Data of

Chapter KK* ebmpilatipq ol S^aWfe Isotope Fractionatloii 

Factors of Geochemical Interest

GEOLOGICAL 440-KK
Data of Geochemistry 

Sixth Edition

MICHAEL FLEISCHER, Technical Editor

Chapter KK. Compilation of Stable Isotope Fractionation 

Factors of Geochemical Interest

By IRVING FRIEDMAN and JAMES R. O'NEIL

GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK

Isotope separation factors for the 

stable isotopes of hydrogen, carbon, 

oxygen, and sulfur are plotted as a 

function of temperature, in degrees Celsius

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1977
UNITED STATES DEPARTMENT OF THE INTERIOR 

THOMAS S. KLEPPE, Secretary

GEOLOGICAL SURVEY 

V. E. McKelvey, Director

Library of Congress Cataloging in Publication Data

Friedman, Irving, 1920-

Chapter KK. Compilation of stable isotope fractionation factors of geochemical interest.

(Data of geochemistry, Sixth Edition, Michael Fleisher, Technical Editor)

(Geological Survey Professional Paper 440-KK)

Bibliography: p.

1. Geochemistry.

I. O'Neil, James R., 1934- , joint author. II. Data of geochemistry, Sixth Edition. III. Title. IV. Series. V. United

States Geological Survey Professional Paper 440-KK. 

QE75.P9 No. 440-KK [QE515] 557.3'08s [551.9] 72-604861

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington, D.C. 20402 

Stock Number 024-001-02942-1
DATA OF GEOCHEMISTRY, SIXTH EDITION

Michael Fleischer, Technical Editor

The first edition of the Data of Geochemistry, by F. W. Clarke, was published in 1908 as U.S. Geological Survey 

Bulletin 330. Later editions, also by Clarke, were published in 1911, 1916, 1920, and 1924 as Bulletins 491, 616, 695, 

and 770. This, the sixth edition, has been written by several scientists in the Geological Survey and in other institutions 

in the United States and abroad, each preparing a chapter on his special field. The current edition is being published 

in individual chapters, titles of which are listed below. Chapters already published are indicated by boldface.

CHAPTER A. The chemical elements

B. Cosmochemistry

C. Internal structure and composition of the earth

D. Composition of the earth's crust, by R. L. Parker

E. Chemistry of the atmosphere

F. Chemical composition of subsurface waters, by Donald E. White, John D. Hem, and G. A. Waring

G. Chemical composition of rivers and lakes, by Daniel A. Livingstone

H. Chemistry of the oceans

I. Geochemistry of the biosphere

J. Chemistry of rock-forming minerals

K. Volcanic emanations, by Donald E. White and G. A. Waring

L. Phase equilibrium relations of the common rock-forming oxides except water, by G. W. Morey

M. Phase equilibrium relations of the common rock-forming oxides with water and (or) carbon dioxide

N. Chemistry of igneous rocks, Part 1, The chemistry of the peralkaline oversaturated obsidians, by 

Ray Macdonald and D. K. Bailey

O. Chemistry of rock weathering and soils

P. Chemistry of bauxites and laterites

Q. Chemistry of nickel silicate deposits

R. Chemistry of manganese oxides

S. Chemical composition of sandstones excluding carbonate and volcanic sands, by F. J. Pettijohn

T. Nondetrital siliceous sediments, by Earle R. Cressman

U. Chemical composition of shales and related rocks

V. Chemistry of carbonate rocks 

W. Chemistry of the iron-rich sedimentary rocks, by H. L. James

X. Chemistry of phosphorites

Y. Marine evaporites, by Frederick H. Stewart

Z. Continental evaporites 

AA. Chemistry of coal

BB. Chemistry of petroleum, natural gas, and miscellaneous carbonaceous substances 

CC. Chemistry of metamorphic rocks

DD. Abundance and distribution of the chemical elements and their isotopes 

EE. Geochemistry of ore deposits 

FF. Physical chemistry of sulfide systems 

GG. The natural radioactive elements 

HH. Geochronology

II. Temperatures of geologic processes

JJ. Composition of fluid inclusions, by Edwin Roedder

KK. Compilation of stable isotope fractionation factors of geochemical interest, by Irving Friedman and 

James R. O'Neil

CONTENTS

Abstract..........................................

Introduction...................................

Terminology..................................

1. The 5 value.........................

2. The fractionation factor, a

3. 103 lna and the A value ..... 

Standards........................................

Page

KK1

1

1

1

1

2

2

Standards Continued

Oxygen.....................................

Hydrogen.................................

Carbon.....................................

Sulfur.......................................

Stable isotope fractionation curves. 

References........................................

Page

KK3

4

5

5

5

9

ILLUSTRATIONS

Page

FIGURE

[Figures 2-49 follow "References"] 

1. Diagram showing the relationship between PDB, SMOW, and other oxygen

standards.............................................................................--............... ............... KK4

2-26. Graphs showing the oxygen-18 fractionation:

2. Carbonate-water paleotemperature scale.

3. Phosphate-water paleotemperature scale.

4. Silica-water paleotemperature scale.

5. Carbon dioxide(g)-water( 1), 8° to 100°C.

6. Carbon dioxide(g)-water( 1), 120° to 350°C.

7. Water(l)-water(v) between 0° and 100°C.

8. Water(l)-water(v) between 0° and 300°C.

9. Water(l)-water(v), solute effects at 25°C.

10. MgCl2 , LiCl, NaCl, and MgSO4 solutions(l)-water(l).

11. NH4C1, NaF, KC1, and CaCl2 solutions(l)-water(l).

12. Carbon dioxide(g)-calcite.

13. Alkaline earth carbonates-water.

14. Dissolved sulfate-water(l) and anhydrite-water.

15. Barite-water.

16. Quartz-water, 200° to 800°C.

17. Quartz-water, 200° to 1,000°C.

18. Feldspar-water.

19. Muscovite-water.

20. Rutile-water.

21. Magnetite-water.

22. Quartz-magnetite.

23. Plagioclase feldspar-magnetite.

24. Muscovite-magnetite, quartz-muscovite, quartz-calcite, and quartz-alkali 

feldspar.

25. Feldspar(An60)-quartz, feldspar(An6 o)-muscovite, feldspar(An60)-pyroxene,

feldspar(An6o)-garnet, feldspar(An60)-amphibole, feldspar(An6o)-olivine, 

feldspar(An60)-biotite, and feldspar(An60)-magnetite.

26. Dolomite-calcite. 

27-33. Graphs showing the carbon-13 fractionation:

27. Dissolved bicarbonate-carbon dioxide(g).

28. Dissolved carbonate-carbon dioxide(g).

29. Carbon dioxide(g)-methane(g) and calcite-graphite.

30. Diamond-graphite, carbon dioxide(g)-diamond, and carbon dioxide(g)-graphite.

31. Carbon dioxide(g)-calcite.

32. Graphite-methane.

33. Dolomite-calcite. 

34-40. Graphs showing the deuterium fractionation:

34. Water(l)-water(v), -20° to +50°C; and water(s)-water(v), -42° to 0°C.

35. Water(l)-water(v), 30° to 350°C.

36. Water(v)-methane(g).

37. Water(v)-hydrogen(g) and methane(g)-hydrogen(g).
VI CONTENTS

FIGURES 34-40. Graphs showing the deuterium fractionation Continued

38. Water(l)-water(v), solute effects at 20°C.

39. Trona-water(l).

40. Water-biotite, water-theoretical biotite, water-hornblende, water-muscovite, 

water-theoretical phlogopite, water-aluminum hydroxide, waterkaolinite, and water-serpentine. 

41-49. Graphs showing the sulfur-34 fractionation:

41. Sulfur dioxide(g)-hydrogen sulfide(aq and g) between 27° and 527°C.

42. Sulfur dioxide(g)-hydrogen sulfide(g) between 287° and 1,000°C.

43. Dissolved bisulfate-hydrogen sulfide(g).

44. Dissolved sul fate-dissolved sulfide, dissolved sulfate-hydrogen sulfide(g), and 

dissolved sulfate-sulfur dioxide(g); hydrogen sulfide(g)-dissolved sulfide 

and dissolved sulfate-dissolved sulfide.

45. Hydrogen sulfide(g)-sulfur(g) and sulfur dioxide(g)-sulfur(g).

46. Pyrite-galena, pyrite-chalcopyrite, pyrite-sphalerite, sphalerite-chalcopyrite, 

and chalcopyrite-galena.

47. Sphalerite-galena.

48. Sphalerite-HS- and galena-HS~.

49. Molybdenite-sphalerite, molybdenite-galena, molybdenite-chalcopyrite, 

molybdenite-pyrite, and molybdenite-pyrrhotite.

TABLES

Page

TABLE 1. Comparison between values of A, a, and 103 lna .......................................................... KK2

2. Experimental determinations of the CO2-water fractionation factor at 25°C ................... 3

3. Absolute deuterium-hydrogen isotope ratios, and 8 values for reference samples........... 5

4. Miscellaneous fractionations............................................................................................... 6
DATA OF GEOCHEMISTRY

COMPILATION OF STABLE ISOTOPE FRACTIONATION FACTORS OF

GEOCHEMICAL INTEREST

By IRVING FRIEDMAN and JAMES R. O'NEIL

ABSTRACT

Selected fractionation factors for D, O18 , C13, and S34 have been compiled from the literature and plotted on a convenient linear temperature coordinate system. Elementary discussions of terminology and 

the problems of isotope standards are presented, together with equations relating the various standards used for reporting O18 values. 

Where data are available at only a few temperatures, the fractionations 

are given in tabular form. For each fractionation factor, a reference 

to the original work is given.

INTRODUCTION

Beginning with the classic paper of Urey (1947), in 

which he calculated stable isotope fractionation factors 

between species of geochemical interest, there has been 

an increasing use of stable isotope variations in natural 

materials for studies in the Earth and cosmic sciences. 

Equilibrium fractionation factors that measure the distribution of a rare stable isotope between two species have 

been determined directly by laboratory experiments and 

also by calculations using the methods of statistical thermodynamics. They have also been inferred from regularities in the stable isotope ratios of natural materials. 

These fractionation factors have been used in geochemistry, meteorology, oceanography, water and aqueoussolution chemistry, cosmochemistry, paleontology, and 

in other scientific fields for a variety of purposes.

We believe that a compilation of selected fractionation 

factors for D, O18 , C13 , and S34, plotted on a convenient 

coordinate system, will be very useful to workers in the 

field and will also focus attention on the state of the art 

of this aspect of stable isotope geochemistry. In addition, 

for the benefit of students and new workers in the field, 

elementary discussions of conventional terminology and 

the problem of isotope standards are presented.

We thank H. G. Thode, Y. Bottinga, and R. H. Becker 

for their helpful comments.

TERMINOLOGY

1. THE 8 VALUE

For most geochemical purposes, knowledge of only the 

difference in absolute isotope ratios between two substances is sufficient. In addition, differences can be measured far more precisely than can absolute ratios. Consequently, this difference, or 8 value, is used almost 

exclusively in the Earth sciences for reporting stable isotope abundances and variations. If the absolute ratios of 

the standards employed are known, then the absolute 

ratio of any sample is readily calculated from its 8 value. 

The 8 value is defined as follows:

RX -R

STD

R

|103 ,

STD

where flx=(D/H)x , (C13/C12 ) X , (O18 /O16 ) X , (S3VS32 )X ,

and so forth, and R$TD * s ^e corresponding ratio in a 

standard. Note that R is always written as the ratio of the 

heavy (rare) isotope to the light (common) isotope. The 

8 value, then, is the difference in isotope ratio between a 

sample and a standard, expressed in parts per thousand, or 

per mil (°/00)- A sample with a 5O18 value of +10.0 is enriched in O18 (or is greater in O18 /O16 ratio) by 10 per mil, 

or 1 percent, relative to the standard. Negative 8 values indicate that the sample is depleted by that amount relative 

to the standard. The 8 value is the quantity actually measured on isotope ratio mass spectrometers.

Over the years, stable isotope geochemists have tacitly 

developed a certain uniformity in the presentation of 

their data. However, there are still a few noteworthy differences. Some workers write 8(O18/O16 ), 8(D/H), and 

so forth, whereas others write SO18 and 8D, and so 

forth, the latter being more common. In the earlier literature 8D values were given in percent, but, because so 

many laboratories now report both 8D and SO18 values 

for the same substances (particularly water), it has become 

standard practice to report both values in per mil to avoid 

confusion. The 8C13 values reported from most laboratories in the Soviet Union are given in percent.

2. THE FRACTIONATION FACTOR, a

The isotope fractionation factor between two substances, A and B, is defined as:

a - RA

aA-B ~ ~ '

KKl
KK2 DATA OF GEOCHEMISTRY

In terms of the quantities actually measured in the laboratory ( 8 values), this expression becomes:

V

1,000 1,000 + 8,4

1 +

A-B

1 +

1,000

1,000

If the isotopes are randomly distributed over all possible 

sites or positions in the species A andfi, the fractionation 

factor ( a ) is related to the equilibrium constant, K, for 

isotope exchange reactions in the following way:

<x=K l/» ,

where n is the number of atoms exchanged. 1 For simplicity, isotope exchange reactions are usually written such 

that only one atom is exchanged. For example, the oxygen 

isotope exchange reaction between CO2 and water vapor 

can be written:

+ H2O18 ^ ^CO218 + H2O16 . 

The equilibrium constant for this reaction is

K =

(HP'8)

This formalism is normally used in the calculation of 

fractionation factors from spectroscopic and thermodynamic data. CO218 means that both oxygen atoms in 

the molecule are O18 . The equilibrium constants for these 

reactions as written are equal to the fractionation factor:

(O18 /O16 )

K= a =

CO,

(O18/O16>

H,O

Values of a are normally very close to unity, typically 

l.OOX. Commonly, isotopic fractionations are discussed 

in terms of the value of X, in per mil ("per mil fractionations"). For example, the sulfur isotope fractionation factor between ZnS and PbS at 200°C is 1.0036. It is accepted 

parlance to state that at 200°C (1) the sphalerite-galena 

"fractionation" is 3.6 (or 3.6 per mil), or (2) sphalerite 

is enriched in S34 by 3.6 per mil relative to galena.

3. 103 lna AND THE A VALUE

It is a useful mathematical fact that 103 ln (l.OOX)S 

X. For the S34 example mentioned above where a =1.0036, 

103 In a = 3.6. That is, 10 s In a is the "per mil fractionation." This logarithm function has added theoretical 

and experimental significance. For perfect gases, In a 

varies as 1/T2 and 1/T in the high- and low-temperature 

limits, respectively (Bigeleisen and Mayer, 1947). In addition, smooth and often linear curves have been found to 

obtain when 103 lna is plotted against 1/T2 for experi-

'Some authors have used the symbol OL' to refer to a measured fractionation factor, 

even though it may not be an equilibrium fractionation.

mentally determined fractionation factors between 

mineral pairs or mineral-water pairs.

The per mil fractionation, 10s In a, is then of prime 

importance in stable isotope geochemistry. This quantity 

is very well approximated by the A value:

That is, merely subtracting S values will be an excellent 

approximation to the per mil fractionation and identical 

to it within the limits of analytical error for values of both 

A 's and 6 's, which are less than about 10. In table 1 a 

comparison between A and 10s In a is presented to illustrate the magnitudes of the approximations. The use of 

A was common in the earlier literature. The definition 

A = 10s In a has appeared in some recent papers. This 

difference in the use of the symbol A is normally of minor 

consequence, and there can be no confusion if the authors 

clearly state how A is calculated. However, as the figures 

in table 1 indicate, it is important to calculate the exact 

10s ln« when the per mil fractionations or the 6 values 

are greater than 10.

A few authors have used another fractionation factor, 

e, defined as e = (a-l)103. Again, for small values of 

e , s S 103 ln « as mentioned previously.

TABLE 1. Comparison between values of A , ot , and 103Jna

8

A

1.00

5.00

10.00

12.00

15.00

20.00

10.00

20.00

30.00

30."n

30.00

30.00

*B

0

0

0

0

0

0

5.00

15.00

25.00

20.00

15.00

10.00

AA-B

1.00

5.00

10.00

12.00

15.00

^.00

5.00

5.00

5.00

10.00

15.00

20.00

IOMntt^_B

1.00

4.99

9,95

11.93

14.89

19.80

4.96

4.91

4.87

9.76

14.67

19.61

a

1.00000

1.00500

1.01000

1.01200

1.01500

1.02000

1.00498

1.00493

1.00488

1.00980

1.01478

1.01980

STANDARDS

Certain irregularities concerning standards, particularly oxygen isotope standards, have developed over the 

years and have been responsible for considerable confusion on the part of workers in the field. Some laboratories are "tied" to each other by acceptance of the 8 

values of certain interlaboratory comparison samples. 

Other laboratories use independent means of arriving at 

8 values. In some cases interlaboratory agreement is 

good, while in others it is poor, even though the laboratories may be "tied" to one another. The reasons for these 

discrepancies are often obscure and usually ignored. With 

the recent rapid growth in the number of laboratories engaged in stable isotope research, informal arrangements 

for interlaboratory standardization are impractical. In the 

future these problems may be resolved by the use of international reference standards being made available by the 

U.S. National Bureau of Standards (Gaithersburg, Md.)
COMPILATION OF STABLE ISOTOPE FRACTIONATION FACTORS OF GEOCHEMICAL INTEREST KK3

and the International Atomic Energy Agency (Vienna, 

Austria).

OXYGEN

There are two internationally accepted reference standards used to report variations in oxygen isotope ratios: 

PDB (Peedee belemnite) and SMOW (Standard Mean 

Ocean Water). The PDB standard is normally used only 

in ocean paleotemperature studies wherein CaCO3 from 

fossil shells is analyzed. The PDB standard is a sample 

of belemnite guard from the Peedee Formation in North 

Carolina and was the laboratory working standard used 

at the University of Chicago during the time that the oxygen isotope paleotemperature scale was developed. Inasmuch as there is confusion in the literature, note also that 

the PDB standard is the solid carbonate, not the acidliberated CO2. The original supply of this standard has 

long been exhausted; however, numerous secondary 

standards have been developed and exchanged among 

workers in the field. The oxygen isotopic composition 

of carbonates is determined by the analysis of CO2 generated from the carbonates by reaction with 100 percent 

phosphoric acid (McCrea, 1950).

There are variations in the carbonate analytical procedures used in different laboratories which bear on the 

question of standards and interlaboratory comparisons. 

Apparent differences in 8 O18 of a carbonate sample can 

arise, depending, for example, on (1) temperature of the 

acid reaction, (2) procedure used to remove organic material (Emiliani, 1966), (3) carbonate to acid ratio (Fontes 

and others, 1965), and, (4) grain size of the carbonate (Fritz 

and Fontes, 1966). Inasmuch as only two-thirds of the 

oxygen is liberated from the carbonate during acid decomposition, these observed variations are not unexpected. In the oxygen isotope analysis of carbonates, identical 

physical and chemical conditions must be operative during preparation of standard and sample so that systematic 

errors will cancel.

The SMOW standard was originally a hypothetical 

water sample with isotope ratios of oxygen and hydrogen 

similar to those of an average sample of ocean water. It 

was defined by Craig (1961) in terms of a National Bureau 

of Standards reference water, NBS-1, as follows:

(018/016 ) SMOW = 1-0<>8 <0»/0«) NBS-I .

Subsequent to this definition, two additional SMOW 

standards have appeared, causing some confusion. In 

most of their papers, Taylor and Epstein of the California 

Institute of Technology have used a standard called 

SMOW against which a sample of Potsdam Sandstone 

(the Caltech internal standard) is +15.50%0. Finally, a 

large quantity of water called SMOW was prepared by 

R. Weiss and H. Craig for the International Atomic 

Energy Agency (Vienna) as one of four standard reference 

waters available to stable isotope geochemists. This latter

SMOW has been analyzed in many laboratories, and the 

oxygen isotope composition has been found by many 

investigators to be identical to the originally defined 

SMOW within the limits of analytical uncertainty 

(±0.05°/oo)- There is some indication that random and significant variations in 5O18 exist between different samplings of the main storage vessels of the NBS water standards.

SMOW is a water standard. In order to relate the oxygen 

isotope composition of nonaqueous substances to it, 

SMOW (or related waters) must be analyzed directly by 

fluorination or carbon reduction techniques. If water is 

analyzed by the CO2-equilibration method, the fractionation factor between CO2 and H2O must be known at the 

temperature of equilibration. In most laboratories, water 

is normally analyzed by the CO2 -equilibration technique. 

For many years the value of 1.0407 measured by Compston and Epstein (1958) and O'Neil and Epstein (1966a) 

has generally been accepted and used to relate oxygen isotope compositions of nonaqueous materials to SMOW. 

However, several recent determinations of this factor indicate that the factor is probably larger than 1.0407 (table 

2). Although it is possible to determine this factor with 

a precision of ±0.0001, it is impossible, owing to the present limitations of mass spectrometry, to determine a factor as large as this with an accuracy of more than ±0.0004 

(approximately 1 percent of the difference in 5 between 

the CO2 and H2O. Therefore, to avoid further confusion, we suggest that a new value of this factor, based on 

an average of 10 determinations, be accepted by everyone working in this field. We propose the value of 

1.0412, which is the average of 10 of the 11 values known 

to us.

Recently, a reference standard of "African Glass Sand" 

(quartz) has been made available through the U.S. National Bureau of Standards as NBS-28. The 8 value of

TABLE 2. Experimental determinations of the CO2-water fractionation 

factor at 25°C

Reference a 10*in a

Compston and Epstein (1958)........................................ 1.0407 39.89

Staschewski (1964)........................................................... 1.0424 41.53

Majzoub (1966)................................................................ 1.0417 40.85

O'Neil and Epstein (1966a)............................................ 11.0412 40.37

Bottinga and Craig (1969).............................................. 1.0409 40.09

Matsuhisa, Matsubaya, and Sakai (1971)....................... 1.0412 40.37

Blattner (1973)................................................................. 1.0417 40.85

Horibe, Shigehara, and Takakuwa (1973)..................... 1.0414 40.57

I. Friedman and J.D. Gleason (unpub. data, 1974)....... 1.0414 40.57

O'Neil, Adami, and Epstein (1975)................................ 1.0412 40.37

R.N. Clayton (unpub. data, 1975).................................. 1.0406 39.80

'Corrected from the published value of 1.0407 using revised mass spectrometer correction 

factors.

NOTE. The average of all the published analyses, excepting the 

value of 1.0424 (Staschewski, 1964), is 1.0412. Bottinga (1968a) has 

calculated values of 1.0409. Bottinga and Craig (1969) have calculated 

a value of 1.0411.
KK4 DATA OF GEOCHEMISTRY

+10.0 reported by Friedman and Gleason (1973) was based 

on their fluorination of two NBS-1 water samples. The 

SO18 value of NBS-28 reported to the authors from several laboratories indicate a range between 9.5 and 9.9.

The relationships between the oxygen isotope standards and the CO2 gases normally prepared from them are 

shown in figure 1. For studies involving only carbonates 

or carbonates and water, some authors choose to use the 

PDB scale exclusively. In his paper establishing the 

SMOW scale, Craig (1961) stated that "The SO18 value 

of Chicago PDB-1 carbonate standard (CO2 from reaction 

with 100 percent H3PO4 at 25°C) is +0.22 per mil on the 

SMOW scale." The correct statement should have been 

that the SO18 value of the CO2 produced by reaction of 

100 percent H3 PO4 with PDB calcite at 25°C is +0.22 per 

mil relative to CO2 equilibrated at 25°C with SMOW 

water. In order to relate the two standards, the fractionation factor for the CO2-H2O equilibration and for the acid 

reaction that produces the CO2 must be known. The uncertainty in these fractionation factors will result in an

SMOW PDB

SC/ 

41.42 

41.20 

+ 40

30.86 

+ 30

+ 20

+ 10

0

7.94

FlGt

\LE SCALE

='CO2 produced by reaction of POB 

-\ with H3PO4 at 25°C 

CO2 in equilibrium with SMOW at 25°C* -

Oxygen in calcite from belemnite guard

from Peedee Formation, North Carolina ^

? 

o

I

In 

*

o

tsro

1

c 

o

'-t-l 

u 

ro

q.

I

O

U

Oxygen in Standard

ionation .01025

i n. *- o 

V 6 «~l U CO I

"

. iviGsn CJcGsn W3t6r

(SMOW)

(0 18 /016 ) H 1.008 (018 /016 ) 

SMOW NBS-1

^Oxygen in NBS-1 water

JRE 1. Relationship between PDB, SMOW, and other oxygen standards.

0

-10

-20

-29.94

uncertainty in the relation between PDB and SMOW. 

The relationship between these two standards has been 

further confused by the fact that some authors have used 

the CO2 liberated from the calcite as the PDB standard 

rather than the solid calcite. To relate 8 O18 values of calcite on the PDB and SMOW scales, the following expressions are used:

8 sMow=1 - 030868 PDB + 30.86, and 

8 PDB=0.970068 SMOW-29.94.

These relationships are based on the following fractionation factors at 25°C:

1.0412 for CO2-H2O,

1.01025 for H3PO4 -liberated CO2 from calcite and, 

1.00022 for H3PO4 -liberated CO2 from PDB-CO2 in 

equilibrium with SMOW.

HYDROGEN

The SMOW standard is also used for reporting hydrogen isotope compositions and was defined by Craig (1961), 

again in terms of NBS-1:

(D/H)sMow= l-050(D/H)NBS_] .

Therefore, by definition 8D of NBS-1 is -47.6 on the 

SMOW scale. When the results of deuterium analyses of 

the four I.A.E.A. standard waters were compared several 

years ago, significant discrepancies in 8 D were apparent. 

The differences were attributed to the use of incorrect 

mass spectrometer correction factors by some investigators. The H3 + contribution to the mass 3 beam cannot be 

determined precisely. Consequently, when this contribution is large ( > 10 percent), the correction may result in 

incorrect 8 values. Some laboratories have circumvented 

this problem, calibrating their machines by accepting 

Craig's 8 D values of -47.6 and -183.3 for NBS-1 and 

NBS-1 A, respectively. Recent measurements by Coplen 

and Clayton (1973) on a high-resolution mass spectrometer (Hs"1" contribution only 0.3 percent) have verified 

Craig's results. Coplen and Clay ton's 8 D for NBS-1 A is 

-183.0+0.5. '

The I.A.E.A. sample of water called SMOW 

has been analyzed in several laboratories and is not identical in D/H ratio to the defined SMOW. Coplen and Clayton (1973), for example, report a 8D value of -1.2. 

Friedman has recently measured the hydrogen isotope 

compositions of 4 separate samples of NBS-1 that he received over the past 20 years and found differences in 8D 

as high as 8°/oo. Therefore some of the interlaboratory 

differences observed may depend on the batch of NBS-1 

standard utilized. An Antarctic water sample is now being 

distributed by the I.A.E.A. This light water has been 

called SNOW and SLAP (Standard Light Antarctic Precipitation). Because the acronyms SNOW and SMOW 

resemble each other too closely, SLAP is to be preferred 

as a designation for this sample.
COMPILATION OF STABLE ISOTOPE FRACTIONATION FACTORS OF GEOCHEMICAL INTEREST KK5

TABLE 3. Absolute deuterium-hydrogen isotope ratios, and 8 values for reference samples

[Leaders (...) indicate no data]

Sample

(D/H) NBS_ r............

(D/H)..n(, .............

v 'NBS-1A

(D/H) .............

^D NBS-1A/SMOW1 ""

^NBS-IA/SMOW1 ' 

SDSLAP/SMOW """

" NBS-1 A/NBS' " "

Horibe and 

Kobayakawa 

(1960)

157±lxlO~6

149±lxl(T6

128±1X1(T6

-182.2

-141.3+2.3

Craig 

(1961)

158±2xl(T6

150±2X10~6

129±2xlO~6

2-47.6

-183.3

Hagemann, Nief, 

and Roth 

(1970)

155.76xl(T6

148.34 xi(T6

89.02±0.05xl(T6

-428.50±1

Brown, Robertson 

and Thurston 

(1971)

157.6+0.3xl(T6

150.1±0.3X1(T6

Coplen and 

Clay ton

(1973)

-183.0±0.5

3 -426.4±l

4 -425.8±l

-142.13

OD vi v is the OD value of X relative to Y. 2De£ined values. 3Compared to SMOW from NBS-1. 'Compared to SMOW, Vienna.

In some of the early United States literature on the 

deuterium abundance in natural materials, a sample of 

Lake Michigan water was used as a standard. The Lake 

Michigan standard is -42.4 on the SMOW scale.

Table 3 lists absolute values of various standards used 

for 8 D as well as ratios of relative deuterium values between common standards.

CARBON

There are a few problems associated with carbon isotope standards. The universally accepted standard for 

reporting carbon isotope compositions is PDB, which is 

no longer available. Two reference standards distributed 

by the U.S. National Bureau of Standards are NBS-20 

(Solenhofen Limestone) and NBS-21 (spectrographic 

graphite). The 8 values given by Craig (1957) for these 

standards are -1.06 and -27.79, respectively. Recent determinations indicate that the latter value is closer to-28.10 

(Mook, 1971; Letolle, 1971; F. C. Tan, unpub. data, 1973; 

J. D. Gleason and I. Friedman, unpub. data, 1973). The 

Solenhofen Limestone standard is actually too fine 

grained to be a good and lasting standard. Care must be 

taken to store it, well-stoppered, in a desiccator to prevent 

exchange between the sample and CO2 in moist air. A 

new carbonate reference standard is being prepared by us 

for distribution by the U.S. National Bureau of Standards.

SULFUR

Troilite from the Canyon Diablo meteorite is the internationally accepted standard used to report 8SM variations. An NBS-120 sulfur reference sample exists, but few 

workers have made use of it. Instead, sulfur isotope geochemists have made interlaboratory exchanges of working standards. The mass spectrometric corrections for 

sulfur dioxide are large, and we suggest that two international reference standards differing in 8 S34 by a large 

amount be used as interlaboratory comparison samples. 

Sulfur hexafluoride, SF6, for mass spectrometric analysis 

of sulfur has been used by Thode, Cragg, Hulston, and

Rees (1971) for S36/S32 , as well as for S34/S32 ratio measurement. The preparation of SF6 has been described by 

Puchelt and Kullerud (1970). Sulfur hexafluoride has 

some advantages over sulfur dioxide for sulfur isotopic 

analysis.

STABLE ISOTOPE FRACTIONATION 

CURVES

We have made this compendium in order to provide 

a single reference work in which stable isotope fractionation factors of geologic interest are presented in a readily 

usable format.

Some features of the curves are:

1. Fractionations (103 lna) can normally be read to ±0.2 

per mil.

2. Temperatures can be read to ±0.5°C on some curves 

and to ±5°C on others.

3. The temperature axes are linear in degrees Celsius.

4. The scale of the graph paper is metric for easy comparison and transposition.

5. Where appropriate, the curves have been drawn using

values of 103 lna recalculated using the CO2-H2O

fractionation factor of 1.0412. (See p. KK3 ) The

corresponding corrected expressions in the figure

captions are indicated with an asterisk.

Titles on the figures designate the systems presented

thereon and are written such that the first-named phase

concentrates the heavy isotope if the value of 1,000 In a

is positive. The curves have been extrapolated beyond the

temperature ranges investigated and even beyond the

range of stability of some minerals. This was done to

provide rough estimates when no other information is

available.

Not all pertinent equilibrium fractionation factors 

that have been measured or calculated are presented here. 

Those determinations which have been clearly superseded by later, more refined determinations (often by the 

same investigators) are not included in the compilation. 

Except for the carbonate-acid fractionation factors, non-
KK6 DATA OF GEOCHEMISTRY

equilibrium isotope effects are not presented. However, 

some of the discrepancies among the experimental curves 

are undoubtedly the result of nonequilibrium or kinetic 

isotope effects, which can often be difficult to recognize. 

The uncertainty in the CO2-H2O fractionation factor 

at 25°C has serious implications both in relating oxygen 

isotope standards and in comparing experimentally determined oxygen isotope fractionation factors. Except for 

the feldspars and micas (O'Neil and Taylor, 1967, 1969), 

rutile (Addy and Garlick, 1974), and magnetite (Bertenrath and Friedrichsen, 1975) the factor 1.0407 was used 

in the determination of the isotopic compositions of the 

waters used in all the experiments. The waters in these 

studies were either analyzed directly or a value of 1.04120 

was used in the original publication. In the compilation

published herein, all the curves with the exception of 

those of Bottinga and Javoy (1973) have been recalculated 

to the newly proposed value of a (1.0412).

The analytical expressions for the temperature dependence of the isotope fractionation factors are given in the 

figure captions, usually in the form given by the original 

authors but recast for consistency. Isolated fractionation 

factors that were determined at only a few temperatures 

are normally plotted on the figure most appropriate to 

the system in question. In these compilations an asterisk 

indicates that the values have been recalculated using the 

CO2-H2O fractionation proposed on page KK3. Those factors for which there is no appropriate figure are listed 

in table 4. In the figure captions T = temperature in 

kelvins; t - temperature in degrees Celsius.

TABLE 4. Miscellaneous fractionations

[Leaders (...) indicate not measured or not calculated]

No. Fractionation

Measured Calculated Reference Remarks

Oxygen

1

2

3

H3PO4 liberated COz-carbonates(s);

CaCOj (calcite) .....................

CaCOs (aragonite) ................

SrCOs....................................

BaCOj ...................................

CaMg(CO3 )2 (dolomite)........

ZnCQs. ..................................

CdCOs...................................

MnCO3 .. ................................

PbCOs. ..................................

MgC03 . .................................

Hydromagnesite-H2O(l )..............

Magnesian calcite-H2O(l). ...........

... 25

... 25

... 25

... 25

... 25

... 25

... 25

... 25

... 25

... 50

0

25

... 25

10.20

10.29

10.43

10.91

11.03

11.24

11.39

10.07

10.08

11.53

137.58

131.69

2.78(10«T-2)-2.89

+0.06 M MgCOj

Sharma and Clayton (1965; corrected by R. N. Clayton (oral

commun., 1972).

... ......do.

... ......do.

... ......do.

... ......do.

... ......do.

... ......do.

... ......do.

... ......do.

... Perry and Tan (1972).

... O'Neil and Barnes (1971).

... ......do.

Tarutani, Clayton, and Mayeda Where M MgCOs=mole percen

(1969). MgCOj in solid solution in

4 Illite-H2O(l)................................... 22

5 H2O(s)-H2O(l)........

6 H20(s)-2.5 M NaCl.

7 H20(s)-H2 0(g)........

8

9 OH-»-HgO(l).

10 C02 (g)-D20(l),

11 C02(g)-C02(l).,

0

-10

0

-5

-10

-15

-20 

25 

25 

15 

25

-53

-50

-43

-30

-25

-20

-10

23.4

3.1

2.2

11.8

12.2

12.6

13.0

13.4

39.2

23.2

-1.03

-.98

-.86

-.69

-.64

-.58

-.51

James and Baker (1976) .

carbonate mineral. 

Gross average of six determinations.

..... O'Neil (1968).

..... Stewart (1974).

...... Matsuo and Matsubaya (1969).

...... ......do.

..... ......do.

..... ......do.

..... ......do.

22.8 Thornton(1962).

......do.

Green and Taube (1963).

Staschewski (1964).

Grootes, Mook, and Vogel (1969).

37.8

-1 .22

-1.17 ......do.

-1.05 ......do.

-.88 ......do.

-.83 ......do.

-.77 ......do.

-.68 ......do.

O18 is concentrated in the liquid 

phase 

Do. 

Do. 

Do. 

Do. 

Do. 

Do.
COMPILATION OF STABLE ISOTOPE FRACTIONATION FACTORS OF GEOCHEMICAL INTEREST KK7

TABLE 4. Miscellaneous fractionations Continued

No. Fractionation tt°C)

10s In a

Measured Calculated Reference Remarks

Oxygen Continued

1 1 CO2(g)-CO2 ( 1 ) Continued

12 C02(g)-C02 (aq) ..............................

13 O (g)-O (aq)

14 Mirabilite(Na2SO4 -10H2O)- 

H20(l) .........................................

15 Gypsum-(hydrate water )-H2O(l)....

16 Grossularite-H2O(l )........ ................

17 Andradite-H2O(l) ...........................

18 Biotite (annite)-H2O(v)...... .............

0

10

20

30

0

10

20

30

40

50

60

1 23

0

25

. 17-57

600

600

400

600

800

-0.42

-.32

-.21

-.06

-1.17

-1.13

-1.09

-1.05

-1.01

-.97

-.92

0.85-0.01(0

2.0

1.4

3.49

-1.60

-3.28

-2.1

-2.1

-1.7

-0.58 Grootes, Mook, and Vogel (1969).

.45 ......do....... .....................................

-.32 ......do............................................

.09 ......do............................................

-.95 Vogel, Grootes, and Mook (1970)

.93 ......do............................................

.90 ......do............................................

.87 ......do............................................

..... ......do............................................

..... ......do............................................

...... ......do............................................

Kroopnick and Craig (1972) ........

..... Stewart (1974)... ............................

..... ......do............................................

Gonfiantini and Fontes (1963).

..... Taylor (1976).

..... ......do.

Bertenrath and Friedrichsen (1975).

..... ......do.

..... ......do.

O18 is concentrated in the liquid

phase.

Do.

Do.

Do.

O18 is concentrated in the liquid

phase.

Do.

Do.

Do.

Do.

Do.

Do.

This expression holds for Oz dissolved in either pure water or

seawater. Where t is in °C.

The fractionation measured was 

between the hydrate water

and the solution.

Do.

The fractionation is independent of the iron ratio in the

mica. The authors have reservations regarding the experimental value of 400°.

Carbon

19 C02(g)-C02(l)

20 Calcite-HCOs-1.............................

21 Aragonite-HCOr 1 ............ ............

22 Argonite^sralcite ............................

23 Gaylussite (Na2COs-CaCO3

 5H,,O)-CO3-2 . ............ ................

24 Trona (Na2CO3 -NaHCO3

 2H20)-C03-2 . ..........................

.. -53

-50

-43

-30

-25

-20

-10

0

10

20

30

.. 20

25

.. 25

.. 25

25

8

18

25

30.5

35

18

25

30.5

0.44

.48

.57

.47

.42

.41

.35

.34

.34

.24

.14

0.035+0.013

0.9+0.2

2.7+0.2

1.8+0.2

3.09

2.50

2.00

1.90

2.00

1.1

.8

.7

...... Grootes, Mook, and Vogel (1969).

..... ......do............................................

..... ......do............................................

..... ......do............................................

..... ......do............................................

..... ......do............................................

..... ......do............................................

..... ......do............................................

..... ......do............................................

..... ......do............................................

..... ......do............................................

C13 is concentrated in the gaseous phase (measured).

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Do.

Emrich, Ehhalt, and Vogel (1970).

Rubinson and Clay ton (1969).

..... ......do.

..... ......do.

0.9 ......do.

..... Matsuo, Friedman, and Smith

(1972).

..... ......do.

..... ......do.

..... ......do.

..... ......do.

..... ......do.

..... ......do.

..... ......do.
KK8 DATA OF GEOCHEMISTRY

TABLE 4. Miscellaneous fractionations Continued

No. Fractionation

25 H2 0(v)-H2S(g) ................................

26 H20(l)-H2S(g).... .............................

27 H2O(s)-H2O(l). ...............................

28 H2 O(s)-2.5 M NaCl.... .....................

30 OH-'-H2O(l). .................................

31 Mirabilite(Na2SO4-10H2OH f~\f 1 \

32 Borax (Na 2B4 O7 -10H2O-H2O(1) ....

33 Gaylussite(Na 2CO3 'CaCO3 

 5H2O-H2 O(1)-.. ........... .................

34 CuSO4 -5H2O-H2O(l) .....................

35 Crystal hydrate-H2O(l): 

CuSO4 . .....................................

SrCl 2 ... ......................................

A1 2 (S04 ) 3 . ...... ...........................

KA1(S04 ) 2 . ................................

BeSO4 . ......................................

36 Gypsum-H2 O(l). .............................

37 Kaolinite-H2O(l)....... ......................

38 Illite-H2O(l). ...................................

39 Montmorillonite-H2O(l)..... ............

40 PbS-S ..............................................

41 H2S(g)-H2S (solution).....................

25

100 

170 

200

25

100 

170 

200 

0

0 

0 

0 

0 

0 

-10

13 5

13 5

0

25

8-35 

18

25

30 5

35

25

25

25

25

25

25

17-57

200

200

200

300

500

20

103 In a

Measured

20.9 

18.4 

23.2 

19.3 

20.6 

23 7

40.0

-1,400

18.8

16.9

0 

-13 1

-13.1

-14.1

-15 1

-21.8

-23 7

-34 4

-35 4

-46.9

-53 5

-15

-34 5

-39 8

-43.9

2 3

.8

1.6

Calculated Reference

Hydrogen

791 Galley, Miller, Atherley, and

Mohn (1972). 

634 ......do. 

536 ......do. 

502 ......do. 

861 ......do.

660 ......do. 

534 ......do. 

492 ......do. 

19.0 Weston (1955).

Posey and Smith (1957). 

17.0 Kuhn and Thurkauf (1958). 

Merlivat and Nief (1966). 

O'Neil (1968). 

Arnason (1969). 

Stewart (1974).

Stewart (1974).

..... ......do

Matsuo, Friedman, and Smith

(1972).

..... ......do.

..... ......do.

..... ......do.

..... ......do.

Heinzinger (1969).........................

..... ..... .do................ ............................

..... ......do................ ............................

..... ......do............................................

..... ......do............................................

..... ......do............................................

..... Fontes and Gonfiantini (1967).

O'Neil and Kharaka (1976)..........

..... ......do............................................

..... ......do............................................

Sulfur

Puchelt and Kullerud ( 1 970).

..... ......do.

..... Sharan, Galas, Lees, and Zhook

(1974).

Remarks

The four waters coordinated to Cu+2 are 57 per 

mil depleted in deuterium relative to the hydrogenbonded water molecule.

in the solution relative 

to the hydrate waters of 

all these salts. 

Do.

Do.

Do.

Do.

Do.

Based on experiment with

29 percent exchange. 

Based on experiment with

28 percent exchange. 

Based on experiment with

82 percent exchange.

'Value has been recalculated, using the CO2 -H2O fractionation of 1.0412.
COMPILATION OF STABLE ISOTOPE FRACTIONATION FACTORS OF GEOCHEMICAL INTEREST KK9

Because of some unresolved discrepancies in the oxygen isotope fractionations between minerals and water, 

it would be unwieldy and confusing to present all possible combinations of oxygen isotope fractionation between mineral pairs. The curves proposed by Bottinga 

and Javoy (1973, 1974) are presented, inasmuch as they 

are self-consistent and take into account much of the experimental work and theoretical considerations. Because 

of the involved manner in which these expressions were 

derived, we made no attempt to correct them for the new 

CO2-H2O fractionation. The quartz-magnetite pair is 

potentially the most useful, and certainly the most sensitive, pair for oxygen isotope thermometry, and the curve 

proposed by Becker (1971) is presented along with that 

of Bottinga and Javoy in figure 20. It is encouraging that 

the two curves are so similar and that the slope for this 

important system is fairly certain.

The stable isotope fractionations presented have not 

been critically evaluated. It is clear from reading the details given in the original references that some systems 

have been examined more thoroughly than others. Presenting all these data together uncritically calls attention 

to the problem areas that require resolution. The calculated fractionation factors for gaseous systems are 

among the most reliable factors presented here. Of the 

minerals investigated, calcite has shown the most consistent oxygen isotope results among several investigations, including equilibrations with water and with carbon dioxide. The stable isotope relations are somewhat 

obscured by experimental difficulties and nonequilbrium effects, but even at our present state of knowledge, 

geologically reasonable temperatures are usually inferred. 

As geothermometers, stable isotope fractionation factors 

continue to show considerable promise for a variety of 

geologic environments. There is enough consistency in 

the natural data to warrant future investigations aimed 

at reconciling some of the discrepancies in the experimental data.

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COMPILATION OF STABLE ISOTOPE FRACTIONATION FACTORS OF GEOCHEMICAL INTEREST KK11

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KK12 DATA OF GEOCHEMISTRY

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irU.S. GOVERNMENT PRINTING OFFICE 1976-7774)34/32
FIGURES 2-49
FIGURE 2

A, Epstein, Buchsbaum, Lowenstam, and Urey (1953):

f (°C) = 16.5-4.3( 8c~ &,)+0-14(8 f - SJ2 " 

B, Craig(1965):

r(°C)= 16.9-4.2(8 c -^)+0.13(8f -^)2, 

where

8 = 8o18 of CO2 from calcium carbonate by reaction with H3PO4 at 25°C, and 

8=8 O18 of CO2 in equilibrium with the water at 25°C. 

The expressions are independent of the standard used.

NOTE. S. Epstein (oral commun., 1975) states that the Craig paleotemperature scale is inincorrect and that the latest scale (Epstein, 1976) corresponds to the 1953 scale within experimental 

error.
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B, O'Neil and Adami (1969) experimental data:

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FIGURE 6

Truesdell (1974) gives the temperature coefficient of the COa-H2O fractionation. The data have 

been plotted assuming that the fractionation at 25°C is 40.37.
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A, The experimental data of Baertschi and Thiirkauf (1960) and of Craig, Gordon, and Horibe 

(1963) were combined in the expression given by Bottinga and Craig (1969):

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B, Majzoub (1971): (0° to 100°C).

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n 

w

2!

2! 

O

o 

o

^5^

DO

:^'

i i i i i i i

W XO
FIGURE 8

A, This expression is based on the experimental data from 134° to 300°C (Bottinga, 1968b; Bottinga 

and Craig, 1968) and the data presented in figure 5 (Y. Bottinga, written commun., 1973):

103 lna = +0.7.664(108T-2 )+1.2051(103T-1 )-3.493. 

B, Uvarov, Sokolov, and Zavoronkov (1962): (0° to 209°C).

103 lna = 7.599(103T-1 )-16.62.
TEMPERATURE, IN DEGREES CELSIUS

. 

o

O

'/-.

H 

W

>

H 

W

w 

H

w 

w 

z

o 

o

W O N< x.O
FIGURE 9

Solid curves from Sofer and Gat (1972). 

Dashed curves from Taube (1954).

NOTE 1. Additional data on these systems by O'Neil and Truesdell (written commun., 1976) 

are not shown but are in agreement with those of Sofer and Gat (1972) and of Taube (1954).

NOTE 2. In these three studies the GOrequilibration method was used to obtain the data. Thus, 

the fractionations actually measured were between COz in equilibrium with pure water and COz 

in equilibrium with the solutions. A value of the fractionation factor between water(l) and water(v) 

was then taken from the literature (fig. 7, this report) to construct the curves.
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 9

o

X

Y 

G 

E

N

10 3 In a 

WATER(l)-WATER(v), SOLUTE EFFECTS AT 25°C
FIGURE 10

Truesdell (1974).

As in figure 9 (note 2), the fractionations measured were between CO2 equilibrated with pure 

water and COg equilibrated with various solutions. From these figures can be obtained the 

oxygen isotope activity ratio of the solutions relative to pure water.
TEMPERATURE, IN DEGREES CELSIUS

to

2

00

n

rM»

n

Z 

»

n

g.

v> 

O

r

d

H

O 

Z 

en

H 

tn 

UO

wo
FIGURE 11

Truesdell (1974).

As in figure 9 (note 2), the fractionations measured were between CO2 equilibrated with pure 

water and CO2 equilibrated with various solutions. From these figures can be obtained the 

oxygen isotope activity ratio of the solutions relative to pure water.
a 

o

69

o

on 

O 

tG 

H

O

as

on

i

> 

H 

W

I C 

CO

NJ 

1 

O

3 

ft

NJ 

t.l

TEMPERATURE, IN DEGREES CELSIUS

3 O O §

1 1

NJ r}

3 ?>

IQ

*

^*

~*

i

s

*

 i

t

0

>

f

/

*

/

/

/

.*

?

^

/

/

AI

*

/

> «

/

^

f *

/

^

^

Z 

ffi

n 

p

en

Ol 

0

/

/

V

X

1'

/

i

it

V

^

1

^:

,

( <*

^

ij

r^

//-

^

^

/ 

^pt

f

T

f

T

^

y|

*

«l

N

\

4

s

^

,;

s

v

\*

%

I*'

V

 «

^4v

^

s

rr

TP

-A

fii

*

\i

\

v

v

\

A

\

S

^

^

^

^

Sj

<

s

4

sJ

V

^

'«

\

,

*^

>

t

s

>

S

*"

N

^

Si

^

'

>

 

^

'

%

<^

v

*j

s

s

s.

^{

^

ta

\

S

^

^

s

^

^

^

^

p

 

s

 

*

^

y*

 .

V

%

ta.

rs

 

^ *

^

^

s

>.

«

^

_

^

^

5

 »

«

^S

 

^

^

^,

s

*

s

*

^

^

s

^

 <

««

*

»*

 a

-»

*N

i^

^

^

 i

 

-

 ^

o

~z

3 11 

o

^* 

3 n o_rNJ

3

O 

n

K

i:

n

i

-1 *

3 n o ih 

-

-

-

--

H -t

§

mo
FIGURE 12

Bottinga (1968a, b) calculation:

103 lna - -1.8034(106T-2 )+10.611(103T- 1 )-2.7798*. 

Circles are data from O'Neil and Epstein (1966b).
TEMPERATURE, IN DEGREES CELSIUS

*» Ul O)

888 8

o

>

*3 

68 

O

2!

g

O

X

5

m00s

v«^

O

r 

n

tn

,**-

'.**

;^_:

^

w o
FIGURE 13

A, O'Neil, Clayton, and Mayeda (1969): (0° to 500°C).

(CaCO3 ) 103 lnot = 2.78(106T-2 )-2.89*,

(SrCO3 ) 103 lna = 2.69(106T-2)-3.24*, and

(BaCO3 ) 103 lna - 2.57(106T~2)-4.23*. 

B, Northrop and Clayton (1966): (300° to 510°C).

Dolomite. KPlnot - 3.20(106T-2 )-1.50*.

This equation represents the average of two consistently different fractionation expressions

for different dolomites.
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 13

1000

900

800

700

600

500

400

300

200

100

-5

BaCO, SrC0 3" 

CaCO,

Dolomite, B

V

s.:s

10 15 

10 3 In a

20

o

X

Y 

G 

E

N

ALKALINE EARTH CARBONATES-WATER
FIGURE 14

Lloyd (1968):

A, (Anhydrite) 103 ln« = 3.88(106T-2 )-2.90*.

B, (Dissolved sulfate) 103 lna = 3.25(106T~2 )-5.10*. 

Mitzutani and Rafter (1969): (110° to 200°C).

C, (Dissolved sulfate) lOMno: = 2.88(106T-2)-3.60*.
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 14

1000

900

800

700

«g eoo

LLI 

U

CO 

LJJ 

LJJ 

DC 

d 

UJ

Q 500

400

300

200

100

O 

X 

Y 

G 

E 

N

10 15 20 25 30

103 In a

DISSOLVED SULFATE-WATER(l) AND ANHYDRITE-WATER

35 40
FIGURE 15

R. Robinson and M. Kusakabe (written commun., 1975):

A, BaS04 -H2 0 10» Ina = 3.0( 10«T~2)-6.79*. 

B, BaSO4 -l M NaCl 103 lna = 2.58(106T-2 )-4.3*. 

C, BaSO4 -l M NaCl+1 M H2SO4 103 lna= 2.64(106T-2 )=)-4.8*.

The BaSO4-l M NaCl and 1 M NaCl+1 M H2SO4 data have been corrected for hydration 

effects. In addition, the BaSO4 -l M NaCl+1 M H2SO4 data have been corrected for exchange 

with HSO 4~ at high temperature.
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 15

1000

900

800

700

600

500

400

300

200

100

O 

X

Y 

G 

E

N

-1 +1 7

103 In a

BARITE-WATER

11 13 15
FIGURE 16

A, Clayton, O'Neil, and Mayeda (1972):

103 lna = 3.38(106T-2 )-2.90* (200° to 500°C), and

103 lna = 2.51(106T- 2 )-1.46*. (500° to 750°C). 

B, Bottinga and Javoy (1973):

103 lna = 4.10(106T-2 )-3.70.

This expression was constructed from a combination of experimental determinations of

other investigators, theoretical considerations, and consistencies in data from natural systems.
TEMPERATURE, IN DEGREES CELSIUS

1 C

ro

OC>

r^

o

u ^

^ =

> »

HW

90

_i O

_»

ro

->

D

CC

^

3 3

KJ 3/

/

i7

/

/i

/-

/

tr

y< /

V/

 / 

cc//

o3

1i

-t

/1

/fV

x/

/4

?

-i

Ji

/^ f />

^?/ ^? ( /

»*

^'t

/t /4 /f /^

,

r

|(

C Cs'

J1Dss

/^/

'.

,* s

?

^

* 

i

{s+

n3

^^

^

»^

/

^<

*

* 

^

,>

^'

 * 

^1 

O O^

* 

*« »^

n*

^BD

.

 

 *

^

Cc

 

I(

10"

*<

p^*

*

W
FIGURE 17

Shiro and Sakai (1972):

This curve results from a combination of Shiro and Sakai's calculation of the partition function 

ratios of a- and jg-quartz, the partition function ratios of water derived from their calculated 

partition function ratios of calcite, and the experimental calcite-water fractionations of O'Neil, 

Clay ton, and Mayeda (1969). A discontinuity occurs at the a to (3 transition temperature 

(573°C) of quartz.

103 ln a = 3.55(106T-2)-2.57* (195° to 573°C), and

103 ln a = 3.23(106T-2 )-2.94* (573° to 1,000°C).
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 17

1000

8

1

8

§

§

8

I

§

8

5

-CK-|8-quartz transition

A,

S

5s

O

X

Y 

G 

E

N

-2 6 

10 3 In a

10 12 14

QUARTZ-WATER
FIGURE 18

O'Neil and Taylor (1967): (350° to 800°C).

A, (Alkali feldspars) 103 lna = 2.91(106T-2 )-3.41. 

B, (Plagioclase) 103 lna = (2.91-0.76B) (10«T-2 )-(3.41-0.14B), 

where

B = mole fraction anorthite. 

Bottinga and Javoy (1973): (500° to 800°C).

C, Alkali feldspar) lOMna = 3.13(106T-2 )-3.70. 

D, (Plagioclase) 103 lna= (3.13-1.04B) (106T- 2 )-3.70, 

where

B = mole fraction anorthite.

NOTE. Sodium and potassium feldspar have identical isotopic properties within the limits 

of analytical uncertainty.
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 18

1000

900

100

-5

o

X 

Y 

G 

E

N

FELDSPAR-WATER
FIGURE 19

O'Neil and Taylor (1969): (400° to 650°C).

103 lna = 2.38(106T-2 )-3.89. 

Bottinga and Javoy (1973): (500° to 800°C).

103 lna= 1.90(106T-2 )-3.10.

NOTE. Muscovite and paragonite have identical isotopic properties within the limits of

analytical uncertainty.
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 19

1000

900

800

700

600

500

400

300

200

100

O 

X 

Y 

G 

E 

N

-5 10 15 

10 3 In a

20 25 30 35

MUSCOVITE-WATER
FIGURE 20

Addy and Garlick (1974): (575° to 775°C). 

103 lna = 4.1(10«T-2)+1.46*.

This curve should show a reversal of slope at low temperature similar to that shown by the 

magnetite-water system. (See fig. 21.)
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 20

1000

900

800

700

600

500

400

300

200

100

O 

X

Y 

G 

E

N

-10 -8 -6 -4 -2 

10 3 In a

RUTILE-WATER
FIGURE 21

A, Becker (1971):

The curve was constructed from the partition function ratio of water derived from the experimental calcite-water fractionations and the calcite reduced partition function ratios of O'Neil, 

Clay ton, and Mayeda (1969), and the average of Becker's maximum and minimum values for 

the reduced partition function ratio for magnetite. The latter was derived from corrected high 

temperature magnetite-water fractionations of O'Neil and Clayton (1964) and theoretical considerations. This curve has been recalculated, using the value of 1.0412 for theCO2-H2O fractionation.

B, Bottinga and Javoy (1973): (500° to 800°C). 

103 lna = -1.47(106T~2 )-3.70.

C, Bertenrath, Friedrichsen, and Hellner (1972):

These fractionations are the results of experiments in the temperature range of 300° to 960°C 

in which hematite was reduced to magnetite in the presence of water at Ni-NiO buffered oxygen 

fugacides. This curve has been recalculated using the value of 1.0412 for the CO2-H2O fractionation.

NOTE. Based on natural data, it is commonly assumed for purposes of geothermometry that 

Aquam-illimenite = 0.95 Aquartz.magnetite . Also see Bottinga and Javoy (1974).
TEMPERATURE, IN DEGREES CELSIUS

s 

> 

o

z

en 

H

k

> 

H

M

JO

MO < XO
FIGURE 22

A, Becker (1971):

This curve was obtained by combining the magnetite-water curve of figure 21 and the quartz-water

curve of Clayton, O'Neil, and Mayeda (1972). 

B, The two curves shown in the figure differ by only 20° or 30°C for per mil fractionations less

than 14.0, but they were constructed from wholly different mineral-water curves.
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 22

1000

900

800

700

600

500

400

300

200

100

\

O 

X 

Y 

G 

E 

N

8 

10 3 Intt

QUARTZ -MAGNETITE

10 12 14 16
FIGURE 23

Bottinga and Javoy (1973): 

A, Anothite-magnetite 

B, Anorthite(75)-magnetite. 

C, Anorthite(50)-magnetite. 

D, Anorthite(25)-magnetite. 

£, Albite-magnetite.

Potassium feldspar has isotopic properties identical to albite within the limits of analytical 

error. The plagioclase-magnetite curves formulated by Anderson, Clayton, and Mayeda (1971) 

are virtually identical to those shown in the figure.
TEMPERATURE, IN DEGREES CELSIUS

 ^ oo

"0

r

> 

oHM

O

o

r

>>

t/D

cn

cn

Ot/D

o

 05

cn 

H

H 

cn

'7\ 

X

_» J_ 

o

TEMPERATURE, I

wo ^ xo
FIGURE 24

A, Muscovite-magnetite. 

B, Quartz-muscovite. 

C, Quartz-calcite. 

D, Quartz-alkali feldspar. 

£, Quartz-alkali feldspar.

Experimental determination by Blattner and Bird (1974).

Expression of O'Neil, Clay ton, and Mayeda (1969) for calcite-water was used in the quartz-calcite 

curve. All the other relationships in this and other curves, except £, are from Bottinga and Javoy 

(1973).
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 24

1000

900

800

700

600

500

o- 400

300

200

100

o

X 

Y 

G 

E

N

MUSCOVITE-MAGNETITE AND QUARTZ-MUSCOVITE, QUARTZ-CALCITE, AND QUARTZ-ALKALI FELDSPAR
FIGURE 25

Bottinga and Javoy (1974).

These curves represent the following fractionations: 

Feldspar(An60 )-quartz, 

f eldspar( An60)-muscovi te, 

feldspar(An60)-pyroxene, 

feldspar(An60 )-garnet, 

feldspar(An60 )-amphibole, 

feldspar(An60)-olivine, 

feldspar(An60)-biotite, and 

f e ldspar( An60)-magne ti te.
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 25

1000

900

800

700

600

500

400

300

200

100

-20

o

X 

Y 

G 

E

N

LDSPAR (An60 )-QUARTZ, -MUSCOVITE, -PYROXENE, -GARNET, 

-AMPHIBOLE, -OLIVINE, -BIOTITE, AND -MAGNETITE
FIGURE 26

A, Sheppard and Schwarcz (1970): (100° to 650°C).

103 lna - 0.45(106T-2 )-0.40.

This curve is constructed from fractionations between coexisting calcite and dolomite in marbles, 

calibrated by the Mg-calcite solvus thermometer.

B, Northrop and Clayton (1966).

C, O'Neil and Epstein (1966b):

lOMna = 0.56(106T-2 )-0.45. 

This curve is based on measurements at only two temperatures, 350° and 400°C.

D, Fritz and Smith (1970):

The constant dolomite-calcite fractionation of +3.1 in the temperature range 25° to 79°C is calculated from data on synthesized protodolomites, using the acid fractionation factor of 1.01025 

for both carbonates. If the acid fractionation factor of 1.01109 is used for dolomite, this value 

becomes +2.3.
TEMPERATURE, IN DEGREES CELSIUS

O 

O

O

s

H

mi 

o

> 

r 

o

H 

tn

W O >< XO
FIGURE 27

A, Malinin, Kropotova, and Grinenko (1967): (23° to 286°C).

This curve is a least-squares fit to the authors' data. 

B, Mook, Bommerson, and Staverman (1974): (5° to 125°C).

103 lna = 9.552(103T- 1 )-24.10. 

C, Emrich, Ehhalt, and Vogel (1970):

NOTE. Data in the insert are given in the following table:

T(°C) 103 In'tt Reference

0

7

10

14

20

20

22

25

25

28

30

9.3±0.4

9.7±0.4

8.4i0.4

9.4±0.4

8.4±0.1

7.6±0.4

7.7±0.3

7.7

8.3

8.5±0.4

6.9±0.4

Deuser and Degens (1967).

Wendt, Stahl, Geyh, and Fauth (1966).

Deuser and Degens (1967).

Wendt (1968).

Emrich, Ehhalt, and Vogel (1970).

Deuser and Degens (1°67).

Vogel (1961).

Thode, Shima, Rees, and Krishnamurty (1965).

Abelson and Hoering (1961).

Wendt (1968).

Deuser and Degens (1967).
TEMPERATURE, IN DEGREES CELSIUS

§

on 

on 

O

r

w 

o

go _

Z o

> -

W ft I ** 

0

yo w 

o

z

o 

o

XM<

o 

w

TEMPERATURE, IN DE

/^

^

op

D&

?

o w & > n
FIGURE 28

Thode, Shirna, Rees, and Krishnamurty (1965) calculation:

The crossover point (10s Ina = 0) occurs at 130°C, and there is a reversal at 425°C 

10s In a--48).
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 28

IUU

on

70

~

W Rn

O

W

UJ

UJ

cc

o

UJ

Q ,-n

z

UJ

cc

D

H

<

CC

S 40

S

UJ hO\S

20

10

0

53

\

\"

\

\

?

iV*

\

\

I

\

'

L

\

*

\

\

\

>j

i

\

I

\

\

\

\

\

V

\

\

I

\

\

V

\

\

(

,

\

,

\

'

I

\ *

\

1

\

'

\

'

s \ *

1

s

0

V

3

\

3 

Ir

\

*

U

\

\

1

\

V

N

V

s

^*

\

1

V

0 1 2 1 4 1

cv^

Ar\.

0

N

6

DISSOLVED CARBONATE-CARBON DIOXIDE(g)
FIGURE 29

Bottinga (1969a):

A, Carbon dioxide(g)-methane(g). 

B, Calcite-graphite.
W

o

oNH

O

XNH 

PI

00s 

V

W 

H

O

> 

r 

oNH

H 

W

O

£

H 

W

TEMPERATURE, IN DEGREES CELSIUS

NO co -t> en 

o o o o

OOOO

> o
FIGURE 30

A, Bottinga (1969b):

Diamond-graphite. 

B, Bottinga (1969b):

Carbon dioxide(g)-diamond.

C, Although carbon dioxide(g)-graphite is given in Bottinga (1969b), the data given in Bottinga 

(1968a) has more internal consistency; therefore, the latter data have been plotted from 0° to 

700°C, and the former from 700° to 1,000°C.
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE

1000

co o

10 12 14

C 

A 

R 

B 

O 

N

468

103 In a 

DIAMOND-GRAPHITE, CARBON DIOXIDE(g)-DIAMOND, AND CARBON DIOXIDE(g)-GRAPHITE

16
FIGURE 31

A, Bottinga (1968b) calculation: (curve).

10slna = -2.9880(106T- 1 )+7.6663(10ST- 1 )-2.4612. 

Note the crossover point at 192°C.

B, Northrop and Clay ton (1966): ( ).

The values shown at 225°, 300°, and 400°C are interpolated values from partial exchange experiments where the percentages of exchange were 7, 20, and 43, respectively.

C, Vogel (1959): (x).

A value of -9.3*0.5 at 20°C is not shown but is in agreement with the value of Emrich, Ehhalt, 

and Vogel (1970).

D, Baertschi (1957): (A).

E, Emrich, Ehhalt, and Vogel (1970): (o).
GEOLOGICAL SURVEY PROFESSIONAL PAPER 44Q-KK FIGURE 31

1000

900

800

700

600

500

400

300

200

100

-13

t

-11 9 -7 -5 

103 In a

-3 -1 + 1

c

A 

R 

B 

O

N

+ 3

CARBON DIOXIDE(g)-CALCITE
FIGURE 32

Bottinga (1969a).
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 32

1000

900

800

700

CO

" 600

LU

500

400

300

200

100

C

A 

R 

B 

O

N

-15 -5 + 5 +15 +25 

103 In a

+ 35 + 45 + 55 + 65

GRAPHITE-METHANE
FIGURE 33

Sheppard and Schwarcz (1970): (100° to 650°C).

lOMna = 0.18(106T-2 )+0.17.

This curve is constructed from fractionations between coexisting calcite and dolomite in marbles, 

calibrated by the Mg-calcite solvus thermometer.
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 33

1000

900

800

700

600

500

400

300

200

100

c

A 

R 

B 

O

N

2 3

10 3 Ina 

DOLOMITE-CALCITE
FIGURE 34

A, Majzoub (1971):

103 lna = 24.844(106T-2)-76.248(103T- 1 )+52.612. 

B, Because of internal consistency, one curve has been constructed from the data of Stewart and

Friedman (1975), Ehhalt and Knott (1965), and Rennow (1970). 

C, Merlivat, Bolter, and Nief (1963). 

D, Merlivat and Nief (1966). 

E, Matsuo, Kuniyoshi, and Miyake (1964).
GEOLOGICAL SURVEY 

50 rr

PROFESSIONAL PAPER 440-KK FIGURE 34

40

30

20

-10

-20

-30

-40

50 70

s

o

2w

-K*

X

^

90 110 130 

10 3 In a

150 170 190 210

WATER(l)-WATER(v) BETWEEN -20° AND + 50°C 

AND WATER(s)-WATER(v) BETWEEN -42° AND O°C

H 

Y 

D 

R 

O 

G 

E 

N
FIGURE 35

A, Merlivat, Bolter, and Nief (1963).

B, Botlinga (1968a).

C, Majzoub (1971).

The data from 0° 10 100°C of Merlivat, Bolter, and Nief (1963) as corrected by Merlivat in Majzoub

(1971) agrees very closely with thai of Majzoub.
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 35

350

300

250

150

100

50

-10

\

10 20 30

10 3 In a

40 50 60

WATER(l)-WATER(v) BETWEEN 30°AND 350°C

70

H 

Y 

D 

R 

O 

G 

E 

N
FIGURE 36

Bottinga (1969a).
TEMPERATURE, IN DEGREES CELSIUS

8

H 

W

^^r

s

w

H

a 

z

w

o 

J o

oo rr

o
FIGURE 37

A, Suess (1949):

Water(v)-hydrogen fractionation.

10s Ina = 467.6(103T-1 )-303.9 (experimental). 

B, Bottinga (1969a):

Water(v)-hydrogen(g) (calculated). 

C, Bottinga (1969a):

Methane(g)-hydrogen(g) (calculated). 

D, Y. Horibe and H. Craig (written commun., 1975).

103 lna = -90.888+181.264(106T-2 )-8.949(1012T-4 ).
GEOLOGICAL SURVEY

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:S

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PROFESSIONAL PAPER 440-KK FIGURE 37

S S

-s

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10 3 In a

1000 1200 1400 1600

WATER(v)-HYDROGEN(g) AND METHANE(g)-HYDROGEN(g)

H 

Y 

D 

R 

O 

G 

E 

N
FIGURE 38

Stewart and Friedman (1975).
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE38

50

H 

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D 

R 

O 

G 

E 

N

WATER(l)-WATER(v), SOLUTE EFFECTS AT 20°C
FIGURE 39

Matsuo, Friedman, and Smith (1972): (8° to 35°C). 

103 lna = -14.20(106T-*)+2.356(10*T- 1 ).
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 39

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10

0 -110 -100 -90 -80 -70 

10 3 In a

-60 -50 -40 -30

H 

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D 

R 

O 

G 

E 

N

TRONA-WATER (1)
FIGURE 40

Suzuoki and Epstein (1976):

(Biotite) 103 Ina = 21.3(106T-2)+2.8;

(Hornblende) 103 lna = 23.9(106T-2)-7.9;

(Muscovite) 103 lna = 22.1(106T~2 )-19.1;

(Theoretical phlogopite) 103 lna = 22.4(106T-2)-27.1; and

(Theoretical biotite) 103 ln« = 22.4(106T-2 )-2.9.

For the mica-water and the amphibole-water systems, the hydrogen isotope fractionations from 

450° to 850°C are a function of temperature and molar fractions of the sixfold coordinated cations, 

regardless of mineral species. The fractionations can be expressed as: 

103 lna (mjnera] wa(er) = -22.4(106T-2)+28.2+(2xA1 -4x Mg -68x Fe ), where x is the molar fraction ot the

cations.
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 40

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CO o o

-60 -40 80 100

WATER-BIOTITE, -THEORETICAL BIOTITE, -HORNBLENDE, -MUSCOVITE, -THEORETICAL 

PHLOGOPITE, -ALUMINUM HYDROXIDE, -KAOLINITE, AND -SERPENTINE

H 

Y 

D 

R 

O 

G 

E 

N
FIGURE 41

Saiki (1957): (27° to 527°C).

The partition function ratios of H2S(g) and H2S(aq) were assumed to be equal.
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440 -KK FIGURE 41

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10 15 20

10 3 Ina

25 30 35

s

U 

L 

F 

U 

R

40

SULFUR DIOXIDE(g)-HYDROGEN SULFIDE(aq AND g) BETWEEN 27° AND 527°C
FIGURE 42

A, Sakai (1968): (287° to 527°C).

B, Thode, Cragg, Hulston, and Rees (1971):

103 ln« = 3.65(106T-2 ) (calculated). 

C, Thode, Cragg, Hulston, and Rees (1971):

103 lna = 4.54(10«T-2 )-0.30 (experimental). 

D, Grinenko and Thode (1970): (o).
"2 3 45678910

103 In a 

SULFUR DIOXIDE(g)-HYDROGEN SULFIDE(g) BETWEEN 287° AND 1,000°C

TEMPERATURE, IN DEGREES CELSIUS

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FIGURE 43

A, Robinson (1973): (200° to 320°C).

10s lna = 5.1(106T-2)+6.3. 

B, Sakai (1968): (27° to 527°C).
c 

o

0 

NJ

0 304 5067 80 103 In tt

DISSOLVED BISULFATE-HYDROGEN SULFIDE(g)

TEMPERATURE, IN DEGREES CELSIUS

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FIGURE 44

Sakai (1968):

A, Dissolved sulfate-dissolved sulfide. 

B, Dissolved sulfate-hydrogen sulfide(g). 

C, Dissolved sulfate-sulfur dioxide(g). 

D, Hydrogen sulfide(g)-dissolved sulfide. 

E, Dissolved sulfate-dissolved sulfide.
GEOLOGICAL SURVEY PROFESSIONAL PAPER 44Q-KK FIGURE 44

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103 Ino

50 60 70 80

DISSOLVED SULFATE-DISSOLVED SULFIDE, -HYDROGEN SULFIDE(g), AND 

HYDROGEN SULFIDE(g) -DISSOLVED SULFIDE AND DISSOLVED SULFATE-

-SULFUR DIOXIDE(g); 

DISSOLVED SULFIDE

S 

U

L 

F 

U 

R
FIGURE 45

Grinenko and Thode (1970):

A, Hydrogen sulfide(g)-sulfur(g). 

B, Sulfur dioxide(g)-sulfur(g).
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 45

400

C/D

D

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LLJ

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HYDROGEN SULFIDE(g)-SULFUR(g) AND SULFUR DIOXIDE(g)-SULFUR(g)
FIGURE 46

Kajiwara and Krouse (1971):

A, Pyrite-galena lOMna = 1.1(106T-2 ). 

B, Pyrite-sphalerite (pyrite-pyrrhotite) 10s In a = 3.0(105T-2 ). 

C, Pyrite-chalcopyrite 103 lna= 4.5(105T~2 ). 

D, Chalcopyrite-galena 10s In a = 6.5(105T~2). 

E, Sphalerite-chalcopyrite (pyrrhotite-chalcopyrite)

= 1.5(105T-2 ).
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 46

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1234567

10 3 In a

PYRITE-GALENA, -CHALCOPYRITE, AND -SPHALERITE; SPHALERITE-CHALCOPYRITE;

AND CHALCOPYRITE-GALENA

s 

u

L 

F 

U 

R
FIGURE 47

Sphalerite-galena:

A, Kiyosu (1973): 103 lna = 8.91(105T-2 )-0.57. 

B, Kajiwara and Krouse (1971): 103 lna = 8.0(105T-2 ). 

C, Czamanske and Rye (1974): 103 lna = 7.0(105T-2 ). 

D, Groctenboer and Schwarcz (1969): 103 lna = 6.6(105T- 2 )-0.1.
TEMPERATURE, IN DEGREES CELSIUS

r c
FIGURE 48

Kiyosu (1973): 50° to 340°C.

A, Sphalerite-HS" 103 lna = l.ll(105T-2)+1.36. 

B, Galena-HS' 10»lno = 7.82(10»T-*)+1.7.
TEMPERATURE, IN DEGREES CELSIUS

8 8

s

C/J

"0

3!

r

M

C/J 

I

O R

r

M

2

i

B 

c/j

i

pa c ^ r c
FIGURE 49

Suvorova (1974).

Experimental:

A, Molybdenite-galena 103 lna = 1.3(106T-2)-0.80. 

B, Molybdenite-sphalerite 103 lna = 0.71(106T-2 )-0.-15.

Calculated: (400° to 750°C).

C, Molybdenite-pyrite 103 lna = 0.48(106T-2 )-0.75. 

D, Molybdenite-chalcopyrite 103 lna = 0.72(106T-2 )-0.70. 

E, Molybdenite-pyrrhotite 103 lna = 0.65(106T-2 )-1.65.
GEOLOGICAL SURVEY PROFESSIONAL PAPER 440-KK FIGURE 49

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MOLYBDENITE-SPHALERITE, -GALENA, -CHALCOPYRITE, -PYRITE, AND -PYRRHOTITE