress of 106 MPa; temperature 291 K.

t e

0. 25 86

0. 50 102

0. 75 112

1 119

2 144

3 161

4 173

5 182

6 188

7 193

8 198

9 203

10 208 11 213 12 217 13 221

14 224

15 228

16 232

17 235

18 238

28 264

56 307

84 324

112 335 140 342 168 348

1 359

2 363

3 366

4 368

5 369

6 369

7 369

8 369

9 370 10 370 11 370

12 370

13 370 14 370 15 370 16 370 17 370 18 371

19 371 20 371

22 371 24 371

26 371

28 371

Dreyer, W. , 1972 [12] 1 359 Tempered; sample and testing conditions same

as above

.

184
400

TIME, t, days (TEMPERED)

20 40

80 160

TIME, t, days (UNTEMPERED)

Figure 3.37 Time-strain relationship for tempered and untempered rock salt (curve numbers correspond to data set numbers in matching table)

.

TABLE 3.37. RELATIONSHIP OF MICROHARDNESS TO INDENTATION DEPTH OF ROCK SALT

[Indentation Depth, h, ym; Microhardness , H, kg mm ^; Load, P, g]

Data

Set Author (s). Year [Ref.] Remarks

Strelkov, P.G., Shpunt, 1 31 10.25

A. A., and Nabutovskaya, 1 65 17.07

O.A., 1967 [15] 2 06 18.89

3 16 20.50

4 54 20.51

6 26 20.54

9 70 20.33

13 70 20.35

19 70 20.15

Strelkov, P.G., et al., 1 44 20.02

1967 [15] 1 85 21.84

2 88 22.77

4 54 20.51

Strelkov, P.G. , et al. , 0. 58 43.42

1967 [15] 0 73 37.28

1 22 30.47

1. 63 29.11

2 05 27.75

2. 46 26.85

2. 74 26.17

3. 57 23.91

3. 85 23.23

4. 12 22.78

6. 26 20.54

NaCl specimen; plastic deformation (e)~0;

dry air with atmospheric humidity (B) < 30%.

Deformed specimen of NaCl; dry atmosphere;

plastic deformation (c) > 0 . 3-0 . 4%

.

NaCl; plastic deformation (e) =0; moist air.

185
0 0.5 2 5 10 20 " 50 " 100 " 200

LOAD, P, g

Figure 3.38. Relationship of microhardness to indentation depth of rock salt (curve numbers

correspond to data set numbers in matching table).

the change in microhardness H of NaCl samples of

nominal purity (Ca^* lO'^-lO"^ mole %) in relation to the quench temperature T. The curve exhibits maxima

and minima attributable to the presence of impurities in

the crystals. At temperatures greater than 873 K

(600°C) the microhardness increases without any

deviations. On reducing the quenching rate, the

microhardness of the samples diminishes and so does the

difference between maximum and minimum values.

Figure 3.40 shows the quench temperature depend- ence of microhardness of NaCl crystals containing

impurities. These data are also from reference [14] and

tabulated in table 3.39. For the purest material no maxima and minima appear, even for very high cooling

rates as indicated by curve 1. It can be seen from this

figure that for a quench temperature of over 873 K

(600° C), the microhardness gradually increases,

independently of the impurity content, and approaches

a constant value on quenching from about the melting

point of the crystal.

3.6. Surface Effects

3.6.1. Joffe Effect

The Joffe effect is the only surface effect considered

here. The Joffe effect is attributed to microfractures in

the surface of the crystals. If surface microfractures are removed either by etching or the chemical polishing

process, the ductility of a crystal is increased significantly. Cleaved crystals are known to fracture after about 2%

elongation, while the maximum elongation for polished,

crystals was 20%. Crystals that were tested in solvent]

show even higher ductility.

The behavior of single halite crystals is strongly

influenced by the surface preparation of the crystal itself] prior to loading and consequent deformation. It is thought that microfractures on the surface of crystalsj cause brittleness. If these microfractures are removed by

either poli^tiing or etching, the ductility of the crystal

increases significantly.

186
TABLE 3.38. QUENCH TEMPERATURE DEPENDENCE OF MICROHARDNESS OF ROCK SALT

[Quench Temperature, T, K; Mlcrohardness , H, kg mm"^]

"f*^^ Author (s), Year [Ref.] T H Remarks

Set

Kishsh, I. and Sharkezl,

I., 1971 [14]

306 0 21 58 379 5 22 02 429 7 22 59 483 9 22 59 530 1 23 52 584 2 24 45 630 9 22 96 681 4 21 97 735 5 22 68 785 6 23 89 839 8 23 76 890 2 23 33 940 3 24 19 990 4 25 68 1040 6 26 112 X 2 X 6 mm NaCl crystals preliminarily

annealed at 923 K and then cooled at 2 deg/

h; both slow and fast quenching used; Zeiss

Model 32 used for microhardness determination with an indentor load of 4 g; 30-40

impressions used for hardness estimation.

36

20.

200 600 1000

QUENCH TEMPERATURE, T, K

Figure 3.39. Dependence of microhardness on quench temperature of rock sah

(curve numbers correspond to data set numbers in matching

table).

187
TABLE 3.39. QUENCH TEMPERATURE DEPENDENCE OF MICROHARDNESS OF ROCK SALT CRYSTALS CONTAINING IMPURITIES

[Quench Temperature, T, K; Microhardness , H, kg mm"^]

Data

Set Author (s) , Year [Ref .

]

Remarks

298 .2 21 .75 374 .6 21 .80 441 .6 21 .91 527 .4 21 .97 578 .4 22 .02 629 .3 22 .07 670 .0 22 .13 731 .1 22 .23 776 .9 22,.28 833 .0 22,.68 934 .3 23 .28 984 .9 23,.89 1035 .6 24 .50

303 .1 22,,20

374,.3 22,,30

471,.0 22,,56

526,.9 22,,76 577 .9 22,,87 629 .0 22,,52 675,.0 22,.27 725.6 22,.97 776,.1 23.,73 832,.3 23.53

883,.3 23,,43 934,.0 23.,83 984,.7 24.,24 1035,.5 24..59

302..8 22.,65 374,.0 22.,96 480.5 23.,76 531.0 24.36

576,.8 24.,82 628.,'3 23.,72 669..8 22..47 730,.4 23.,37 781,.0 24.,03 832,.1 23.,88 883..2 23,,63 933..9 24.,03 989..8 24.,39 1035..4

Kishsh, I. and Sharkezi,

I., 1971 [14]

Kishsh, I. and Sharkezi,

I., 1971 [14]

Kishsh, I. and Sharkezi,

I., 1971 [14]

Sample and testing conditions same as those

of Table 3.17; impurity introduced but total

impurity is under 10"' mole %.

Sample same as above; Ca 10" mole %.

Sample same as above; Ca 10 -10 mole %.

Kishsh, I. and Sharkezi,

I., 1971 [14]

302.7

378.9 480.3

530.9

576.5 628.0

679.8

725.0

785.4

831.5

882.9

933.7 989.6

1035.3

22.85

23.26

24.16 24.81

25.32 24.37

22.77

23.97 25.33

24.83 24.18

24.44 24.74

24.89

Sample same as above; Ag"*" 10 ' mole % + Ca"*"^ 10" mole %.

188
200 600 1000

QUENCH TEMPERATURE, T, K

Figure 3.40. Dependence of microhardness on quench temperature of impure

rock salt crystals (curve numbers correspond to data set numbers

in matching table).

Stokes, Johnston, and Li [3] have studied the Joffe

effect on NaCl crystals. Their data are tabulated in table

3.40 and shown in figure 3.41. A plot of the resolved

shear stress versus percent strain is given for differently

prepared single NaCl crystals. Curves for the following

conditions are presented:

1. Fresh cleaved crystal.

2. Polished crystal deliberately "painted" and showing

a stain.

3. Polished crystal showing a stain and exposed to humid atmosphere.

4. Unstained polished crystal after one day in dry air.

5. The same as curve 4.

6. Unstained polished crystal after eight days in dry

air.

7. Unstained polished crystals after three months in

dry air. An interesting feature of the data in figure 3.41 is that

storage time seems to play no part in the ductility of

polished crystals. For details concerning the test, see the section on the measurement methods.

3.7. Effect of Nuclear Irradiation on

Mechanical Properties of Rock Salt

Ionizing radiation leads to a significant variation of the

stress-strain properties of rock salt. The effect of

radiation varies with temperature, the time of radiation,

the radiation dose, as well as with the type of salt considered and the dimensions of the specimen.

3.7.1. Effect on Stress-Strain Behavior

Bradshaw et al. [13] performed uniaxial compression

testing on bedded salt and dome salt to evaluate the

effects of radiation on stress-strain behavior, maximum

compressive stress, and yield stress. The tests were first run at 293 K and then at 473 K using radiation doses of 0,

10^, 10^ 10^, and 5 XlO^ R, respectively. Three samples

each of dome salt of two cases: ( 1) bedded salt with force

applied perpendicular to bedding planes, and (2) bedded

salt with force applied parallel to bedding planes, were

considered. Their values are presented in Tables 3.41

and 3.42 and have been plotted in figures 3.42 and 3.43,

respectively. Figure 3.42 shows the stress-strain curves

for different exposure doses and the force applied

perpendicular to bedding planes at 293 K. Figure 3.43

shows the relationship between radiation dose and

maximum compressive stress and yield stress at 293 K.

These investigations indicate the following trends:

1. The maximum compressive stress of rock salt exposed to 5 X 10^ R is less than that of unirradiated salt

for both bedded and dome salt.

2. At exposures of 5 X 10^ R and 473 K, there is little difference between the stress capacities of bedded and

dome salt.

3. The yield stress of dome salt is higher than the yield

stress of bedded salt for radiation doses < 3 X 10^ R.

Studies by Demidova and Gol'denberg [10] have

shown that generally the yield limit of NaCl crystal

irradiated at room temperature increases with irradiation

189
TABLE 3.40. STRESS-STRAIN RELATIONSHIP OF ROCK SALT CRYSTAL HAVING DIFFERENT SURFACE CONDITIONS

[Resolved Shear Stress, T, MPa; Strain, e, %]

^ Author(s), Year [Ref.] T e Remarks

Set

Stokes, R.J., Johnston,

T.L. , and Li, C.H. , 1959

[3]

0.23

0.55

0.75

0.87

0.94

0.98

1.04 1.08

1.18

1.22 1.26

,43

,47

,51 0.51

0.66

,88

,15 1.48

1.87

2.14

2.47

Cleaved NaCl crystals; all tests (Data Sets

1-7) done on a conventional hard tensile

machine at what is assumed to be room tem- perature .

Stokes, R.J. , et al.

,

1959 [3]

0.29

0.65

0.85

1.04 1.14

1.25

1.36

3.97 3.89

3.98

3.97 4.13

4.35

4.62

Polished NaCl crystals deliberately "painted"

and showing a stain.

Stokes, R.J. , et al.

,

1959 [3]

0.22

0.58

0.73

0.83

0.86

0.96

1.04

1.09

4.80

4.77

4.99

5.20

5.48

5.86

6.24

6.51

Polished NaCl crystals showing a stain and

exposed to a hximid atmosphere.

Stokes, R.J., et al., 1959 [3]0.19

0.43

0.77

0.88

0.97

1.03

1.13

,22

,3450

71 1.92

2.16

2.47 2.70

3.07 3.50

9740

88

30

70

142

7100

2951

7

7.89 7.82

7.86 7.91

7.90

8.17

8.61 9.05

9.43

10.08

10.68

11.22 11.81

12.34

12.77 13.30

14.00

14.91

15.77

17.01

18.26

19.50

21.08

22.50

23.86

25.28

26.87 28.40

29.78

Unstained polished crystals of NaCl after

1 day in dry air.

190
TABLE 3.40. STRESS-STRAIN RELATIONSHIP OF ROCK SALT CRYSTAL HAVING DIFFERENT SURFACE

CONDITIONS (continued)

Author (s), Year [Ref.] T e Remarks

5 Stokes, R J . , Johnston , u .

z

oy An Unstaxneci poiisnea NaLX di- L C i- -L T.L. , and Li, c.H., iyjy u.jz Qy / u in dry air

•

r 1

1

[3] r\ 7 Q U . / o

Qy DO

n Q

1

u . yx Qy D /

1 m Qy

fiQ

i . Uo xu 101 fii

i . iZ xu1 A /i Q

± . ZU 1 A xu Q 7 o /

1 "3 "3 1 . J J XX JD l.DD 1 0 xz n 7 U / 12 82

O 1 Q Z . ii5 13 80 2.50 14 77 2.88 15 80

J . Z J 16 89

J . 3Z 17 92

•3 Q 0 J . oZ 18 90

/. IT 20.01

/.4 . J 21 34

^ . y 22 64

6 Stokes, R J . , et al . , U . lo 13 09 Unstained polished NaCl crystals alter o

T n c n r "3 1 (J . 4b 13 07 days in dry air.

\J »0 / 13 22

A 7 7 13 33

n Q A U . OD 13 65

1 n "3 X . U J 14 03

1 "30 14 57

X . J 3 15 16

X1 Q ^ . y J 15 97 2.33 16 94 2.67 17 97

Oft 19 16

J . tz 20 36 21 55

• XiJ 22 75

4 . J_> 23 89 24 88

7 btoKes, K J .

, et ax . , u . xu 17 90 Unstained polished NaCl crystals after 3 n "3^ 17 88 months in dry air.

n 7 0 u . / z 17 86

n QQ u . y 0 17 90

X . Uo 18 06

X . X4 18 17

1 0 "3 X . Z J 18 38

T "3 7 X . J / 18 71

X . 4(5 18 92

X . O / 19 63 2.04 20 60 2.36 21 41

2.72 22 33 3.08 23 14 3.45 23 95 3.75 24 43 4.11 25 33 4.38 25 94

191
Curve

No

.

Cond it ion Cleaved cryst

Polished Crys

Deliberately

Exposed to bumi

Polished Crys'

4 After one day

5 After one day After eight da;

7 After three mo

• Refe

I-*— 40/0—

J"

STRAIN. €, %

Figure 3.41. Stress-strain relationship of salt crystals having different surface conditions.

192
TABLE 3.41. RADIATION EFFECTS ON STRESS-STRAIN RELATIONSHIP OF ROCK SALT

[Compressive Stress, ai,MPa; Strain, e, In/ln]

Data

Set Author(s), Year [Ref .

J

0 1 Remarks

1 Bradshaw, R.L. , Limpson, 10 . 6 0 . 006 2" X 2" cubes of bedded salt; force applie

F.M., Boegly, W.J., Jr., 13 . 8 0 . 009 perpendicular to planes of stratification

Kubobta, H. , Parker, F.L., 15 . 7 0 .011 d L. L (JVJIU l-ClUpC L d L U.1- C , LiLlX J. J- CHJJ_cl LC^ . and Struxness, E.G., 19 . 0 0 . 016

Tr\An rill 1968 L13j . 5 0 . mlU/i

Z J

c

. 0 0 .026

25 2 0 .031

26 1 0 .036

26 7 0 041

1

1

1 0 046

z / z 0.051

Z / 3J 0 056

0 7 Z / OJ 0 061

2 Bradshaw, R.L. , et al.

,

cJ U 0 002 Sample similar to above; irradiated to

Q 0 006 10^ R. iz 0 009

T /, 14 J 0 010

± / 0 016

onZU U 0 021

Zl oy 0 026

Z J

cJ 0 031

24 7 0 036

25 5 0 041

ZD o 0 046

Z J

Q 0 051

25 6 0 056

25 6 0 061

QJ Bradshaw, R.L. , et al.

,

9 0 002 Sample similar to above; irradiated to lybo l-L-ii 11 3 0 006 10' R. 15.0 0 009

16 9 0 Oil

20 5 0 016

23 1 0 021

25 0' 0 026

26 5 0 031

27 5 0 036

28 0 0 041

28 0 0 046

28 0 0 051

28 0 0 056

27 9 0 061

/. Bradshaw, R.L,, et al.,. 5 3 0 002 Sample similar to above; irradiated to lyoo L-L^J 11 5 0 005 10^ R. 15 4 0 009

17 3 0 Oil

20 9 0 016

23 3 0 021

25 3 0 027

26 3 0 031

27 1 0 036

27 3 0 041

26 6 0 046

25 7 0 051

25 1 0 056

24 8 0 061

c Bradshaw, R.L., Limpson, 5. 27 0 002 Sample similar to above; irradiated to

r • M, , Boegiy , w . J .

, Jr .

,

10. 95 0 006 5 X 10^ R. Kubota , H. , Parker , F . L .

,

15. 20 0 009

and Struxness, E.G.

,

17. 57 0. Oil

XyOO 10AQ n^i LJ-JJ 21. 20 0 016

22. 8 0 021

23. 8 0 026

24. 3 0 031

23. 8 0. 036

22. 7 0. 041

21. 1 0. 046

19. 5 0. 051

18. 5 0. 055

193
0.00 0.02 0.04 0.06

STRAIN, €, in/in

Figure 3.42. Effect of radiation on.the stress-strain behavior of rock salt (curve numbers correspond to

data set numbers in matching table).

194
TABLE 3.42. MAXIMUM COMPRESSIVE AND YIELD STRESS OF ROCK SALT FROM HUTCHINSON,

KANSAS, AND GRAND SALINE, TEXAS

All results have been rounded off to the nearest .69 MPa and standard deviation to the nearest .34 MPa.

(After Bradshaw [13], 1968)

Type of Salt Exposure

Dose (R)

Maximum

Compressive

Stress MPa

Yield

Stress MPa

At 293 K

Beddea Parallel 0 28 95 - 3 45 17 23 - 2 07

10^ 31 03 3 45 17 23 1 03

10' 31 72 + 2 76 18 62 + 1 72 10° 31 72 + 1 03 23 44 + 1 72

5 X lO' 24 13 + 0 34 18 62 + 1 38

Bedded Perpendicular 0 27 58 + 2 76 15 86 + 2 07 10^ 26 20 + 3 45 12 41 + 1 72 10' 28 27 + 2 76 15 86 + 3 45

10° 27 58 + 2 76 16 55 + 3 45

5 X 10° 24 13 + 2 76 16 55 + 2 07

Dome 0 38 61 + 0 69 19 99 + 1 03

10° 36 54 + 0 69 19 99 + 1 03 10' 35 16 + 1 38 20 68 + 0 69

10° 28 27 + 1 38 18 62 + 0 69

5 X 10° 24 13 + 3 45 17 93 + 1 39

Bedded Parallel

Bedded Perpendicular

Dome

At 473 K

0 26.89

5 X 10° 23.44

0 24.82

5 X 10° 22.75

0 24.82

5 X 10° 21.37

± 1.38 11.03 ± 1.39

± 2.76 13.10 ± 1.72

± 0.69 11.03 ± 0.69

± 2.76 14.48 ± 1.03

± 3.45 13.10 ± 1.03

± 2.07 15.86 ± 1.03

Bedded Parallel: bedded salt, force applied parallel to the planes

of stratification.

Bedded Perpendicular: bedded salt, force applied perpendicular to the plane of stratification.

195
o

a.

b" 40

CLO

u

X

Dome

Dome

Bedded Parallel

Bedded Perpendicular

Compressive Strength

Yield Strength

10° 10' 10

RADIATION DOSE, R

8

Figure 3.43. Relationship between maximum compressive stress and

radiation dose.

dose; at low doses the temperature hardening mechanism

controls while at higher doses a temperature insensitive

mechanism prevails. They also observed that even before

two hours of irradiation had occurred, the strain was

elastic while the failure was brittle. Only at rupture a small local plastic strain was evident. Whisker crystals

irradiated for two or more hours revealed macroscopic

plastic flow only if they had first been subject to plastic

strain. A substantial difference in the extent of the

variation in the ultimate strength of crystals of different

diameters was shown as the radiation dose was varied

[8] . The ultimate tensile stress capacity of NaCl whisker

crystals, measuring 18 yum in diameter, was observed to increase first and then decrease, passing through a maximum at an irradiation time of about eight hours as shown in figure 3.44 with the corresponding values in

table 3.43. Specimens measuring 86 fim in diameter

under the same conditions exhibited a gradual increase

in the degree of hardening with dose.

Figure 3.45 is also taken from Demidova and

Gol'denberg [10] and shows that another effect of

radiation is the change in the nature of crystal whisker

fracture. The corresponding values are tabulated in table

3.44. Prior to exposures the specimens fail in a plastic

mode whereas the exposed specimens fracture primarily

in a brittle mode.

3.7.2. Effect on Young's Modulus

The relationship between radiation dose and Young's

modulus as investigated by Bradshaw et al. [13] is given

in table 3.45 and plotted in figure 3.46. There is a general

increase in modulus of elasticity with increase in

radiation dose but this trend is irregular and inconsistent.

3.7.3. Effect on Creep

In addition to the static tests, the creep rate resulting

from the application of a constant force of 17.237 MPa

for 100 minutes was measured by Bradshaw et al. [13].

Figure 3.47 shows the creep curves for bedded salt with

the corresponding values given in Table 3.46. The

irradiated salt which received 5 X 10^ R was stronger as shown by less creep.

3.7.4. Effect on Hardness

The hardness of NaCl crystals increases on irradiation.

Small irradiation doses, however, produce very little hardening compared to coloration. Demidova and

Gol'denberg [10] observed that: (1) two hours of

exposure to x-rays result in hardening of crystal

whiskers, and (2) the degree of hardening increases as the diameter diminishes.

196
TABLE 3.43. DEPENDENCE OF ULTIMATE TENSILE STRESS CAPACITY OF NaCl CRYSTAL

WHISKER ON IRRADIATION TIME

[Irradiation Time, t, hrs; Tensile Stress, CTf, MPa]

Data

Set Author (s), Year [Ref.] t at Remarks

1 Demidova, N.N. and -0.08 2 .89 NaCl whisker crystals measuring 10-100 ym

Gol'denberg, S.U., 1975 1.91 5 .61 in diameter cultivated from solution using

L

'-^ J 3.81 10 .06 the Amelinck method j specimens irradiated

7.78 16 .94 at room temperature j this data obtained

11.87 10 84 for a specimen with a diameter of 18 ym.

15. 96 3 .88

2 Demidova, N.N. and 0.09 1 20 This data obtained for a specimen with a Gol'denberg, S.U., 1975, 2.07 2 29 diameter of 86 m.

[8] 3.95 2 99 8.07 4 24 15.96 5 46

o

0.

IRRADIATION TIME, t, hrs

Figure 3.44. Dependence of ultimate stress capacity of NaCl crystal whiskers on irradiation time (curve

numbers correspond to data set numbers in matching table).

197
TABLE 3. 4 A. EFFECT OF RADIATION ON TENSILE STRESS-STRAIN BEHAVIOR OF NaCl CRYSTAL WHISKER

[Tensile Stress, a^, MPa; Strain, e, %]

Data

Set Author (s), Year [Ref.] Remarks

Demidova , N.N. and

Gol'denberg, S.U.,

1975 [8]

Demidova, N.N. and

Gol'denberg, S.U.,

1974 [10]

15

.

1. 74

17

.

1. 75

16. 75 5.08

18. 80 5. 92

17. 98 6. 75

16. 75 9.,24 19. 20 11..76 17. 97 13.42

16. 75 15.,08 17. 96 16.,75 19.,20 19.,26 20.0 20..93 20.,8 23.,43 20.,0 25..09 21..23 27..60 21.22 30..10 22.04 30.94

23.,26 33..44 21.,22 35.10

22.,45 36..77 20.4 38..43 23.,75 40..11 23,,80 42.62

24.,63 48,.07 25,,48 51,.70 26.31 53..52 26,,73 55,.36 26,,73 58,,97 26,,73 60,,79 27,,15 64,,42

27,,99 66,.24 28.83 68,,96

29,,67 71,.69

30.,09 75,.32

31.,34 77,.13

31,,77 80,,77

32..60 84,.4 32,.61 87,.13

5 .24 0 .11

12..57 0 .23

19,.89 0,.33

29..30 0 .46

38,.71 0 .57 44 .99 0 .69 55 .45 0 .79

61,.73 0 .89 72 .73 1 .01

79,.51 1 .12

87,.87 1 .22

Unexposed; NaCl crystal whiskers grown

by Amelinck method from solution and

tested on a tensile machine; specimen

diameter 13.7 \l.

Exposed; NaCl crystal whiskers grown

by Amelinck method from solution and

irradiated directly on a tensile machine with unfiltered x-radiation for

2 hours; diameter of crystal whisker

used 26 \i.

198
STRAIN, €, % (IRRADIATED)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Q

LU

STRAIN, €, % (UNIRRADIATED)

Figure 3.45. Effect of radiation on tensile stress-strain behavior of a NaCl crystal whisker (curve numbers

correspond to data set numbers in matching table).

199
TABLE 3.45. YOUNG'S MODULUS OF ROCK SALT FROM HUTCHINSON, KANSAS, AND GRAND SALINE, TEXAS

All results have been rounded off to the nearest .69 MPa and the standard deviation

to the nearest .34 MPa.

(After Bradshaw [13], et al.)

Type of Salt Exposure

Dose, D (R)

Modulus of Elasticity, Es GPa

At 293 K Bedded Parallel 0 2 41 + 0 41

10^ 2 21 0 41

10' 2 41 + 0 14 10° 2 48 + 0 62

5 X 10 °

Bedded Perpendicular 0 2 48 + 0 80

10° 2 41 0 69 10' 2 62 + 0 26 10° 2 62 0 41

5 X 10° 2 55 - 0 76

Dome 0 3 45 + 0 34 10° 3 52 + 0 82 10' 4 27 0 41 10° 3 81 + 0 28

5 X 10° 4 06 + 0 83

At 473 K

Bedded Parallel 0 0 62 + 0 07

5 X 10° 0 83 + 0 14

Bedded Perpendicular 0 0 90 + 0 07

5 X 10° 0 90 + 0 07

Dome 0 0 96 + 0 07

5 X 10° 1 10 + 0 07

200
TABLE 3.46. EFFECT OF IRRADIATION ON CREEP PROPERTIES OF ROCK SALT

[Time, t, min; Strain, e, (in/in) x 10^]

°f'^ Author(s), Year [Ref.] t £ Remarks

Set

Bradshaw, R.L., Limpson, 0.9 9.00

F.M., Boegly, W.J., Jr., 1.4 10.50

Kubobta, H., Parker, F.L. 2.9 10.88

and Struxness, E.G., 6.4 11.26

1968 [13] 10.3 11.57

15.5 11.53

26.6 11.92

40.8 11.95

60.6 11.98

80.1 12.29

100.2 12.31

Bradshaw, R.L. , et al.. 0.9 6.25

1968 [13] 1.4 10.25

1.9 11.38

4.6 14.63

8.3 15.14

12.5 15.65

21.7 15.91

30.8 16.31

50.6 16.47

70.4 16.75

90.2 17.04

Bedded salt with force applied perpendicular

to planes of stratification; constant load

of 17.237 MPa.

Similar conditions as Data Set 1; irradiated to 5 X 10^ R.

toO

X

40

30

Force applied perpendicular to planes of stratification. Constant load of 17.24 MPa.

o Unirradiated

• Irradiated (5 x 10^ R)

20 40 60

TIME, t, minutes

80 100

Figure 3.47. Effect of radiation on tlie creep of rock salt (curve numbers

correspond to data set numbers in matching table).

201
Figure 3.48 from Inabe and Takeuchi [9] shows the

relationship between Vickers hardness and x-ray dosage

for specimens annealed and reheated up to 600 °C and

then cooled. The corresponding values are tabulated in

table 3.47.

3.7.5. Evaluation of Data

At this stage the published data do not permit the

generation of recommended values of the mechanical

properties of rock salt. The available data are contradictory and even though measurements seem to have been

carefully conducted, the nature of the material under

consideration makes it difficult to characterize it adequately.

TABLE 3.47. VICKER'S MICROHARDNESS OF NaCl CRYSTALS AS A FUNCTION OF X-RAY DOSE

[X-Ray Dose, 10^ R; Change in Vicker's Microhardness , AHv, kg mm ^]

Data

Set Author (s). Year [Ref.]

Dose

10 5r Remarks

1 Inabe, K. and Takeuchi, 0.09 0 21 NaCl crystals grown in air by Kyropoulos

N., 1973 [9] 0.30 0 A5 technique from a melt reagent grade material

1.05 0 81 Specimens annealed in air at 923 K for 80 2.05 1 08 hours and slowly cooled at 293 K/hr. 3.06 1 00

2 Inabe, K. and Takeuchi, 0.09 0 10 NaCl crystals grown as indicated above; howN., 1973 [9] 0.31 0 20 ever they were reheated to 873 K and allowed

1.03 0 49 to cool on an asbestos plate.

2.01 0 55 3.00 0 50 4

X-RAY DOSE, X 10^ R

3.48. Effect of radiation on the microhardness of rock salt (curve

numbers correspond to data set numbers in matching table.)

202
3.8. References

[1] Glossary of Geology, American Geological Institute (1974).

[2] Voronov, F.F., and Grigor'ev, S.B., "Influence of Pressures Up

to 100 kbar on Elastic Properties of Silver, Sodium and

Cesium Chlorides," Sov. Phys. Solid State, 18(2), 325-8

(1976).

[3] Stokes, R.J., Johnston, T.L., and Li, C.H., "Environmental

Effects on the Mechanical Properties of Ionic Solids with

Particular Reference to the Joffe Effect," Office of Naval

Research, Sixth Technical Report, Project NONR-2456(00)

NR 032-451 (1959).

[4] Morris, C.E., Jamieson, J.C., and Yarger, F.L., "Ultrasonic Measurements at Elevated Pressures (9 GPa) to Determine

Poisson's Ratio and other Elastic Moduli of NaCl and

NaF,"J.Appl. Phys., 47(9), 3979-86 (1976).

[5] Cera, F., "Review of Salt Tectonics in Relation to the Disposal

of Radioactive Wastes in Salt Formation," Geological

Society of America Bulletin, 83, 3551-74 (1972).

[6] Wu, C. and Phillips, G.C., "Seismic-Wave Propagation from

Salt Dome Environments," VESIAC State of the Art Rept.

4410-79-X, 58 pp. (1964).

[7] Heard, H.C., Abey, A.E., Bonner, B.P., and Duba, A., "Stress- Strain Behavior of Polycrystalline NaCl to 3.2 GPa,"

Lawrence Livermore Laboratory Rept. UCRL-5I743, 16 pp. (1975).

[8] Demidova, N.N. and Gol'denberg, S.U., "Role of the Scaling Factor in Radiation Variation of the Stress-Strain Properties

of NaCl Whisker Crystals," Izv. Vyss. Ucheb. Zaved. Fiz., 12, 123-4, 1975; English Translation: Plenum Pub. Corp.

(1975).

[9] Inabe, K. and Takeuchi, N., "Dislocation and Radiation

Hardening of NaCl Single Crystals," Jap. J. Appl. Phys.,

12(6) (1973).

[10] Demidova, N.N. and Gol'denberg, S.U., "Radiation Hardening

of NaCl Crystal Whiskers," Izv. Vyss. Ucheb. Zaved. Fitz.,

4, 139-41 (1974); English Translation: Plenum Pub. Corp.

(1975).

[11] Sanchez, C, Lioma, I.S., Jargiu, F., and AguUo-Lopez, F., "Influence of the Aggregation State of Ca^"*" Ions on the Coloring and Hardening Behavior of NaCl: Ca^"*"," Crystal

Lattice Defects, 6, 227-32 (1976).

[12] Dreyer, W., "The Science of Rock Mechanics, Vol. I," Tran. Tech. Publications, 29-164 (1972).

[13] Bradshaw, R.L., Limpson, F.M., Boegly, W.J., Jr., Kubota, H., Parker, F.L., and Struxness, E.G., "Properties of Salt Important in Radioactive Waste Disposal," Geol. Soc. Am.,

Special Paper 88 (1968).

[14] Kishsh, I. and Sharkezi, I., "Change in the Microhardness of

Alkali Halide Crystals on Quenching," Sov. Phys., 16(5)

827-31 (1972).

[15] Strelkov, P.G., Shpunt, A.A., and Nabutovskaya, O.A., "Use of NaCl Crystals as Hardness Standards," Zavod. Lab., 34(5)

599-601 (1967).

[16] Frankel, J., Rich, F.J., and Homan, C.G., "Acoustic Velocities

in Polycrystalline NaCl at 300 K Measured at Static Pressures from 25 to 27 kbar," J. Geophys. Res., 81(35),

6357-63 (1976).

[17] Baar, C.A., "Applied Salt-Rock Mechanics I, The in Situ Behavior of Salt Rocks," Developments in Geotechnical

Engineering, 16A, 34 (1977).

[18] Dames & Moore, White Plains, NY, Consultants Rept.

Y/OWI/TM-36, Vol. 4, "Baseline Rock Properties—Salt,"

of work entitled "Technical Support for GEIS: Radioactive

Waste Isolation in Geologic Formations," prepared for Union Carbide, April 1978.

[19] Burke, P.M., "High Temperature Creep of Polycrystalline

Sodium Chloride," Stanford Univ., PhD. Thesis (1968).

[20] Handin, J., "An Application of High Pressure in Geophysics:

Experimental Rock Deformation," Trans. ASME, 75,

315-24 (1953).

[21] Heard, H.C., "Steady-State Flow in Polycrystalline Halite at 2

Kilobars," (Heard et al., Editors), American Geophysical

Union Monograph 16, 191-209 (1972).

[22] LeComte, P., "Creep in Rock Salt," J. Geol., 73, 469-84

(1965).

[23] Nair, K. and Deere, D.V., "Creep Behavior of Salt in Triaxial Extension," in Third Symposium on Salt (Rau and Dellwig,

Editors), Vol. 2, N. Ohio Geological Society, Inc. (1970).

[24] Ode', H., "Review of Mechanical Behavior of Salt Relating to Salt Dome Genesis," (Braunstein, J.D. and O'Brien, G.D.,

Editors), Diapirism and Diapirs. Mem. 8, Am. Assoc. Petroleum Geologists (1968).

[25] Thompson, E.G., "An Experimental Technique for the

Investigation of the Flow of Halite and Sylvinite," Univ. of Texas-Austin, Ph.D. Thesis (1965).

Symbols and Units

Symbol Name Unit

P Pressure MPa, GPa

P Density kg m"' pjp Compression dimensionless

E Young's modulus GPa

G Shear modulus GPa

K, Bulk modulus GPa

M Poisson's ratio dimensionless

V Velocity m s"' T Shear stress GPa

e Strain, also true strain %, in/ in

e Creep, also strain rate r» a Compressive stress MPa, GPa

(a, - Oi) Differential stress MPa, GPa

t Time min, h, s H Hardness kg mm"2

T Temperature K

Tensile stress MPa

AL Change in length cm

Conversion Factors

Pressure

To convert from to Multiply by

MPa lb in"2 (psi) 1.45138 X 102 MPa kbar IX 10-2 GPa lb in"2 (psi) 1.45138X 105 GPa kbar 10 bar 10 X,103

Density

To convert from to Multiply by

kg • m ' lb • fr3 0.06243

kg • m"^ g

•' cm"' LXlO-3

Temperature

To convert from to Subtract K °c 273.15

203
4
Chapter 4

Thermophysical Properties

J. M. Yang*

Contents

Page

4.1. Introduction 206

4.2. Review of Measurement Methods for Thermophysical Properties 206

4.2.1. Measurement Methods for Thermal Conductivity 206

4.2.1.1. Absolute, Longitudinal Steady-State Heat Flow Method 206

4.2.1.2. Comparative, Longitudinal Steady-State Heat Flow Method 206

4.2.1.3. Absolute, Radial Steady-State Heat Flow Method 207

4.2.1.4. Flash Method 207

4.2.2. Measurement Methods for Thermal Expansion 207

4.2.2.1. Push-Rod Dilatometers 207

4.2.2.2. Interferometers 208

4.2.2.3. X-Ray Methods 209

4.3. Thermal Conductivity 209

4.4. Thermal Diffusivity 211

4.5. Thermal Linear Expansion 211

4.6. Effect of Nuclear Irradiation on Thermophysical Properties 212

4.7. References 217

Symbols and Units 221

Conversion Factors 221

* Center for Information and Numerical Data Analysis and. Synthesis, Purdue University, 2595 Yeager Road, West Lafayette, Indiana 47906

205
4.1. Introduction

In this chapter the thermophysical properties (thermal conductivity, thermal diffusivity, and thermal linear

expansion) of rock salt are discussed. Recommended

values which were generated from the analysis and

synthesis of the available experimental data are presented. In spite of the fact that the study of molten

salts has increased notably in the past thirty years,

experimental data on molten rock salt are still very

scanty. As a consequence, no recommended values were

generated for thermal conductivity above the melting

point. Recommended values of the thermal diffusivity were derived by correlating the recommended values of

thermal conductivity, specific heat, and thermal

expansion. In those cases where the reported values are not adequately substantiated by experimental data or where the material cannot be uniquely characterized, the

term "typical" values is used. No attempt was made to estimate the thermal diffusivity beyond the melting

point.

The data sets upon which the recommended values are based are shown in the various figures for the respective

properties. Additional data sources are given as references.

4.2. Review of Measurement Methods for

Thermophysical Properties

Many different methods and variations for measuring

the thermophysical properties of solids have been

developed, especially in the past fifty years. In this

section, only the methods that are frequently used for

measuring rock salts will be described and discussed.

It is noted that the only commonly used method for

measuring thermal diffusivity, the flash method, is often

employed (together with independently-obtained specific heat values) to obtain thermal conductivity values.

This method will be discussed in section 4.2.1. entitled

"Measurement Methods for Thermal Conductivity".

4.2.1. Measurement Methods for Thermal

Conductivity

4.2.1.1. Absolute, Longitudinal Steady-State Heat Flow

Method

In the absolute, longitudinal heat flow method, the

experimental arrangement is so designed that the flow of

heat is nearly entirely in the axial direction of a rod (or

disk) specimen. The radial heat loss or gain of the

specimen can either be prevented or minimized and

evaluated. Under steady-state condition and assuming no

radial heat loss or gain, the thermal conductivity is determined by the following expression which is from

the one-dimensional Fourier-Biot heat-conduction equation

k = -^

(4.1) AAT

where k is the average thermal conductivity corresponding to the average temperature V2 {T1 + T2), AT= T2-T1,

q is the rate of heat flow, A is the cross-sectional area of

the specimen, and Ajc is the distance between points of

temperature measurements for Ti and T2.

In this method, the specimen used is in the form of a

relatively long rod or disk (for poor conductors) so as to produce an appreciable temperature drop along the

specimen for precise measurement. A source of heat at a constant temperature is supplied at one end of the rod (or one side of the disk). Heat flows axially through the rod

(or disk) to the other end (or side) where a heat sink at a lower constant temperature is located. The radial heat

loss or gain of the rod (or disk) should be negligible. In

order to calculate the thermal conductivity from

equation (4.1), it is necessary to measure the rate of heat

flow into and/or out of the rod (or disk), the cross- sectional area, the temperature of at least two points

along the rod (or of two sides of the disk), and the

distance between these points (or the thickness of the

disk) . This method has been used for most measurements

below room temperature. General reviews of the lowtemperature measurements and experimental techniques have been presented by White [83,84] . For

details of some of the useful low-temperature apparatus

the reader may consult references [85-96]

.

While this method is inherently capable of high

precision and accuracy, experience has shown that

uncertainties of approximately one percent are attained

at room temperature and lower. This figure rises to three

percent at high temperatures.

4.2.1.2. Comparative, Longitudinal Steady-State Heat Flow

Method

In this method a reference sample (or samples) of

known thermal conductivity is placed in series with the

unknown specimen with hopefully the same rate of heat

flow through both the reference sample and the

specimen. Under such ideal conditions, the thermal

conductivity of the specimen is given by

AAAT/Ax)

_ A (AT/ Ax) (4.2)

where the subscript r designates the reference sample.

206
This method may be divided into two distinct groups:

the "long-specimen" type [97-99] for measuring the

thermal conductivity of good conductors, and the

"short-specimen" type [36,101-104] for measuring

poor conductors.

Comparative methods have the advantages of simple

apparatus, easier specimen fabrication, and easier

operation. Their disadvantages include additional meas- urement errors due to the required additional measure- ment of temperatures and thermocouple separations,

difficulty in matched guarding against radial heat loss (or

gain), and lower accuracy due to the additional

uncertainty in the conductivity of the reference sample,

the conductivity mismatch between specimen and

reference sample, and due to the interfacial thermal

contact resistance. These have been carefully analyzed

by Laubitz [105] and Flynn [106]. The accuracy of the

method is limited by the uncertainties in the reference

material used. Normally this may be as high as two or three percent.

4.2.1.3. Absolute, Radial Steady-State Heat Flow Method

This method uses a specimen in the form of a right

circular cylinder with a coaxial central hole, which

contains either a heater or a heat sink, depending on

whether the de red heat flow direction is to be radially

outward or inwf d. In the earlier experiments and also in

many later designs [107-110], end guards are not

employed. The effect of heat losses from the ends of the

specimen is minimized by using a long specimen and

monitoring the heater power within only a small section

of the specimen away from the ends.

The guarded cylindrical method employing end guards

at both ends of the specimen to prevent axial heat losses was developed by Powell [111] and first reported in 1939

for measurements on Armco iron at high temperatures.

In this method the specimen is composed of stacked disks

with a coaxial central hole containing either a heater or a heat sink. Temperatures are measured either by thermocouples or by an optical pyrometer.

The thermal conductivity is calculated from the

expression

^

qln{r2/ri)

" 2wl{T,-T2) ^^'^^

where / is the length of the central heater and Ti and T2 are temperatures measured at radii n and r2, respectively.

For details of some of the useful apparatus employing

the guarded cylindrical method, the reader may consult

references [111-117]. The uncertainties in this method

are normally those encountered in the absolute radial

method.

4.2.1.4. Flash Method

The flash method is a variant of the absolute,

longitudinal transient heat flow method using a small

thin disk specimen. In this method, a flash of thermal

energy is supplied to one of the'surfaces of the disk

specimen within a time interval that is short compared

with the time required for the resulting transient flow of

heat to propagate through the specimen. This method

was developed by Parker, Jenkins, Butler, and Abbott

[118] and reported in 1961.

In use, a heat source such as flash tube or laser

supplies a flash of energy to the front face of a thin disk

specimen and the temperature as a function of time at the

rear face is automatically recorded. The thermal

diffusivity is obtained from the thickness of the

specimen, /, and a specific time, i , at which the back

face temperature reaches half its maximum value by the

expression

a = 1.37 ly-ivH,^^ (4.4)

The thermal conductivity of the specimen is then

calculated by the relation

k = pacp (4.5)

where k is the thermal conductivity, p is the density,

and Cp is the specific heat at constant pressure.

Subsequent improvements on this method have been

made [119,110] by the application of corrections for the

finite pulse-time effect and the radiation-loss effect. Current capabilities exhibit an uncertainty of the order

of five to ten percent depending on sample transparency

and temperature level.

4.2.2. Measurement Methods for Thermal

Expansion

4.2.2.1. Push-Rod Dilatometers

The push-rod dilatometer method for measuring

thermal expansion is experimentally simple, reliable, and

easy to automate [ 121] . With this method, the expansion

of the specimen is transferred out of the heated zone to an extensometer by means of rods (or tubes) of some

stable material. The expansion of the specimen is given

by —AL (AL)3 - = Co — + ci (4.6)

where (AL)a is the apparent change in length as calculated from the difference between the extensometer

readings at two different temperatures, and Co and Ci are

calibration constants for the system. If the reference rod

207
is made the same length as the push rod and a second

specimen placed on the base plate, the dilatometer will measure the difference between the specimens [122].

The difference, or differential expansion is given by

(AL)2 (AI),

Co

(AL)a

+ Ci. (4.7)

When used this way the dilatometer can have a very high

sensitivity. This technique is also very useful for quality

control measurements and for studying phase transitions.

One of the most common sources of error in using

dilatometers is the measurement of temperature. All too

often the temperature that is measured is not the

temperature of the specimen. If a thermocouple is used,

care must be taken to ensure that its junction and

specimen are the same temperature; they can be at different temperatures even if in contact with each

other. Another common source of error, especially for

flexible materials or materials near their softening

temperatures, is deformation under the load of the push

rod. Special techniques such as increasing sample

diameter, reducing push rod pressure, and using

horizontal mounts must be used for these soft materials.

The uncertainty of this method depends on the quality

of the push rod used and precision of construction.

Results of two or three percent uncertainty may be

achieved routinely.

4.2.2.2. Interferometers

These methods are based on the interference of

monochromic light reflected from two surfaces [123]

that are separated by a specimen or by the combination of

a specimen and a reference material. The general

condition for interference is

2nL cos 6/= NXlv (4.8)

where n is the index of refraction of the atmosphere

between the surfaces, L the distance between the two

surfaces, d the angle between the direction of the

incident rays and the direction normal to the surfaces, N

the order of interference, and kp the wavelength of the

light in vacuum. Monochromatic light sources that may

be used include cadmium, helium, mercury, and sodium

low-pressure discharge lamp [ 124] and a stabilized He-Ne

laser [125].

If slightly inclined surfaces are illuminated with

collimated light and viewed at normal incidence (0= Ofor

all rays) , fringes of equal inclination are observed. When

the surfaces are flat the fringes will be straight; otherwise

they are determined by the contour of the surfaces. This

type of interference is used in the Fizeau interferometer

[126] . If plane-parallel surfaces are illuminated with an

extended source (0 will vary), fringes of equal inclination are observed. This type of interference (concentric

rings) is used in the Fabry-Perot interferometer [127].

When an interferometer is used to measure thermal

expansion, the expansion of the specimen is given by

2nL cosd

(4.9)

where ANis the number of the fringes that pass a fiducial

mark and Are is the change of refractive index. A useful

approximation for the refractive index is

TrP

n= 1 + (n.,-1) p-j (4.10)

where rij- is the index at the reference temperature 7^- and

the reference pressure Pj-- In vacuum or in sufficiently

low-pressure atmosphere

AL ktj A/V

2L cosd (4.11)

In a Fizeau interferometer (straight fringes) the fractional part of AA' is easily determined from measure- ments of the position of the fiducial mark between two

fringes. In a Fabry-Perot interferometer (circular

fringes) the fractional part, v is given by

nLdj,

PA.,

(4.12)

where dp is the diameter of the pth fringe (counted from

the center of the concentric pattern) and /is the focal

length of the lens that forms the pattern. If measure- ments are made on the second and fourth fringes, the

fractional part is

V =

3(^2 - dl

dl - do

(4.13)

The number of fringes that move past a reference point

during the expansion of a specimen can be counted by

eye or automatically by photographic [128] or photoelectric [129] techniques. Another way of determining

A is by finding the value of A^at each temperature. This can be done by using at least three different wavelengths

[124]. From eq (4.8) it can be seen that

(A^l+I^l)Al = {N2+V2)k2 = (A^3+l^3)A3 (4.14)

where A^i, N2, and A^a are the fringe integers and J^i, V21 and V3 are the fringe fractions for each of the three

wavelengths. In the method of exact fractions a value is

208
guessed for A^i (~2aL/Xi) and using the measured

value of Vi the values of (A^2+|i'2) and (A^s+^s) are

calculated. This procedure is repeated with different

values of A^i until the calculated values of V2 and P3 agree

with their measured values. If is known, then

AL AN An

N

(4.15)

The Fizeau interferometer can be used to measure

either the absolute or relative expansion of a specimen.

In the relative method a pedestal of one material fills most of space within a ring or cylinder of a second

material. The pedestal is preferably made of a reference

material. While the ring supports the optical flat, the

interference is formed by reflections from the optical flat and the top surface of the pedestal. Since the reflecting

surfaces are close together this method has three

advantages: (1) the fringes are bright and well defined;

(2) the change of the refractive index of the gas within

the small space does not affect the measurements; and

(3) longer specimens can be used with a corresponding

increase in sensitivity. The thermal expansion is given by

FALl \j,AN L.TALl An

(4.16) n

where the subscripts s and r refer to the specimen and

reference materials. When the last term can be

ignored.

4.2.2.3. X-Ray Methods

These methods are based on the diffraction of a coUimated beam of monochromatic x-rays that is scattered by atoms in a crystal lattice. The Bragg law

X = 2d(hkl)sind (4.17)

gives the condition for constructive reflection of the

incident radiation. Here d is the separation of the lattice

planes, h, k, and / are the Miller indices for the planes,

and 6 is the angle measured between the direction of the

incident or reflected beam and the planes. Except for a small correction due to refraction, the measurement of

expansion is independent of wavelength such that

Ad(hkl)

d(hkl)

- -COS0A0 =

sin^i sin02

sin02 -(4.18)

where d\ and 62 are the angles of incidence of the beam

with the crystal plane at temperatures T\ and T2,

respectively.

The thermal expansion of crystalline materials can be

accurately measured with x-ray cameras and diffractometers under conditions that preclude the use of any

other method, as when the specimens are very small,

weak, and/ or irregular in shape. These methods are also

unique in that they can easily be used to determine the

principal coefficients of thermal expansion of anisotropic crystals and permit direct observation of phase

changes. There is a further advantage in that measure- ments with x-rays do not include effects that are observed in measurements on bulk specimens. The

problems associated with heating the specimen and

accurately measuring its temperature in both x-ray cameras and diffractometers are discussed in several

articles [131-133].

Unique x-ray techniques exist for special situations.

In particular, the use of the Bond technique for single

crystals [134] has resulted in a sensitivity of 10"^ in

measurements of Aa/a [135]. In this technique the

specimen is rotated between equivalent diffracting

orientations on either side of the incident beam. The

value of 6 thus obtained is unaffected by any specimen

eccentricity, absorption, and zero errors, and errors due

to specimen tilt and beam axial divergence are minimized.

The inherent accuracy of this technique is extremely

high for well characterized and stable materials.

4.3. Thermal Conductivity

The thermal conductivity of different samples of rock

salt can be different by four orders of magnitude,

depending on the temperature region. This variation is dependent upon the degree of lattice imperfection, the

various treatments before the measurement, and the

kind and the amount of impurities present in the sample.

Figure 4.1 shows several types of thermal conductive

behavior of rock salts with different treatments. Group 1 represents the thermal conductivity of high-purity rock

salt [1-8,16]. Based on the data in this group,

recommended values for pure rock salt were generated

for temperatures above 100 K and are tabulated in table

4.1. Those tabulated values below 100 K are merely

typical values. The recommended values are considered

accurate to within + 5%. Rock salts which were annealed

at different temperatures are represented by group 2

[9,10]. The thermal conductivity of samples with

different amounts of Na [2] and NaOH [7,8] are shown

in group 3 and group 4, respectively. Data for rock salts which were melted, treated with CI2, and recrystallized are also shown, group 5 [7]. Finally, data for rock salts with unknown impurities are represented by group 6

[5,11].

It should be noted that at temperatures below 100 K,

the thermal conductivity of rock salt is inversely

proportional to the quantity of the added impurity.

However, at temperatures higher than 100 K, the

thermal conductivity seems to be insensitive to the

impurity content.

209
10^

> 10

'e

>-Io

3O

z

o

o

Hi 10 ' X

I10-2

)6'

TYPICAL

RECOMMENDED

SYMBOL REF.

7

7

7

8

8

8

GROUP

GROUP 3 O

9

9

9

10

2

2

GROUP 6

B

B<

e

e

>

(DmO

9

A

7

7

II

5

5

V 2

1 M.P. 1074 K1 II 1 1 1 1 Mill

10rl

I 10 10'

TEMPERATURE, K

Figure 4.1. Thermal Conductivity of Rock Salt.

10- 10"

210
TABLE 4.1. RECOMMENDED VALUES OF THE THERMAL CONDUCTIVITY OF ROCK SALT*

[Temperature, T,K; Thermal Conductivity, k, Wm~'K~']

T k T k

0.4 0.95 25 191

0.5 1.78 30 130

0.6 3.13 40 75.0

0.7 4.97 50 54.0

0.8 7.40 75 34.9

0.9 10.0 100 24.3

1 14.0 150 15.0

2 99.3 200 10.9

3 270 250 8.24

4 443 293 6.65

5 595 300 6.57

6 735 400 4.80

7 820 500 3.67

8 880 600 2.98

9 870 700 2.47

10 836 800 2.08

15 502 900 1.85

20 306 1000 1.67

*Those below 100 K are typical values.

There are a number of additional references where the

thermal conductivity of rock salt, either pure or impure,

is reported [12-15, 17-43, 45, 136-140, 148-152].

4.4. Thermal Diffusivity

There are very few experimental data available for the

thermal diffusivity of rock salt. Consequently, the

thermal diffusivity values are derived from the recom- mended values of the thermal conductivity, the specific

heat, and the density computed from the recommended

thermal expansion values.

The equation used to calculate the thermal diffusivity can be expressed as

where a is the thermal diffusivity, k is the thermal

conductivity, Cp is the specific heat at constant pressure,

and p is the density. The density at temperature Tcan be

calculated from the equation [44]

(4.20)

where Po ( = 2.16 g/cm^) is the density of rock salt at room temperature (293 K), and AL = L-Lq, L and Lq

being the lengths at temperature T and at room

temperature, respectively.

The thermal diffusivity values so calculated are

plotted in figure 4.2 and tabulated in table 4.2. The

values in the temperature region above 100 K can be

considered with the uncertainty of +5%. Some experimental data for the thermal diffusivity of high-purity

rock salt [33,43] are also exhibited in the figure for

comparison. It can be seen that the recommended values

agree with the experimental data quite well. Other

references on the thermal diffusivity of rock salt are

[46,47].

4.5. Thermal Linear Expansion

The quantity reported here for the thermal linear

expansion of rock salt is the percent expansion, which is defined as AL/Lo{%), where AL - L-Lq, and L and Lq

are the lengths at temperature T and at room temperature (293 K), respectively. In figure 4.3 the recom- mended values of the thermal linear expansion and the

selected experimental data sets which were used to generate the recommended values are shown. These

recommended values are considered with the uncertainty of + 5% . The recommended values are also tabulated in

table 4.3, and can be represented approximately by the

following equations:

AL/Lo = -1.064 + 3.025 X

+ 1.471 X lO-^P - 8.559 X lO-^iP (4.21)

(293^ r<600 K)

AL/Lo = -1.161 + 4.030 X lO'^T (4.22) - 4.554 X 10-^ P + 1.285 X lO-^P (4.22)

(600^r<1074 K)

and

AL/Lo = -8.5462 + 0.012169 T (1074 K< 7) (4.23)

211
TABLE 4.2. RECOMMENDED VALUES OF THE THERMAL DIFFUSIVITY OF ROCK SALT*

[Temperature, T,K; Thermal Diffusivity, 10~''m^s~M

Solid Solid

T T ct

10 301 293 0.0353

15 136 300 0.0349

20 36.7 400 0.0249

25 15.9 500 0.0186

50 0.952 600 0.0149

75 0.356 700 0.0123

100 0.192 800 0.0103

150 0.0955 900 0.00915

200 0.0628 1000 0.00827

250 0.0459

*Those below 100 K are typical values.

Theoretical calculation of the thermal expansion of

rock salt in the temperature range 0-300 K was

conducted by White [69] using the Gruneisen relation;

his results agreed with the experimental data.

Strictly speaking, the concept of thermal linear

expansion does not apply to liquids and/or materials in

the molten state. However, for ease of presentation and

ease of comparison with room temperature dimensions,

the quantity AL/Lq, instead of the volumetric expansion, is presented also for the molten state. (For practical

purposes, the volumetric expansion, AV/Vo, can be

equated to 3 AL/Lq). These values are calculated from

volumetric thermal expansion data which were obtained

from density measurements.

The theoretical calculation of the thermal expansion

of molten rock salt was carried by Vilcu et al. [57,58] and

Lu [56] using Significant-Structure theory of liquid.

Their results agreed well with the experimental data.

Additional experimental data on the thermal linear

expansion are given in references [28,41,48-50,

61-82,100,141-147].

4.6. Effect of Nuclear Irradiation on

Thermophysical Properties

Experimental data on the thermophysical properties

of rock salt which has been irradiated are lacking. Only

three data sets on the thermal conductivity were

reported [10] , and no information on the thermal linear

expansion and the thermal diffusivity could be found in

the literature. Therefore, no recommended values for

these thermophysical properties are generated. However, the available thermal conductivity data are plotted

in figure 4.4 and tabulated in table 4.4. The recommended and typical curves for high-purity rock salt without nuclear irradiation (from section 4.2) are reproduced in figure 4.4 for comparison. All three sets are for specimens (Optovac sodium chloride) with ap- proximate OH"' concentration of 3 ppm and Tfirradiated, with 3.8 X lO'^F centers/cm^ (curve 1), 5.6

X10"F centers/cm3 (curve 2), and 7.6 X IQi^F cen- ters/cm^ (curve 3). It is seen from figure 4.4 that

irradiation drastically reduced the thermal conductivity

of rock salt at cryogenic temperatures. No data are

available at or above room temperature.

212

TABLE 4.3. RECOMMENDED VALUES OF THE THERMAL LINEAR EXPANSION OF ROCK SALT

[Temperature, T,K; Thermal Linear Expansion, AL/L5,%]

T AL/Lj T AL/L„

5 -0.772 600 1.371

10 -0.772 700 1.878

15 -0.772 800 2.430

20 -0.771 900 3.034

25 -0.771 1000 3.699

50 -0.759 1074 4.528

75 -0.722 1100 4.840

100 -0.666 1200 6.057 150 -0.521 1300 7.274 200 -0.352 1400 8.490

250 -0.168 1500 9.707

293 0.000 . 1600 10.924 400 0.448 1700 12.141 500 0.896 y 1750 12.750

214
TT

TYPICAL FOR UN-IRRADIATED

HIGH PURITY ROCK SALT CURVE SYMBOL REF.

1 c 10

2 n 10

3 A 10

RECOMMENDED FOR UN-IRRADIATED

HIGH PURITY ROCK SALT

M.R 1074 K -1

10

Figure 4.4.

10 10 10^

TEMPERATURE , K

Thermal Conductivity of Irradiated Rock Salt.

10"

215
TABLE 4.4. EXPERIMENTAL DATA ON THE THERMAL CONDUCTIVITY OF

ROCK SALT AFTER NUCLEAR IRRADIATION

[Temperature, T,K; Thermal Conductivity, k, Wm~^K~M

Curve 1 Curve 2 Curve 3 X lO'^F centers/ cm^) (5.6 X 10^^ F centers/cm^

)

(7.6 X lO'^F centers/c

T k T k T k

1.26 5 _ 19 1..33 2

.

43 1. 26 2.10

1.26* 5 _ 1,.47* 2

.

fil ox 1. 35* 2.70

1.35* f. 1,.53* •3 J . X1 J 1. 44* 3.17

1.35* 7/ . 18 1,.58* "Jo

.

oo 1. 63* 4.24

1.55* 9^ 1,.70 A 1

L

1. 84* 5.65

1.55 1 1 XJ. 1,.95* o . J -J 2. 05 7.02

1.75* 1 L no 2,.13* 7 o / 2. 40* 10.40

1.82* 1 c; X J . 9n 2,.41 1XVJn . 70 2. 57* 11.00

1.92* 18

.

An 2,.68* X J . 1xun 2. 91* 11.60

2.02* 20

.

sn 3,.04* 1 t; XJ • 7n 3. 41 14.70

2.09* ^ . 7n 3,.38* 1xofi . An 3. 41* 18.00

2.29 ^ o . An 3,.69* 9n Qn 3. 79* 16.70

2.41* nn 4,.18* 9 A ftn 4. 13* 16.40

2.73* 3D . An 4,.64 9 7 An 3..72* 20.70

2.73* 38

.

00 5,.16* J X . 7n 4. 28* 18.30

3.03* 44

.

70 5,.44* An 4. 51* 20.00

3.37* 48

.

90 6,.05* 40. 90 5. 01* 23.10

3.56 55

.

50 6,.73* 46

.

40 5..57 26.20

3.95* 64

.

20 7,.35 51

.

70 6..08* 30.90

4.24* 72. 80 7.. 75* 57

.

60 6..87* 37.00

4.55* 78

.

30 8,.47* 62

.

00 7..77* 45.10

5.06* 50 8,.77* 66

.

60 8..94 54.00

5.53* 103

.

00 9 .09* 71

.

60 9..76* 63.60

6.15* 115

.

00 9 .75* 77

.

00 11..60* 81.90

6.84 X J\J . nn 11 .00 Tn 12..90* 92.90

7.74* XHO 1 LP, . nn 12 .50* 1XUn'^J . nn 14..40 105.00

8.02* 165

.

00 13 .90* 115

.

. 00 15.,90* 113.00

9.07* xou 1 fin

.

nn 15 .40* 1X 9fi ^ o . nn 17,.70* 115.00

9.57* 204

.

00 17 .20 133

.

00 19..30 118.00

10.40 220

.

00 18 .40 133

.

00 21.,50* 111.00

11.60* 9 A

1

14 X . nn 20 .10* 1 Tn nn 25.,60 96.40

12.90 254.,00 21 .60* 128..00 27.,50* 91.40

14.60 254..00 23 .20 119..00 32.,80 68.50

20.10 212..00 31 .40* 87..60 26.30* 151..00 33 .10 77..20 36.80 77..20 48 .90* 46..50 43.20* 56..80 63 .80 36..80 56.40* 37. 50

61.60 31..90

*Not plotted in the figure.

216
4.7. References

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and KCl as Standard Materials in the Measurement of Thermal Conductivity in the Temperature Range 80-460

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841]

[2] Klein, M.V. and Caldwell, R.F., "Low Temperature System for Thermal Conductivity Measurements," Rev. Sci. Instrum., 37(10), 1291-7 (1966).

[.3] Lemanov, V.V. and Smirnov, I. A., "Thermal Conductivity of NaCl Single Crystals Containing Ca Impurities," Fiz. Tverd.

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[4] Singh, D.P. and Verma, G.S., "Variational Calculation of the Three-Phonon Umklapp Resistivity," Phys. Status Solidi, B59(l), 291-6 (1973).

[5] Schwartz, J.W., "Phonon Resonances in Some Alkali Halides Doped with Divalent Ions," Northwestern University, Ph.D.

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[6] Worlock, J.M., "Thermal Conductivity and Phonon Scattering

in Alkali Halide Crystals Containing Colloidal Particles," Cornell University, Ph.D. Thesis, 163 pp. (1963). [Univ.

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[7] Klein, M.V., "Phonon Scattering in Sodium Chloride Containing Oxygen," Phys. Rev., 122(5), 1393-402 (1961).

[8] Rosenbaum, R.L., Chau, C.K., and Klein, M.V., "Thermal

Conductivity of Alkali Halide Crystals Containing the Hydroxide Ion," Phys. Rev., 186(3), 852-64 (1969).

[9] Taylor, A., Albers, H.R., and Pohl, R.O., "Effect of Plastic Deformation on the Thermal Conductivity of Various Ionic

Crystals," J. Appl. Phys., 36(7) 2270-8 (1965).

[10] Aldrich, R.E., Burke, W.J., and McCarthy, K.A., "Resonant Phonon Scattering in Colored Sodium Chloride Crystals," Solid State Commun., 5(11), 899-903 (1967).

[ 1 1] Shvidkovskii, E.G. and Zakharov, V.M., "Thermal Conductivity

of Sodium Chloride at Helium Temperatures," Sov. Phys.-

Dokl., 12(4), 335-6 (1967).

[12] Eucken, A., "Uber die Temperaturabhangigkeit der Warmeleitfahigkeit fester Nichlmetalle," Ann. Physik, 34(2), 185-221

(1911).

[13] McCarthy, K.A. and Ballard, S.S., "Thermal Conductivity of Eight Halide Crystals in the Temperature Range 220 to 390

°K," J. Appl. Phys., 31(8), 1410-2 (1960).

[14] Birch, F. and Clark, H., "The Thermal Conductivity of Rocks

and Its Dependence Upon Temperature and Composition,"

Am. J. Sci.. 238, 529-58 (1940).

[15] Barclay, J. A., Rosemblum, S.S., and Steyert, W.A., "Low

Temperature Thermal Conductivity of Some Composite

Materials," Cryogenics, 16(9), 539-43 (1976).

[16] Petrov., A.V., Tsypkina, N.S., and Logachav,Yu. A., "Temperature Dependence of Thermal Conductivity in Alkali Halide

Salts at Elevated Temperatures," Sov. Phys. -Solid State, 16(1), 39-42 (1974).

[17] Stephens, D.R., "High Temperature Thermal Conductivity of Six Rocks," USAEC Repi. UCRL-7605, 19 pp. (1963).

[N64- 1.5.399]

(18] Fedorov, V.I. and Machuev, V.I., "Thermal Conductivity of Fused Salts," High Temp., 8(4), 858-60 (1970).

[19] Singh, D.P. and Verma, G.S., "Role of Longitudinal and

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(1973)

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Behavior of Lattice Thermal Conductivity of Crystals at High

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[.30[ Wilson, H.W., Beahm, K.W., and Cooper, W.J., "Determination and Analysis of the Potentialties of Thermal Energy

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217
[42] Smith, N.O., "The Difference Between and Cj, for Liquids

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220
Symbols and Units Conversion Factors

Symbol Name Unit

A Cross-sectional area of the specimen m*' A

Aj. Cross-sectional area of the reference sample m'^

Co,Cl Calibration constants dimension!ess Cp Specific heat at constant pressure J Kg IS. J€L Separation of the lattice planes

(eq 4.

1

m

dp Diameter of the pth fringe m

f Focal length of the lens m

h,k,l Miller indices dimensionless

k Thermal conductivity WT —1 1/"—! W m ^ I

Kj. Xllcllllai CUIlUUCHVlly Ul lllc lcit;iClH.-C sample w III rv

Li Length at temperature T m

J Length of the specimen m

r Length of the reference sample m

Lo Length at room temperature (293 K) m

A T AT - T T m

/\J /I „ Thermal linear expansion /o

I 1 pnfftri of trip rpntral ripatpr m

A/ /V Order of interference dimensionless

A/ AI A/ 'Vl,/V2,/V3 Fringe integers dimensionless A A/ Number of fringes that pass a fiducial mark dimensionless

n Refractive index dimensionless

A « L-nange ot retractive index dimensionless

p Pressure atm (use Pa) Rate of heat flow watt

''l,''2 ixaaii m

1 i^mnprQ 1 1 1 fp

1 1,1 2 Temperatures \r A T Zii - i 2 - i 1

1/y Volume at temperature T m^

Volume at room temperature (293 K) m^

AK AF = F - Fo m^

AF/Fo Thermal volumetric expansion %

Ax Distance difference m

Greek

symbols

1 nermal uiiiusivity m s u Angle degree K Wavelength m

X"V \X/ VV aVclCllciliX a VP 1 pn or t ri ni lirrril in \7Qr'iiiim KJi ll^lll 111 VclL-LILilll m

I' The fractional part in Fabry-Perot

interferometer dimensionless

Fringe integers dimensionless

p Density kg m"^

Density at room temperature (293 K) kg m^^

Thermal conductivity

To convert from to Multiply by

W m-i K-i BtuiT h-> ft"! F-' 0.5777908

W m-i K-i caliT s"' cm"! C-i 2.38846 X lO"'

Thermal diffusivity

To convert from to Multiply by

m2 S-' cm2 s-i 10" m2 S-' ft2 s-i 10.7639 m2 S-' m2 h-i 3600

221
^
Chapter 5

Optical Properties

H. H. Li*

Contents

Page

5.1. Introduction 224

5.2. Measurement Methods for Optical Properties 224

5.3. Refractive Index and Absorption Coefficient 226

5.4. Effect of Nuclear Irradiation on the Optical Properties 232

5.5. References 238

Symbols and Units 240

Conversion Factors 240

* Center for Information and Numerical Data Analysis and Synthesis, Purdue University, 2595 Yeager Road, West Lafayette, Indiana 47906

223
5.1. Introduction

Optical properties of a material are of fundamental

importance to the description of interactions between

electromagnetic radiation and the material. They relate

both the absorptive and dispersive characteristics of the

material and have a wide range of applications in science

and technology. In this chapter, the available information on the refractive index and absorption coefficient of

rock salt are reviewed and discussed. For the refractive

index, the available data are adequate for data evaluation

and the generation of recommended values. In the case of the absorption coefficient, the situation is different in

that this property is influenced by a number of factors,

notably the thermal history of the crystal, the irradiation

history, the impurity contents, the physical environment, etc. As a consequence, no recommended values

could be generated. Only qualitative discussions and a few typical graphical presentations are given.

5.2. Measurement Methods for Optical

Properties

The response of a nonmagnetic solid with isotropic or cubic symmetry to incident electromagnetic radiation can be generally described in terms of two optical

constants, which are related to each other through

dispersion relations.

These two optical constants can consist of either (1)

the refractive index, n, and the extinction coefficient. A:, or (2) and €3 which are, respectively, the real and

imaginary part of the complex dielectric constant e. These two pairs of constants are related as follows:

2in{X)k{k)

[nHX) -kHk)] +

(5.1)

In the transparent wavelength region where the

absorption can be neglected, the refractive index of the

material can be directly determined in a number of

ways. The basic principle of such measurements is rather simple. It makes use of the dispersive nature of

the material and the wavefront reconstruction of the

electromagnetic radiation after the radiation has passed

through the dispersive medium. Depending on the

shape of the dispersive element and the environmental

medium surrounding it the reconstructed wavefront is detected through angular displacement, interference

order advanced, distant moved or the refractive index of

embedding medium changed. The following table

summarizes these methods.

Shape of

Crystal

Quantity to be

Observed

Prism Deviation angle

Plane parallel Interference order

plate

Scratch on

plate

Lens

Irregular

Apparent depth

Focal length

Refractive index

of embedding

medium

Principle

Snell's Law

Interference

order depends on thickness

Optical path

increase in

the plate

Lens maker

formula

Contrast

disappears

when crystal

and medium

have same

refractive index

In general, refractive index obtained by prism method

is reported to the fifth or sixth decimal place, interfer- ence method gives three to four decimal places, the other

methods yield no more than three decimal places. For a comprehensive and concise review of these methods, the

reader is referred to the text in refs. [74 and 75]

.

For a crystal of sufficient thickness so that the

reflection from the rear surface can be neglected, the

absorption coefficient can be determined by using a simple exponential law:

-ad. (5.2)

where and Toe are, respectively, the reflectivity and

transmission at normal incidence, a the absorption

coefficient, and d the thickness of the sample. However,

the sample to be measured is not always thick and the

reflection from the rear surface is not always negligible.

The observed reflectance and transmission of a trans- parent plate is the resultant of multiple reflections

and transmission at the boundary surfaces. In terms of

Too and Rx, the observed transmission and reflectivity of

a plate sample (not a thin film) can be expressed as:

[(l-/?J2 + 4/?^ sin^^]e-«''

T= ;—

rz; (5.3)

1 Rle-^'^d

and

R = R {1- e'"')

1- Rle-

(5.

224
where

"A

k

R

n'

n

-1 tan

2k

n^ + k^ - I

'

47r '

{n-n'y+k^

refractive index of surrounding medium,

1 for air or vacuum.

In the differential technique, a dual-beam spectrometer is used to compare the transmissions of a thick sample

{Ts and d^) and a reference sample (T^ and d^). An

optical wedge is added to the reference beam and its transverse position is so adjusted as to balance the

transmitted intensity of the sample beam. The transmission of the wedge, T^, is then measured. The relation of

the three measured transmissions is therefore

hence, by using eq (5.3)

(5.6)

It appears that if we know /?a> and either n or k, the

remaining one can be calculated by this relation. But this

is only limited to the transparent region where direct

measurement of n can be made. It is obvious that the key

parameters T and R are usually difficult to measure

accurately, because of influencing surface conditions,

such as flatness, aging, oxide layers, absorbed gas, etc. However, this method is self contained at a given

wavelength.

Precise determination for small absorption coefficients, in the order of lO"^ or lower, was considered

impossible until the laser source becanie available. As the

bulk absorption becomes smaller than surface losses

measuring the former requires amplification of the

absorption effect, which, in turn, requires high-level

energy input to the sample. The two commonly used

methods are the laser calorimeter [76] and the

differential technique [77].

In the laser calorimeter, the absorbed energy is measured in the form of heat. It can be shown that the

bulk and surface loss, i.e., the total absorption, is related to the absorbed energy, Ea, by

aL + 2o =

(5.5)

provided aL <C 1, where L is the sample length through

which a laser beam passes, and o the surface loss. £3 can

be calculated using the specific heat, the mass of the

sample and the measured temperature rise. The

transmitted energy can be determined using a black body

and the temperature rise. In order to separate the bulk

and surface absorptions, the total absorption of a series

of samples of different thickness, cut from the same piece

of material and polished in the same way must be

measured. A plot of total absorption versus sample

thickness will give a straight line with slope a and

intercept 2a. Although this method yields very accurate

results and is used to measure absorptions as low as 10"^

cm"^, it covers only a limited wavelength range. For a wider wavelength range measurement, the differential

technique is used.

T„=t'»^<^ (-L_«-? L]

(5 7)

where Ac? = d^ -d, , and

The accuracy of the method depends strongly on the

accuracy of the values for refractive index and

transmission. While the former can be determined with

high accuracy, the accuracy of the latter parameter

depends on the instrument utilized. A +1% uncertainty is generally expected. This imposes a limit,

the order of 1 X 10"^ cm"^ to the lowest value for

absorption coefficient to be measured.

Beyond the transparent region in the high absorption

region where neither n and k is accessible, one has to rely on the reflection spectrum from which the optical

constants can be derived by the Kramers-Kronig analysis

[78] or by the multiple-oscillator fit based on the

Lorentz theory [79]

.

The Kramers-Kronig relations are derived from the

dispersion relation in that the phase angle 0(a>) of the

complex reflectivity R{(o) is determined based on the

observed reflection spectrum:

"R(aj) =/?(w)ei^('"), (5.9)

where w is the frequency of radiation and P is the

principal value of the Cauchy integral. Based on the

amplitude, R{(o), and phase angle of the reflectivity, the

refractive index and absorption index can be calculated

according to the following

. ^ 1 - R(aj)

"^""^ "

l + /?(to) - 2v^)cos0(a>) (5-^^)

and

225
(5.12)

In principle, the calculation of 6 requires a complete

reflection spectrum with frequency ranging from zero to

infinity. In practice, R is measured only for a limited

spectral range. In order to use eq (5. 10) , extrapolation of

R{(o) beyond the measured range must be made based on

certain approximations. Consequently, errors are introduced in 6 and hence in n and k. It is clear that the

accuracies of optical constants derived from the

reflection spectra depend strongly on the accurate

determination of reflectivity. Unfortunately, measure- ments on the latter are inherently inaccurate because of

experimental difficulties. Typical errors reported for

reflectivity observations are one to ten percent. This

will reflect an error of about one to ten percent in the

calculated optical constants depending on the stability

of the light source and the quality of reference mirror

used.

In the Lorentz theory, the refractive index and

absorption index are related to the oscillator frequencies,

ftj •, the oscillator strengths, s •, and the damping factors,

'II' ii\ T^', by the expressions:

2nk - S

SjTj (co/ftjj)

[1 - (a;/w;)|2]2 + 7^2 ((o/(o.y

(5.13)

(5.14)

where 6;^ is the optical dielectric constant. The resulting n and k have to satisfy the observed reflectivity by the

relation

R{<v) n {a)) - 1 + ik(co)

n{aj) + I + ik{oj) (5.15)

It is clear that this approach requires knowledge of the

oscillator frequencies which in general is not complete.

This leaves no choice but to use only the observed

predominant ones. Nevertheless, this method, similar to the Kramers-Kronig analysis, yields good approximations to the properties under consideration.

5.3. Refractive Index and Absorption

Coefficient

Pure rock salt is uniformly transparent from 0.2 /xm in

the ultraviolet to 12 /um in the infrared. In the region of

15 /xm the absorption increases rapidly. Rock salt in

i

moderately thin pieces may be expected to transmit

several percent of the light up to wavelengths as long as 26.0 jum. However, a plate 1 cm in thickness is completely opaque to radiation of wavelengths greater

than 20 /xm. A

Rock salt has long been a favorite material for infrared

spectroscopy. It polishes easily and, although hygroscopic, can be protected by evaporated plastic coatings. It shows excellent dispersion over its entire transmission

range. It has been difficult, however, to obtain natural

rock salt crystals of sufficient size and purity for making

optical components. As crystal-growing techniques

advanced, synthetic sodium chloride crystals have been

grown up to 11.3 kg in weight commercially, making this

material readily available for large optical parts and

stimulating the design and construction of infrared

instruments.

Measurement of the refractive index of sodium

chloride dates back to 1871, when Stefan [1] determined

the refractive indices of a rock salt prism for solar lines B

,

D, and F. Since then, a large amount of data in the

transparent region have been contributed by a number

of investigators, among which are Martens [2] , Paschen

[3] , and Langley [4,5] . They used either the deviation

method or interferometry in their experiments. It was

not until 1929 that measurements were carried out

beyond the transparent region in the infrared. Kellner

[6] determined refractive indices of NaCl in the 23-35

fXm region, based on information on transmission and

reflection of thin specimens. In the vacuum ultraviolet

region, Rossler and Walker [7] observed the region

from 0.0476 to 0.2480 /xm, and Miyata and Tomiki [8,9]

studied from 0.10 to 0.25 /xm. Additional measurements on the refractive index were reported in ref. [10-37].

Data on the refractive index are now available from

0.0476 /xm up to 300 /xm and at 2000 ixm.

A collective plot of the available data is shown in figure

5.1., where the reference number for the data source is designated by the number in a circle. In the interest of

visual clarity not all the available data are plotted in the

figure. Furthermore, most of the UV and IR data were

determined from the analysis of the reflection spectra. It was found that refractive index data in the transparent

regions for colorless natural rock salt are in close

agreement with those for synthetic crystal with

discrepancies occurring at the fourth decimal place.

Beyond the transparent regions, in the vacuum

ultraviolet and infrared regions, investigations were

mainly concerned with the characteristic absorptions.

Predominant absorption peaks in the ultraviolet region were measured by Hilsch and Pohl [38] , Schneider and

O'Bryan [39] and by Ramachandran [40] . Fundamental

infrared absorption peaks were reported by Lowndes and

Martin [36] , and Karheuser [41] . Observation of the

226
227
refractive index carried out in the millimeter wavelength

region was used to determine the static dielectric

constant of the material. Dianov and Irisova [33]

determined the refractive index at a wavelength of 2

millimeters. The static dielectric constant, using the

relation = re^, is in close agreement with that obtained

by other methods. The selected absorption peak values

taken from these works are given below:

Ultraviolet absorption peaks occur at:

0.050 Aim,

0.100 Aim,

0.128 yum,

0.158 /xm

Infrared absorption peaks occur at:

40.50 Mm (LO mode),

60.98 Mm (TO mode),

120.34 Mm,

And the dielectric constants are:

high frequency dielectric constant €^ = 2.33,

static dielectric constant = 5.99.

The temperature coefficient dn/dT is available over a

large part of the transparent region of NaCl. Notable are those measured by Micheli [42] (from 0.202 to 0.643

Mm), Liebreich [43,44] (from 0.656 to 8.85 Mm), and

Kolosovskii and Ustimenko [45] (for 10.6 Mm). These

data are plotted in figure 5.2. Li [46] , in 1976, reduced the then available experimental data on the refractive index and dn/dT to a common temperature of 293 K and after careful critical evaluation and analysis adopted a formula, eq (5.16), for

the calculation of dn/dTiox the temperature range 293 + 50 K

Recommended values calculated from eqs 5.16 and

5.17 are shown in figures 5.2 and 5.3 and are tabulated

in table 5.1. It should be noted that values tabulated in

table 5.1 are for a pure crystal. Unfortunately, there are no systematic measurements on the refractive index of

impure and defective crystal of NaCl reported. However,

the refractive indices of an impure crystal are likely to be

higher than the values in table 5.1. Investigations of the absorption coefficient are generally classified into three broad wavelength

regions: the ultraviolet, the infrared, and the transparent region. In the ultraviolet region, the investigations are concerned with the exciton states in the crystal and

the determination of the Urbach-rule parameters.

Roessler and Walker [7] determined the absorption

index of NaCl in the spectral range from 0.047 to 0.248

Mm by a Kramers-Kronig analysis of the reflectance

spectrum. The surfaces of the specimen examined were

near perfect as evidenced by the strong temperature

dependence of reflectance in the exciton region and the

appearance of spin-orbit split doublets. Kobayashi and

Tomiki [47] studied the effects of impurities on the

absorption coefficient and found significant differences

between crystals in the spectral range from 0.171 to 0.231 Mm. The main sources of such discrepancies were

the presence of hydroxyl ions and dislocations in the

crystals. The inclusion of the OH" is also reflected by

the presence of an absorption band at 2.8 Mm in the near infrared region. Miyata and Tomiki [8,9] and

Tomiki, Miyata and Tsukamoto [48] studied the

absorption of NaCl in the region of 0.156 to 0.205 nm

for the purpose of determining the Urbach-rule

parameters and finding the features characteristic of the

intrinsic tail. Systematic observation and analysis gave

the empirical relations of the parameters:

dn 6.118 X*

2a =-11.91(n^-l)- 0.50+ 0.02496)^

+

199.36

(A2 _ 3718.56)2' (5.16)

where dn/dT is in units of 10"^ K"i and A. is in niu.

Similarly a Sellmeier type dispersion equation, (eq

5.17), was used to evaluate refractive index at 293 K in

the wavelength region 0.20-30.0 wm:

+

2 = 1.00055 +

0.38696 W

\2 - (0.128)2 + \2 _ (0.158)2 ^ \2 _ (40.50)2

3.17064 A2 0.30038 A2

+ A2 - (60.98)2 + A2 - (120.34)2 ' (5.17)

where A is in units of Mm.

0.19800 A2

A2 - (0.050)2

0.25998 A2

+

+

0.48398 A2

A2 - (0.100)2

0.08796 A2

£0 = 8.025 eV

^0 = 1.2 X lO'o cm-i

hoj = 0.0095 eV

aso = 0.741

and led to the expression of the absorption coefficient

for the intrinsic tail as:

A(E,T) = Aoexp [ -a^ (T) (Eo-E)/kT] (5.18)

2 kT hcj

where (T) = Og^ tank'2 kTMeasurements of an absorption coefficient for the

infrared region were made for the purpose of studying

the optically active lattice vibrations. On the short

wavelength side of the reststrahlen band, multiphonon

228
I

in•o

IC

T3

6.0

4.0

2.0

0.0

-2.0

-4.0

1 \ \

1 I I I I

-6.0

REF.

PROVISIONAL1 I TTT

MEAN —

TEMP.(K)

325

293

232

332

335

332

270 _

300

RECOMMENDED

I I I I I J II I I I I 0.1 I 10 WAVELENGTH, X,/im

Figure 5.2. Temperature Coefficient of Refractive Index of Rock Salt

100

229
1.90

1.80

1.70

1.60 X

UJo

- 1.50

liJ >

< 1.40

UJ

1.30

1.20

I.IO

10 -I

7

\

\

TTT

I ' r I—

\^

/-PROVISIONAL

345681 2 34568 10 WAVELENGTH , X ,/i.m

Figure 5.3. Recoiranended Refractive Index of Rock Salt

3 4

230
Table 5.1. Recommended Values on the Refractive Index and Its Temperature

Derivative for Pure Rock Salt at 293 K*

Aymdn/dT

10 ^ K

' Xym

dn/dT

10 ^ K

0.200 1 .789 4.6 3.500 1..5230 -3.3

0.204 1 .770 3.4 4.000 1,.5217 -3.3

0.208 1 .754 2.5 4.500 1,.5203 -3.2

0.212 1 .739 1.8 5.000 1..5188 -3.2

0.216 1 .726 1.2 6.000 1,.5153 -3.2

0.220 1 .714 0.7 7.000 1,,5112 -3.1

0.224 1 .704 0.3 8.000 1.,5064 -3.1

0.228 1 .694 -0.0 9.000 1.,5009 -3.0

0.232 1,.686 -0.3 10.000 1.,4947 -2.9

0.236 1,.678 -0.6 10.200 1.,4934 -2.9

0.240 1,.671 -0.8 10.400 1,,4920 -2.9

0.244 1..664 -1.0 10.600 1.,4906 -2.9

0.248 1,.658 -1.2 10.800 1.,4892 -2.9

0.252 1,.6525 -1.3 11.000 1.,4877 -2.8

0.258 1..6447 -1.5 11.200 1,,4862 -2.8

0.264 1.,6376 -1.7 12.000 1,.4800 -2.7

0.270 1.,6312 -1.8 13.000 1,,4713 -2.6

0.276 1,,6254 -2.0 14.000 1.,4618 -2.5

0.282 1.,6201 -2.1 15.000 1..451 -2.3

0.290 1,,6137 -2.2 16.000 1..439 -2.1

0.300 1,.6066 -2.3 17.000 1..427 -1.8

0.320 1.,5950 -2.5 18.000 1..413 -1.5

0.340 1..5859 -2.7 19.000 1,.398 -1.2

0.360 1..5785 -2.8 20.000 1..382 -0.8

0.380 1..5724 -2.8 22.000 1..344 0.1

0.400 1..5674 -2.9 23.000 1..323 0.8

0.450 1..5580 -3.0 24.000 1.,299 1.5

0.500 1,.5515 -3.1 25.000 1..273 2.5

0.550 1..5469 -3.1 26.000 1..24 3.5

0.600 1..5434 -3.2 27.000 1..21 4.9

0.700 1,.5386 -3.2 28.000 1..17 6.4

0.800 1..5356 -3.2 29.000 1..13 8.4

0.900 1..5335 -3.2 30.000 1..09 10.8

1.000 1..5320 -3.3

1.250 1..5296 -3.3

1.500 1..5282 -3.3

1.750 1,.5272 -3.3

2.000 1..5265 -3.3

2.500 1..5253 -3.3

3.000 1..5241 -3.3

* Estimated uncertainties for n; ±0.006 in region 0.20-0.25 ym; ±0.0005 in 0.25-

0.35 ym; ±0.0001 in 0.35-10.0 ym; ±0.003 in 10.0-15.0 ym; ±0.006 in 15.0-25_.0 ym;

±0.02 in 25.0-30.0 ym. Estimated uncertainties for dn/dT in units of 10 ±0.8 in 0.20-0.24 ym; ±0.2 in 0.24-4.0 ym; ±0.4 in 4.0-15.0 ym; ±0.6 in 15.0-

20.0 ym; ±0.9 in 20.0-30.0 ym.

absorption, in which a photon is absorbed and two or more phonons are generated, can occur and lead to absorption coefficients that range from 10 * cm ' to 100

cm-', depending on the number of phonons generated.

Recent measurements [49] on NaCl have shown that the

absorption coefficient can be represented in the muhiphonon absorption region by the expression:

A = Ao exp i-u/uo) (5.19)

where Vq - 56.0 cm"', and Aq - 24273 cm '.

It is not known if the two exponential relations (eqs

5.18 and 5.19) hold for the visible and near infrared

regions. If they do, the absorption in the transparent

region will be negligible. In a real situation, however,

there are always traces of residual impurities and

imperfections in the available crystal, consequently the

absorption is noticeable though it is negligibly low as a

rule.

Absorption data in the transparent region are very

scanty. The reason is that absorption in this region is very low and its effects are thus unnoticeable in most

applications. However, at high energy levels many

unfavorable effects due to absorption take place.

Unfortunately, investigations of absorption coefficient

at the high energy level were made only at a few wavelengths of interest to laser applications. Harrington and

Hass [50] studied the temperature dependence of
multiphonon absorption at wavelength 10.6 /xm from room temperature to near the mehing point by a calorimetric method. His results are higher than those in

the intrinsic tail. Deutsch [49] using a differential

technique with a dual beam spectrometer measured an

absorption coefficient for the wavelength region from

11.7 to 20 ^m at room temperature. The predicted value

at wavelength 10.6 /im obtained by fitting the measured

values is 1.1 X 10"^ cm"i which agrees well with the

measured value of 1.3 X 10"^ cm~^ reported by Horrigan

and Rudko [51]. This value was believed to conform to the values in the intrinsic tail. No noticeable improvement in the values could be obtained by improvements

in purity and growth techniques. Califano and Czerny

[52] examined the region, 11-14 fxm, at room

temperature. Barker [53] measured the region, 11-20

)um, at temperature from 300 K up to 1105 K, 31

degrees beyond the melting temperature of NaCl. Their

room temperature values agreed with those predicted by

eq (5.4).

Owens [54] measured the room temperature absorption index at three wavelengths, 2.50, 8.02, and 32.3

/um. By combining his measurement with others

reported in the literature [11,12,14,55,56] in the

wavelength range from 10 to 10'' /xm, he found a constant background loss corresponding to a residual

value in absorption coefficient of 1 X 10-*. The origin of

this loss, which appeared to be independent of

temperature is unknown. It is most probably due to imperfections in the crystals. A summary of the

knowledge to date on the absorption index of rock salt is shown in figure 5.4. Based on the above review of available data, the most

probable values of intrinsic bulk absorption coefficients

of a pure NaCl crystal at 293 K are derived as follows:

Wavelength range Absorption coefficient, cm"^

0.165 - 0.173 Mm

0.25 - 9.00 Mm

9.0 - 30 Mm

Use eq (5.3)

Usually negligibly small

Use eq (5.4)

Values derived and recommended in this way are also

given in table 5.2. It should be noted that recommended

values in table 5.2 are for a pure crystal. Crystals with

impurities, other defects, and unfavorable surface

conditions yield absorption coefficients in the transparent region which are expected to be noticeable. At the

absorption center wavelengths, such absorption coefficients become extraordinarily large and unpredictable,

depending upon the amount of foreign substances and

the extent of defects.

While rock salt in the form of a pure chemical

compound is clear and colorless, rock salts with

impurities and defects reveal a variety of colors; gray to

black, red, brown, yellow, green, blue, and violet. In

table 5.3, a few typical natural colored rock salts are displayed together with the corresponding causes [57]

.

Most of the colors are caused by impurities, while some

of the yellow, blue and violet colors owe their origin to radiation. Effects of radiation on the optical properties

of rock salt will be discussed in a later section.

5.4. Effect of Nuclear Irradiation on the

Optical Properties

Nuclear radiations either corpuscalar or electromagnetic are known to alter the properties of materials. The

results of the interaction of energetic radiation with

matter are to create microscopically many types of

defects which lead to the observable changes of

macroscopic properties. These involve such stable

primary defects as vacancies, interstitials and dislocations which may be detected optically in a variety of

colored absorption bands. These bands are located

primarily in the visible region and therefore are easily

recognized by the induced color. Generally the effect of

nuclear radiation on the optical properties of rock salt is the coloration produced in the crystal. The strongest

absorption band occurs at 0.465 fxm where the crystal

turns yellow after being irradiated.

Color centers can be generated in a crystal in a variety

of ways. The most important ones are: (1) exposure to ionizing radiation, (2) addition of impurities to produce

coloration, and (3) imposition of electrolytic action to produce coloration. All of these processes occur in nature. However, the first process is primarily

concerned with the effect of nuclear radiation on the

properties. The term, ionizing radiation, includes all sources that can generate free electrons and holes in the

crystal. The energies range from photons of a few eV,

through x-rays and 7 -rays up to high energy protons of

400 MeV. However, so far as the effect on the optical

properties is concerned, studies showed that radiations

of high energies produce similar results as those by lowenergy radiations. They both cause color centers of the same nature. The problem of "the effects of nuclear

irradiation on the optical properties of rock salt" is therefore reduced to the studies of the F-center and F- aggregate centers of rock salt. Detailed discussion of the

subject of color centers is beyond the scope of the

present work. For a comprehensive and concise review

of the color centers, the interested readers are referred

to the excellent articles by Seitz [60], Compton and

Robin [61] , Schulman and Compton [62] , and Crawford

and Slifkin [63] . Only a few typical examples pertinent

to rock salt will be presented.

Irradiation with any type of ionizing radiation

including ultraviolet light will produce an F-center

232
233
Table 5.2. Calculated Values on the Intrinsic Absorption

Coefficient for Pure Rock Salt at 293 K

A, ym a, cm '

0.165 4525

0.166 1217

0.167 332

0.168 92 0.169 26 0.170 7.4 0.171 2.2 0.172 0.63

0.173 0.19

5.3 6 X 10 ^° 10.6 1.1 X 10

TABLE 5.3. COLOR AND CAUSE OF NATURAL ROCK SALT

Color Family

Black

Grey

Red

Yellow

Brown

Green

Blue

Violet

Cause

38.64% NaCl

55.35% insoluble matter

Clay inclusions in either large

aggregates or microscopical particles

Iron compounds

Due to radiation or iron compounds

Bituminous inclusions often arranged

in regular layers

Copper

Due to radiation

Due to radiation

together with a number of other centers, mostly the F- aggregate centers. Figure 5.5 shows a typical absorption

spectrum of an irradiated NaCl crystal in the wavelength region from 0.2 to 1.2 fxin where absorption is otherwise negligibly low. The absorption peaks at 0.210,

0.465, 0.545, 0.595, 0.720, and 0.823 are, respectively,

identified as V3, F, Rj, R2, M, and N centers. The above centers are usually created at a low level of

irradiation. At a high level of irradiation, a strong

absorption band appears at 0.57 /zm corresponding to the

absorption of colloidal sodium particles. The appearance

of this adsorption band is generally accompanied by the

diminution of F-absorption. The radiation-induced

formation of colloidal sodium particles can amount to 0.001 to 0.1 atomic weight percent range. In one case of

study [69], it was noted that the hydroxyl ions in the

crystal may play some role in the formation of colloidal

particles.

F-center production is the result of the capture of an

electron by a negative ion vacancy. The F-absorption at 0.465 jum corresponds to an electron transition from the

ground state to ap excited state. The half-width of the F- absorption is temperature dependent, it is smallest at low

temperatures and the peak of the band shifts toward

shorter wavelengths with decreasing temperature. The

M-center is the simplest among the F-aggregate centers.

It consists of two adjacent F-centers with its main axis

oriented in the <110> plane. Because of anisotropic

distribution of the axis of the center, the M-absorption

shows dichroism. An R-center consists of three adjacent

F-centers occupying an equilateral triangular array in a <111> plane of the NaCl structure. The N-center

consists of four neighboring F-centers occupying a parallelogram array or a tetrahedral array. The V-center

is due to the halogen molecular ion occupying two

adjacent negative ion vacancies.

Kobayashi [64,65] studied the relationship between

the behavior of the color centers and the density change

during thermal annealing for sodium chloride crystals^

irradiated with 350 MeV protons with a total flux of Ix^

10^^ protons/cm^. Figure 5.6 shows the changes of

concentration of color centers and the change ofj

density, A n, of the crystal as a function of annealing

temperature. It can be noted that, while below 475

the density of the irradiated crystal remains constants

significant changes in the intensity of respective

234
UJ

_l

<

o

>-<

CD

o:<

LdO

Q.

ITO

V)

CQ

<

0.2 0.6 0.8

WAVELENGTH, X, /tm

Figure 5.5. Typical Absorption Spectrum of Irradiated Rock Salt

absorption bands are observed. It implies that in this

region no noticeable annealing of vacancies takes place,

while the continuous decreases of F and V3 bands and

the growths of the F-aggregate absorption bands are the

results of thermal agitation which leads to the

redistribution of the vacancies to form more clusters. It appears that the final products of such redistribution of

vacancies are the R centers and other stable clusters.

When all of the color centers are converted to R

centers and clusters, a further increase of temperature

will anneal the vacancies out as indicated by the

simultaneous drop of A p and intensity of R-absorption

band. At a temperature of 515 K, where all color centers

have disappeared, the remaining Ap is due to the

existence of other types of stable vacancy clusters.

Beyond this point, A p decreases almost linearly with

increasing temperature and the crystal is completely

recovered at 673 K.

It can be said that the nuclear radiation effect on the

optical properties is to increase the absorption coefficient particularly at the color centers. A well known

method to study the formation of defects induced by

radiation in rock salt is to obtain the so-called F-coloring

curve, which shows the variation of the F-center

concentration with irradiation dose. Hodgson, Delgado

and Rivas [66] investigated the gamma-ray produced F- coloring curve for NaCl at and above room temperatures. The dose rate was approximately 350 R/ min,

produced by bombarding 1.8 MeV electrons on a gold

target. The results are shown in figure 5.7. The curves corresponding to temperatures 293, 323, and 373 K

show the increasing F-center concentrations and the ap- proaching saturations at the respective temperatures.

At temperatures above 373 K, the respective curves

lave a broad maximum which decreases as the temperature increases. This change is due to the formation of

F-aggregate centers in accordance with the data shown

in figure 5.6. Jain and Lidiard [67] , in the study of the

growth of colloidal centers in irradiated alkali halides,

calculated the growth of F-center concentration as a function of dose as given in figure 5.8. It can be seen that

the F-center concentration reaches its saturation at quite

a low dose and is very temperature dependent. It should

be noted that in all cases the saturated F-center

concentration decreases with increased temperature.

There are two contributing factors, the thermal

235
bleaching and the optical bleaching. The thermal

bleaching is actually the thermal annealing caused by

energy absorption. The optical bleaching can be obtained

either from radiation of appropriate frequency or from

luminescence caused by the excitation of the electrons.

Both of the bleaching effects are present at any

operational condition.

Nowick [68] investigated the growth of the F band in

NaCl crystals with 1.2 MeV gamma-ray irradiation using

a C0*° source. Crystals of different origins, heat

treatments, and states of deformation were measured.

While deformation has a small effect on the concentration of F-centers in the early stage of F band growth, the

effect on the later stage is large. The growth of F band in

the undeformed and annealed crystals appears to satu- rate rapidly at about 10^^ F-center/cm^ and continue to grow slowly and linearly with time. The deformed crystals, however, continue to grow at a considerably higher

rate in the later stage of irradiation time as shown in

figures 5.9 and 5.10. Furthermore, the deformed crystals cannot be completely bleached; the R band remains.

Based on the available information on the F-center in- vestigation, it was concluded that F-center coloration at room temperature proceeds in two distinct stages:

(1) The first stage consists of a rapid filling of the

vacancies and vacancy clusters present in the crystal

prior to irradiation.

(2) The second stage consists of the creation of new

vacancies at a slow rate and their transformation into Fcenters. The effect of deformations is to create new dislocations

and possibly to help disperse the precipitated impurities

with the consequence of more F-centers creation.

Compton [69] observed the coloration of synthetic

and natural NaCl crystals with C0*° gamma-ray and 1.3

MeV electron irradiations. It was found that these

0 10 20 HOURS

IN IRRADIATION TIME

Figure 5.7. F-center color curves obtained for

NaCl sample temperatures between

20 and 300 °C at a dose rate of

approximately 350 R/min [66].

irradiations produced the colloid band, at 0.565 /zm, in

the synthetic crystals but not in natural crystal. This

colloid band became much stronger than F-center

absorption at high doses. Through various thermal

treatments given the natural crystal prior to their

coloration, it was found that the hydroxyl ions played an

important role in the conversion of F-centers into

colloids.

Observations of Nowick [68] and Compton [69] may

provide clues regarding the nature of blue rock salt. In

the deformed rock salt, the optically unbleachable R236
UJ

LUO

2

O

h-O

<K

libi

_lO

2

"0.00 0.05 0.10 0.15 0.20 0.25

DOSE IN DISPLACEMENTS /ANION

Figure 5.8. The predicted dose dependence of

F- center concentration in NaCl at

temperatures of 398, 423 and 448 K

[67].

A-As Received

S-Deformation 4.3%

C-Deformation 8.5%

I I I I I I I 20 30 40 50

TIME (minutes)

70

Figure 5.9, Early stage of F-band growth for

irradiated NaCl crystals [68].

band covers a broad spectral range centered at about 0.6

/xm. The presence of hydroxyl ions in the crystal seem to be essential in the formation of the colloid band, at 0.565

)um, by irradiation. As both absorption bands contribute

to the blue appearance of the crystal, it may be possible to conclude that the blue rock salt is the consequence of

nuclear irradiation on a rock salt crystal which contains

hydroxyl ion substituted lattice defects which was

plastically deformed in the geological past.

Not only does the F-center concentration depend on

temperature and radiation dose, but it also varies with

the incident energy of radiation. Figure 5.11 is a plot of

the number of F-centers produced per proton versus the

energy of the protons [70]. It was also observed in the

case of intense irradiation that the peak of F-center

absorption was slightly shifted toward shorter wavelength. This may be due to the high concentration of

lattice defects and an associated interaction between

them [71]. Data on the effect of neutron exposure on the

optical properties on rock salt is rather scanty. Available

information [72] indicates that neutron bombardment is more effective in producing defects.

From the available information on the color center

investigations, it is noted that neither F-center nor F- aggregate center absorption bands have been found to extend into the 10.6 /Ufn region when observed by the

usual spectrometric methods. However, Lipson, Ligor,

and Martin [73] , measured the absorption coefficient at 10.6 jLtm by CO2 laser calorimetry for NaCl crystals

irradiated with C0*° gamma-rays. It was found that the

absorption at 10.6 /im increased upon irradiation.

2.5

E 2.

O

I

'o

1.5 —

1.0

0.5

0.0

A-As received

B-Deformation 4.3%

C-Deformation 8.5%

1

10 20 30

TIME (hours)

40

Figure 5.10. The same F-band growth curves

as in Figure 5.9 carried out

to a much longer irradiation

time [68].

100 200 300 400

ENERGY OF PROTONS IN M*v

Figure 5.11. Number of F-centers produced by one proton

per cm path In NaCl irradiated with 10 protons/cm^ [70].

237
Through a careful analysis, they concluded that the

increase in absorption at 10.6 jum after irradiation is associated with the F-aggregate centers. In general, it can be safely said that the effect of

nuclear radiation on the optical property of rock salt is to increase the absorption coefficient across the spectrum,

with much greater absorption at the color centers. The

effects resulting from crystal irradiation are, however,

influenced by many factors:

a. The thermal history of the crystal,

b. The irradiation history of ihe crystal,

c. The origin of the crystal,

d. The energy of the radiation,

e. The dose rate of the radiation,

f. The length of exposure (the total dose),

g. The physical environment (temperature, pressure,

radiation), and

h. The impurity contents of the crystal.

Whatever the factors are, the result is the coloration of

the crystal. Although the colored crystal may be

bleached optically or thermally, some of the defects will

remain as permanent damage to the crystal. The most

important of such defects is the creation of additional

impurities which result from the primary bombardment

of particles and/ or when their products are stopped by

the crystal.

5.5. References

[I] Stefan, J.M., "The Influence of Heat on the Light Refraction of Sohds," Sitzungsber. Akad. Wiss. Wien, 2, 63, 223-45

(1871).

[2] Martens, F.F., "The Dispersion of Uhraviolet Radiation," Ann. Phys., 6, 603-40 (1901).

[3] Paschen, F., "The Dispersion of Rock Sah and Sylvite in

Infrared," Ann. Phys., 26, 120-38 (1908).

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238
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239
Symbols and Units

Symbol Name Units

A Absorption coefficient cm ' d Sample thickness cm E Energy eV

£3 Absorbed energy eV

ht4i Energy of light quantum eV

k Absorption index or extinction

coefficient dimensionless

LO, TO Longitudinal and transverse

optical phonon modes

n Refractive index dimensionless

R Reflectivity dimensionless

T Temperature K

T Transmission dimensionless a Intrinsic absorption coefficient cm"' Ap Density change cm"'

eo Static dielectric constant dimensionless

e Dielectric constant dimensionless

\ Wavelength nm

6 Phase angle radius A Light frequency s~'

Conversion Factors

W dvclcllglll

To convert jrom to Multiply by

Mm A 10*

240
Chapter 6

Electrical and Magnetic Properties

R. A. Matula*

Contents P3ge

6.1. Introduction 242

6.2. Methods of Measuring Electrical and Magnetic Properties 242

6.2.1. Methods of Measuring Electrical Conductivity 242

6.2.2. Methods of Measuring Dielectric Constant 242

6.2.3. Methods of Measuring Dielectric Strength 242

6.2.4. Methods of Measuring Magnetic Susceptibility 242

6.3. Electrical Conductivity 243

6.3.1. Solid State, Temperature Dependence 243

6.3.2. Liquid State, Temperature Dependence 252

6.3.3. Solid State, Pressure Dependence 254

6.3.4. Aqueous Solutions 254

6.4. Dielectric Constant 254

6.4.1. Real Part of the Dielectric Constant 254

6.4.2. Tangent of the Loss Angle 261

6.5. Dielectric Strength 261

6.6. Magnetic Susceptibility 276

6.7. Effect of Nuclear Irradiation on Electrical and Magnetic Properties 276

6.7.1. Effect of Nuclear Irradiation on Electrical Conductivity 276

6.7.2. Effect of Nuclear Irradiation on Dielectric Constant and Strength 277

6.8. References 278

Symbols and units 282

Conversion Factors 282

* Center for Information and Numerical Data Analysis and Synthesis, Purdue University, 2595 Yeager Road, West Lafayette, Indiana 47906

241
6.1. Introduction

There have been extensive measurements made on the

electrical properties. In most cases an effort was made to

critically evaluate the available data and come forth with

recommended reference values. When this was not possible, selected sets of data are presented as typical cases with the ; ita presented in both tabular and graphical

form for ease of use. The difficulty in developing

recommended values arises from the uncharacterized

nature of the samples reported and the large changes in

the properties due to impurities. Because of these

difficulties, data for pure and doped sodium chloride

have been included.

The very meaning of "rock salt" gives an indication of

the variation in composition to be expected. The

percentage of NaCl in "rock salt" ranges from 17% to 99+% with a range around 96% being a typical value;

typical values of impurities are water 0.17-0.5%,

anhydrite 0.1-80%, other salts 0.08-0.5%, carbonates

0.01-0.2%, and sulfate 0.1-10% [128]. In addition,

numerous liquid and gaseous inclusions are known to be

in rock salt. Preceding the presentation and discussion of the data, a brief discussion is given of methods of measurement for

the purpose of pointing out the basic idea of the methods

and giving references for additional information for the

interested reader.

6.2. Methods of Measuring Electrical and

Magnetic Properties

6.2.1. Methods of Measuriiig Electrical

Conductivity

The electrical conductivity in the solid state is determined by measuring the resistance of a slab of

material of known dimensions. The resistance is found

by placing the material between metallic electrodes and

finding the current flowing for a given known electric

potential. To aid in obtaining good contacts Aquadag, a

colloidal dispersion of graphite, is sometimes put on the

faces of the material on which the metallic contacts are to be placed. Details of measuring the conductivity in the

solid state can be found in references [112, pp. 26-35; 5,

p. 1005; and 2, p. 1497]. A discussion of electrode

behavior in the determination of ionic conductivity is given in reference [113]. The error inherent in the

measurement of the electrical conductivities with the 4- probe method can be of the order of +0.1%.

In the liquid state there are three main types of cells used to measure the electrical conductivity. With theUshaped capillary type the liquid material is contained

entirely within the cell. With the dip-type cell the

capillaries are immersed in the liquid material. The third

type uses electrodes immersed in the liquid material.

Additional details are in references [46, pp. 875-6; 114,

p. 3; and 115, pp. 583-6]. The errors inherent in the

measurement of the electrical conductivities in the

liquid state can be as high as several percent for the diptype cell because of the problem of parasitic conduction,

but for the U-type cell, where this problem is not present,

it can be of the order of 0.1%.

6.2.2. Methods of Measuring Dielectric Constant

The general idea behind the determination of the real and imaginary parts of the dielectric constant is the

measurement and comparison of a capacitor containing

the dielectric material and the same capacitor without

the dielectric. In different frequency regions, different

experimental methods are used. At lower frequencies,

typically 10^ to 10^ Hz, bridge methods are applicable. At

higher frequencies resonant circuit methods can be used

while at frequencies greater than the order of 100 MHz

transmission line methods are used while at higher

frequencies, waveguide and cavity resonator methods

can be used. Details can be found in references [69, pp. 315-6; 116, chapter 3, pp. 109-68; 117, chapter 2, pp. 21-38; 118, p. 1; 119, pp. 47-122; 72; and 120, pp. 364-390] . The inherent inaccuracy in the measurement

of the dielectric constant can be of the order of 0.1% or

better.

6.2.3. Methods of Measuring Dielectric Strength

The dielectric strength is the maximum electric field strength a material can withstand before the onset of a rapid increase in electrical conduction. The dielectric

strength is measured by increasing the voltage applied to a specimen and noting when conducting paths form.

Additional details can be found in references [121, pp. 6-7; and 81, pp. 2, 3, 6, and 7] . One writer [98, p. 103]

points out that the variation in the breakdown voltage can be held to within +5% as well as for the sample

thickness thus giving an uncertainty in these quantities

alone that should not exceed +10%.

6.2.4. Methods of Measuring Magnetic

Susceptibility

The magnetic susceptibility of sodium chloride has

been measured using the Faraday method which is also

known as the non-uniform field method. The principle

behind this method is the measurement of a force, using

a sensitive balance, on a small specimen suspended

between pole pieces in which the magnetic field and its

spatial derivative do not vary very much. The sensitivity

using this method is high with an accuracy that can be

242
attained of +0.1%. Additional details can be found in

references [122, pp. 428-30; 123, pp. 11-8; and 124, pp. 458-9]

.

In the Gouy method or uniform field method, a long

sample is suspended between pole pieces such that one

end of the sample is in the region of maximum field

strength and the other end in a region where the field is minimal. The force is measured by a balance and the

force is proportioned to the square of the maximum field

strength. Generally the accuracy using this method can

be + 1% which can be improved to an accuracy of +0.1%

[124, p. 454]. Additional details can be found in

references [122, pp. 429-30; 123, pp. 3-10; and 124, pp. 456-7]

.

6.3. Electrical Conductivity

6.3.1. Solid State, Temperature Dependence

Evaluated data are given for the intrinsic electrical

conductivity of pure sodium chloride in the solid state. The evaluated data are given in table 6.1 and shown on

figure 6.1. Table 6.2 gives the experimental data for data

sets used specifically to develop the evaluated data as well as other selected data in order to illustrate the

behavior for pure sodium chloride, sodium chloride with

known amounts of dopants, and naturally occurring rock

salt. A discussion of some features of the data follows

before describing how the evaluated data were arrived

at.There are several characteristics of the conductivity

data as a function of temperature that bear mentioning.

The conductivity increases as the temperature increases

and, moreover, does so by orders of magnitude from

room temperature of 293 K (or 10Vr=3.41) to the

melting point of 1074 K (or lOV 1-0.931). This large

change suggests plotting the conductivity on a logarithmic scale. Another feature of the data is that there are distinct

regions where log {oT) is linear when plotted as a function of T'^ (cur\re 15). This is further illustrated in

the literature both for pure and doped sodium chloride

[7, fig. 1; 15, fig. 1; and 16, fig. 1] . In addition, theoretical considerations lead to the conclusion that in three

conductivity regions, one of which is the intrinsic, log

(ctT) versus T"^ is linear [4] . Based on the consideration

that much of the data in the literature are presented as log (o-T) as a function of 10^/ T", it was decided to plot

figure 6.1 similarly.

On figure 6.1, it is observed that below the melting

point to perhaps 10^/T'~1.3, there is a limiting line

below which data do not extend. This is the intrinsic

region applicable to the pure material (parts of data sets

4, 5, 7, 8, 9, and 15). Several of these data sets are for

pure sodium chloride. Jain and Dahake [4] (curve 7)

presented data on spectroscopically pure material, Etzel

and Maurer [5] (curve 9) presented results from

measurements on pure sodium chloride, and Trnovcova

et al. [8] (curve 15) also gave measurements on pure

material. It should be noted that very close to the melting

point, a behavior different from the extension of

linearity of the intrinsic-region behavior is evident

(curve 5 for 10Vr<1.0).

Other features are also evident in figure 6.1. Specimens doped with impurities exhibit differences in

the value of the conductivity (curves 3, 6, 10, 11, 12, and

14). Specimens that come from natural crystals show a wide variation (curves 4 and 16). Other conditions are

for a single crystal (curve 1), pellet (curve 2), disk

specimen made under pressure (curve 5) , a single crystal

with low background impurity (curve 8) , and a specimen

called "rock salt" by the author (curve 13). For the same

impurity, the conductivity increases as the impurity

content increases (curves 11 and 12).

Recent measurements of the DC resistivity by Olhoeft

[127] (curves 17-20), made at 295 K on halite cored

from a Carlsbad, New Mexico corehole, show a variation

between subsamples. In addition, data for the real part of

the complex resistivity as a function of frequency are

also presented and range from 5.16X10^ fim to 1.86 X

10^ flm at a frequency of 10^ Hz. This can be compared

to the estimate based on dielectric measurements of the

Laboratory for Insulation Research [60] at 298K. Using

a frequency of 10^ Hz, a value for the real part of the

dielectric constant of 5.90 (see data set 1 in table 6.7), a value of tan 8 of <1 X 10"* [60, p. 302] , and the relation

between this resistivity and the dielectric properties (and

TABLE 6.1. EVALUATED DATA FOR THE INTRINSIC ELECTRICAL CONDUCTIVITY OF

SOLID, PURE SODIUM CHLORIDE

[Temperature, T, K; Electrical Conductivity, a, S m~']

T a. ^ . . xntrinsic

825 2.06 X lO^" 850 4.27 X 10_'* 875 8.47 X 10

"* 900 1.62 X

10"' 925 2.98 X 10_' 950 5.31 X 10 ' 975 9.19 X 10"' 1000 1.54 X

10"^

243
0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50

10^/ T, K''

Rgure 6.1. Electrical conductivity of solid sodium chloride (temperature dependence).

244
TABLE 6.2. EXPERIMENTAL DATA ON THE ELECTRICAL CONDUCTIVITY OF SOLID SODIUM CHLORIDE

(Temperature Dependence)

[Temperature, T,K; Electrical Conductivity, a, S m

Data

Set Author(s), Year [Ref.] IOVt log(aT) Remarks

1 Torkar, K., 1965 [1]

Torkar, K. , 1965 [1]

Radhakrishna , S. and

Karguppikar, A.M.,

1973 [2]

1,.250 -0.952

1,.301 -1.137

1,.304 -1.242

1,.451 -1.668

1,.626 -2.082

1.,818 -3.124

2,,202 -4.849

2,.265 -5.177

2,,448 -6.069

2..862 -7.944

3.,153 -9.221

1.,650 -2.625

1.,979 -4.248

2.,302 -5.902

2.,739 -7.872

3.,116 -9.264

1.,287 0.267

1.,354 -0.150

1. 363 -0.283

1. 397 -0.400

1. 439 -0.467

1.,464 -0.567

1.,489 -0.600

1. 532 -0.683

1.5A9 -0.800

1. 574 -0.867

1. 591 -0.933

1. 624 -0.983

1. 641 -1.067

1. 667 -1.150

1. 709 -1.217

1.,726 -1.300

1. 759 -1.367

1. 793 -1.483

1. 827 -1.617

1. 869 -1.850

1. 920 -2.017

1. 970 -2.183

1. 996 -2.367

2. 030 -2.500

2. 072 -2.650

2. 105 -2.800

2. 156 -3.033

2. 215 -3.250

2. 257 -3.483

2. 308 -3.700

2. 359 -3.983

2. 426 -4.233

2. 485 -4.517

2. 544 -4.800

2. 612 -5.033

2. 679 -5.233

NaCl single crystal; measured in air using

isothermal method; data points extracted

from figure; analytically, temperature dependence, a = 2.5 exp(-20,700/RT)

NaCl pellet; measured in air using isothermal

method; data points extracted from figure;

analytically, temperature dependence a = 1.0 exp(-20,700/RT)

.

NaCl crystals Sb-doped to 0.0080 (80 ppm)

;

crystals grown from melt by Kyropoulos technique starting with BDH-AR grade salt, Sb

then diffused by heating the crystal in Sb

vapor at 973 ± 5 K for about 6 days, the

NaCl and Sb metal sealed together in quartz

tube after evacuating to approx 10 ' torr; impurity content estimated by mass spectroscopic analysis; data points of log(aT) versus 10 ^/T extracted from figure; conductivity measurements incorporated a GR 1644-A

Mf2 bridge; specimens prepared for measurements by coating two opposite faces of

crystal with thin coating of aquadag and

crystal placed between two platinum plates.

245
TABLE 6.2. EXPERIMENTAL DATA ON THE ELECTRICAL CONDUCTIVITY OF SOLID SODIUM CHLORIDE

(Temperature Dependence) (continued)

Data

Set Author(s), Year [Ref.] 10 Vt log(aT) Remarks

Phipps, T.E., Lansing,

W.D. , and Cooke, T.G.

,

1926 [3]

0.947

0.953

0.950

0.970

0.980

0.993

1.010

1.031

1.060

.093

.107

,110

.148

.160

.175

.209

1.210

1.210

1.226

1.235

1.237

1.260

1.265

1.260

1.282

1.321

1.330

1.363

1.410

1.431

1.481

1.530

1.561

1.670

1.682

1.747

1.795

1.796

1.984

1.871

1.774

1.686

1.430

1.373

1.121

1.057

0.589

0.448

0.336

0.115

-0.068

-0.304

-0.255

-0.589

-0.645

-0.808

-0.759

-0.780

-0.848

-1.022

-1.225

-1.192

-1.184

-1.484

-1.597

-1.631

.934

.008

.250

.425

.676

-3.008

-3.228

-3.496

-3.635

-3.706

NaCl natural crystal (Navarre), rock salt;

resistances from 0 to 0.5 Mfl measured using

telephone and drum-wound conductivity bridge

with a Leeds and Northrup 1000 Hz microphone

hummer as source of ac, from 0.5 to 100 Mf2 Wheatstone bridge method used with 8 V dc

used in range of lower resistances and 110

V dc used for the highest resistances; un- certainty in temperature 1 or 2 K; composite

data of 3 experiments with different crystals

extracted from table; at 10 Vt = 1.28 (T = 781 K) slope changes in log a versus lO'/T

plot.

Phipps., T.E., et al. 0.948 1.866 NaCl; material obtained from S.A. Braley of

1926 [3] 0.950 1.724 the Analytical Division of Chemical Lab. of

0.950 1.729 the University of Illinois and had been

0.970 1.623 twice crystallized, twice centrifuged, and

0.980 1.405 dried at temperatures near the melting point;

0.980 1.415* specimen prepared by pressing the powdered

1.000 1.306 salt into disks using 8000 atmospheres and

1.010 1.128* disks were quite transparent; disk specimen

1.000 1.130 1.5 mm thick; resistances from 0 to 0.5 Mf2 1.030 1.009 measured using telephone and drum-wound con- 1.060 0.638 ductivity bridge with a Leeds and Northrup

1.110 0.209 1000 Hz microphone hummer as source of ac, 1.110 0.193 from 0.5 to 100 Mfi Wheatstone bridge method

1.116 0.192 used with 8 V dc used in range of lower re1.160 -0.166 sistances and 110 V dc used for the highest

1.160 -0.200 resistances; uncertainty in temperature 1 or

* Not shown in figure.

246
TABLE 6.2. EXPERIMENTAL DATA ON THE ELECTRICAL CONDUCTIVITY OF SOLID SODIUM CHLORIDE

(Temperature Dependence) (continued)

Data

Set Author(s), Year [Ref.] 10 Vt log(aT) Remarks

5 Phipps, T.E., Lansing,

(cont.) W.D., and Cooke, T.G.,

1926 [3]

1.200

1.210

1.289

1.310

1.310

1.360

1.399

1.410

1.447

1.447

1.460

1.530

561

600

670

691

740

810

810

0.447

0.546

0.975

1.141

1.238

1.410

1.686

1.655

1.860

1.764

1.902

2.235

540

561

897

140

240

542

624

2 K; composite data of three runs with

different high-pressure disks extracted

from table; at 916 K slope changes in log

a versus IOVt plot; first value of IOVt

1.310 taken with ac, second value taken

with dc.

Jain, S.C. and

Dahake, S.L., 1964 [4]

Jain, S.C. and

Dahake, S.L., 1964 [4]

1.205 0.458 NaCl single crystal; Ba-doped to concentra1.243 0.309 tion 0.0045 at.%; grown from melts of BDH

1.292 0.128 analar NaCl using Kyropoulos method; barium

1.343 -0.076 impurity added in form of chloride to melt;

1.421 -0.382 concentration of barium estimated approx by

1.514 -0.745 comparing ionic conductivity (in impurity

1.592 -1.097 range) of Ba-doped NaCl with corresponding

1.690 -1.528 conductivity of NaCl containing known con- 1.802 -2.049 centration of nickel; rapidly quenched; thin

coating of aquadog applied to two opposite

faces and crystal put between two plates

made of a platinum-rhodium alloy; measurements performed in an atmosphere of pure

nitrogen to avoid oxidation of graphite

electrodes; measurements performed using dc

pulse and ballistic galvanometer; data

points of log(oT) versus 10^/T extracted

from a figure; accuracy of conductivity 5% at lowest temperature used and 1% at higher

temperatures

.

1.018 1.262 Spectroscopically pure NaCl; impurity con1.034 1.000 centration 0.00015 at.%; grown from melt at

1.050 0.870 Johnson Matthey spectroscopically pure NaCl

1.070 0.765 using Kyropoulos method; rapidly quenched

1.081 0.608 from 973 K at about 200 K min ^ ; thin coat1.091 0.504 ing of aquadog applied to opposite faces

1.154 -0.097 and then specimen put between two plates

1.160 -0.202* made of a platinum-rhodium alloy; measure1.191 -0.437 ments performed in an atmosphere of pure

1.222 -0.751 nitrogen to avoid oxidation of graphite

1.233 -0.803 electrodes; measurements performed using dc

1.248 -0.986 pulse and ballistic galvanometer; data points

1.264 -1.117 of log(aT) versus 10^/T extracted from a 1.316 -1.535 figure; accuracy of conductivity 5% at

* Not shown in figure.

247
TABLE 6.2. EXPERIMENTAL DATA ON THE ELECTRICAL CONDUCTIVITY OF SOLID SODIUM CHLORIDE

(Temperature Dependence) (continued)

Data

Set Author(s), Year [Ref.] 10 Vt log(oT) Remarks

7 Jain, S.C. and

(cont.) Dahake, S.L., 1964 [4]

1.358

421

520

645

755

870

-1.770

-2.057

-2.396

-2.840

-3.257

-3.753

lowest temperature used and 1% at higher

temperatures

.

Jain, S.C. and

Dahake, S.L., 1964 [4]

Etzel, H.W. and

Maurer, R.J., 1950 [5]

1.175

1.207

1.255

1.307

1.360

1.434

1.498

1.656

1.741

1.820

1.01

1.04

1.09

1.15

1.18

1.22

1.25

1.32

1.41

1.48

1.55

1.63

1.67

1.75

-0.226 NaCl single crystal; background impurity

-0.382 content 0.0010 at.%; grown from melt of BDH

-0.591 analar NaCl using Kyropoulos method; rapidly

-0.825 quenched from 973 K at about 200 K min~'

;

-1.033 thin coating of aquadag applied to opposite

-1.267 faces and then specimen put between two -1.527 plates made of a platinum-rhodium alloy;

-2.125 measurements performed in an atmosphere of

-2.464 pure nitrogen to avoid oxidation of graphite

-2.854 electrodes; measurements performed using dc

pulse and ballistic galvanometer; data

points of log(aT) versus 10 ^/T extracted

from a figure; accuracy of conductivity 5%

at lowest temperature used and 1% at higher

temperatures

.

1.120* Sample designation N; pure NaCl; impurities

0.783 <0. 00001 B, <0.000dl Be, <0. 00001 Cr,

0.362 <0. 00001 Cu, <0. 00001 Fe, <0. 00001 Li,

-0.136 <0. 00001 Si, <0.0001 Ag, <0.0001 Al,

-0.519 <0.0001 As, <0.0001 Ba, <0.0001 Ca, <0.0001

-0.736* Cd, <0.0001 Co, <0.0001 Hg, <0.0001 K,

-0.921 <0.0001 Mg, <0.0001 Mn, <0.0001 Ni, <0.0001

-1.208 P, <0.0001 Pb, <0.0001 Sb, <0.0001 Sn,

-1.587 <0.0001 Ti, <0.0001 Zn, <0.0001 Zr, and Mo

-1.846 V, and W not detected; Eimer and Amend

-2.115 Tested Purity NaCl source of material; single

-2.437 crystal grown from melt by Kyropoulos method

-2.623 using platinum crucible; cleaved into cubes

-2 . 955 approx 1 cm on an edge and annealed in an atmosphere of helium at 1043 K (heating

rate 6 K min ') for 1 h, slowly cooled to room temperature at 1 K min ^ (for pure

crystal and one containing 0.0002 mole fraction Cd conductivity not altered when cooling rate changed to either 3 K min ^ or 0.3

K min ^

, conductivity of a quenched pure

crystal rapidly cooled in air by removing

it from oven at 1043 K was same as that of

crystal cooled at 1 K min ^); then cleaved

into plates approx 1 mm thick; electrodes

used were either platinum evaporated on

crystal surfaces in a vacuum or colloidal

graphite painted on in alcohol solution

(both materials yielded identical results)

;

during measurements crystals mounted between

platinum clad nickel electrodes in a quartz

tube; measurement method used a ballistic

* Not shown in figure.

248
TABLE 6.2. EXPERIMENTAL DATA ON THE ELECTRICAL CONDUCTIVITY OF SOLID SODIUM CHLORIDE

(Temperature Dependence) (continued)

Data

Set

Author(s), Year [Ref.] IOVt log(aT) Remarks

9 Etzel, H.W. and

(cont.) Maurer, R.J. , 1950 [5]

galvanometer which measured charge passing

through crystal on application of square

pulse of voltage of known magnitude and

duration; accuracy of conductivity estimated

as ±5%.

10 Etzel, H.W. and

Maurer, R.J., 1950 [5]

11 Etzel, H.W. and

Maurer, R.J., 1950 [5]

1.A8 -1.658 Sample designation K; crystal grown from

1.55 -1.940 melt containing 0.01 at.% KCl , expected con1.62 -2.260 centration of KCl in crystal was about 0.1

1.70 -2.580 of its concentration in melt.

1.48 -1.157 Sample designation H; mole ratio Cd/Na 1 x 1.55 -1.445 10 ^; single crystal grown from melt by

1.62 -1.743 Kyropoulos method using platinum crucible;

1.69 -2.079 source materials were Eimer and Amend Tested

1.76 -2.426 Purity NaCl and Baker and Adamson CdCl ; 1.83 -2.771 cleaved into cube approx 1 cm on an edge and

1.90 -3.046 annealed in an atmosphere of helium at 1043 K (heating rate 6 K min ') for 1 h, slowly

cooled to room temperature at 1 K min '

,

then cleaved into plates approx 1 mm thick;

electrodes used were either platinum evaporated on crystal surfaces in a vacuum or colloidal graphite painted on in alcohol

solution (both materials yielded identical

results) ; during measurements crystals

mounted between platinum clad nickel electrodes in a quartz tube; measurement method

used a ballistic galvanometer which measured

charge passing through crystal on application

of square pulse of voltage of known magnitude

and duration; accuracy of conductivity estimated as ±5%.

12

13

14

Etzel, H.W. and 1. 48 0.,208 Similar to the above specimen and conditions

Maurer, R.J. , 1950 [5] 1. 55 -0.,100 except sample designated as A and mole ratio

1. 62 -0.,428 Cd/Na 68.6 x 10 ^ with duplicate analysis

1. 69 -0.,785 giving 64.0 x 10 ^. 1. 76 -1.,064

1. 84 -1.,471

1. 90 -1.,803

Seelen, D.

,

1924 [6] 1. 293 -1.,456 Rock salt; compilation of results reported

1. 486 -3. 088 by this author in this paper; data extracted

1. 745 -4.,479 from table.

2. 113 -6.,001

2. 680 -8.,568

3. 413 -12. 197

Dreyfus, R.W . and 1. 49 -0.,64 Sample number L20A; specimen with CaCl2

Nowick, A.S. , 1962 [7] 1. 61 -1.,20 added; metallic impurity concentration

1. 72 -1.,71 0.0100 ± 0.0030 and determined by semiquanti1. 81 -2.,21 tative spectroscopic analysis; specimen size

1. 92 -2. 82 1 cm by 1 cm by 0.04 cm; specimen prepared

2. 00 -3. 12 by adding CaCl2 to reagent grade NaCl and

2. 08 -3.,48 grown by Bridgman technique; cooled from

2. 13 -3.,78 range of 343 to 573 K down to 203 K at

249
TABLE 6.2. EXPERIMENTAL DATA ON THE ELECTRICAL CONDUCTIVITY OF SOLID SODIUM CHLORIDE

(Temperature Dependence) (continued)

Data

Set

Author (s). Year [Ref.] 10 Vt log(aT) Remarks

14 Dreyfus, R.W. and

(cont.) Nowick, A.S., 1962 [7]

15 Trnovcova, V., Marianl,

E. , and Polak, K.

,

1974 [8]

16 Lehfeldt, W. , 1933 [9]

2.22 -4.24

2.27 -4.59

2.41 -5.20

2.47 -5.71

Z . j1 —J . yo 2.60 -6.52

0 71 "7 m

2.76 -7.33

2.91 -8.14

3.06 -8.95

3.34 -10.37*

* Not shown in fij

1.030 0.930

1.049 0.692

1.074 0.560

1.099 0.242

1.112 0.151

1.149 -0.179

1.187 -0.537

1.212 -0.892

1.231 -0.955

1.237 -1.014

1.262 -1.167

1.306 -1.382

1.381 -1.664

1.443 -1.940

1.512 -2.219

1.587 -2.526

1.656 -2.802

1.737 -3.109

1.818 -3.444

1.912 -3.838

1.994 -4.199

2.069 -4.559

2.156 -4.949

9 9 1 Q

2.300 -5.607

2.362 -5.934

2.438 -6.263

2.500 -6.560

2.575 -6.859

2.625 -7.125

1.088 0.454

1.107 0.301*

1.144 0.189*

1.181 0.077

1.228 -0.136*

1.246 -0.240*

1.302 -0.406

1.321 -0.461*

1.339 -0.613*

1.386 -0.728*

cooling rate of 0.3 K min ; data taken with

increasing temperature; data points extracted

from figure; accuracy of temperature ±0.1

± 0.005 T with T in °C.

Pure; contains 2 x 10 molar percent bivalent metals; thermal treatment of annealing

for 2 h at 1023 K and quenching employed in

most measurements; sample equipped with

graphite contacts and a dc voltage of 10 V applied for measurements; measured in an

inert atmosphere of dry argon; data extracted

from smooth curve.

Naturally occurring rock salt; estimated

Inaccuracy ±10%; data points extracted from

figure.

* Not shown in figure.

250
TABLE 6.2. EXPERIMENTAL DATA ON THE ELECTRICAL CONDUCTIVITY OF SOLID SODIUM CHLORIDE

(Temperature Dependence) (continued)

Data

Set Author(s), Year [Ref.] IOVt log(aT) Remarks

16 Lehfeldt, W, , 1933 [9]

(cont.)

1.414

1.451

1.488

1.525

1.553

1.572

1.609

1.646

1.702

1.748

1.776

1.804

1.841

1.869

-0.832*

-0.990

-1.196*

-1.304

-1.507*

-1.561*

-1.718*

-1.875

-2.073*

-2.340*

-2.541

-2.645*

-2.801*

-2.905

*Not shown in figure.

17 Olhoeft, G.R., 1978

[127]

3.39 -5.73 Subsample 1; halite salt cored from 786 m

deep in ERDA #9 corehole at Carlsbad, New

Mexico; core cut into 4 subsamples; salt

crystals in core had undetectable impurity

levels but cracks and grain boundaries con- tained large amounts of impurities; disc

geometry 1.7 cm thick and 10.6 cm diam;

sample holder was 3-terminal brass configuration with 3.8 cm diam guarded electrode under

8.5 kPa uniaxial load; measured in 3% relative humidity; accuracy ±5% in resistivity;

accuracy in dielectric permittivity ±0.65%;

p = 1.57 X lO^f^m for DC conditions.

18 Olhoeft, G.R., 1978

[127]

19 Olhoeft, G.R., 1978

[127]

20 Olhoeft, G.R., 1978

[127]

3.39 -5.08 Similar to the above specimen and conditions

except subsample 2 and p = 3.58 x lO^fim.

3.39 -5.57 Similar to the above specimen and conditions

except subsample 3 and p = 1.09 x lO^flm.

3.39 -5.43 Similar to the above specimen and conditions

except subsample 4 and p = 7.92 x lO^fim.

frequency) [60, p. 294], a value of 3.05 X 10" nm is obtained for fresh sodium chloride crystals from

Harshaw.

The evaluated data for the intrinsic conductivity of

pure sodium chloride were based on the data from data

set 15. The result of a least-squares fit gave

o = 2.637 X lO'o (6 1) intrinsic 7p g \" /

(T'inK,a intrinsic in S m " which is applicable over the

temperature range of 825 K to 1000 K. The values given

in table 6.1 were calculated from equation (6.1). The

Least Square Polynomial Equation Curve Fit (LSPE)

program at the Purdue University Computing Center was

utilized to obtain equation (6.1). This program utilizes

the F-statistic to optimize the order of a polynomial fit to

data. The order of the polynomial is successively

increased until a maximum is found in the F-statistic.

LSPE was applied to the intrinsic conductivity data for

the data applying to pure sodium chloride (data sets

7,9,15); the best fit to \og{oT) versus lOVT data

resulted in a linear relation for each of these data sets. Of

these three, data set 15 was selected as the one on which

to base the evaluated data; the standard deviation of the

data about the regression line is 3.27 X 10"^ for the fit to the linear form log(a7) versus 10V T. Data set 7 was not

used since it is higher than the other two sets and has

more scatter. Of the remaining two sets, data set 15 has

slightly less scatter and was, therefore, selected. The

difference between the evaluated data and the conductivity data for curve 15 can be as high as 10%. Furthermore,

even though the data in table 6.1 can be regarded as

251
evaluated data, it should be recognized that systematic

variations from sample to sample can be large for pure

sodium chloride. The difference between the evaluated

data for conductivity and curve 9 can be as high as 15%

while for curve 7 it is typically 45%.

Additional data for the electrical conductivity of solid

sodium chloride appear in references [15-30] . A review

article of ionic conductivity in solids [31] reports both

general references as well as references pertaining to sodium chloridtj.

6.3.2. Liquid State, Temperature Dependence

Evaluated data are given for the electrical conductivity of liquid sodium chloride. The evaluated data are given

in table 6.3 and are shown in figure 6.2 which shows the

general trend of the data. Data from references [32 and

33] formed the general base on which the evaluated data were developed and table 6.4 gives the experimental data

from these references. A discussion of how the evaluation was arrived at follows.

The evaluated data for the electrical conductivity of

liquid sodium chloride were specifically based on the

data of Ketelaar and Maenaut [33] (curve 2) because

their use of the capillary U-type cell in air did not involve

parasitic conduction. On figure 6.2, it is noted that the

data of Van Artsdalen and Yaffe [32] (curve 1) is higher

than the data of Ketelaar and Maenaut [33] (curve 2) in the higher temperature region. Also shown are data of

Ketelaar and Maenaut [33] (curves 3 and 4) taken with a dip cell with these data higher than their data taken

with the U-type cell in air. These higher data have been

demonstrated to be due to parasitic conduction, i.e., the

cell walls conduct when using the dip-type design for

the measurements, which leads to a higher conductivity

[33 and 46, pp. 875-6] . The result of a least-squares fit to the data of Ketelaar and Maenaut (data set 2) was

-3.9323 X 102 + 11 269 X IQ-^T

-3.9452 XlOi'^P (6.2)

{T in K and a in S m^') which is valid over the

temperature range of 1090 K to 1300 K. The computer

program LSPE, which was previously described in the

discussion of the temperature dependence of the

electrical conductivity of solid sodium chloride, was used

for the least-squares fit. The standard deviation of the

1000 1050 1100 1150 1200 1250 1300

TEMPERATURE, K

Figure 6.2. Electrical conductivity of liquid sodium chloride.

1350

252
TABLE 6.3. EVALUATED DATA FOR THE ELECTRICAL CONDUCTIVITY OF LIQUID SODIUM CHLORIDE

[Temperature, T, K; Electrical Conductivity, a, S m~ '

]

T a 1090 366.4 HOC 369.0 1200 390.9 1300 405.0

TABLE 6.4. EXPERIMENTAL DATA ON THE ELECTRICAL CONDUCTIVITY OF LIQUID SODIUM CHLORIDE

[Temperature, T,K; Electrical Conductivity, o, S m M

Data

Set

Author (s), Year [Ref.] Remarks

XU / J 308 .87

XU / / Q

. O 344 .97

XU / 7 0 358.04

XU1 n7Q/ y . 0 358 .21

XUOX Z 360 .57 XUOX 360 .60

XU1 OQ7 X1 364 .31

1091 .0 364 .41

1100 .6 366 .01

u 371 .45

n 376 .62

o 380 .41 XXD J

ao 385 .02

1179 ft 386 .37

1XXOH- 1 RZl f,D 391.54

XXOO 391 .29

XX7_J D 394 .16

/. 396 .80

1XZU907/ u 397 .01

x^ ^ u 401 .51

1 9AA ftD 406 .53

1 9A =^ XZH J

0

L. 406 .16

1 9/i 407 .19

1 9ftn 415 .95

1XZO9R'^J 417 .01

X1 9QA A 7 H 418 .01

XU7 J 367 .2 xuy J 367 .65

1XXU1 n J 371 .1 XXU J 369 .4 Tim XXU J 370 .25 XXX J 373 .7 XXZ J 372 .9 XXZ J 373 .77 1123 372 .9 1123 374 .0 1125 .6 376 .5 1133 376 .2 1143 378 .4 11A8 382 .5 1148 379 .6 1173 385 .3 1173 .6 387 .1 1198 391 .4 1223 394 .1 1223 395 .1 1223 395 .6 1248 398 .5 1273 402 .2 1273 401 .1 1273 402 .6 1298 404 .5

Van Artsdalen, E.R. and

Yaffe, I.S., 1955 [32]

Ketelaar, J. A. A. and

Maenaut, P.P.E., 1972

[33]

100 NaCl; liquid state; quartz dip-type capillary conductance cell used for measurements;

resistance measured using Leeds and Northrup

precision "Jones" bridge with frequencies of

200 to 20,000 Hz and a variation in resistance

<0.5%; linear extrapolation to infinite frequency made of measured resistance versus

frequency ^ to obtain inductance-free resistance; cell constant order of 300-500 cm

^ and recalibration after 2 or 3 days use showed

constant did not change by more than 0.3% and on average about 0.1%; cell calibrated in

demal aqueous potassium chloride solution at

298 K; temperature could be maintained to better than ±0.1 K up to 1273 K with a thermal

gradient of no more than 0.2 K over height of

melt, usually about 6.35 cm (2.5 in); data

taken going up and down in temperature scale,

no difference observed in measurements; data

extracted from table; authors presented equation for conducting as a = -0.1697 + 0.6259t - 1.953t^, O in Q ^ cm \ t in °C, std dev = 0.006 J^~^cm \ and valid within 1083-1303 K.

Each impurity does not exceed 0.003%; Baker

analyzed reagent; liquid state; capillary U-_

type cell in air used; cell constant 2500 cm

^ and determined using a normal solution of potassium chloride at 298 K; cell constant

checked after every series of measurements,

variation never exceeded 3%; resistances measured at a frequency of 10 hHz; higher values

of measurements using dip-cell explained as due to parasitic conduction; data extracted

from table.

253
TABLE 6.4. EXPERIMENTAL DATA ON THE ELECTRICAL CONDUCTIVITY OF LIQUID SODIUM CHLORIDE (continued)

Data

Author (s). Year [Ref.] T a Remarks

Set

Ketelaar, J. A. A. and 1223.3 446.5

Maenaut, P.P.E., 1972 1272.9 469.8

[33]

Similar to the above specimen and conditions

except dip-cell used, cell constant 2520 cm ^, and data extracted from figure.

Ketelaar, J. A. A. and

Maenaut, P.P.E., 1972

[33]

1113.3 376.9

1173.5 400.2

Similar to the above specimen and conditions

except cell constant 1520 cm

data about the regression line is 1.01 X 10~^. The

uncertainty assigned to the evaluated data is +3%

because Ketelaar and Maenaut found a variation of the

cell constants within that value.

Additional data for the electrical conductivity of liquid

sodium chloride appears in references [34-44]. Two

documents which give a compilation of information and

an assessment of the data are references [45 and 46]

.

6.3.3. Solid State, Pressure Dependence

Selected experimental data are given for the pressure

dependence of the electrical conductivity of solid sodium

chloride. These selected data are given in table 6.5 and

are shown in figure 6.3. Pierce [47] (curves 1-6) reported extensive data for

doped sodium chloride. Shimizu [13] (curves 7-10)

reported data over a lesser range of pressure for a single

crystal. Observation of these data on figure 6.3 which are

plotted as log a as a function of pressure shows that

above 550 K there is a single straight line that would be

applicable to the data at each temperature.

Other investigators have contributed information to the pressure dependence of the electrical conductivity.

Beyeler and Lazarus [14] presented data for single

crystal sodium chloride at 923 K and at 953 K for log

(a I) as a function of pressure. Cleaver et al. [48]

reported data at 1093 K but the data were presented on

the log o axis such that absolute values cannot be

determined. Biermann [21] presented data for the

resistance ratio as a function of pressure and, in

addition, data for the pressure coefficient of electrical

conductivity as a function of temperature. Another data source for the pressure dependence of the electrical

conductivity is reference [49] . Murri and Doran [59]

studied the effects of shock waves on the electrical

conductivity of sodium chloride. Homan et al. [125]

reported the conductivity ratio as a function of

pressure.

Evaluated data are not given for the pressure

dependence of the electrical conductivity because of the

lack of confirmatory data on well-characterized materials.

6.3.4. Aqueous Solutions

Data for the electrical conductivity of aqueous

solutions of sodium chloride for various concentrations

and temperatures appear in references [50-56] . Two

early compilations appear in references [57 and 58]

.

6.4. Dielectric Constant

6.4.1. Real Part of the Dielectric Constant

Evaluated data are given for the real part of the

dielectric constant of pure sodium chloride in table 6.6

and are shown on figure 6.5. Figure 6.4 shows the

frequency dependence over a range of 1 X 10^ Hz to 2.5X

10^° Hz and figure 6.5 shows the temperature dependence. The curves shown on these two figures come from

references [60-67] and have been selected to show

various characteristics including the variation at room

temperature for pure sodium chloride and for naturally

occurring samples. The numerical data, together with

information on sample characterization, for the curves shown on the two figures are given in table 6.7. The data in figure 6.4 show interesting features. The

measurements of the Laboratory for Insulation Research

[60] (curve 1) made at room temperature on a commercial crystal from Harshaw show that the data are constant. The data of the Laboratory for Insulation

Research [60] (curve2) andofBreckenridge [61] (curve

3) are also for Harshaw crystals with the measurement

temperature 358 K. The data for both curves are close

to each other and show an upturn as the frequency is decreased below 10* Hz. Above that frequency the data are constant to 10^° Hz. This rise at low frequencies is due to interfacial polarizability which is not included

in the real part of the dielectric constant [69, £p.

316-7]. Data for halite cored from a Carlsbad, New

Mexico corehole are given in ref. [127] for four

subsamples and show a variation of 10^ Hz from 7.012

to 8.705.

254
0

0 100 200 300 400 500 600 700 800 900 1000

PRESSURE, MPa

Figure 6.3. Electrical conductivity of solid sodium chloride (pressure dependence).

255
TABLE 6.5. EXPERIMENTAL DATA ON THE ELECTRICAL CONDUCTIVITY OF SOLID SODIUM CHLORIDE

(Pressure Dependence)

[Pressure, P,MPa; Electrical Conductivity, a, S m ^]

Data

Set Author(s), Year [Ref.] Remarks

Pierce, C.B., 1961 [47]

Pierce, C.B., 1961 [47]

Pierce, C.B., 1961 [47]

Pierce, C.B., 1961 [47]

Pierce, C.B., 1961 [47]

Pierce, C.B., 1961 [47]

Shimizu, K. , 1962 [13]

(T=473 K)

0 .0 199 .6 -6.347

394 .8 -6.545

598 .6 -6 . 759

810 .8

(T==513 K)

4 .2 -5.196

250 .5 -5 . 523

458.5 - S 7Q

636 .8 -5.977

891 .5 -6.233

fT= 297 .1 598 .6 —L son 908 .5 -L 7 S6

(T=

573 .1 -2 . 767

755 .7 -2 .866

(T==481 K)

2 .7

2 .7 -5 . 204

15 .6 J . ^ -7 U 49 .7 -5.347

101 .1 -5.433

173 .6 -5.552

250 .4 344 .3 -5 7Qn

433 .9 -5.861

510 .7 -5.975

596 .1 —fi 07 S 677 .2 -ft 1 7A 771.1 — O . iC. OO 830 .8

(T==773 K)

302 .7 -2.011

588 .5 -2.167

844 .5 -2.337

(T= 473 K)

0 .4 -7.962

19 .5 -7.988

38 .6 -8.003

58 .9 -8.017

0.02 mole percent CaCl2; crystal grown by

Kyropoulos method; measurements made using ac bridge technique with 1 hHz input to a General

Radio 706 capacitance bridge; measurement tem- perature 473 K.

The above specimen and conditions except mea- surement temperature 513 K.

The above specimen and conditions except mea- surement temperature 594 K.

The above specimen and conditions except mea- surement temperature 773 K.

0.09 mole percent CaCl2; crystal grown by

Kyropoulos method; measurements made using ac bridge technique with 1 hHz input to a General

Radio 706 capacitance bridge; measurement tem- perature 481 K.

The above specimen and conditions except mea- surement temperature 773 K.

Single crystal prepared by Kyropoulos method;

specimen 1 mm by 5 mm by 8 mm; annealed in

NaCl powder at 873 K for 6 h and slowly coded

to room temperature; electrodes applied with

silver paint; conductivity measurements made

for increasing and decreasing pressures Dy means of a capacitance bridge at 1 hKz at con- stant temperature; specimen compressed in a silicone oil by an oil injector and pressure

measured with a calibrated Bourdon- type gauge;

data points extracted from figure; measurement

temperature 473 K.

256
TABLE 6.5. EXPERIMENTAL DATA ON THE ELECTRICAL CONDUCTIVITY OF SOLID SODIUM CHLORIDE

(Pressure Dependence) (continued)

Data

Set

Author (s)

,

Year [Ref.] P a Remarks

8 Shimizu, K. , 1962 [13] (T= 533 K) The above specimen and conditions except

0.9 -5.680 measurement temperature 533 K. 19.9 -5.702

39 .

5

-5.720

59 .

2

-5.738

9 Shimizu, K. , 1962 [13] (T= 553 K) The above specimen and conditions except

0.9 -5.371 measurement temperature 553 K. 20.2 -5.388

39.5 -5 .406

59.5 -5 .425

10 Shimizu, K. , 1962 [13] (T= 573 K) The above specimen and conditions except

0.6 -5.120 measurement temperature 573 K. 20.4 -5.136

40.1 -5.158

59.5 -5.172

1 1 mill 1 1 mill 1 1 iiiiiij 1 1 mill i i iiiiii| i i iiiiii 1 1 mm 1 1 mill i i iiiiii i i iiiiii // .."

1 1 iiiiii 1 1 1 mm 1 1 Ill 1 1 mm i 1 1I mini 1

10 10^ lO' 10* 10= 10^ 10^ 10^ 10^ I0'° lO" FREQUENCY , Hz

Figure 6.4 Real part of the dielectric constant of sodium chloride (frequency dependence).

257
Figure 6.5. Real part of the dielectric constant of sodium chloride (temperature dependence).

TABLE 6.6. EVALUATED DATA FOR THE REAL PART OF THE DIELECTRIC

CONSTANT OF PURE SODIUM CHLORIDE

[Frequency, V, Hz; Temperature, T, K; Real Part of the Dielectric Constant, e']

V

T = 298K T = 358K

1 X 10^ 5.90 6.01

1 X 10^ 5.90 6.01

1 X lO" 5.90 6.01

1 X 10^ 5.90 6.01

1 X 10^ 5.90 6.01

1 X 10' 5.90 6.01

1 X 10^ 5.90 6.01

1 X 10^ 5.90 6.01

1 X 10^" 5.90 6.01

258
TABLE 6.7. EXPERIMENTAL DATA FOR THE REAL PART OF THE DIELECTRIC CONSTANT OF

SODIUM CHLORIDE

[Frequency, V,Hz; Temperature, T,K; Real Part of the Dielectric Constant, e']

Data

Set

Author (s). Year [Ref.] Remarks

Laboratory for Insulation

Research, 1954 [60]

Laboratory for Insulation

Research, 1954 [60]

(T=298 K)

1 X 10^ 5 .90

1 X 10^ 5,.90

1 X

10"* 5,.90

1 X 10 = 5,.90

1 X 10^ 5..90

1 X 10^ 5,,90

2 .5 X 10'" 5,.90

(T=358 K)

1 X 10^ 6..35

1 X 10^ 6..11

1 X

10'* 6..00

1 X 10^ 5,.98*

1 X 10^ 5..98*

1 X 10^ 5,.98*

2,,5 X 10" 5,.97*

Fresh crystals from Harshaw; dried over phosphorus pentoxide; data extracted

from table.

Fresh crystals from Harshaw; dried over phosphorus pentoxide; data extracted

from table.

* Not shown in figure.

Breckenridge, R.G.,

1948 [61] 9.86

9.54

1.17

1.14

9.81

9.53

8.21

(T=358 K)

10

10 2 10"

10^

10 = 10^

10'

8.71 X 10-

6.36*

6.09

5.98

5.98

5.92*

5,97

5.96

5.95

Commercial crystal from Harshaw Chemical

Co., Cleveland, Ohio; specimen approx

0.5 in square and about 0.020 in thick;

electrodes applied by painting crystal

faces with duPont Silver Paste No. 4351;

probable error about 2%; data extracted

from figure.

DeGiura, V. and

Spinolo, G., 1968 [62]

Lowndes, S., 1966 [63]

Haussuhl, S., 1957 [64]

* Not shown in figure.

T

(V=5xl0^ Hz)

293 5.92

(v=10'

1.5

90

290

-10' Hz)

5.43

5.57

5.90

(v=10^-

293

2x10' Hz)

5.87

Measurement method used a three-terminal

system kept under vacuum. General Radio

1615A bridge used; data extracted from

table; data reported is average on sev- eral specimens with maximum variance

within ±0.02; temperature specified as room temperature, 293 K assigned.

Optically flat single crystal discs with

vacuum-deposited gold electrodes on the

faces; measurements made in a threeterminal cell system with frequency at

10^ to 10^ Hz ; crystals showed no impurity

polarization mechanisms; uncertainty

±0.02 at the three temperatures; data

extracted from table.

Single crystal; measurements conducted

in a frequency range of 10= to 2 x lO' Hz

and in a temperature range of 293 to 383 K; measurement temperature applying

259
TABLE 6.7. EXPERIMENTAL DATA FOR THE REAL PART OF THE DIELECTRIC CONSTANT OF

SODIUM CHLORIDE (continued)

Data

Set

Author (s), Year [Ref.] Remarks

6 Haussuhl, S., 1957 [64]

(cont .

)

7 Jones, B.W., 1967 [65]

8 Eucken, A. and Buchner,

A., 1935 [66]

9 Matsonashvile, B.N.,

1958 [67]

(v=lxlO'

296

Hz)

5.86

293 5.62

(v=8 .50x10' Hz)

304 5.72

307 5.72

313 5.73

318 5.73

327 5.75

339 5.76

348 5.79

357 5.80

367 5.81

374 5.83

383 5.84

392 5.87

399 5.88

407 5.89

416 5.90

432 5.94

446 5.95

462 5.99

474 6.00

482 6.02

500 6.08

514 6.10

to tabular data not explicitly stated,

293 K assumed.

Naturally occurring sample; 0.7 ppm

divalent ions; single crystal; flat

plate specimen of about 1.0 cm x 1.0 cm

X 0.1 cm with metallic electrodes put on; dielectric constant measured using a geometrical technique in association with a three terminal transformer bridge system;

pressures up to 7 kbars used; low frequency dielectric constant at zero pressure reported; data extracted from

table; uncertainty 1% or less.

Slab specimen; from natural crystal;

data extracted from table; uncertainty

±0.01.

Single crystal; grown by Kyropoulos technique; slabs sawed from crystals by using

water-wetted wire saw; ground and polished

using dehydrated alcohol to disk shape;

plane parallel to within 1-2 ym; transparent and crossed polaroids showed no perceptible internal stresses; measured

in vacuum; data extracted from smooth

curve.

The data in figure 6.5 show several features. There is a spread in the data at room temperature for pure material

(curves 4, 5, 6, and 9). The data of Lowndes [63] (curve

5) show the variation with temperature for temperatures

below room temperature. Above room temperature the

data of Matsonashvili [67] (curve 9) appear to show a

variation that increases faster than linearly at the higher

temperatures. Naturally occurring specimens also have a spread (curves 7 and 8).

The evaluated data for the real part of the dielectric

constant at room temperature were based on data set 1 in

figure 6.4 and confirmatory evidence given in reference

[74, table IV-1] for the room temperature values at 8.9,

35.4, and 116 GHz which were all 5.90. The values up to

358 K were based on data set 2 together with information on the slope from data sets 5 and 9 as well as information on the temperature coefficient quoted in reference [74,

table IV-3] . The evaluated data for pure sodium chloride

are given in table 6.6 and between 298 K and 358 K are represented by

e' = 5.354 + 0.001833 T (6.3)

with Tin K. Considering the difference beween equation

(6.3) and the data of curve 9, an uncertainty of 3.5% is assigned to e'. Additional data for the real part of the dielectric

constant appear in references [68, 70-74, 76, and 80],

with reference [12] containing data for doped sodium

260
chloride, halite, granulated purified salt, and fine flake

salt. Data over a frequency range of 2.96X10'^ Hz to 1.17

X 10^^ Hz appear in reference [79] and were calculated

from the magnitude and phase angle of the reflectance

which was measured at 300 K. Data for a 10% solution

are reported in reference [78] . Data for the temperature

coefficient of the real part of the dielectric constant

appear in references [66, 74, 75, and 80] and data on the

rate of change with temperature appear in reference

[76] . Data for pressure coefficient appear in references

[77 and 80] , on the rate of change with pressure in

references [76] , and the variation with pressure in

reference [65] . In reference [80] measurements of the

real part of the dielectric constant, its pressure and

temperature coefficients, were performed on the same

samples.

6.4.2. Tangent of the Loss Angle

Selected experimental data are given for the tangent of

the loss angle, tan 8, of sodium chloride. These selected

data are tabulated in table 6.8 with the frequency

dependence shown in figure 6.6 and the temperature

dependence shown in figure 6.7. The frequency dependence, figure 6.6, contains some

general features for various conditions. There are several curves for the pure material. The results reported by

Haven [82 anc 83] (curve 5) were for a very pure

single crystal measured at a temperature of 383 K with

the data decreasing from 1.55 X 10"* at 52.3 Hz to 4.44x10-5 at 1.04 X 10^ Hz. Nearby at 1 X 10^ Hz is the

data point reported by Vodop'ianov and Galibina [85]

(curve 8) which applies to a pure specimen at 293 K. In

a higher frequency range, the data also of Vodop'ianov

and Galibina [85] (curve 9) show data for pure material

generally decreasing and going from 1.36 X 10-" at 1.718 X 105 Hz to 2.3 X 10-5 at 1 X 10^ Hz. Similarly, a decrease in tan 6 with an increase in frequency is evident for the data of Bayley [84] (curve 7) which apply

to pure rock salt; the values are higher than for the pure

material. The data of Nevald [86] (curve 1) and of

Breckenridge [61] (curve 6) both show an increase in

tan 8 at the upper end of their respective frequency

intervals; the former data apply to an unstrained

specimen of sodium chloride with the upturn starting at

1 X 10^ Hz and the latter data apply to a commercial

crystal from Harshaw with the increase applying to the

last point at 7.64 X 10^ Hz. The data for the Harshaw

crystal are higher than the data for the unstrained

crystal.

Specimens with doping or dislocations show some

interesting features. The data of Radhakrishna and

Karguppikar [2] (curves 3 and 4) apply to Sb-doped

sodium chloride crystal with curve 3 for a temperature of

393 K and curve 4 for a temperature of 493 K. The

magnitude of tan 8 is higher than for previous curves

discussed. Nevald [81] (curve 2) reported data for a specimen having a dislocation density of 5 X 10' cm"^

and the shape of the curve is concave downward. Data for

halite cored from a Carlsbad, New Mexico corehole is given in ref. [127] for four subsamples and show a variation in tan 8 of:

Hz Variation in tan 6

10 1.1411 to 3.3953

103 0.2909 to 0.4997

10* 0.4239 to 0.6510

106 0.2175 to 0.3639

The temperature dependence, figure 6.7, shows the

general trend of the data and illustrates the point that

data for pure specimens have lower values of tan 8

compared to specimens with impurities (compare

curves 10, 15-17 with curves 11 and 12), and illustrates

the effect of frequency (curves 13 and 14) with the

higher frequency giving higher values of tan 8

Evaluated data are not given for tan 8 because of the

large change in tan 8 caused by impurities and the lack of

confirmatory evidence on well-characterized materials.

Documents containing additional ^data of tan 8 in

addition to the particular data sets discussed above are references [2,11,12,60,67,74,81-9]

.

6.5. Dielectric Strength

Evaluated data for the dielectric strength of bulk,

pure, unstrained sodium chloride are given in table 6.9. Figure 6.8 shows the temperature dependence of the

dielectric strength and figure 6.9 shows the thickness

dependence. Table 6.10 contains the numerical data,

together with information on sample characterization,

for the curves shown on the two figures. Before stating

the basis of the evaluated data, a discussion of some

features of the data is given.

There are several noteworthy characteristics of the

temperature dependence of the dielectric strength. The

dielectric strength increases in value from low temperatures to reach a maximum slightly above room

temperature and then decreases (curves 1, 4, 11, and 12).

The data at room temperature show quite a variation.

Nevald [81] (data set 1) reported a value of 139 MV m'^

at 302 K for a sodium chloride single crystal, von Hippel

and Lee [90] (data set 4) gave 164.7 MV m-' at 295.5 K

for pure sodium chloride. Caspari [91] (data set 8)

reported a value of 146 MV m-^ at 296 K for a single

crystal from Harshaw Chemical Co. with the applied field

in the [100] direction; in contrast, he reported 142 MV

m"^ for the field in the [110] direction (data set 9). The

261
10 10^ 10^ lO'' 10^ 10® 10^ 10® 10® lo' FREQUENCY, Hz

Figure 6.6. Tangent of the loss angle of sodium chloride (frequency dependence).

262
Figure 6.7. Tangent of the loss angle of sodium chloride (temperature dependence).

263
TABLE 6.8. EXPERIMENTAL DATA FOR THE TANGENT OF THE LOSS ANGLE OF SODIUM CHLORIDE

[Frequency, v,Hz; Temperature, T,K; Tangent of the Loss Angle, tan 5]

Data

Set

Author (s). Year [Ref.] tan 6 Remarks

1 Nevald, R. , 1964 [81]

2 Nevald, R., 1964 [81]

(T = 293 K)

2,,36 X 10 2 3.45 X 10"-

2,.70 X 10^ 3.19 X io~-

3,,31 X 10^ 2.99 X io~-

4.,06 X 10^ 2.73 X 10"-

4.,97 X 10^ 2.44 X io~-

6.,09 X 10^ 2.18 X io~-

9.,14 X 10^ 1.86 X 10"-

1..12 X 10^ 1.73 X io~-

1,,37 X 10' 1.60 X 10"-

1..47 X 10' 1.50 X 10"-

1..92 X 10' 1.34 X 10"-

2,.52 X 10' 1.17 X 10"-

3,.30 X 10' 1.04 X

10"-

4..33 X 10' 0.915 X 10"-

5..67 X 10' 0.850 X

10"-

7,.95 X 10' 0.720 X 10"-

8..50 X 10' 0.687 X 10'-

1,.27 X 10- 0.590 X 10"-

2,.05 X 10- 0.493 X

10"-

3,.51 X 10- 0.396 X 10"-

4..92 X 10- 0.363 X

10"-

7,,37 X 10- 0.364 X

10"-

1..45 X 10 = 0.332 X

10"-

2

.

.66 X 10 = 0 . 332 X 10

4.,56 X 10 = 0.332 X

10"-

1.,02 X 10^ 0.333 X 10"-

2..01 X 10^ 0.464 X 10"-

3,,22 X 10^ 0.529 X 10"-

5,.92 X 10^ 0.659 X io~-

1,.09 X 10^ 0.790 X

10"-

1,.86 X 10^ 0.953 X

10"-

(T = 293 K)

1..31 X 10' 2.36 X 10"-

1,.71 X 10' 2.62 X 10"-

2,,55 X lO' 3.21 X

10"-

4,.34 X 10' 4.06 X 10"-

8..45 X 10' 5.04 X 10"-

1..10 X 10- 5.43 X

10"-

1..14 X 10- 5.57 X 10"-

1,.76 X 10- 5.70 X

10"-

2,.30 X 10- 5.76 X 10"-

3,.00 X 10- 5.89 X 10"-

3,.67 X 10- 5.89 X 10"-

4,,49 X 10- 5.89 X 10"-

5,.86 X 10- 5.90 X

10"-

8,.18 X 10- 6.03 X 10"-

1,,00 X 10 = 6.03 X io~-

1,.14 X 10 = 6.09 X 10"-

1,.95 X 10 = 6.29 X 10"-

2,.23 X 10 = 6.42 X 10"-

2 .91 X 10 = 6.42 X 10"-

3,.81 X 10 = 6.36 X io~-

4 .35 X 10 = 6.36 X 10"-

5 .69 X 10 = 6.23 X 10" -

NaCl unstrained; flat specimen 2.5 x 1x0.1 cm' cleaved from blanks,

gold electrodes evaporated over both

sides, and tin foil pasted to the

gold electrodes with low-loss oil;

smooth data extracted from figure;

measurement temperature specified

as room temperature, 293 K assigned.

Similar to the above specimen and

conditions_except dislocation density

5 X lO' cm ^ and specimen designated

as I.

264
TABLE 6.8. EXPERIMENTAL DATA FOR THE TANGENT OF THE LOSS ANGLE OF SODIUM CHLORIDE (continued)

Data

Set

Author (s). Year [Ref.] tan 6 Remarks

ran L ox J 7 . 44 10^ 6 . 10 10"'* (cont .

)

9 .09 X 10 = 5 .97 X

10"'*

1 .78 X 10^ 5 .25 X 10 "

4 . 26 X 10^ 4,.34 X

10''*

6 .81 X 10^ 3,.89 X 10" "

1 .02 X 10' 3,.37 X 10""

]_ . 74 X 10' 2

,

. 85 X 10""

2 .44 X 10' 2

,

. 52 10""

3 Rsdhs-kr istins, , S . and (T = 393

KflTPimn'ilf.^iT LxCL L ^LI L> -1- Ivd J- y A Mi 1 < 1,.25 X 10^ 1,. 05 X 10"^

1973 \l^ 1,, 68 X 10=^ 7

,

, 30 X 10"'

2,, 26 X 10 2 5

,

, 56 X 10"'

2,,52 X 10^ 5

,

, 57 X 10"'

2

,

.81 10' 5,, 78 X 10"'

3

.

.92 X 10' 4.,02 X 10"'

5

,

.36 X 10' 2

,

,96 X 10"'

5,, 88 X 10' 2

,

, 56 10"'

U 1 45 lO' 2 79 X lO"'

7,.47 X 10' 1,,95 X 10"'

8.,20 X 10' 1.,63 X 10"'

1.,02 X 10^ 1.,36 X 10"'

1,,40 X 10' 9.,62 X

10"'

2,,02 X 10' 6.,58 X 10 '

2.,57 X lO' 5.,80 X 10"'

NaCl crystals doped with Sb; crystals

grown from melt by Kyropoulos technique starting with BDH-AR grade salt,

Sb then diffused by heating the

crystal in Sb vapor at 973 ± 5 K for

about 6 days, the NaCl and Sb metal

sealed together in quartz tube after

evacuating to approx 10 ' torr ; impurity content estimated by mass spectroscopic analysis; before mea- surements crystals quenched from

approx 673 K; for measurements thin

coating of aquadog made and crystals

held in vacuum of 10 ' torr; m mea- surements made by GR 1615-A capacitance bridge combined with GR 1311-A

Audio Oscillator, for higher frequencies a PM 5100 Philips Oscillator

used in conjunction with capacitance

bridge; data points of log(tan 6) versus log(frequency) extracted

from figure.

Radhakrishna , S. and (T = 493 K)

Karguppikar, A.M., 6,.47 x 10' 7,.26 X 10" 1 1973 [2] 7,.50 X 10' 5,.84 X

10"^

8,.70 X 104,.96 X 10"^

9,.71 X 10' 4,.37 X 10"^

1,.05 X 10" 3,.78 X 10"^

2..03 X 10" 1,.77 X 10"!

2,.58 X 10" 1,.71 X

10"'

5,.30 X 10" 7,.69 X 10"'

1,,03 X 10" 3,.60 X 10"'

Haven, Y., 1953 (T = 383 K)

[82,83] 5.,23 X 10 1,.55 X 10""

7.,56 X 10 1..34 X 10""

1.,02 X 10' 1,.24 X 10""

1,.36 X 10' 1..11 X 10""

1,.97 X 10' 9..95 X 10 =

2,.85 X 10' 8,.58 X 10" =

4.,60 X 10' 7.,98 X 10 =

6.,90 X 10' 7,,14 X 10" =

9.,98 X 10' 6.,64 X 10" =

1,,44 X lO' 6,,17 X 10 =

1,,87 X 10' 5,.94 X 10" =

2..80 X 10' 5..32 X 10 =

4,.36 X 10' 5,.32 X 10" =

7,,30 X 10' 4,.95 X 10" =

Similar to the above specimen and

conditions

.

Very pure; single crystal; smooth

data extracted from figure.

265
TABLE 6.8. EXPERIMENTAL DATA FOR THE TANGENT OF THE LOSS ANGLE OF SODIUM CHLORIDE (continued)

Data

Set

Author (s). Year [Ref.] tan (5 Remarks

5 Haven, Y., 1953

(cont.) [82,83]

6 Breckenridge, R.G.,

1948 [61]

Bayley, P.L., 1933 [84]

Vodop'ianov, K.A. and

Galibina, G.I., 1958

[85]

Vodop'ianov, K.A. and

Galibina, G.I., 1958

[85]

1,.02 X 10- 4,.95 X 10 ^

1,.70 X 10- 4 .77 X 10-5

2,.75 X 10- 4,. 78 X 10-5

5,.14 X 10- 4,.44 X 10 5

7,. 71 X 10- 4,.44 X 10-5

1,.04 X 10^ 4 .44 X

10-5

(T = 358 K)

1

,

.09 X 10^ 1,. 11 X 10-^

1,.20 X 10 3 1,.19 X 10-2

1..03 X 10- 8,.93 X 10 '

1,,00 X 10^ 3,.58 X 10 '

1,.09 X 10^ 6,.35 X 10--

9

,

.42 X 10^ 3,.68 X 10--

8..11 X 10' 3,.68 X 10"-

7,.64 X 10' 3,.04 X 10 '

(T = 293 K)

1

,

,04 X 103.,50 X 10--

1

.

, 14 X 10' 3,,41 X 10--

2,,04 X 10' 3,,18 X 10"-

2,,86 X 10' 3,,08 X 10 -

3.,43 X lo' 3,,02 X 10"-

1.,33 X 10^ 1,,65 X

10--

1.,46 X 10^ 1,,58 X

10--

1,,98 X 10^ 1,,49 X 10--

2..30 X 10^ 1.,49 X

10--

(T = 293 K)

1 X 10^ 6.4 X 10" 5

(T = 293 K)

1.718 X 105 1.36 X 10"-

3.784 X 105 9.6 X 10 5 6.714 X 105 5.5 X 10" 5 2.158 X 10^ 3.0 X 10 5 7.998 X 10^ 3.1 X 10" 5 1.00 X 10' 2.3 X 10" 5

Commercial crystal from Harshaw

Chemical Co., Cleveland, Ohio; specimen approx 0.5 in square and about

0.020 in thick; electrodes applied

by painting crystal faces with

duPont Silver Paste No. 4351; probable error ±0.0003; data extracted

from figure except max tan 6 at 600 Hz from text.

Pure rock salt; specimen 0.9 mm thick;

sawed from larger block almost parallel to natural cleavage planes;

from Ward's Natural Science Establishment; colored amber by 40 min

exposure to x-rays; data points,

before and after exposure to x-rays,

extracted from figure; no difference

in data noted due to x-ray exposure;

temperature assumed to be 293 K.

Pure; grown by Kyropoulos method from

melt of chemically pure material;

data extracted from table; measurement temperature specified as room

temperature, 293 K assigned.

Pure; grown by Kyropoulos method

from melt of chemically pure material;

data extracted from figure; measurement temperature presumably room

temperature, 293 K assigned.

tan 6

10 Breckenridge, R.G.,

1950 [86]

(V = 1 X 10' Hz) 0.18 mole percent CdCl2; concentration

303 .9 8.6 X 10 It of impurity ion determined polaro305 .9 9.4 X 10 •i graphically using method of standard

310 .6 1.03 X 10 3 additions; NaCl from Harshaw Chemical

313 .0 1.11 X 10 3 Co., Cleveland, Ohio; c.p. grade of

315 .8 1.11 X 10 3 CdCla used; specimen prepared by

318 .1 1.27 X 10 3 coating pure crystal of approx 0.02

322 .1 1.51 X 10 3 in by 0.5 in by 0.5 in with thin

324 .9 1.67 X 10 3 layer of impurity and heating for

329 .2 2.14 X 10 3 several hours at approx 25 K below

333 .5 2.46 X 10 3 melting point until impurity evenly

338 .7 3.01 X 10 3 distributed; measurements made at

347 .0 3.96 X 10 3 1 kHz; data points extracted from

356 .4 5.54 X 10 3 figure

.

266
TABLE 6.8. EXPERIMENTAL DATA FOR THE TANGENT OF THE LOSS ANGLE OF SODIUM CHLORIDE (continued)

Data

Set

Author (s). Year [Ref.] tan 6 Remarks

360 .3 6.88 X 10-5

363 .9 7.51 X 10 5 366 .2 7.51 X 10 5

369 .0 9.24 X 10 5 372 .1 1.066 X

10"^

374 .5 1.200 X 10"^

376 .8 1.342 X 10-2

381 .9 1.578 X 10" 2

385 .1 1.759 X 10" 2

385 .8 1.932 X 10-2

388 .2 2.128 X 10"2

391 .3 2.302 X 10-2

394 .8 1.9 X 10-2

395 . 2 2.703 X 10-2

399 .1 2.7 X 10-2

403 .9 3.9 X 10-2

407 .0 4.7 X 10-2

410 2 5.9 X 10"^

416 .5 7.9 X 10-2

420 .8 1.15 X 10 ^ 424 .4 1.46 X 10 ^ 425 .9 1.66 X 10 ' 429 .5 1.97 X 10 ' 431 .1 2.37 X 10 ^ 435 .4 3.07 X 10 ^ 439 .3 3.70 X 10 ^ 440 .9 4.29 X 10 ^ 444 .8 5.51 X 10 ^ 446 .7 5.98 X 10 ' 450 .6 7.00 X 10 ^ 452 .6 7.67 X 10 ^ 454 .9 9.04 X 10 ^ 456 .8 9.79 X 10 ^ 458 .8 1 053

461 .9 1 230

(V = 1 X 10^ Hz)

296 5.9 X 10 ^ 325 5.2 X 10 ^ 355 6.1 X 10" = 364 6.2 X 10 ^ 377 6.2 X

10-=

384 4.6 X 10 =

397 5.5 X 10 = 406 6.3 X 10 = 425 7.2 X 10 = 435 5.6 X 10 = 455 1.07 X 10-^

466 1.25 X 10-^

482 1.93 X 10-^

492 2.35 X 10-^

518 3.12 X 10-^

540 4.64 X 10-^

547 4.81 X 10-^

562 5.75 X 10""

574 6.34 X 10-^

581 6.85 X 10-^

10 Breckenridge, R.G.,

(cont.) 1950 [86]

11 Vodop'ianov, K.A. and

Galibina, G.I., 1958

[85]

Pure; grown by Kyropoulos method from

melt of chemically pure material;

data extracted from figure; data

reported for two different specimens

with data obtained on increasing

temperature.

267
TABLE 6.8. EXPERIMENTAL DATA FOR THE TANGENT OF THE LOSS ANGLE OF SODIUM CHLORIDE (continued)

Author (s), Year [Ref.] T tan 6 Remarks

12 Vodop'ianov, K.A. and

Galibina, G.I., 1958

[85]

13 Matsonashvil i, B.N.,

1958 [67]

(v = 1 X 10^ Hz)

14 Matsonashvili , B.N.,

1958 [67]

15 Westphal, W.B. and

Sils, A., 1972 [12]

A A A 1.62 X

10'"

/i 7 A 2.12 X 10""

5.19 X

10""

\V - 1 X 10' Hz)

9QQ 6.4 X 10 " HQ 7.1 X 10'"

jX J 7.5 X 10""

T 9 7 7.5 X 10" "

"^A 1 J4 1 7.5 X

10""

354 9.3 X 10""

357 1.01 X

10"

7A7 1.12 X

10"'

"3 7 0 J / Z 1.12 X 10"'

9 70 1.12 X 10"'

T Q 0 JO J 1.12 X 10"'

TOO 1.25 X

10"'

/.in 1.43 X 10"'

{V - I3 . jU X 10^ Hz)

zy D 3.5 X 10

jUd 3.6 X 10

T 1 7 3.5 X 10

JZo 3.6 X 10""

"5 "5 A 3.6 X 10""

"3 A 1 3.6 X

10~"

T ^ 1 J jl 3.6 X 10""

1 Q _)DO 3.5 X 10""

1 Q 7 Joz 3.5 X10""

4zy 3.7 X 10""

A /. 0 4.0 X

10""

4DO 5.4 X 10""

A 7 O 5.5 X10""

40l 6.2 X

10""

A Qft 4c5i3 6.3 X 10""

504 6.3 X 10""

512 6.5 X

10""

7.4 X 10""

T 7.6 X 10" " 8.1 X

10""

_)4D 8.5 X 10""

9.0 X

10""

J JO 9.0 X 10""

(V = 1 X 10^ Hz)

295 3 X 10"'

347 6.7 X 10" 2 383 1.84 X 10"'

432 3.26 X 10"'

478 7.61 X 10"'

591 8.020

The above specimens except data

taken with decreasing temperature.

Single crystal; grown by Kyropoulos

technique; slab sawed from crystal

by using water-wetted wire saw; ground and polished using dehydrated

alcohol to disk shape; plane parallel

to within 1-2 ym; transparent and

crossed polaroids showed no perceptible internal stresses; measured

in vacuum; data taken on heating;

data points extracted from figure.

Similar to the above specimen and

conditions except different frequency

and data taken on heating.

0.075 at.% BeCls; data points ex- tracted from figure.

16 Westphal, W.B. and

Sils, A., 1972 [12]

(v = 1 X 298

335

382

426

10^ Hz)

4 X 10 "

7 X 10_"

1.6 X 10_'

2.9 X 10 '

Similar to the above specimen and

conditions

.

268
TABLE 6.8. EXPERIMENTAL DATA FOR THE TANGENT OF THE LOSS ANGLE OF SODIUM CHLORIDE (continued)

Data

Set

Author (s). Year [Ref.] T tan 6 Remarks

16 Westphal, W.B. and 492 3.9 X lO"^

[cont .

)

Sils, A., 1972 [12] 518 4.4 X 10~'

553 1.2 X 10 ^ 586 2.0 X 10 ^ 625 4.9 X 10 ^

17 Westphal, W.B. and (v = 1 X 10^ Hz) 1.23 at.% BiCl3; data points exSils, A., 1972 [12] 295 4.7 X 10~^ tracted from figure.

341 5.9 X 10 ^ 380 1.76 X 10 ' 419 3.63 X 10 ^ 461 5.59 X 10 ^ 500 1.030

533 1.730

269
350

325
271
TABLE 6.9. EVALUATED DATA FOR THE DIELECTRIC STRENGTH OF BULK, PURE, UNSTRAINED SODIUM CHLORIDE

[Temperature, T, K; Dielectric Strength, MV m~']

T Dielectric Strength

293 125-175

TABLE 6.10. EXPERIMENTAL DATA FOR THE DIELECTRIC STRENGTH OF SODIUM CHLORIDE

[Temperature, T,K; Thickness, t,iJm; Dielectric Strength, MV m ^]

Data

Set

Author (s). Year [Ref.]

Dielectric

Strength Remarks

1 Nevald, R., 1964 [81] 477 133

176

202

229

277

302

345

355

86

92

97

100

107

111

126

139

139

134

NaCl single crystal; from Harshaw Chemical;

slabs 5 to 8 mm thick cleaved from crystal

blanks of approx 1 cm^ cross section, an- nealed for several hours at 750 K and slowly

cooled; cavity, approx 3 mm in diam and

average thickness 90 ym, etched into center

of one side and chemically polished with

ether to a mirrorlike surface free of

scratches; after drying and cleaning gold

electrodes evaporated in high vacuum on both sides; data extracted from table; 37 samples used: at 4 K spread in breakdown

voltage 5 MV m ' based on 5 samples, at

77 K 5_MV m~^ with 6 samples, at 133 K

5 MV m ' with 4 samples, at 176 K 6 MV m

^ with 2 samples, at 202 K_4 MV m"^ with 3 samples, at 229 K 5 MV m ^ with 3 samples,

at 277 K 4 MV m~^ with 4 samples, at 302 K

3 MV m~^ with 3 samples, at 345 K 5_MV m~' with 3 samples, and at 355 K .4 MV m~^ with

4 samples; author regorts maximum breakdown

strength at 140 MV m ^ at 337 K; identical

data reported in table for specimen annealed,

no deformation, and counted dislocation

density of 2 x 10 ' cm ^.

Nevald, R., 1964 [81] 77 185

229

266

298

340

388

97

109

116

124

142

119

94

Similar to the above specimen and conditions

except deformed by compression of 2.5% or bent with radius 1 cm, counted dislocation

density 1.1 x 10^ cm , at 77 K spread in

breakdown voltage 8 MV m ^ based on 9 samples, at 185_K 5 MV m ' with 2 samples, at

229 K 9 MV m ^ with 3 samples, at 266 K

7 MV m ' with 2 samples, at 298 K 7 MV m~^

with 4 samples, at 340 K 15 MV m~^ with 6 specimens, and at 388 K 10 MV with 5 samples.

Nevald, R. , 1964 [81] 77 220

298

345

137

129

115

94

Similar to the above specimen and conditions

except deformed by compression 10%, counted

dislocation density 1.0 x 10^ cm ^ at 77 K spread in breakdown voltage 12_MV m ' based

on 11 samples, at 220 K 7 MV m ' with 7 samples, at 298 K 8 MV m~' with 7 samples,

and at 345 K 10 MV m~^ with 4 samples.

4 von Hippel, A. and

Lee, G.M, , 1941 [90]

100.7

211.8

295.5

328.4

360.0

394.4

420.5

85.0

126.2

164.7

168.8

146.9

96.3

67.6

Pure NaCl (rock salt) ; data points extracted

from figure.

von Hippel, A. and 110.2 119.2

Lee, G.M., 1941 [90] 200.8 152.2

0.004 at.% AgCl in rock salt; data points

extracted from figure.

272
TABLE 6.10. EXPERIMENTAL DATA FOR THE DIELECTRIC STRENGTH OF SODIUM CHLORIDE (continued)

Data

Set

Author (s). Year [Ref.]

Dielectric

Strength Remarks

5 von Hippel, A. and

(cont.) Lee, CM., 1941 [90]

von Hippel, A. and

Lee, G.M., 1941 [90]

298.2

351.7

384.8

117.0

202.1

296.7

353.1

395.8

201.7

167.5

115.5

200.1

233.0

246.9

157.9

67.5

0.017 at.% AgCl in rock salt; data points

extracted from figure.

von Hippel, A. and

Lee, G.M., 1941 [90]

204.7

298.1

346.3

373.8

8 Caspari, M.E., 1955 [91] 296

9 Caspari, M.E., 1955 [91] 296

290.6

272.9

146.9

103.1

146

142

0.046 at.% AgCl in rock salt; data points

extracted from figure.

NaCl single crystal from Harshaw Chemical

Co.; crystal plates of <0.25 mm thickness

and about 1 cm^ area cut from same single

crystal, ground to proper thickness, and

polished on soft silk moistened with NaCl

solution; evaporated gold electrodes applied

to flat specimens; direction of applied

field [100]; data reported is average for 5 specimens; data extracted from table; max

154 MV m \ min 135 MV m \ standard deviation 0.064; max deviation about ±7.5%,

about 2.5% of this may be due to random

errors in voltage and thickness determination.

Similar to the above specimens and conditions

except direction of applied field [110], max dielectric strength 151 MV m '

, min

138 MV m and standard deviation 0.048.

10

11

Caspari, M.E., 1955 [91] 293

von Hippel, A. and

Alger, R.S., 1949 [92]

99

121

138

159

175

191

206

224

239

255

268

280

291

303

311

319

330

334

175

82

89

96

102

109

116

123

130

137

143

150

156

160

162

164

164

164

164

Crystal between glass slides; approximate

values reported; data extracted from table;

measurement temperature specified as room

temperature, 293 K assigned.

Pressed-on ball bearing electrodes; dc

dielectric strength; data extracted from

figure

.

273
TABLE 6.10. EXPERIMENTAL DATA FOR THE DIELECTRIC STRENGTH OF SODIUM CHLORIDE (continued)

Data

Set

Author (s), Year [Ref.] Dielectric

Strength Remarks

340 162

344 158

352 153

362 143

372 134

382 123

390 113

396 104

402 94

410 85

418 75

422 69

428 60

432 58

170 63

183 70

203 80

222 89

238 98

255 106

265 113

273 118

284 122

292 125

300 129

304 131

311 134

321 135

331 134

341 133

356 132

370 128

384 124

396 119

411 112

429 106

453 95

467 87

480 81

500 72

522 62*

540 53*

559 44*

575 36*

585 31*

601 24*

11 von Hippel, A. and

(cent.) Alger, R.S., 1949 [92]

12 von Hippel, A. and

Alger, R.S., 1949 [92]

Cavity, evaporated metal electrodes; dc

dielectric strength; data extracted from

figure.

13 von Hippel, A. , 1932

[93]

* Not shown in figure,

293 150 Results of measurements on several natural

crystals and a synthetic NaCl specimen; max deviation ±10 MV m ^ or ±6.6%; measure- ment temperature not given explicitly,

assumed to be 293 K.

274
TABLE 6.10. EXPERIMENTAL DATA FOR THE DIELECTRIC STRENGTH OF SODIUM CHLORIDE (continued)

Data

Set

Author (s), Year [Ref.]

Dielectric

Strength Remarks

14 Pikalova, I.S., 1967

[94]

(T=

0.36

0.48

0.54

0.76

1.03

1.21

1.64

2.00

2.42

3.00

3.97

293 K)

10320*

6780*

5470*

3670*

2490*

1860*

1310*

1060*

933*

933*

684

Rock salt; measurement carried out using

dc ; data extracted from figure; measurement

temperature not given explicitly, assumed

to be 293 K.

* Not shown in figure.

15 Vorob'ev, A.A. , Vorob'ev,

G.A., and Murashko, L.T.,

1963 [95]

(T=293 K)

2.9

5.1

6.9

8.3

10.0

11.7

13.7

16.3

17.4

20.3

744

543

464

392

352

319

285

291

268

268

Rock salt; electric field in [100] direction; small electrodes used; data extracted

from figure; measurement temperature specified as room temperature, 293 K assigned.

16 Vorob'ev, A.A., et al.

1963 [95]

(T=293 K)

5.7 386

9.7 308

15.1 252

20.0 241

Similar to the above specimen and conditions

except electric field in [111] direction.

17 Vorob'ev, A.A. , et al.

1963 [95]

(T=293 K)

10.0 263

15.1 224

20.0 213

35.1 173

40.3 168

50.0 151

Similar to the above specimen and conditions

except electric field in [110] direction.

275
work of von Hippel and Alger [92] showed that the

electrodes used to measure the dielectric strength have

an effect on the numerical values. Data from press-on

ball bearings (data set 11) resulted in a value of 160 MV

at 291 K while cavity, evaporated metal electrodes

(data set 12) gave 125 MV m-i at 292 K. With a crystal

between glass slides, Caspari [91] (data set 10) reported an approximate value of 175 MV m~i at 293 K. For

results on several natural crystals and a synthetic one, von Hippel [93] (data set 13) reported a value of 150

MV m-K

In contrast to pure material, data for specimens with

impurities deliberately added or deformed show other

features. In 1941, von Hippel and Lee [90] (data sets 4-7) presented data for the dielectric strength for

varying amounts of silver chloride in sodium chloride.

For temperatures below room temperature, the dielectric

strength increases as the amount of silver chloride

increases and the maximum in the dielectric strength

shifts to a lower temperature. Above room temperature

the slope of the decrease shows a tendency to become

more pronounced as the amount of silver chloride

increases. Nevald [81] (data sets 1-3) investigated the

effect of deformation. A deformation by compression of

10% (data set 3) shows a curve decreasing in value form

77 to 345 K,

Figure 6.9 for the thickness dependence shows the

general features of the data. Of particular note is the

orientation dependence shown by Vorob'ev et al. [95]

(data sets 15-17) demonstrating that the dielectric

strength increases as the electric field is in the [100],

[111], and [110] directions.

The range of values at room temperature for the

dielectric strength given in table 6.9 as the evaluated data

is based on the lowest and highest values reported for

bulk, pure, and unstrained sodium chloride; evaluated

data are not given in addition to room temperature since

several effects mentioned above lead to a variation in

the dielectric strength and also data on wellcharacterized materials are lacking.

In addition to the data discussed above, data are contained in references [91,96,97]. A review article in

which the author discusses many aspects of dielectric

strength in alkali halide crystals is reference [98]

.

6.6. IVIagnetic Susceptibility

Evaluated data for the temperature dependence of the

magnetic mass susceptibility of pure sodium chloride are given in table 6.11 and shown on figure- 6. 10 together

with experimental data. Table 6.12 contains the

numerical data, together with information on sample

characterization, for the experimental data shown on

figure 6.10. A discussion of the data is given before

stating the basis of the evaluated data.

The data indicate that at room temperature and below

the magnetic susceptibility is constant. In 1914, Ishiwara

[99] (curve 1) reported data on a small crystal from

Merck over the temperature range 123 to 291 K, with

the data showing a constant behavior. The data are negative making sodium chloride a diamagnetic substance. He also reported data on a large crystal ot rock

salt (curve 2), which are close to the data on the small

crystal, and also showed constant behavior. Data on solid

material at or near room temperature were reported by

Hoare and Brindley [101,102] (curve 4) and by Kido

[103] (curve 5) with the data of the latter differing from

the data of Ishiwara by no more than 3.5%. Data from

measurements on aqueous solutions were given by

Ikenmeyer [100] (curve 3). In 1974, Smirnov et al. [104] made the point that the temperature coefficient of

the magnetic susceptibility, within the experimental

error, was zero for crystals of sodium chloride.

The evaluated data were based on the data of Ishiwara

(curve 1) for a solid sample and were arrived at by taking an average of that data. The uncertainty in the data is assigned a value of 3.5% since the data of Kido is within

that percentage.

Additional data for the magnetic susceptibility appear

in references [105,106, and 126]. A previous compilation of molar magnetic susceptibility values for sodium

chloride in aqueous solutions appears in reference [ 107]

.

6.7. Effect of Nuclear Irradiation on

Electrical and Magnetic Properties

6.7.1. Effect of Nuclear Irradiation on Electrical

Conductivity

Pearlstein [108] studied the effect of proton bombardment on the electrical conductivity of sodium chloride.

The material received a 350 MeV fluence of 10^^ protons

cm '2 at room temperature and the conductivity was measured over the range of 398 to 743 K. The

conductivity was decreased by the bombardment. Upon

heating the material the conductivity anneals in several

distinct temperature ranges. At room temperature, the

initial conductivity is restored after all the heat

treatments; at higher temperatures it is only about 75%

restored. Further work on proton bombardment was

reported by Pearlstein and Ingham [109] in which

sodium chloride was bombarded at 350 MeV and several

days later the conductivity was measured as the

temperature was increased at a constant rate of 1.25 K

min Three different proton fluences of 2.6 XlO^'*, IX

10^^, and 2.6 X 10^^ protons cm"^ were used. The

276
conductivity decreased to a minimum at 423 K and

increased to its pre-bombardment level at just below 623

K.

6.7.2. Effect of Nuclear Irradiation on Dielectric

Constant and Strength

Ishiguro et al. [110] studied the effect of x-ray

irradiation on tan 6. If a specimen is either plastically

deformed or quenched, x-rays darken the crystal and the

anomalous dispersion peak at 393 K disappears. When

the specimen undergoes either heating or illumination,

the peak reappears.

Mineav et al. [Ill] exposed single-crystal sodium

chloride whiskers to x-rays and found the dielectric

strength decreased with an increase in the concentration

of F-centers that were produced by the irradiation.

TABLE 6.11. EVALUATED DATA FOR THE MAGNETIC MASS SUSCEPTIBILITY OF PURE SODIUM CHLORIDE

[Temperature, T, K; Magnetic Mass Susceptibil.ity , Xf^ mass'

^ TM^ ^1

T ^M,inass

125 -6.28

150 -6.28

200 -6.28

250 -6.28

291 -6.28

roE

o

IUJ 200 300 400 500 600

TEMPERATURE, K

Magnetic mass susceptibility of sodium chloride.

C9 0 100

<

Figure 6. 10.

277
TABLE 6.12. EXPERIMENTAL DATA FOR THE MAGNETIC MASS SUSCEPTIBILITY OF SODIUM CHLORIDE

[Temperature, T,K; Magnetic Mass Susceptibility, mass> 10 ' kg M

Data

g^j. Author (s), Year [Ref.] T M,mass

Remarks

1 Ishiwara, T., 1914 [99] 123.,2 -6 ^0 From Merck; small crystal, data extracted

143,,4 -6,.26 from table.

165..6 -6,.30 183,.8 -6

,

. 22

210..2 -6 . 28

229

,

,0 -ft . J J. 244,.2 -6 . 27 269,,2 -6 . 35

291,,4 -6

,

. 27

2 Ishiwara, T., 1914 [99] 122.,2 -6

,

. 32 Rock salt; large crystal; data extracted

142..2 -6 . 31 from table.

165.,0 -6,.37 188..8 -6,.31 207..6 -6

,

.32 227..8 -6 . 32 248..8 -6,.30 263.,8 -6,,31

271..2 -6 . 27 292..4 -6 . 26

3 Ihenmeyer, K., 1929 293 -6

,

.438 From measurements on aqueous solutions; mea-

[100] surement temperature assumed to be 293 K; data extracted from table.

4 Hoare, F.E and 293 -6

,

. 49 Material supplied by British Drug Houses,

Brindley

,

G.W., 1934 Ltd., of grade A.R. standard; measurement con- [101,102] ducted on crystalline material; number of

samples used was 4; Gouy method used; temperature specified as room temperature, 293 K assigned; data of molecular diamagnetic sus- ceptibility (30.2 ± 0.14 X 10~^) extracted

from table; average deviation from mean of

molecular diamagnetic susceptibility ±0.14 x 10~^; molecular weight of NaCl 58.44277 from

1971 atomic weights of the elements.

5 Kido, K., 1932 [103] 282 -6,.36 Solid material; data extracted from table.

6.8. References

[1] Torkar, K., "Studies of Preparation and Properties of Active

Alkali Azides and Barium Azide and Effects of this Activity on Thermodynamic and Thermochemical Data," Graz Univ.,

Austria, 12 pp. (1965). [AD 463 784]

[2] Radhakrishna, S. and Karguppikar, A.M., "Defect Centers in Antimony Doped Sodium Chloride Crystals," J. Phys. Chem.

Solids, 34(9), 1497-505 (1973).

[3] Phipps, T.E., Lansing, W.D., and Cooke, T.G., "Temperature

Conductance Curves of Solid Salts. I. The Halides of Sodium," J. Amer. Chem. Soc, 48, 112-25 (1926).

[4] Jain, S.C. and Dahake, S.L., "Ionic Conductivity of Sodium

Chloride Crystals Doped with Nickel and Other Impurities,"

Indian J. Pure Appl. Phys., 2, 71-9 (1964).

[5] Etzel, H.W. and Maurer, R.J., "The Concentration and

Mobility of Vacancies in Sodium Chloride," J. Chem. Phys.,

18(8), 1003-7 (1950).

[6] Seelen, D., "On the Electrical Conductivity of Rock Salt

Crystals," Z. Phys., 29, 125-40 (1924).

[7] Dreyfus, R.W. and Nowick, A.S,, "Ionic Conductivity of Doped Sodium Chloride Crystals," Phys. Rev., 126(4),

1367-77 (1962).

[8] Trnovcova, V., Mariani, E., and Polak, K., "Association

Reactions Between Nickel Ions and Vacancies in Sodium

Chloride Crystals," Czech. J. Phys., B, 24, 765-73 (1974).

[9] Lehfeldt, W., "About the Electrical Conductivity of Single

Crystals," Z. Physik., 85, 717-26 (1933).

[10] Melik-Gaikazyan, I.Ya., et al., "Effect of Annealing on the Absorption Spectra and Electrical Conductivity of Crystalline Lead Doped Sodium Chloride and Potassium Chloride,"

Opt. and Spectre, 9(1), 43-4 (1960).

[11] Trnovcova, V., Mariani, E., and Lebl., M., "Electrical Conductivity and Dielectric Relaxation of Sodium Chloride

Crystals Doped with Vanadium," Phys. Status Solidi, A,

31(1), K43-K46 (1975).

[12] Westf hal, W.B. and Sils, A., "Dielectric Report," Massachusetts Inst, of Tech., Cambridge, Mass., 243 pp. (1972). [AD

746 686]

[13] Shir.iizu, K., "Effect of Hydrostatic Pressure on Ionic Conductivity of Sodium Chloride," Rev. Phys. Chem., Jap., 31(2), 67-72 (1962).

278
[14] Beyeler, M. and Lazarus, D., "Influence of the Hydrostatic Pressure on the Electric Conductivity of Sodium Chloride in the Intrinsic Domain," Solid State Commun. 7(20), 1487-9

(1969).

[15] Nadler, C. and Rossel, J., "Measurement and Interpretation of the Ionic Conduction in Alkali Halides," Phys. Status Solidi A, 18(2), 711-22 (1973).

[16] Dreyfus, R.W. and Nowick, A.S., "Energy and Entropy of Formation and Motion of Vacancies in Sodium Chloride and

Potassium Chloride Crystals," J. Appl. Phys., 33(1), 473-7

(1962).

[17] Dryden, J.S. and Meakins, R.J., "Electrical Conductivity of Certain Crystalline Materials After Grinding," 171, 307-8

(1953).

[18] Kobayashi, K. and Tomiki, T., "Studies on the Preparation of Pure Alkali Chlorides," J. Phys. Soc. Japan, 15(11),

1982-90 (1960).

[19] Trnovcova, V., "Ionic Conductivity and Cation Self-diffusion

in Sodium Chloride Crystals Doped with Calcium or Cadmium," Czech. J. Phys., B, 19, 663-76 (1969).

[20] Bhatia, R., "The Conductivity of Direct Compression Materials and Its Relation to Hardness in Aged Compacts," Rutgers

University, New Brunswick, N.J., Ph.D. Thesis, 152 pp. (1976).

[21] Biermann, W., "The Pressure Dependence of Electrical Conductivity of Alkali Halides, I.," Z. Phys. Chem., 25,

90-107 (1960).

[22] Tammann, G. and Veszi, G., "Electrical Conductivity of Salts

in Single Crystals and Crystalline Conglomerates," Z. Anorg.

Allg. Chem., 150, 355-80 (1926).

[23] Benrath, A. and Wainoff, J., "On the Electrical Conductivity

of Salts and Salt Mixtures," Z. Phys. Chem., 77, 257-68

(1911).

[24] Rautenfeld, P., "The Conduction of Electricity in Crystals," Ann. Physik, 72, 617-28 (1923).

[25] Rautenfeld, F., "Correction and Addendum to my Paper on the Conduction of Electricity in Crystals," Ann. Physik, 75(4),

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281
symbols and Units

Symbol Name Unit

Tangent of the loss angle dimensionless

T Temperature K

£ Real part of the dielectric constant dimensionless

V Frequency Hz

0 Electrical conductivity S m-'

^ intrinsic Intrinsic electrical conductivity S m-i

^ M, mass Magnetic mass susceptibility m' kg-' P Electrical resistivity fl m

Conversion Factors

Temperature

To convert from to Use K "C K- 273.15 K °F (K - 273.15)9/5 + 32

Electrical Conductivity

To convert from to Multiply by

S m-i n 'cm-' 10-2 Sm-' n 'in-' 2.54X10-2

Sm-i n 'ft-' 3.048X10-1

Sm-i n 'cmil-ift 1.66243X10-9

S m-' (mA cm)-' 1X10 "

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Physical Properties Data for Rock Salt

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Supplement No. 1 to Vol. 6 ENERGETICS OF GASEOUS IONS

by H. M. Rosenstock, K. DraxI, B. Steiner, and

J. T. Herron, National Bureau of Standards

Provides a comprehensive body

of critically evaluated information on ionization potentials, ap- pearance potentials, electron affinities and heats of formation of gaseous positive and negative

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for Formation of Gaseous Positive Ions," NSRDS-NBS 26.
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