NBS SPECIAL PUBLICATION 260-55

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

Standard Reference Materials:

ENTHALPY AND HEAT CAPACITY

STANDARD REFERENCE MATERIAL:

MOLYBDENUM SRM 781,

FROM 273 TO 2800 K
NATIONAL BUREAU OF STANDARDS

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ia i Bureau of Stanaartin

SEP 2 7 Wf

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Standard Reference Materials:

too ENTHALPY AND HEAT CAPACITY STANDARD REFERENCE

7 7 MATERIAL: MOLYBDENUM SRM 781, FROM 273 TO 2800 K

D.A. Ditmars, A. Cezairliyan, S. Ishihara,

and T.B. Douglas

Physical Chemistry Division

Institute for Materials Research

National Bureau of Standards

Washington, D.C. 20234

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

\J . S , NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued September 1977
Library of Congress Cataloging in Publication Data

United States. National Bureau of Standards.

Physical Chemistry Division. Enthalpy and heat capacity standard reference material.

(Standard reference materials) (National Bureau of Standards

special publication ; 260-55)

Supt. of Docs, no.: CI3. 10:260-55

1. Molybdenum—Thermal properties—Tables. 2. Enthalpy—Tables.

I. Ditmars, D. A. II. Title. III. Series: United States. National Bureau

of Standards. Standard reference materials. IV. Series: United States. National Bureau of Standards. Special publication ; 260-55. QC100.U57 no. 260-55 [QD181.M7] 602' Is [546'.534'56] 77-608175

National Bureau of Standards Special Publication 260-55

Nat. Bur. Stand. (U.S.), Spec. Publ. 260-55, 80 pages (Sept. 1977)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1977

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Price $2.20—Stock No. 003-003-01836-8
PREFACE

Standard Reference Materials (SRM's) as defined by the

National Bureau of Standards are "well-characterized materials, produced in quantity, that calibrate a measurement

system to assure compatibility of measurement in the nation."

SRM's are widely used as primary standards in many diverse

fields in science, industry, and technology, both within the

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measurement system is carried out through the mechanism and

use of SRM's. For many of the nation's scientists and technologists it is therefore of more than passing interest to

know the details of the measurements made at NBS in arriving

at the certified values of the SRM's produced. An NBS series

of papers, of which this publication is a member, called the

NBS Special Publication - 260 Series is reserved for this

purpose

.

This 260 Series is dedicated to the dissemination of

information on all phases of the preparation, measurement,

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or desirable, in scientific journal articles. This enables

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and to learn details of techniques and methods utilized for

work entailing the greatest care and accuracy. It is also

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information not found on the certificate so that new applications in diverse fields not foreseen at the time the SRM

was originally issued will be sought and found.

Inquiries concerning the technical content of this

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National Bureau of Standards

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J. Paul Cali, Chief

Office of Standard Reference Material

iii
OTHER NBS PUBLICATIONS IN THIS SERIES

Catalog of NBS Standard Reference

Materials ( 1975-76 edition), R. W.

Seward, ed., NBS Spec. Publ. 260 (June

1975). $1.50*

Michaelis, R. E., and Wyman, L. L.,

Standard Reference Materials: Preparation of White Cast Iron Spectrochemical Standards, NBS Misc. Publ.

260-1 (June 1964). COM74-1 1061**

Michaelis, R. E., Wyman, L. L., and

Flitsch, R., Standard Reference Materials:

Preparation of NBS Copper-Base Spectrochemical Standards, NBS Misc. Publ. 260-2

(October 1964). COM 74-11063**

Michaelis, R. E., Yakowitz, H., and Moore, G. A.,

Standard Reference Materials: Metallographic

Characterization of an NBS Spectrometric

Low-Alloy Steel Standard, NBS Misc. Publ.

260-3 (October 1964). COM74-1 1060**

Hague, J. L., Mears, T. W., and Michaelis, R. E.,

Standard Reference Materials: Sources of

Information, NBS Misc. Publ. 260-4 (February

1965). COM74-11059

> Alvarez, R., and Flitsch, R., Standard Reference

Materials: Accuracy of Solution X-Ray Spectrometric Analysis of Copper-Base Alloys, NBS

Misc. Publ. 260-5 (March 1965). PB168068**

Shultz, J. I., Standard Reference Materials:

Methods for the Chemical Analysis of White

Cast Iron Standards, NBS Misc. Publ. 260-6

(July 1975). COM74-11068**

Bell, R. K., Standard Reference Materials: Methods for the Chemical Analysis of

NBS Copper-Base Spectrochemical Standards,

NBS Misc. Publ. 260-7 (October 1965).

COM74-11067**

Richmond, M. S., Standard Reference

Materials: Analysis of Uranium Concentrates at the National Bureau of

Standards, NBS Misc. Publ. 260-8 (December

1965). COM74-11066**

Anspach, S. C, Cavallo, L. M., Garfinkel,

S. B., Hutchinson, J. M. R., and Smith,

C. N., Standard Reference Materials:

Half Lives of Materials Used in the

Preparation of Standard Reference Materials of

Nineteen Radioactive Nuclides Issued by the

National Bureau of Standards, NBS Misc.

Publ. 260-9 (November 1965). COM74-1 1065**

Yakowitz, H., Vieth, D. L., Heinrich, K. F.

J., and Michaelis, R. E., Standard

Reference Materials: Homogeneity Characterization on NBS Spectrometric Standards II: Cartridge Brass and Low-Alloy Steel, NBS

Misc. Publ. 260-10 (December 1965).

COM74- 11064**

Napolitano, A., and Hawkins, E. G.,

Standard Reference Materials: Viscosity of Standard Lead-Silica Glass,

NBS Misc. Publ. 260-1 1 (November

1966). NBS Misc. Publ. 260-11**

Yakowitz, H., Vieth, D. L., and Michaelis,

R. E., Standard Reference Materials:

Homogeneity Characterization of NBS

Spectrometric Standards III: White

Cast Iron and Stainless Steel Powder

Compact, NBS Misc. Publ. 260-12(September

1966). NBS Misc. Publ. 260-12**

Spijkerman, J. I., Snediker, D. K., Ruegg,

F. C, and DeVoe, J. R., Standard

Reference Materials: Mossbauer Spectroscopy

Standard for the Chemical Shift of Iron Compounds, NBS Misc. Publ. 260-13 (July 1967).

NBS Misc. Publ. 260-13**

Menis, O., and Sterling, J. T., Standard

Reference Materials: Determination of Oxygen

in Ferrous Materials - SRM 1090, 1091, and

1092, NBS Misc. Publ. 260-14 (September 1966).

NBS Misc. Publ. 260-14**

Passaglia, E., and Shouse, P. J., Standard

Reference Materials: Recommended Method of

Use of Standard Light-Sensitive Paper for Calibrating Carbon Arcs Used in Testing Textiles for

Colorfastness to Light, NBS Misc. Publ. 260-15

(June 1967). (Replaced by NBS Spec. Publ.

260-41.)

Yakowitz, H., Michaelis, R. E., and Vieth,

D. L., Standard Reference Materials:

Homogeneity Characterization of NBS

Spectrometric Standards IV: Preparation and Microprobe Characterization

of W-20% Mo Alloy Fabricated by

Powder Metallurgical Methods, NBS

Spec. Publ. 260-16 (January 1969).

COM74-11062**

Catanzaro, E. J., Champion, C. E., Garner,

E. L., Marinenko, G., Sappenfield, K.

M., and Shields, W. R., Standard Reference

Materials: Boric Acid; Isotopic and Assay

Standard Reference Materials, NBS Spec. Publ.

260-17 (February 1970). 65 cents*

iv
Geller, S. B., Mantek, P. A., and Cleveland, N. G.,

Standard Reference Materials: Calibration of

NBS Secondary Standard Magnetic Tape (Computer Amplitude Reference) Using the Reference

Tape Amplitude Measurement "Process A,"

NBS Spec. Publ. 260-18 (November 1969). (See

NBS Spec. Publ. 260-29.)

Paule, R. C, and Mandel, J., Standard Reference

Materials: Analysis of Interlaboratory Measurements on the Vapor Pressure of Gold (Certification of Standard Reference Material 745), NBS

Spec. Publ. 260-19 (January 1970). PB190071**

Paule, R. C, and Mandel, J., Standard Reference

Materials: Analysis of Interlaboratory Measurements on the Vapor Pressures of Cadmium and

Silver, NBS Spec. Publ. 260-21 (January 1971).

COM74-11359**

Yakowitz, H., Fiori, C. E., and Michaelis, R. E.,

Standard Reference Materials: Homogeneity

Characterization of Fe-3 Si Alloy, NBS Spec.

Publ. 260-22 (February 1971). COM74-1 1357**

Napolitano, A., and Hawkins, E. G., Standard

Reference Materials: Viscosity of a Standard

Borosilicate Glass, NBS Spec. Publ. 260-23

(December 1970). 25 cents*

Sappenfield, K. M., Marineko, G., and Hague, J.

L., Standard Reference Materials: Comparison

of Redox Standards, NBS Spec. Publ. 260-24

(January 1972). $1.00*

Hicho, G. E., Yakowitz, H., Rasberry, S. D., and

Michaelis, R. E., Standard Reference Materials:

A Standard Reference Material Containing

Nominally Four Percent Austenite, NBS Spec.

Publ. 260-25 (February 1971). COM 74-1 1356**

Martin, J. F., Standard Reference Materials:

National Bureau of Standards-US Steel

Corporation Joint Program for Determining

Oxygen and Nitrogen in Steel, NBS Spec. Publ.

260-26 (February 1971). 50 cents*

Garner, E. L., Machlan, L. A., and Shields, W. R.,

Standard Reference Materials: Uranium

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Spec. Publ. 260-27 (April 1971). COM74-

11358**

Heinrich, K. F. J., Myklebust, R. L., Rasberry, S. D., and Michaelis, R. E., Standard Reference

Materials: Preparation and Evaluation of

SRM's 481 and 482 Gold-Silver and GoldCopper Alloys for Microanalysis, NBS Spec.

Publ. 260-28 (August 1971). COM71-50365**

Geller, S. B., Standard Reference Materials: Calibration of NBS Secondary Standard Magnetic

Tape (Computer Amplitude Reference) Using

the Reference Tape Amplitude Measurement

"Process A-Model 2," NBS Spec. Publ. 260-29

(June 1971). COM71-50282**

Gorozhanina, R. S., Freedman, A. Y., and

Shaievitch, A. B. (translated by M. C. Selby),

Standard Reference Materials: Standard

Samples Issued in the USSR (A Translation

from the Russian), NBS Spec. Publ. 260-30 (June

1971). COM71-50283**

Hust, J. G., and Sparks, L. L., Standard Reference

Materials: Thermal Conductivity of Electrolytic

Iron SRM 734 from 4 to 300 K, NBS Spec. Publ.

260-31 (November 1971). COM7 1-50563**

Mavrodineanu, R., and Lazar, J. W., Standard

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for High Accuracy Spectrophotometry, NBS

Spec. Publ. 260-32 (December 1973). 55 cents*

Wagner, H. L., Standard Reference Materials:

Comparison of Original and Supplemental SRM

705, Narrow Molecular Weight Distribution

Polystyrene, NBS Spec. Publ. 260-33 (May

1972). COM72-50526**

Sparks, L. L., and Hust, J. G., Standard Reference

Materials: Thermal Conductivity of Austenitic

Stainless Steel, SRM 735 from 5 to 280 K, NBS

Spec. Publ. 260-35 (April 1972). 35 cents*

Cali, J. P., Mandel, J., Moore, L. J., and Young,

D. S., Standard Reference Materials: A Referee

Method for the Determination of Calcium in

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(May 1972). COM72-50527**

Shultz, J. I., Bell, R. K., Rains, T. C, and Menis,

O., Standard Reference Materials: Methods of

Analysis of NBS Clay Standards, NBS Spec.

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Spec. Publ. 260-39 (May 1972). 55 cents*

McAdie, H. G., Garn, P. D., and Menis, O.,

Standard Reference Materials: Selection of

Thermal Analysis Temperature Standards

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760), NBS Spec. Publ. 260-40 (August 1972).

65 cents*

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Wood, L. A., and Shouse, P. J., Standard Refer- ence Materials: Use of Standard Light-Sensitive

Paper for Calibrating Carbon Arcs Used in

Testing Textiles for Colorfastness to Light, NBS

Spec. Publ. 260-41 (August 1972). COM72-

50775**

Wagner, H. L., and Verdier, P. H., eds., Standard

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Iron-Chromium-Nickel Alloy, NBS Spec. Publ.

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Schooley, J. F., Soulen, R. J., Jr., and Evans, G. A.,

Jr., Standard Reference Materials: Preparation

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(December 1972). COM73-50037**

Greifer, B., Maienthal, E. J., Rains, T. C, and

Rasberry, S. D., Standard Reference Materials:

Powdered Lead-Based Paint, SRM 1579, NBS

Spec. Publ. 260-45 (March 1973). COM73-

50226**

Hust, J. G., and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and

Electrical Resistivity Standard Reference Materials: Austenitic Stainless Steel, SRM's 735 and

798, from 4 to 1200 K, NBS Spec. Publ. 260-46

(March 1975). $1.00*

Hust, J. G., Standard Reference Materials: Electrical Resistivity of Electrolytic Iron, SRM 797,

and Austenitic Stainless Steel, SRM 798, from

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1974). COM74-50176**

Mangum, B. W., and Wise, J. A., Standard Refer- ence Materials: Description and Use of Precision

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Burke, R. W., and Mavrodineanu, R., Standard

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Acidic Potassium Dichromate Solutions as an

Ultraviolet Absorbance Standard, NBS Spec.

Publ. 260-54 (in press).

Ditmars, D. A., Cezairliyan, A., Ishihara, S., and

Douglas, T. B., Standard Reference Materials:

Enthalpy and Heat Capacity; Molybdenum

SRM 781, From 273 to 2800 K, NBS Spec. Publ.

260-55 (in press).

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i
CONTENTS

Page

1. Introduction 2

2. Samples 3

2.1 Sample Characterization. ..... 3

2.1. a Qualitative Spectrochemical Analyses 3

2.1.b Spark-Source Mass Spectrometry 3

2.1. c Electronic Characterization (RRR) ratio). ..... 6

2.2 Sample Preparation and Assignment . 8

2. 2. a Adiabatic-Receiving-Calorimeter Range

(1173 to 2100 K) 8

2.2.b Bunsen-Ice-Calorimeter Range

(273 to 1173 K) 9

2.2.c High-Speed, Pulse-Calorimeter Range

(1500 to 2800 K) 9

3. Calorimetric Apparatus and Procedure 9

3.1 Bunsen Ice Calorimeter

(Temperature Range: 273.15 to 1173 K) 10

3.1. a Apparatus 10

3.1. b Procedure 10

3.2 Adiabatic Receiving Calorimeter (Temperature

Range: 1173 to 2100 K) . . . . 11

3. 2. a Apparatus 11

3.2. b Procedure 14

3.3 High-Speed Pulse Calorimeter (Temperature

Range: 1500 to 2800 K) 14

3. 3. a Apparatus 14

3.3.b Procedure 15

vii
Page

4. Enthalpy and Heat-Capacity Measurements 16

4.1 Bunsen Ice Calorimeter: H - H 16

1 A I i • 1_) K

4.2 Adiabatic Receiving Calorimeter: H - H 18

i zyo.ijK

4.3 High-Speed Pulse Calorimeter: C , .1500 to 2800 K 22

5. Smoothing the NBS Data 23

6. Reliability of the NBS Data 35

6.1 Error Due to Sample Impurity 35

6.2 Bunsen-Ice-Calorimeter Data 36

6.3 Adiabatic-Receiving-Calorimeter Data 37

6.4 Pulse-Calorimeter Data 38

7. Comparison of NBS Heat Data on SRM 781 Molybdenum with Data on

Molybdenum Metal of Previous Investigators and Compilers .... 41

8. Acknowledgements 56

9. References 57

Appendix 63

viii
LIST OF TABLES

Table Pag

1 Qualitative spectrochemical analyses of the molybdenum

samples, in mass percent 4

2 Mass-spectrometric analysis of a representative specimen

from the SRM-781 molybdenum lot 5

3 Residual resistivity ratios for OSRM SRM-781 6.35-mm-O.D.

molybdenum rods 7

4 Chronological order of experiments performed on SRM-781

molybdenum specimens Dl, D2 and D3 17

5 Enthalpy data (referred to 273.15 K) on the SRM-781

molybdenum sample 19

6 Enthalpy data (referred to 298.15 K) on the SRM-781

molybdenum sample 20

7 Heat-capacity results on the SRM-781 molybdenum sample in

the temperature range 1500 to 2650 K 24

8 Heat-capacity results on the SRM-781 molybdenum specimen

Dl in the temperature range 2250 to 2800 K, series Dl-T 26

9 Coefficients of the spline representation of heat_capacity

(equation (7)) of SRM-781 molybdenum for C /J-mol 1 -K 1 29

P

10 Coefficients and constants of the spline representation of

relative enthalpy (equation (8)) of SRM-781 molybdenum for

ElJ-mol 1 30

11 Summary of error estimates for pulse-calorimeter data on

SRM-781 molybdenum 39

12 Heat-capacity results on SRM-781 molybdenum (specimen D2)

at 2000 K, as a function of specimen-heating rate 39

13 Average percent difference over the range 1500 to 2650 K

between smooth representations of heat capacity of different

SRM-781 molybdenum specimens and different experiment series. 42

14 Chronological compilation of literature references containing

original or compiled data on the enthalpy or heat capacity

of molybdenum metal chiefly in the temperature range 273.15 K

to 2800 K 44

15 Symbol and citation key for relative enthalpy data displayed

in figure 6 52

ix
LIST OF TABLES (continued)

Table Page

16 Symbol and citation key for heat-capacity data displayed

in figure 7 52

17 Symbol and citation key for relative enthalpy and heatcapacity correlations displayed in figures 8 and 9 55

Al Calculation of estimated impurity levels in OSRM SRM-781

6.35-mm-O.D. molybdenum rod, specimen No. 12 63

A2 Enthalpy data for two empty (90Pt-10Rh) containers 64

A3 Hemispherical total emittance of the SRM-781 molybdennm

specimen in the temperature range 1730 to 2760 K 65

A4 Corrections for molybdenum (s) to convert enthalpy and

heat-capacity data between IPTS-48 and IPTS-68 temperature

scales 66

A5 Enthalpy relative to 273.15 K and heat capacity of SRM-781

molybdenum computed from equations (8) and (7) 67

LIST OF FIGURES

Figure Page

1 Deviation of NBS relative-enthalpy data on SRM-781

molybdenum from unified spline representation 31

2 Deviation of NBS heat-capacity data on SRM-781 molybdenum

from unified spline representation 32

3 Deviation of all NBS pulse-calorimeter, heat-capacity data

on SRM-781 molybdenum from unified spline representation 33

4 Total hemispherical emissivity of SRM-781 molybdenum

measured in pulse-calorimeter experiments 34

5 Dependence at 2000 K of calculated heat capacity of SRM-781

molybdenum (specimen D2) on specimen-heating rate 40

6 Deviation of directly-measured molybdenum enthalpy data

appearing in the literature from unified spline representation of present NBS data for SRM-781 molybdenum 50

x
LIST OF FIGURES (continued)

Figure Page

7 Deviation of directly-measured molybdenum heat-capacity

data appearing in the literature from unified spline

representation of present NBS data for SRM-781 molybdenum. ... 51

8 Deviation of enthalpy correlations appearing in the

literature from unified spline representation of present

NBS data for SRM-781 molybdenum 53

9 Deviation of heat-capacity correlations appearing in

the literature from unified spline representation of

present NBS data for SRM-781 molybdenum 54

xi

Standard Reference Materials

:

ENTHALPY AND HEAT CAPACITY STANDARD REFERENCE MATERIAL:

MOLYBDENUM SRM 781, FROM 273 TO 2800 K

D. A. Ditmars, A. Cezairliyan, S. Ishihara , and T. B. Douglas

Institute for Materials Research, National Bureau of Standards

Washington, DC 20234

Abstract

The relative enthalpy of NBS Standard Reference Material No. 781

(99.95 mass-percent pure, polycrystalline molybdenum: a metallic, hightemperature enthalpy and heat-capacity standard) has been measured with

two differently designed, receiving-type calorimeters in the temperature

ranges 273 to 1173 K and 1173 to 2100 K, respectively. The smoothed

enthalpy data derived from these measurements are believed to have an

inaccuracy not exceeding 0.6 percent at any temperature in these ranges.

The heat capacity of Standard Reference Material No. 781 has also been

measured in the temperature range 1500 to 2800 K using a millisecondresolution pulse technique with resistive self-heating. This technique

measured, in addition, hemispherical total emittance. In this highest

temperature range, the smoothed heat-capacity data are believed to be in

error by no more than 3 percent. A complete description of all the NBS

experimental techniques and a detailed analysis of all suspected sources

of errors are presented. Equations representing the smoothed NBS enthalpy

and heat-capacity data for SRM-781 molybdenum in the range 273.15 to

2800 K are presented along with a table of these data calculated from

the equations at selected temperatures. A bibliography of all known

publications on the enthalpy and heat capacity of molybdenum has been

compiled. The NBS-measured enthalpy and heat-capacity data for molybdenum

have been compared with those of all the principal investigators and

compilers reported in the literature.

Key Words: Drop calorimetry; emittance; entbalpy; heat capacity;

high-speed measurements; high temperature; molybdenum; pulse calorimetry;

standard reference material; thermodynamic functions.

a Deceased.

1
1. Introduction

Calorimetric standard reference materials are employed to verify

the continued, correct functioning of individual calorimeters and to

provide a meaningful basis for intercomparing calorimeters of similar

or different design. The principal criteria for choosing these standard

reference materials ("SRM's") are that they be readily available in forms

of high purity and stability, that the thermal property for which each

was chosen be accurately known, and that they themselves contribute no

extraneous heat effects which would significantly affect the inaccuracy

or imprecision of measuring the thermal properties.

The National Bureau of Standards has played a leading role in

developing and promoting such SRM's for applications in combustion

calorimetry, solution calorimetry and differential thermal analysis [l]

a

. Since 1970, the National Bureau of Standards has also offered pure

synthetic sapphire (C1-AI2O3) as an SRM for enthalpy and heat-capacity

measurements over the temperature range 273 to 2250 K. This certification of a-Al203 was based upon relative-enthalpy measurements on this

material carried out at NBS [2,16].

Due to significant advances in high-temperature materials and

measuring technology in recent years, a need has arisen for enthalpy and

heat-capacity SRM's usable at temperatures above 2250 K. In addition,

> many of the newer high-temperature techniques for measuring thermophysical

properties are restricted to materials which are more amenable to physical

shaping than 01-AI2O3 and which exhibit metallic electrical conductivity.

Molybdenum was chosen from among the candidate refractory materials for

a high-temperature enthalpy and heat-capacity SRM since it possesses all

the required qualities described above. Its high melting point (2894 K)

[3] affords a considerable extension of the temperature range above that

covered by CI-AI2O3. Also of importance is the fact that there exists

a considerable published body of thermophysical data for molybdenum

(see section 7). The extensive documentation of its physical, chemical,

and thermal properties in the literature lends confidence in the choice

of it as an SRM.

The National Bureau of Standards Office of Standard Reference

Materials ("OSRM") has obtained a quantity of annealed, polycrystalline

molybdenum rod in diameters 3.18 and 6.35 mm. Specimens chosen at

random from this material were used in relative-enthalpy measurements on

molybdenum over the temperature ranges 273.15 to 1173 K and 1173 to

2100 K. Two different designs of receiving-type calorimeter were used

in these measurements. Up to 1173 K, a Bunsen ice calorimeter was used

and above this temperature (there being negligible overlap of these two

temperature ranges), an adiabatic receiving- type calorimeter was used.

In addition, the heat capacity of another specimen chosen from the same

OSRM lot was measured over the temperature range 1500 to 2800 K. The

Figures in brackets refer to literature references in section 9 of this

paper

2
data up to 2800 K were obtained by using a millisecond-resolution

pulse-calorimetric technique employing resistive self-heating of the

specimen. This technique simultaneously measured the heat capacity and

the hemispherical total emittance. In the following sections, all details

of the thermal measurements with the three calorimeters are described.

All the NBS enthalpy and heat-capacity data are critically examined to

evaluate causes affecting their imprecision and overall inaccuracy. The

NBS relative-enthalpy and heat-capacity results are compared with all

significant original data on these properties reported in the literature

for molybdenum.

2. Samples

The molybdenum for the enthalpy and heat-capaCity measurements was

chosen from the stock of 3.18-mm and 6 . 35-mm-diameter rods made available

by the NBS Office of Standard Reference Materials as SRM-781. These had

been obtained from the General Electric Company where they were made by

sintering high-purity powder, swaging, grinding to final diameter and

annealing at 1725 K in a high vacuum. Two specimens of 3.18-mm-diameter

rod, denoted as specimens "A" and "C", were used in the measurements;

also, two specimens of 6 . 35-mm-diameter rod, called specimens "B" and

"D". In addition, a few enthalpy measurements above 1173 K were made

on a specimen (designated "E") , machined from a rod of 3-pass electronbeam zone-refined polycrystalline molybdenum obtained from the Materials

Research Corporation (MRC) of Orangeburg, NY. Specimen "E" was classified

by MRC as being of "MARZ grade"3 and having a purity of 99.992 mass

percent

.

2.1 Sample Characterization

2.1. a Qualitative Spectrochemical Analyses

Portions of three specimens - A and B (OSRM sample) and E (MRC

sample) - were analyzed separately. The results are given in table 1.

In the case of specimen E, special care was taken to remove all surface

contamination, to consume the sample completely in the arc excitation and

to use a high-purity reference sample of molybdenum. This analytical

technique does not account for the important non-metals, but indicated

a total metallic impurity level less than 0.02 percent for specimens A

and B and a lesser metallic impurity level for specimen E, consistent

with the supplier's claimed purity.

2.1.b Spark-Source Mass Spectrometry

A specimen from the OSRM lot from which specimens A and B were

taken was first etched in nitric acid, then washed with distilled water

and boiled in distilled water to clean the surface. This specimen was

then presparked to identify and remove any remaining surface contamination.

Use of company or trade-names does not imply recommendation by the

National Bureau of Standards.

3
Table 1

Qualitative spectrocheraical analyses of the molybdenum

samples, in mass percent

OSRM Sample (SRM-781) MRC Sample

Elems n t Specimen A

(3.18mm diam. rod)

Specimen B (6.35mm diam. rod)Specimen E (triple-zonere fined)

Al

%

0.001 - 0.01

%

0.001 - 0.01

%

?

Ca < 0.001 < 0.001 < 0.0001

Cu < 0.001 < 0.001 < 0.0001

Fe 0.001 - 0.01 0.001 - 0.01 < 0.0001

Mg < 0.001 < 0.001 < 0.0001

Mo > 10 > 10 > 10

Si < 0.001 < 0.001 < 0.001

The following elements were also analyzed for, but not detected: Ag, As, Au, B, Ba,

Be, Bi, Cd, Ce, Co, Cr, Ga, Ge , Hf, Hg, In, Ir, La, Mn, Na, Nb , Ni, Os , P, Pb, Pd,

Pt, Rh, Ru, Sb, Sc, Sn, Sr, Ta, Te , Th, Ti, Tl, U, V, W, Y, Zn, and Zr . The estimated

limit of detection of any alkali metal is 0.005 percent.

4
Table 2

Mass - spectrometric analysis of a representative specimen

from the SRM-781 molybdenum lot

Elements Measured*5 Elements Showing Interference*

5

Element

Impurity

level a Element

Impurity

level a Element

Impurity

level a Element

Impurity

level 3

Ag 1 Sb 0.5 Ar <20 N <10

Al 7 Si 40 Au <10 Nb <3

As 2 V 0.4 B <0.1 Ni <20

Ca 9 W 56 Ba <1 0 <30

Cr 12 Zn 0.26 C <3 Os <6

Cu 15 Cd <8 Pd <6

Fe 40 CI <0.1 Pt <4

Ga 0.1 Co <7 Re <1

K 20 Cs <0.2 Rh <0.2

Mn 2 In <0.5 S <1

Mo (matrix) Ir <3 Sc <0.3

P 0.6 Li <0.3 Sn <30

Rb 0.3 Mg <31 Ta <25

Parts per million (ppm) by mass.

and He were not analyzed for and interference was complete for F, Ne, Na, and Ti . In

addition to the elements listed, the following were reported as "not detected" and were estimated to be present - if at all - in amounts not exceeding 1 ppm (some estimated at substantially lower levels; e.g., Be <0.01 ppm.): Ac, Be, Bi , Br, Ce , Dy, Er, Eu, Ge , Gd,

Hf, Hg, Ho, I, Kr, La, Lu, Nd, Pa, Pb, Pm, Po , Pr, Pu, Ra , Ru, Se, Sm, Sr, Tb , Tc , Te , Th,

Tl, Tm, U, Xe, Y, Yb , and Zr . "Interference" refers to the obscuring of lines for a given element by Mo matrix lines and lines from other impurities.

5
The mass-spectrometric results are given in table 2. Note the nearcompleteness of the coverage of the elements, and particularly, the low

levels of low-atomic-weight elements. The apparent enthalpy and heat

capacity of molybdenum would be particularly affected by the presence of

these elements; see section 6.1. This analytical technique indicated a

total impurity of 0.02 percent by mass of the elements detected, and set

a total upper limit of 0.02 percent by mass for the elements (except F,

Ne, Na, and Ti) partially masked by major interference.

2.1.c Electronic Characterization (RRR ratio)

Measurement of the residual resistivity ratio (RRR: the ratio of

the electrical resistivity of a metallic specimen at the ice point to

its resistivity at the normal boiling point of helium) has been applied

for estimating the concentration of metallic impurities and defects in a

metallic specimen [4,5]. The RRR's of sixteen specimens of 6.35-mmdiameter molybdenum rod chosen from the OSRM lot were measured using an

eddy-current decay method [83, 84, 85]. In this method, prior cleaning

and annealing of the specimens was important. The specimens were chosen

randomly from the 6 . 35-mm-diameter rods (no 3 .18-mm- diameter rods were

included) but bore no known relation to specimens B and D discussed

above. They were cleaned with ethyl alcohol, then heavily electroetched

to remove surface contamination. A pure molybdenum electrode in an

electrolyte of sulfuric acid and methyl alcohol was used. Annealing for

one hour at 1273 K in a high vacuum, followed by slow cooling, did not

yield stable RRR's. The adopted conditions, a minimum of two annealing

treatments of two hours duration each at 1473 K followed by slow cooling,

did result in RRR values stable within the resolution of the RRR measurements, however. The results of these measurements are presented in table

3. Note that specimen Nos. 2, 4, 9, 11, 13, and 14 seem to form a

fairly homogeneous group with a mean RRR of 70.4 and a standard deviation

of a single observation of 0.7. Also, specimen Nos. 5, 6, 7, 10, 12,

15, 16, and 17 form a somewhat-less homogeneous group with a mean of

58.1 and a standard deviation of a single observation of 1.6. Two

specimens, Nos. 3 and 8, have RRR's of higher value. There is no

known reason for this segregation.

Since the observed RFR values did not agree well with prior observed

RRR values for other metals with similar impurity levels typified by

tables 1 and 2, a hypothetical calculation of the possible overall

impurity level was carried out. In this calculation (see table Al), the

maximum total metallic Impurity level has been derived under the

following assumptions: 1) Ca, Mg, and Si are assumed to be absent or at

least to make no substantial contribution to the residual resistivity,

2) Despite the evidence of the qualitative spectrochemical analysis

(table 1), various other transition-metal contaminants are present,

namely Ni, Al, and Co at levels equal to those observed for Fe; and Nb,

Ta, W, and Zr are present at some common, unspecified atomic concentration,

3) Nb, Ta, W, and Zr have equal specific effects on the residual resistivity at 4 K equal to 0.3 ]sQ*em per atomic percent of impurity [7].

See table Al
Table 3

Residual resistivity ratios for OSRM SRM 781 6.35-mm O.D.

molybdenum rods

d

O pc (-_L Illfci 11 INU •

p V

D 4 K

vjIU U.}J ±

2

b

70.6 70.6

J 80.9

4 69.4 69.4

5 57.5 57.5

6 58.3 58.3

7 60.7 60.7

8 77.8

9 69.9 69.9

10 57.4 57.4

11 71.1 71.1

12 55 .8 55.8

13 70.1 70.1

14 71.2 71.2

15 59.4 59.4

16 56.7 56.7

17 59.2 59.2

Mean 66.6 70.4 58.1

c

s 8.4 0.7 1.6

For an explanation of this grouping, see text, section 2. I.e.

Specimen 1 was used as the electrode material in etching the other specimens.

Computed standard deviation of a single observation.

These specimen numbers are valid only within the context of the residualresistivity-ratio measurements and bear no relation to specimen designations

accompanying the heat-measurement data.
The atomic fraction of each of the elements Nb, Ta, W, and Zr

calculated under these assumptions is 0.0307 atom percent (see table Al)

.

Expressing these fractions as mass percentages and adding the levels of

Fe, Ni, Co and Al, yields an estimated overall metallic impurity level

of 0.216 mass percent. Thus, under these assumptions , the OSRM SRM-781

molybdenum samples may be considered at least 99.78-mass percent pure.

Note that this calculation is based on the RRR of only specimen No. 12.

Specimen No. 3 (RRR = 80.9) under the same assumptions, will have

impurity levels about two thirds of those listed in table Al . This

would correspond to a purity of 99.85 mass percent. The levels of

impurity implied by the RRR characterization far exceed those found by

the spectrochemical and mass-spectrometric analyses detailed in tables

1 and 2. The cause of the disagreement is not known. Because it was

felt to be much more reliable, the mass-spectroscopically-measured purity

has been accepted as the purity of SRM-781.

2.2 Sample Preparation and Assignment

The molybdenum specimens A, B, C, D, and E mentioned above were

subjected to preliminary cleaning and additional annealing prior to the

enthalpy and heat-capacity measurements. The following sections describe

these preparatory procedures and the assignment of the specimens to the

three measuring ranges and calorimeters used in this investigation.

2. 2. a Adiabatic-Receiving-Calorimeter Range

(1173 to 2100 K)

Relative enthalpy measurements on each of the specimens A, B, and

E were made in an adiabatic receiving calorimeter in the temperature

range 1173 to 2100 K. Specimen A, which consisted of four sections of

OSRM SRM-781 molybdenum rod, 3.18 mm in diameter and 25.4 mm in length,

was first etched with HN0 3

, then with HC1 and subsequently cleaned in

boiling distilled water. After this treatment, the surface apparently

discolored when in contact with room air, but without detectable weight

gain; Specimen A was excluded from extended contact with room air thereafter. It was then annealed for two hours at 1473 K and 1.3 kPa pressure

of argon. Specimen B, a single section of OSRM SRM-781 molybdenum rod,

6.35 mm in diameter and 25.4 mm in length was cleaned in the same manner

but was not specially annealed. Note, however, that the first enthalpy

measurement on it was made only after it had been held at about 1700 K

for about 40 minutes and this circumstance may have affected its annealing.

At least, a repetition of this heating did not change its enthalpy

significantly (see table 6). Specimen E, the high-purity MRC molybdenum,

was cleaned with solvents and boiling distilled water but was neither

etched nor annealed prior to the heat measurements on it. After heat

measurements in the temperature range 1173 to 2100 K were completed,

specimen A was combined with specimen C, described below, and the combination treated as one composite specimen in all subsequent heat measurements .

8
2.2.b Bunsen-Ice-Calor imeter Range

(273 to 1173 K)

Relative enthalpy measurements in this temperature range were

carried out on a composite specimen consisting of specimens A and C

together. Specimen C comprised four sections of the 3 . 18-mm-diameter

OSRM SRM-781 molybdenum rod, each 50.8 mm long. These were chemically

etched and cleaned in the same fashion as specimen A, and subjected to

the same annealing treatment described for specimen A, above.

2.2.c High-Speed, Pulse-Calorimeter Range

(1500 to 2800 K)

Heat-capacity measurements over the temperature range 1500 to 2800 K

were performed on three separate segments of specimen D. For this

purpose, specimen D, a segment of 6 . 35-mm-diameter OSRM SRM-781 molybdenum

rod, was divided into three equal segments of length 76 mm each. These

segments are designated as specimens Dl, D2, and D3. Each of these had

a central cylindrical portion (including the entire segment axis) removed by an electro-erosion technique. This resulted in three tubes of

wall thickness 0.5 mm. The outer surface of each of these three tubular

specimens was then highly polished to reduce heat loss due to thermal

radiation during the high-temperature experiments. Before the start of

these experiments, the three specimens were heat-treated by subjecting

each of them to 20 heating pulses during each of which a maximum temperature of about 2500 K was attained.

3. Calorimetric. Apparatus and Procedure

The enthalpy and heat-capacity measurements of the present

investigation were carried out over three temperature ranges in three

calorimeters of different design and operating principle. The sections

which follow describe these apparatuses briefly under headings appropriate

to each apparatus and provide further literature references to more

detailed descriptions. Also covered are special operational features of

value in evaluating the molybdenum data of this study and further details

on the physical preparation and handling of the specimens during the

measurements. See section 2.1 for details concerning the elemental

characterization of the various molybdenum specimens.

9
3.1 Bunsen Ice Calorimeter

(Temperature Range: 273.15 to 1173 K)

3.1. a Apparatus

The enthalpy, relative to the enthalpy at 273.15 K, of molybdenum

specimens A and C, combined, was measured over the temperature range

273.15 to 1173 K with a Bunsen ice calorimeter. This is a highly precise

type of phase-change, receiving calorimeter in which an amount of energy

to be measured causes the melting of ice in a spatially confined icewater system. The amount of ice melted (or some quantity proportional

to this) is then taken as the measure of this energy. This method and

the apparatus employed at NBS have been described previously in considerable detail [2, 8, 9, 10]

.

Briefly, a sample whose relative enthalpy is to be measured is

first suspended in the isothermal zone of a controlled-temperature

furnace until it reaches a steady temperature. It is then dropped in

almost free fall into a re-entrant well of the calorimeter. The heat

transferred to the calorimeter as the sample cools to the calorimeter

temperature (very nearly 273.15 K) melts a portion of the calorimeter

ice. The resulting change in volume of the calorimeter's confined

ice-water system is measured with a sensitive mercury dilatometer.

.Calibration [9, 10, 11] of the calorimeter (i.e., measuring the proportionality between the energy transferred to the calorimeter and the ensuing

volume change of the ice-water system referred to above) is carried out

with accurately measured quantities of electrical energy converted to

heat in a specially-designed electrical heater which fits within the

calorimeter well. In this measurement technique, samples are usually

encapsulated in order to guarantee their integrity and to prevent their

reaction with the furnace atmosphere. Separate enthalpy measurements on

an empty container are made ever the same furnace temperature range as

obtained in the measurements on the container-pl -s-sample in order that

the reproducible but unknown heat lost during the fall may be accounted

for. It is not necessary to know this heat loss during the fall explicitly

if one can assume that it is the same for a full as for an empty container.

It then cancels when the empty-container measured heat is subtracted from

that for the container-plus-sample.

3.1.b Procedure

Specimens A and C, comprising a total mass of 20.8297 grams of

molybdenum (approximately 0.2 moles), were hermetically sealed in a 0.3

mm-wall, (90 Pt-10 Rh) container together with helium at several hectopascals3 pressure at room temperature. Since it was not practical to

measure separately the relative enthalpy of the container actually used

to hold the molybdenum, the required empty-container enthalpies (see

section 3.1. a) were derived from existing enthalpy measurements (table A2)

1.3 hFa = 1 mm Hg,

10
made on two entirely comparable containers of very nearly the same mass

during a prior enthalpy study (a-Al^, SRM 720 [2].) A total of

fourteen enthalpy measurements at ten temperatures uniformly covering

the temperature range of the ice calorimetric measurements were made on

the encapsulated specimens. The emtpy-container measurements consisted

of a total of twenty measurements on two empty containers in the same

temperature range. Container masses were routinely checked before and

after each measurement to preclude the possiblity of unsuspected leaks

or losses of container material.

The furnace temperature was measured up to 773 K by a platinum

resistance thermometer, and above 773 K by two homogeneous Pt/ (90 Pt-10 Rh)

thermocouples. The thermometer and both thermocouples were calibrated

by the Temperature Section of NBS on the scale IPTS-48 but all readings

were corrected [12] to the basis of IPTS-68 [13]. Both thermocouples

were compared up to 773 K with the thermometer in place in the calorimeter furnace, and a slight adjustment in their calibrations (0.1 K at

and above 773 K) was made to avoid a temperature discontinuity at 773 K.

3.2 Adiabatic Receiving Calorimeter

(Temperature Range: 1173 to 2100 K)

3. 2. a Apparatus

The enthalpy, relative to the enthalpy at 298.15 K, of molybdenum

specimens A, B, and E (taken separately) was measured in the temperature

range 1173 to 2100 K with an adiabatic receiving calorimeter. This

apparatus, depicted and partially described in one prior publics tion

[14], has been used in several other high-temperature enthalpy studies,

notably of tungsten (to 2600 K) [15], aluminum oxide (SRM-720) [16], and

beryllium aluminate (Be0-Al203) [17]. Since considerable operating

experience has been gained with this calorimeter and some modifications

to it have been made since the prior description [14], somewhat more

detail will be given here for this apparatus than for either of the two

other calorimeters used in the present study.

The apparatus (see figure 1 of reference [14]) consists of an

adiabatic calorimeter positioned above a controlled- temperature, inductionheated furnace and optically separated from it by a shutter. An

encapsulated specimen of the substance under investigation is suspended

by a tungsten wire in the furnace until it reaches a steady temperature.

This temperature is measured with an automatic optical pyrometer. The

shutter is momentarily opened and the capsule is then rapidly lifted a

distance of 0.8 m into the adiabatic calorimeter. The shutter is manually

opened and closed on the same timed sequence during all experiments.

The energy transferred to the calorimeter from the specimen and container

while within the calorimeter causes the temperature of the central measuring portion of this calorimeter to rise to a new steady level while

a surrounding shield is simultaneously heated to maintain the temperature

differences between this central portion and the shield at a minimum

(adiabatic principle) . The measured specimen energy is calculated as

11
the product of the observed temperature rise of the calorimeter and its

total heat capacity (a small correction is made for calorimeter heat

leak). Calibration of the calorimeter (i.e., measurement of its total

heat capacity under adiabatic conditions) is carried out in separate

experiments using accurately measured quantities of energy converted to

heat in an electric heater situated within the calorimeter. Separate

measurements on the heat content of the empty specimen containers are

made at each specimen-measuring temperature. Subtraction of the emptycontainer heat-content values from the corresponding heat-content data

for the specimen-plus-container yields the heat content of the specimen

alone. This assumes that the heat loss to the surroundings during the

lift into the receiving portion of the calorimeter is a function of

container temperature and surface emissivity only and that all lifts

take place in time intervals of equal length. The container is exposed

to a room-temperature zone outside of the calorimeter for about 0.1

second during its transfer from the furnace to the calorimeter.

The central measuring portion of the adiabatic calorimeter consists

of two concentric cylinders, the inner one of nickel avd the outer one

of copper. These are thermally coupled to each other through a common

circumferential ring of 8 mm thickness and located between the cylinders

at mid-height. This feature delays the temperature response of the

outer (copper) surface of this central measuring portion by several

minutes and reduces the temperature control problems, at moderate or

high rates of heating, associated with the surrounding adiabatic shield.

A guard jacket surrounds the adiabatic shield and is controlled at a

temperature slightly below that of the shield. The calorimeter heat leak

is thus kept small and almost constant throughout its temperature range.

The rise in the calorimeter temperature during an experiment is

measured with a copper resistance thermometer wound around and cemented

onto the copper cylinder. This has been compared with a platinum

resistance thermometer calibrated by the Temperature Section of the NBS

.

Control of the shield and guard is achieved using the information

provided by copper resistance thermometers wound on and cemented to

these bodies. The adiabatic calorimeter has a total heat capacity of

about 2900 joules per kelvin and operates in the range 298 to 338 K.

The electrical energy supplied to the calorimeter during calibration is

calculated from the observed voltage, current, and active time interval

of a heater element situated within the calorimeter. This energy is

also corrected for the observed calorimeter heat leak. The calorimeter

has been electrically calibrated eight times to date and the standard

deviation of the accumulated calibration data points from a smooth

representation is estimated to be + 0.004 percent.

12
The induction-heated furnace consists of a central hollow graphite

core (to couple with the induction coil) with surrounding concentric

layers of carbon black (25 nanometer particle size) and fine silicon

carbide powder, the entirety contained within a heavy-wall quartz tube.

The carbon black and silicon carbide are used for thermal insulation

inside the quartz tube since they do not appreciably couple with the

working coil below 2300 K. After thoroughly degassing the furnace parts

by heating to 2800 K_under high vacuum, the calorimeter and furnace are

operated in a 1 cm3 s

1 flow of argon at 13.3 kilopascals pressure.

Around the quartz tube is a water-cooled copper working coil shaped as

a solenoid with closer turn spacing near the ends to decrease the

temperature gradient near the furnace core, where the capsule hangs.

One-half centimeter below the lower limit of the normal capsule

position at the center of the furnace is a diaphragm with a 3.18 mm hole.

An automatic optical pyrometer is focused up through this hole onto the

bottom of the capsule for temperature measurement and control of the

furnace. The pyrometer has been periodically calibrated by the Optical

Radiation Section of the NBS . The uncertainty of this instrument is now

estimated (95-percent confidence limits) to be +0.9 K at 1200 K,

+0.8 K at 1350 K, +0.8 K at 1500 K, +1.3 K at 1675 K, and +3.0 K at 2475 K.

Since the furnace temperature measurement is the most critical measurement, extra effort and frequent checks have been exercised to see that

the conditions of the environment during the use of the pyrometer simulate those during its calibration and that the system optics are clean.

An exploratory graphite probe the size of the specimen container

was used to measure the temperature gradient along the furnace axis.

This test showed that the temperature along this axis is uniform to

+2.5 K for 20 centimeters upwards from the lower limit of the normal

container position at 2300 K after two hours furnace warm-up time.

The capsule lifting device, a small servo motor, is driven by an

operational amplifier signal, so chosen as to provide an upwards

acceleration of constant magnitude for the first half of the lift of the

hot capsule from the furnace to the calorimeter. The tension in the

lifting wire is constant during the first half of the lift and is

essentially zero during the second half of the lift. The total time of

the lift is monitored by an interval timer gated by the amplifier signal.

It does not vary by more than +2 ms out of 600 ms

.

13
3.2.b Procedure

The relative enthalpy measurements on specimens A, B, and E in the

adiabatic receiving calorimeter were completed prior to the measurements

in the Bunsen ice calorimeter described above. The specimen masses were:

A, 8.20415 grams; B, 8.18014 grams; E, 13.95978 grams. During these

experiments, each specimen was contained within a molybdenum capsule

with a closely fitting (but not hermetically sealed) lid in the argon

atmosphere of the furnace and calorimeter. Both the capsule and the lid

were machined from a molybdenum rod claimed to be of 99.95-percent purity.

Specimen and capsule masses were measured before and after each enthalpy

measurement. The mass of specimen A did not vary by more than 0.06

milligrams below 2000 K. At 2000 K, a total mass increase of 0.30 milligrams (0.004 percent) was observed for this specimen and at 2100 K, the

total specimen mass had increased by 0.40 milligrams (0.005 percent)

above its initial value. The assumption was made that this mass increase

was due to carbon from the furnace atmosphere. It was considered too

small to warrant a correction. Specimens B and E, which were not

subjected to these high temperatures, showed no mass increase.

Twelve furnace temperatures nearly uniformly covering the range

from 1170 to 2100 K were chosen. A table of random numbers selected by

a computer was used to arrange these furnace temperatures in a chronological sequence. This method of determining the temperature sequence

'of the experiments was followed so as to avoid the possible introduction

of a bias into the measurements arising from gradual changes in the

condition of the furnace insulation or in the automatic optical pyrometer.

A total of twenty-seven relative-enthalpy measurements were made, most

of them (twenty) on specimen A; four measurements were made on specimen

B and three on specimen E.

Since the final calorimeter temperature is in general not equal to

the reference temperature (298.15 K) , a small correction is necessary

in order to refer the measured enthalpies to this reference temperature.

The maximum value of this correction occurred in an experiment at 2100 K

and amounted to 2 percent of the net measured heat at this furnace

temperature. In this instance, the final temperature of the adiabatic

calorimeter was 315.65 K. These corrections were applied using the

molybdenum heat-capacity evaluations of references [18] and [19] and are

believed to be in error by no more than 5 percent, thus contributing an

error to the corrected specimen enthalpy not exceeding 0.1 percent.

3.3 High-Speed Pulse Calorimeter

(Temperature Range: 1500 to 2800 K)

3. 3. a Apparatus

The heat capacity and hemispherical total emittance of molybdenum

specimen D were measured in the temperature range 1500 to 2800 K using a

millisecond-resolution pulse technique which employed resistive selfheating of the specimen. The apparatus used in this technique and the

method of calculating the heat capacity from the observed quantities

14
have already been described in considerable detail [20,21]. Briefly, the

tubular specimen is heated in a vacuum or inert-gas atmosphere from room

temperature to high temperatures (above 1500 K) in less than one second

by passing an electric current pulse through it. Simultaneously, measurements are made (with millisecond resolution) of the potential difference

across a standard resistor placed in series with the specimen, the axial

potential drop along the specimen and the specimen temperature. The

specimen current is determined from the measured potential difference

across the calibrated standard resistor. The axial potential drop across

the middle one third of the specimen is measured between spring-loaded,

knife-edge probes. A rectangular (0.5 x 1.0 mm) hole in the wall at the

middle of the tubular specimen provides an approximation to blackbody

conditions for optical temperature measurement. The specimen temperature

is measured at the rate of 1200 times per second with a high-speed photoelectric pyrometer [22] focused on this hole along a diametral axis normal

to the tube axis. The digital data acquisition system used to record

all the measurements is capable of recording a set of signals corresponding to temperature, potential drop and current approximately every

0.4 millisecond with a full-scale signal resolution of about one part in

8000.

3.3.b Procedure

The heat-capacity measurements were performed on three tubular

specimens which had been fabricated from adjacent segments of specimen D.

These were designated specimens Dl, D2 and D3. Specimen geometries and

other details are given in section 2.2.c.

In order to optimize the operation of the pyrometer, the entire

temperature interval in which these heat-capacity measurements were

carried out (1500 to 2800 K) was divided into six smaller intervals (or

"ranges") as follows:

Range I: 1500 to 1650 K Range IV: 2000 to 2250 K

Range II: 1650 to 1800 K Range V: 2250 to 2650 K

Range III: 1800 to 2000 K Range VI: 2300 to 2800 K

In each of these smaller intervals a different absorbing filter was used

in the high-speed, photoelectric pyrometer. At least four pulse experiments were performed in each temperature interval, save interval VI in

which only two were performed. A single pulse experiment normally

provides sufficient data to permit calculation of the heat capacity and

hemispherical total emittance throughout the entire interval. All

specimens were measured at least once in each temperature interval except

that only specimen Dl was measured in the sixth interval.

15
The chronological sequence of the 31 experiments which were performed on specimens Dl, D2 and D3 is summarized in table 4 to show the

total number of experiments performed on each specimen. All the experiments (except number 12) in the range 1500 to 2650 K were conducted with

the specimen in a vacuum environment at approximately 1.3 x 10 5 hectopascals ('vlO 5 torr) total pressure. Because of the relatively high

vapor pressure of molybdenum at high temperature, the experiments (numbers

13 and 14) in which the specimen was heated to temperatures above 2650 K

(Range VI) were conducted with the specimen in an argon environment at

about atmospheric pressure. Also, one of the experiments (number 12)

in Range V was performed in an argon environment. A comparison of the

results of experiments 11 and 12, one with the specimen in vacuum and

the other in argon, respectively, does not show any difference in the

measured property. Optical measurements performed on the sample chamber

window before and after the pulse experiments did not show any change in

its transmission. Also, mass measurements before and after the complete

set of pulse experiments for each specimen failed to detect any change

in specimen mass. The electrical resistance of each specimen was

measured at room temperature both before and after the pulse experiments,

using a Kelvin bridge. Current and potential-drop measurements on each

specimen during the pulse experiments provided the data for determination

of the electrical resistivity of SRM-781 molybdenum at 1500, 2000, and

2500 K.

To study the effects which may be attributable to the specimen

'heating rate, seven experiments (numbers 20 to 26) in the temperature

Range IV were conducted on specimen D2 using different heating rates

from 1200 to 8000 K*s The results are discussed in section 6.4.

These experiments were performed to demonstrate the effect of heating

rate on the measurements and the data were not used in the final smoothing

of the molybdenum heat-capacity data.

The duration of the current pulses in the experiments (excluding

experiments 20 to 26) ranged_from 400 to 560 ms and the heating rates

ranged from 5100 to 6800 K's l

. Radiative heat loss from the specimen

amounted to approximately 1 percent of the total energy input at 1500 K,

2 percent at 2000 K, 5 percent at 2500 K, and 8 percent at 2800 K. The

magnitude of the current pulses ranged from 1800 to 2500 A.

4. Enthalpy and Heat-Capacity Measurements

4.1 Bunsen Ice Calorimeter: (H - H )

1 L 1 5 . ID Jx

In any accurate drop calorimetry, including the present work, the

relative enthalpy of the empty sample container is measured separately.

This permits accounting for both heat lost in subsequent enthalpy measurements on the container-plus-sample and for the heat content of the

container itself. Since it was not practical in the present case to

separately measure the relative enthalpy of the container actually used

to hold the molybdenum, the required empty-container enthalpies were

derived from enthalpy measurements on two entirely comparable empty

containers used in a previous study [2], These data are repeated for

16
Table 4

Chronological order of experiments performed on

SRM-781 molybdenum specimens Dl, D2, and D3

Range

Code

Temp . Range

K

Specimen Dl Specimen D2 Specimen D3

First

Series

Second

Series

Third

Series

First

Series

Second

Series

I 1500-1650 1 6 15 27

II 1650-1800 2 7 16 28

III 1800-2000 3 8 17 29

IV 2000-2250 4 9 18 (20-26)

C 30

V 2250-2650 5 10 ll,12b

19 31

VI 2300-2800 13

b

,14

b

The numbers 1 to 31 indicate the sequence of experiments in the cbronological

order performed.

b These experiments only carried out in argon gas at atmospheric pressure. All

other experiments carried out in vacuum (1.3*10 5 hFa)

.

Heating-rate tests. These experiments excluded in smoothing the

heat-capacity data. See table 12.

17
convenience in table A2. In order to reduce the effect of random errors

in these enthalpy data on the empty container, they were smoothed by

fitting an equation to them by the method of least squares (equation (1)

of reference [2]). This equation is:

E

T

" ^273.15

= ^•529744 )( 10_8 )(2

7 -273.15)

3

+ (8 .068654) (10

_5

) (T-273.15) 2

+ (1.901653) (7-273.15) - (34 .94647) (7-273 .15) /T, (1)

in which H is given in J and temperature, Tt in K (IPTS-68).

The individual measurements on the container-plus -sample are listed

in column 2 of table 5 in the order in which they were measured. These

represent the total mercury mass, ^tot.» forced into the calorimeter

during an experiment. These data correspond to temperatures slightly

different than those of column 1 (average difference = 0.4 K and no

difference exceeded 1 K) . Therefore, the corrections, &7?tot.' given in

column 3 must be added to the data of column 2 in order that the gross

observed heats (£gross> column 4) derived from column 2 correspond to

the temperatures of column 1. These corrections were calculated using

tabulated heat-capacity data on the container materials and the molybdenum

sample [23,24], along with the real observed sample temperatures and a

calorimeter calibration constant of 270.49 joules per gram of mercury [11].

The gross observed heats, 5gross» °f column 4 were derived by multiplying

the mass of mercury (column 2 plus column 3) by this same calibration

constant. The container heat values (Gcont . > column 5) were calculated

from equation (1) using the temperatures of column 1. The net measured

sample heats (H - #273.15* column 6) were calculated by subtracting

column 5 from column 4 and converting to a molar basis (atomic weight =

95.94 [25]). Columns 7 and 8 give the deviations, 6(#y - #273-15)> °f

the net enthalpy data from smooth values (6 = net - smooth) calculated

from equation (8) . The predominance of negative values for the deviations arises from the fact that equation (8) was fit simultaneously to

three sets of heat data, of which table 5 comprises but one set. See

section 5 for details of smoothing the data.

4.2 Adiabatic Receiving Calorimeter: (H - #OOQ -.c v)

The results of the. enthalpy measurements on molybdenum in the

range 1170 to 2100 K are tabulated in table 6. The temperatures of

column 1 are the actual furnace temperatures to which the heat data of

column 4 correspond. Column 2 gives the (random) chronological order in

which the heat data were obtained on the specimens of column 3. This

random order of the measurements was determined with the aid of a table

of random numbers in order to eliminate bias in the measurements due to

possible changes in the quality of the furnace insulation or a possible

gradual change in the automatic optical pyrometer. Columns 4 and 5 give,

respectively, the results of the heat measurements on the container-plussample (5gross ) and the empty container (£> Cont.)' A single day's experiments usually consisted of four heat measurements at a single temperature;

two on the container-plus-sample and two on the empty container.

18
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21
The last measurement of a day was always made on the same system as the

first measurement of that day. Prior investigation had indicated that

one probable cause of difference between these first and last measurements

of a day was a gradual change in the temperature distribution along the

furnace core (even though the apparent container temperature was unchanged) . This difference, for the present measurements, averaged 0.05

percent and did not exceed 0.10 percent of the empty-container heat. In

order to reduce the contribution of this suspected gradual change in

temperature distribution to the overall measurement imprecision, the

measured empty-container heats appear in column 5 corrected to their

expected values at the actual time of the corresponding container-plussample heat measurements.

The net measured sample heat (Hrp - #298. 15» column 6) was calculated

by subtracting column 5 from column 4 and converting to a molar basis

(atomic weight = 95.94 [25]). Specimen A had an initial mass of

8.20415 g. After the measurement at 2000 K (seventh in the series) its

mass was observed to have increased by 0.3 mg to 8.20445 g and thereafter, to have stayed essentially constant. It was assumed that this

apparent mass increase was due to pickup of carbon from the susceptor.

It was calculated that the error incurred by neglecting the carbon nature

of this addition would introduce an error into the molar enthalpy,

Hrp - #298 . 15' no greater than 0.016%. This was considered negligible

and was not corrected for. Specimens B and E, which were not subjected

v to the highest temperature, did not change in mass.

The derivation of the smoothed enthalpy values from the data of

column 6 is described in section 5. Prior to smoothing and calculating

the deviations, S(HT - #2 73. 15> " (% ~ #273 . 15)meas . ~

(Hrp - #27 3 . is) smooth' appearing in columns 7 and 8, the data of column 6

were all augmented by an amount, #298 15 ~ #273. 15 K

= 593.6 J»mol 1 to

convert them to the base temperature 273.15 K. This enthalpy increment

was derived from a provisional smoothing of relative enthalpy data on

the same sample taken in the range 273.15 to 1173.15 K (see_section 4.1

and table 5) . It agrees very well with the value 594 J'mol 1 derived

by Reilly and Furukawa [18] from their analysis of the low- temperature

heat-capacity data for molybdenum. The predominance of positive values

for the deviations of columns 7 and 8 arises from the fact that equation

(8) was derived from a simultaneous fit to three sets of data, of which

table 6 comprises but one set.

4.3 High-Speed Pulse Calorimeter: C , 1500 to 2800 K

The experimental results on the heat capacity of SRM-781 molybdenum

in the temperature range 1500 to 2800 K are given in tables 7 and 8,

while the results on the hemispherical total emittance are given in

table A3. In table 7, columns 2, 4, 6, and 8 give values of Cp while

columns 3, 5, 7, and 9 give the deviation of these values from the

corresponding smooth values of Cg calculated from equation (7)

;

60p = (C ) ~(Cp) sinoo th* Two series of heat-capacity measurements,

designated "first" (F) and "second" (S), were carried out on specimen Dl

.

22
Note that all heating rates for the experiments of tables 7 and 8

exceeded 5000 K«s . Two series of measurements were also carried out

on specimen D2. The second series, the data for which are tabulated

separately as table 12, was performed to investigate the effect of heating

rate on the heat-capacity data (see section 6. A). The data of table 12

were not included in any final smoothing of the heat-capacity data for

SRM-781. Complete details of the procedure for calculating heat capacity

and hemispherical total emittance from the measured current, potential

drop, and temperature during the pulse-heating and radiative-cooling

periods have been given in reference [21] . In the calculation of Cp,

using equation (2) of reference [21], values of potential drop (e)

and current (i) are first calculated from smooth functions at the temperature at which C-g is desired. These functions are polynomial smoothing

functions of temperature which are fitted to the e and i data recorded

at 0.4 ms intervals (see section 3. 3. a). A correction is included in

each heat-capacity datum for heat loss by thermal radiation. This correction was based on temperature data recorded during the cooling period.

See section 3.3.b for details on the radiative heat losses. Coolingperiod data were not adequate to permit evaluation of hemispherical

total emittance for experiments 2, 15 through 18 and 20 through 30. The

measurements on the three specimens yielded the following average values

for the electrical resistivity of SRM-781 molybdenum (units, \iQ.*cm) : 5.45 at 293 K, 38.1 at 1500 K, 53.3 at 2000 K, and 69.0 at 2500 K.

5. Smoothing the NBS Data

As a first step in obtaining one unified representation of the

enthalpy and heat-capacity data presented in Section 4., the relativeenthalpy data obtained with the Bunsen ice calorimeter (table 5, column

6) and with the adiabatic receiving calorimeter (table 6, column 6) were

individually smoothed. To accomplish this, each of these sets of

enthalpy data was fitted by the method of least squares with several

different functions, having up to five disposable constants. The

functions chosen to represent these enthalpy data were the ones yielding

a minimum standard deviation of residues of those tried and are as

follows:

H

T

- E273.\S = " 2333.9 + (25.79244)?1 + (1.73410 x 10~ 3 )T2 -

862.870 InT (2)

The unit of H is J*mol "S the range of applicability of equation

(2) is 1173.15 K > T > 273.15 K.

Standard deviation of percent residues = 0.28%, and

^"#298. 15 = " (6.18063 x 10

3

) + (21.6641)7 + (3.24129 x 10~3 )T

Z

+

(1.590 x 10

6

) exp (-16000 /T) (3)

The unit of H is J*mol ^ / the range of applicability of equation

(3) is 2100 K > T > 1170 K

Standard deviation of percent residues = 0.13%.

23
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26
The heat-capacity data obtained with the pulse calorimeter (tables 7 and

8) were fitted by the method of least squares with the third-degree

polynomial function of temperature, given below:

C = - 3.0429 + (4.7215 x 10~ 2

)T - (2.3139 x

10~ 5 )T

2

+ (4.7090 x

p

' > -9 3

10 )T (4)

The unit of C is J'mol "*"'K "S the range of applicability of

equation (4) Pis 2800 K > T > 1500 K.

Standard deviation of percent residues = 0.5%.

Note that equation (4) was not used further in deriving the unified data

representation. Equations (2) and (3) were differentiated to derive the

corresponding best representations of heat capacity for the individual

enthalpy data sets. Smooth heat capacities were then calculated from

these derived heat-capacity functions at 50 K intervals from 250 to

2100 K. The heat-capacity data measured directly with the pulse

calorimeter (tables 7 and 8) were next combined by arithmetically averaging them at each temperature in 50 K intervals from 1500 to 2800 K.

The smooth heat capacities derived from the enthalpy data and the

average measured heat capacities of the pulse calorimeter measurements

were then assigned weights based on a preliminary estimate of the overall

inaccuracy of the heat-capacity values. Each smooth heat-capacity value

derived from the ice-calorimeter data was assigned unit weight. The

smooth heat-capacity values derived from the adiaba tic-receiving-calorimeter data were all assigned the weight 0.500, and the averaged, measured

heat-capacity data obtained from the pulse-calorimeter data were all assigned

the weight 0.167. Note that the data of the adiabatic receiving calorimeter and that of the pulse calorimeter overlapped from 1500 to 2100 K.

All these weighted heat-capacity data were then fitted, using the method

of least squares, with a cubic spline function having four knots and of

the form,

C = I a/ + I \ff-V+ ' <5) r v=0 v=l

in which (T-Q ) +

= 0 for T <_ G

v

« The knot temperatures, 0 V

, were chosen

near suspected inflection points in the heat-capacity function or near

overlap temperatures of the different experimental techniques.

27
a

o = + 1 .6078753 X 10

a

l = + 4 .2064833 X 10

a

2 = - 6 .4321802 X 10

a

3 = + 3 .8567377 X 10

b

l = - 3 .2183846 X 10

b

2

6 .2727966 X 10

b

3

+ 6 .5829329 X 10

\

+ 3 .2467912 X 10

(6)

The coefficients of this cubic spline function for C J'mol ^"'K ^

and the values of the knot temperatures are as follows:

"

+1 _ -1 -1

J'mol «K

-2 -1 -2

J'mol *K

-5 -1 -3

J*mol 'K

-8 _

n -l -4

J'mol 'K

-8 -1 -4

J-mol *K ; 0 = 500 K

"9 J'mol

-1

'K~

4

; 0

2 = 1000 K

~10 J'mol

_1

'K~

4

; 0

3 = 1500 K

-8 _ -1 "4 n j r

The standard deviation of residues_of the heat-capacity data for this

spline function is 0.058 J'mol 1 "K 1

, based on 62 degrees of freedom.

An equivalent representation of the heat-capacity data can be obtained

by expanding this spline function and collecting terms to yield functions

of the form,

C = S c/V

(7) r v=0

corresponding to each of the five temperature intervals defined by the

four knots. The coefficients of the heat-capacity functions given by

equation (7) for Cp J-mol 1 *K 1 are presented in table 9. The enthalpy

of SEM-781 molybdenum relative to its enthalpy at 273.15 K can be obtained

by integration of the heat-capacity functions, equation (7). This integration yields enthalpy functions of the form,

4

Hm

~ #273 15 " K + s d T

V

(8)

v=0

in which Kv

is the enthalpy at the (knot) temperature starting the u'*

1

interval relative to the enthalpy at 273.15 K. The enthalpy at 273.15 K

is assigned the value zero. The coefficients of the enthalpy functions

given by equation (8) for H J-mol * and the values of the constants

are given in table 10. Values of enthalpy and heat capacity for

SRM-781 molybdenum at a series of temperatures in the range 273.15 to

2800 K have been computed from equations (8) and (7) and are given in

table A5. Figures 1, 2, and 3 show the deviations of the NBS-measured and

smoothed enthalpy and heat-capacity data (tables 5, 6, 7 and 8 and

equations (2), (3), and (4)) from the spline representations (equations

(8) and (7)). In figure 1, there is a systematic difference of about

0.2 percent between the enthalpy curve representing equation (3) (above

1200 K) and the unified spline representation (baseline) . This is a

result of the spline-fitting process which simultaneously gave weight to

28
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34
pulse-calorimetrically measured heat-capacity data of this study above

1500 K as well as the smooth heat-capacity values derived from equations

(2) and (3).

The hemispherical total-emit tance data (table A3) were fitted with

a linear function of temperature (IPTS-68 [13]) using the method of

least squares. This function is:

e = 9.40 x

10~ 2

+ 8.21 x

10~5

T, (9)

in which the range of applicability is 2700 K > T > 1700 K. Figure 4

shows the emittance data and smooth values calculated from equation (9)

6 . Reliability of the NBS Data

The overall inaccuracy of the relative-enthalpy and heat-capacity

data for the SRM-781 molybdenum sample (insofar as these data are

considered to represent pure molybdenum metal) contains a component

arising from chemical impurities in the sample as well as the usual

random and systematic components associated with each of the three

individual calorimeters used in the heat measurements. The effect of

sample impurity will be considered first and it will be shown that this

source of error is smaller than other sources of error. This will be

followed below by consideration of heat-measuring errors. These error

estimates will then be combined to yield values for the overall inaccuracy of each of the three sets of heat data.

6.1 Error Due to Sample Impurity

All calculations of the enthalpy and heat-capacity data (tables

8, 5, 6, and 7) were made assuming a sample purit}^ of 100 percent. The

small amount of impurities actually present (tables 1, 2, and Al) introduce error chiefly by making the real sample one or more phases whose

average heat capacity per unit mass differs slightly from that of the

nominal pure material (molybdenum) . This assumes that no latent heats

of phase change are introduced by the impurities. A simple way to

estimate the order of magnitude of this "error" is to make the approximation that all the impurity elements have the same heat capacity per

gram atom as molybdenum. Thus if one were to replace all the impurities,

atom-for-atom, by molybdenum, the percentage change in sample mass should

be a measure of the change in both the enthalpy and heat-capacity. The

effect on this basis can be calculated from table 2: the "elements

measured" indicate a net error of +0.02 percent and the upper limits of

the "elements showing interference", and additional +0.03 percent, for a

total error of +0.05 percent. Hydrogen, which was not analyzed for, could

produce a much greater error. One hundred ppm hydrogen impurity, for

instance, would introduce an error on the order of +1 percent. However,

molybdenum is not known to form stable hydrides and it is believed that

hydrogen was present at a much lower level. As noted in table Al, the

electronic characterization of samples A and B was interpreted as indicating a greater impurity level (0.2% by mass) than did the other two

35
analytical techniques. However, the amounts of impurities postulated

in the interpretation (table Al) would, on the above basis, introduce a

total error of only +0.01% due to their high atomic weights.

6.2 Bunsen-Ice-Calorimeter Data

A detailed estimate of possible systematic errors for enthalpy

measurements made with the ice calorimeter has been given in a previous

publication (see section A of reference [2].) Since the measuring

system of the present study is identical to that described in reference

[2], the same quantitative estimate applies. To briefly summarize,

systematic error may arise from the calibrations of the potentiometer

and the resistance bridge used with the furnace temperature-measuring

elements, as well as from the calibrations of the measuring elements

themselves. Also, calibration error in the analytical balance used to

weigh the mercury reservoir before and after each experiment as well as

the sample and sample container could be a source of systematic error.

Two remaining sources are the calorimeter calibration constant and a

possible difference in the heat loss of the full and empty containers

during the drop into the calorimeter. The arithmetic sum of all the

systematic errors ascribed to these sources plus that calculated above

for sample impurity is 0.11 percent at 1200 K.

Figure 1 indicates that two enthalpy measurements at 323.15 and

373.15 K deviate considerably from all the others in the series (up to

three times the standard deviation of residues) . A re-calculation of

the standard deviation of the ice-calorimeter data, neglecting these two

measurements, yields 0.06 percent for this index of the imprecision of

the measurements. Adding this index, taken at a 99-percent confidence

level, to the estimated maximum systematic error (0.11 percent at 1200 K)

yields 0.3 percent as an estimate of the overall inaccuracy of the

enthalpy data. The inaccuracy in the heat-capacity values obtained by

differentiating equation (2) is believed not to exceed 0.5 percent up to

1000 K.

Comparison of the heat capacity at 2.73.15 K derived from equation

(2) with the value of heat capacity at 273.15 K derived from a careful

analysis of all the low- temperature (below 300 K) heat-capacity data

reported for molybdenum in the literature [18] yields a difference in

heat capacity at this temperature of 0.01 percent. Although the lowtemperature samples were undoubtedly of a different composition and

history than SRM-781, such close agreement does lend confidence to the

validity of the present measurements.

36
6.3 Adiabatic Receiving-Calorimeter Data

Past experience with this calorimeter has indicated that the major

source of inaccuracy in enthalpy measurements above 1200 K arises from

error in measuring the average temperature of the sample in the furnace.

An approximation commonly made (and it is followed in this discussion)

is to assume that the error in pyrometrically determined temperatures is

proportional to the square of the absolute temperature. The estimated

pyrometric uncertainties listed in section 3. 2. a approximately obey this

temperature dependence and yield an uncertainty of 2.5 K at 2300 K. To

this must be added the additional error in realizing the average temperature of the sample. On the basis of an earlier determination of the

temperature profile of the furnace core at 2300 K, an approximate calculation indicated that near 2300 K, the temperature of the bottom of the

sample container (which is what the pyrometer measures) may be as much

as 0.5 K different from the average temperature of the sample. Assuming,

therefore, an overall temperature error of 3 K at 2300 K and of the same

sign and proportional to the square of the temperature at other temperatures, the smoothed results of the enthalpy measurements (equation (3))

indicate an error in (Hm - #298. 15^ varying from 0.1 percent at 1200 K

to 0.15 percent at 2000 K and an error in C

p varying from 0.15 percent

at 1200 K to 0.3 percent at 2000 K.

Some of the error in pyrometric temperature measurements may be

due to the calibration of the absorbing filters used for the different

ranges. In proceeding to successively higher temperatures a point is

reached at which a calibrated absorbing filter is required in the radiation

path and the adjusted pyrometer current abruptly assumes a much lower

value. It is then instructive to examine a mono tonically-varying property

(e.g. enthalpy) to see if a discontinuity appears at this point. In the

present study, such a current change did occur between 1500 and 1600 K.

Examination of the unsmoothed enthalpy data in this temperature range

(figure 1) discloses no enthalpy differences which exceed the usual

precision of measurement. Therefore, there is no evidence for the

existence of a filter-dependent pyrometer error. A second such current

shift took place between 2000 and 2100 K but it is felt that the lack of

enthalpy data at more than one temperature in the range 2100 K and above

would make any conclusions about an enthalpy discontinuity between 2000 K

and 2100 K unreliable.

Further evidence of the reliability of the optical pyrometry in

the present study can be obtained from the measurements on a specimen of

a-Al

2 03 (NBS SRM-720 [16].) The enthalpy of this material was measured

once at 1170 K (before experiment 1) and once at 1700 K (after experiment 27) . The results agreed with the highly consistent earlier results

T16] to 0.05 percent or better, providing evidence that the pyrometry

did not substantially deteriorate during the measurements on molybdenum.

37
Addition of the observed standard deviation of residues for the

enthalpy data (from equation (3); taken at a 99-percent confidence level)

to the maximum estimated inaccuracy in enthalpy due to temperature error

(0.15 percent at 2000 K) and the estimated inaccuracy due to sample

impurity (0.05 percent) yields an estimate of the overall inaccuracy in

the enthalpy measurements of 0.6 percent. The inaccuracy in the heatcapacity values derived from equation (3) by differentiation is believed

to be about 1 percent.

Although error in sample-temperature measurements certainly seems

to be the most serious one in heat measurements similar to those of the

present study, there is a remote chance that a substantial part of the

large disagreement among the many investigators of the enthalpy and heat

capacity of molybdenum (see section 7) is due to a real difference between some samples of the pure, annealed metal. The present enthalpy

data on molybdenum include an enthalpy measurement on a sample with a

very different history (sample E; see section 2) at each of the temperatures 1170, 1699 and 1900 K (table 6). The agreement within 0.15 percent

between Samples A (SRM-781) and E at these three temperatures is some

evidence that the massive annealed metal has a reproducible enthalpy and

heat capacity.

6.4 Pulse-Calorimeter Data

^ The procedural details for estimating the errors in the measured

and computed quantities in high-speed experiments using the present

measurement system have been given in a prior publication [21]. In the

present work, specific terms in the error estimates were recomputed

whenever circumstances warranted. The error estimates, summarized in

table 11, indicate an estimated overall inaccuracy in the heat capacity

not exceeding 3 percent. This figure represents twice the sum of two

components: the standard deviation of residues of the best fit to the

heat-capacity data (equation (4)) and the estimated systematic errors

(table 11) combined in quadrature.

The rate at which the tubular specimen is heated in a pulsecalorimetric heat-capacity measurement has a significant effect upon the

heat capacity calculated from the potential-drop, current and temperature

data. The effect of specimen-heating rate was investigated in the series

of experiments 20 through 26 in temperature Range IV (see section 3.3.b).

The results at 2000 K are representative of those over the entire temperature range and are given in table 12 and figure 5. Low heating rates,

dT/dT, (below 4000 K-s

-1

) yield larger values of the calculated heat

capacity. This effect is believed to be related to the existence of

larger temperature gradients in the specimen at low heating rates and to

the fact that the specimen temperature and its time derivative measured

at the mid-region differ from the corresponding effective values for the

entire specimen. To take experimental data at heating rates less than

4000 K-s 1 would introduce a source of systematic error. All the heatcapacity data of tables 7 and 8, upon which equations (4) and (7) are

based were taken at heating rates in excess of 5000 K*s .

38
Table 11

Summary of error estimates for pulse-calorimeter data on SRM-781 molybdenum

Measured or Derived

Quantity Imprecision Inaccuracy

Temperature (at 2000 K)

Specimen current

Specimen potential drop

Hemispherical total emittance

Heat capacity

0.3 K

0.03%

0.04%

2%

5K

0.1%

0.1%

5%

Imprecision of a set of data for some property measured as a function of temperature

refers to the standard deviation of residues of a smooth function of temperature fitted

to the data set by the method of least squares

'inaccuracy refers to twice the arithmetic sum of the imprecision and the estimated

systematic errors (systematic errors combined in quadrature)

Table 12

Heat-capacity results3 on SRM-781 molybdenum (specimen D2)

at 2000 K, as a function of specimen heating rate

dT/dt Pk—r

K-s- 1 J-mol-^K-l

1230 37.89

2040 37.12

2840 36.91

3920 36.77

5270 36 .77

6510 36.72

8010 36 .75

a These are experiments 20-26

39
Figure 5. Dependence at 2000 K of calculated heat-capacity

of SRM ?8l molybdenum (specimen D2 ) on specimen-heating; rate.

40
In order to detect significant differences among the heat-capacity

values for the three different specimens and also for different experimental series (see tables 7 and 8), the heat-capacity data in the range

1500 to 2650 K were fitted separately for each experimental series and

each specimen. The fitting procedure employed a third-degree polynomial

in temperature with the method of least squares and resulted in four

heat-capacity functions. The standard deviation of residues for each of

these four functions was in the range 0.3 to 0.5 percent. The percent

differences of these heat-capacity functions, taken pairwise, is given in

table 13. In this table, the differences are tabulated in pairs. Each

upper pair member represents the average algebraic percent difference

between the pair of functions indicated in the table margins. Each lower

pair member represents the average absolute percent difference between

the same pair of functions. These differences all lie in the range 0.1

to 0.6%. Since these differences are comparable to the imprecision of

the heat-capacity measurements, it is concluded that no significant

differences exist between the heat-capacity data of different specimens

and different experimental series.

The electrical resistivity of all specimens was measured before and

after the pulse experiments (but after the pre-experimental pulse conditioning; see section 3.3.b). These resistivity data agreed within 0.1 percent,

indicating that no significant irreversible structural or chemical changes

had taken place in the specimens as a result of their being heated to

temperatures in excess of 2650 K.

7. Comparison of NBS Heat Data on SRM-781 Molybdenum with Data on

Molybdenum Metal of Previous Investigators and Compilers

Interest in the thermodynamic properties of molybdenum has had

many different motivations and has spanned a period of nearly a century

and a half. As a result, there now exists in the literature a considerable body of enthalpy and heat-capacity data for this material. The

earliest thermal measurements known to the present authors were made by

Regnault [27] and by De la Rive and Marcet [26]. These were part of an

attempt by these early investigators to verify and extend the foundations

of the efforts by Dulong and Petit to correlate the heat-capacity

behavior of the elements. Almost a century later, the refractory qualities

of molybdenum were valued and the metal was widely studied for applications in thermionic devices [86, 87]. Most recently, it has found use

as a structural and alloying component in applications for advanced

power-generating and propulsion systems [46, 88], It has also been

considered as a candidate high-temperature standard reference material

[68], the application to which the present investigation is addressed.

Finally, there has been a continuing concern with the deviation of its

high-temperature heat capacity from the classical Debye heat capacity

[86, 66, 21, 89]. Attempts to explain the deviation have included the

contributions of anharmonicity , point defects and electronic excitations

at temperatures well above 0D

. Most of the heat-capacity studies have

been carried out on the solid phase above room temperature. A very few

extend down to liquid helium temperature and still fewer include the liquid

phase. There have also been several attempts to correlate all the heatcapacity data available at a given time.

41
Table 13

Average percent difference^ over the range 1500 to 2650 K

between smooth representations^ of heat capacity of different

SKM-781 molybdenum specimens and different experiment series

D3 D2-F Dl-S

Dl-F

0.48

0.48

-0.07

0.16

0.18

0.21

Dl-S

0.31

0.35

-0.24

0.24

D2-F

0.55

0.55

The indices ± and j_ refer to the experiment series listed in the table

margins and summarized in table 7.

b^=^- I [ (*~C (T ) - jc(T))/5 C(T)}; N temperatures, T. are

P V=l p

v pv p

v

uniformly spaced in the range 1500 to 2650 K.

cUpper figures are average algebraic percent differences, lower figures

are average absolute percent differences.

These smooth representations not given in text.

42
One task of the present study of molybdenum as a standard reference

material has been the compilation of a comprehensive bibliography giving

all known literature references to date containing either original or

compiled and critically-evaluated data on the enthalpy or heat capacity

of this material in the solid range above 273.15 K. This bibliography

is contained within section 9 and further information on each individual

investigation is given in table 14. In some instances, as this table

shows, data have been repeated by the same author (s) in several citations,

sometimes in a different guise. For completeness, all such citations

have been included and the duplication of data has been noted in the last

column of this table. This does not apply to the data compilations

(pre-starred entries of columns 1 and 2) . For these, only the most recent

data compilation by each author in question has been cited. Columns 4

and 5 of table 14 indicate which property (enthalpy or heat capacity)

was actually measured or compiled by each investigator.

The smoothed, composite enthalpy and heat capacity of SRM-781

molybdenum derived in the present study (equations (8) and (7), respectively) have been compared with most of the original measured enthalpy

and heat-capacity data appearing in the references of table 14. (Some

of the earliest references were considered unreliable due to uncertainties

in temperature measurements and sample purity and were therefore omitted.)

These comparisons are given in figures 6, 7, 8, and 9. Figures 6 and 7

present, respectively, the comparisons for measured values of the enthalpy

of molybdenum relative to 273.15 K and measured values of the heat capacity

of molybdenum taken from the literature. In both these figures, the

original data points have been represented insofar as possible. A few

investigators, however, have given their data exclusively in the form of

smooth functions and these have been included as well. In no case do

the curves appearing in figures 6 and 7 represent smooth versions of any

set of data points concurrently appearing in these figures. In a few

instances in which the representation of multiple measurements at very

closely-spaced temperatures (< 50 K apart) by a single investigator would

have obscured the figures, these data were averaged to preserve the overall trend in the investigator's data while still giving a clear representation. An example of this is the data of [81] (figure 7) which comprise

37 individual measurements of heat capacity in a 500 K interval. A few

data points fell outside the chosen ordinate limits of these figures.

The deviations of these points have been printed directly above or below

them. All data have been corrected [12] to their values on the temperature scale IPTS-68 [13]. A convenient table (A4) for effecting such

corrections for molybdenum in those cases in which the data are expressed

on IPTS-48, was calculated using reference [12] with equation (7) of the

present work and appears in the present Appendix. All enthalpy data

which were originally referred to 298.15 K have been referred to 273.15 K

using the enthalpy increment (#298.15 K ~ #273. 15 k) = 593.6 J mol 1 (see section 4.2). The NBS-measured heat data on SRM-781 molybdenum have

been omitted from figures 6 and 7 but the range of these NBS-measured

enthalpy and heat-capacity data have been indicated by the dotted horizontal lines. It seems unlikely to the present authors that the great

dispersion of the literature enthalpy and heat-capacity data can be ascribed wholly to variations in sample purity. This dispersion probably

arises from large systematic errors in temperature measurement.

43
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47
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48
These literature enthalpy and heat-capacity data for molybdenum

provide, in any event, a formidable task for the data compiler. Nine

such compilations are known to the present authors and these are compared

(with the exception of compiler reference [71]; see table 14) to the

present NBS results on SRM-781 molybdenum in figures 8 (enthalpy) and 9

(heat-capacity). With regard to figure 8, note that the compilations of

Goldsmith, et al . [46] and Stull and Sinke [39] have been omitted; the

former, because no values were given; the latter, for clarity since the

values given by Stull and Sinke are virtually identical with those of

Schick [53] below 1500 K and with those of Kelley [23] above 1500 K. In

figure 9, reference [39] is only displayed in the interval 1400-1600 K

for the same reasons. Note that the deviations of some compilations

(notably, those of Kelley [23], Hultgren [24] and Kirillin [54]) are

negative and very large (on the order of 20 percent) near the melting

point. The present NBS measurements agree very well with the most

recent correlation [61]

49
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50
T

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 r

300 500 700 900 1.100 1.300 1.500 1.700 1.900 2,100 2.300 2.500 2.700

77K

Figure 7. Deviation of directly-measured molybdenum heat-capacity data appearing in the literature from unified spline representation of present NBS data for SRM-781 molybdenum. Baseline is equation (7). Dotted lines indicate limits of dispersion

of NBS pulse-calorimetric, heat capacity data. See table 16 for

explanation of symbols.

51
Table 15

Symbol and citation key for relative enthalpy data displayed in

figure 6

Symbol Re f er enc e Year 1 n ve s x 1 era x or (, s ) urisiinai iNumuer 01

Data Points

o J 7 J O "Usc» ex ai. l i> %J 1 V J J Bronson, et al. jo

CI L3 5J 1 y i

1* Jaeger ft Veenstra 1 J AL i r^7i 1 Q < 1 DoHfialH j?. Will 31

CIv7 Tii.nl 1 Q C ^ 1 V J 0 lucks oc ueem 1 ( U -J

1 O cC n i\ox nen yD 1

J 70I Al^i11^1111 1 1 n 0+ a 1 L 111 | o l» _L •

id)

I 701 ijcl id! cvd f rill

1964 Conway, et al.

L59J 1 9o5 Gezairliyan 9

[66] 1968 Kirillin, et al. 24

[72] 1971 Berezin, et al. 29

A [76] 1972 Oettine; ft Navratil

[77] 1973 Bondarenko, et al.

Table 16

Symbol and citation key for heat-capacity data displayed in figure 7

Symbol Reference Year Investigator ( s

)

Original Number

of Data Points

C [33] 1929 Cooper ft Iane;stroth

B [42] I960 Boe;ffS ft Wiebelt

€ I960 Lehman 12

0 [44] 1 960 Rasor ft McClelland 36

R 1 960 Rudkin

T [49] 1 961 Taylor ft Finch

I, [55] 1963 Lowenthal

[59] 1965 Cezairliyan 9

A [60] 1965 Filippov ft Yurchak 8

O [64] 1968- Filippov, et al. 32

z [21] 1 970 Cezairliyan, et al.

M [69] 1 970 Makarenko, et al.

K [79] 1973 Kraftmakher

[80] 1973 Mebed, et al. 7

• [81] 1975 Chekhovskoi ft Kalinkina

—

37

52
+5

+4

+3

+2

+1

0

-1

-2

-3

-4

i—i—i—I—I—I—i—i—I—i—i—i—i—I—i—I—I—i—i—i—i—i—i—i—

i i i i i i i i i i i i i i i i i i i i i 6 8 10 12 14 16 18 20 22 24 26 28

7V(Kx102

)

Figure 8. Deviation of enthalpy correlations appearing in the

literature from unified spline representation of present NBS

data for SRM-781 molybdenum. Baseline is equation (8). See

table 17 for explanation of symbols.

53
r/(Kxio 2

)

Figure 9- Deviation of heat-capacity correlations appearing

in the literature from unified spline representation of present

NBS data for SRM-781 molybdenum. Baseline is equation (7).

See table 17 for explanation of symbols.

54
Table 17

Symbol and citation key for relative enthalpy and heat-capacity

correlations displayed in figures 8 and 9

Symbol (fig. 8)

Hp at—c an ac itv

Symbol (fig. 9)

Reference Year Compiler

a

a

[39]

[23]

[46]

[53]

[54]

[24]

[61]

[18]

1955

I960

1961

1962

1963

1965

1966

Stull & Sinke

Kelley

Goldsmith, et al.

Schick

Kirillin, et al.

Hultgren

JANAF Tables

Reilly & Furukawa

S

H

R

a

Not shown on figure 8 (see section 9)«

55
8 . Acknowledgements

Several members of the professional staff of the National Bureau

of Standards made substantial contributions to the present work.

E. D. West designed and built the high-temperature adiabatic receiving

calorimeter. R. E. Michaelis of the NBS Office of Standard Reference

Materials furnished samples A, B, C and D and coordinated their several

characterizations. Together with R. K. Kirby, he coordinated all other

aspects leading to the certification and issuance of molybdenum as an

NBS Standard Reference Material. The spectrochemical analyses were

performed by Virginia C. Stewart (samples A and B) and Martha M. Darr

(sample C) ; the mass-spectrometry by C. W. Mueller and R. J. Paulsen;

and the electronic characterization and its interpretation by V. A. Deason

and R. L. Powell (NBS, Boulder). E. Lewis, Jr. carried out the pyrometer

calibrations; and M. L. Reilly provided a computer program for analysis

of the adiabatic-receiving-calorimeter data. The computer program for

spline-fitting the composite NBS molybdenum heat data was developed by

J. Rosenblatt of the NBS Statistical Engineering Section. Substantial

portions of the present investigation were carried out under the sponsorship of the Air Force Office of Scientific Research.

56
9. References

[1] NBS Special Publication 260, Catalog of NBS Standard Reference

Materials, 1975-76 Edition. Available from Superintendent of

Documents, U.S. Government Printing Office, Washington, DC 20402.

[2] Ditmars, D. A., and Douglas, T. B., J. Res. Nat. Bur. Stand. (U.S.),

75A (Phys. and Chem.), No. 5, 401 (Sept. -Oct. 1971).

[3] Cezairliyan, A., Morse, M. S., and Beckett, C. W., Rev. Int. Hautes

Temper, et Refract., 7_, 382 (1970).

[4] Kunzler, J. E. , and Wernick, J. H., Trans. Metal. Soc. AIME, 212 , 856 (1958).

[5] Kunzler, J. E., Electrical Properties of Metals and the Importance

of Purity, Chapter 9 in Ultra-High-Purity Metals, Am. Soc. for

Metals (1961).

[6] Landolt-Bornstein, Zahlenwerte und Functionen, 6th ed., (Springer,

Gottingen, 1959).

[7] Archer, R. S., Briggs, J. Z., and Loeb, C. M., Jr., Molybdenum,

(Climax Molybdenum Co., 1953).

[8] Douglas, T. B., and King, E. G., High-Temperature Drop Calorimetry,

Chapter 8 in Experimental Thermodynamics, Volume I, Calorimetry of

Non-Reacting Systems, p. 293, J. P. McCullough and D. W. Scott,

Eds. (Butterworths, London, 1968). See also NBS Special Publication

No. 300, vol. 6, p. 181 (1970).

[9] Ditmars, D. A., Int. J. Appl. Rad . Isotopes, 2_7, 469 (1976).

[10] Ginnings, D. C, Douglas, T. B., and Ball, A. F . , J. Res. Nat.

Bur. Stand. (U.S.), 4_5, No. 1, 23 (1950), RP2110.

[11] Furukawa, G. T., Douglas, T. B., McCoskey, R. E., and Ginnings, D. C,

J. Res. Nat. Bur. Stand. (U.S.), _5_7_, No. 2, 67 (1956), RP2694

[12] Douglas, T. B., J. Res. Nat. Bur. Stand. (U.S.), 73A (Phys. and

Chem.), No. 5, 451 (Sept. -Oct. 1969).

[13] The International Practical Temperature Scale of 1968, Metrologia,

5_, 35 (1969).

[14] West, E. D., and Ishihara, S., A Calorimetric Determination of the

Enthalpy of Graphite from 1200 to 2600 °K in Advances in Thermophysical Properties at Extreme Temperatures and Pressures, p. 146,

ASME, New York, (1965). See also NBS Special Publication No. 300,

vol. 6, p. 220 (1970) .

57
[15] West, E. D., and Ishihara, S., National Bureau of Standards Report

No. 9803, National Bureau of Standards, U.S. Department of Commerce,

(Jan. 1, 1968).

[16] Certificate: Standard Reference Material 720, Synthetic Sapphire

(AI2O3), National Bureau of Standards, U.S. Department of Commerce,

(1970)

[17] Ishihara, S., and West, E. D., J. Res. Nat. Bur. Stand. (U.S.), 8 OA

(Phys. and Chem.), No. 1, 65 (Jan. -Feb. 1976).

[18] Reilly, M. L., and Furukawa, G. T., Critical Analysis of the HeatCapacity Data of the Literature and Evaluation of Thermodynamic

Properties of Cr, Mo, and W from 0 to 300 K, NSRDS-NBS (to be

published)

.

[19] Starrett, K. F . , and Wallace, W. E., J. Am. Chem. Soc ., 80_, 3176

(1958).

[20] Cezairliyan, A., J. Res. Nat. Bur. Stand. (U.S.), 75C , (Eng. and

Inst.), No. 1, 7 (Jan. -Mar. 1971).

[21] Cezairliyan, A., Morse, M. S., Berman, H. A., and Beckett, C. W.,

J. Res. Nat. Bur. Stand. (U.S.), 74A (Phys. and Chem.), No. 1, 65

(Jan. -Feb. 1970).

i22] Foley, G. M. , Rev. Sci. Instr., 41_, 827 (1970).

[23] Kelley, K. K., Contributions to the Data on Theoretical Metallurgy.

XIII. High-Temperature Heat-Content, Heat-Capacity, and Entropy

Data for the Elements and Inorganic Compounds, U.S. Bureau of Mines

Bull. 584, (1960).

[24] Hultgren, R., Desai, P. D., Hawkins, D. T., Gleiser,M., Kelley, K. K.

and Wagman, D. D., Selected Values of the Thermodynamic Properties

of the Elements, American Society for Metals, Metals Park, OH (1973).

[25] Atomic Weights of the Elements 1975, Pure and Appl. Chem., 47 (1),

75 (1976).

[26] De la Rive and Marcet, Ann. Chim. Phys. [2], 75, 136 (1840).

[27] Regnault, V., Ann. Chim. Phys. [2], 73., 5 (1840).

[28] Defacqz, E., and Guichard, M., Ann. Chim. Phys. [7], 24_, 139 (1901).

[29] Stucker, N., Sitzb. Kbnig. Akad. Wiss., Wien, 114 , 657 (1905).

[30] Wlist, F. A., Meuthen, A., and Durrer, R., Forsch. Gebiete.

Ingenieurv. , 204 (1918).

[31] Stern, T. E., Phys. Rev., .32 (2), 298 (1928).

58
[32] Bronson, H. L., and Chisholm, H. M., Proc . Nova Scotia Inst. Sci.,

17 (4), 44 (1929).

[33] Cooper, D., and Langstroth, G.O., Phys . Rev., 21 (2), 243 (1929).

[34] Bronson, H. L., Chisholm, H. M., and Dockerty, S. M., Can. J.

Res., 8, 282 (1933) .

[35] Jaeger, F. M., and Veens tra, W. A., Rec. Trav. Chim. Pay-Bas,

53 (6), 677 (1934).

[36] Jaeger, F. M., and Veens tra, W. A., Proc. Roy. Acad. Sci.

Amsterdam, 37_, 61 (1934).

[37] Redfield, T. A., and Hill, J. H. , U.S. AEC ORNL-1087, (Sept. 24,

1951) .

[38] Kothen, C. W., Dissertation, Ohio State Univ., available from

Univ. Microfilms (Ann Arbor, Mich.) as Publ . No. 23697, 93 pp.

(1952); Smooth data also available in Dissertation Abstracts 17 , 2842 (1957).

[39] Stull, D. R., and Sinke, G. C, in Thermodynamic Properties of the

Elements, Advances in Chemistry Series - No. 18, Am. Chem. Soc .

Washington, DC (1955).

[40] Lucks, C. F., and Deem, H. W., WADC Tech. Rept. 55-496 (1956),

ASTIA Document AD 97185.

[41] Rasor, N. S., and McClelland, J. D., WADC Tech. Rept. 56-400,

part I (March, 1957), ASTIA Document AD 118144.

[42] Boggs, J. H., and Wiebelt, J. A., U.S. AEC TID 5734 (Feb., 1960).

[43] Lehman, G. W., WADD Tech. Rept. 60-581 (July, 1960), ASTIA Document

AD 247411, PB160804.

[44] Rasor, N. S., and McClelland, J. D., J. Phys. Chem. Solids 15_, 17

(1960) .

[45] Rudkin, R. L., Res. and Dev. Tech. Rept. USNRDL-TR-433 (June 20,

1960), PB 155892.

[46] Goldsmith, A., Waterman, T. E., and Hirschhorn, H. J., Handbook of

Thermophysical Properties of Solid Materials, Revised Ed., V. I:

Elements, Armour Research Foundation, Chicago, the MacMillan Company,

New York, (1961)

[47] Kirillin, V. A., Sheindlin, A. E., and Chekhovskoi, V. Ya., Soviet

Physics Doklady, 139 (3), 557 (1961); (translated from Dokl. Akad.

Nauk. SSSR, 139 (3), 645 (1961)).

59
[48] Lazareva, L. S., Kantor, P. B., and Kandyba, V. V., Phys . Metals

and Metallog. (USSR), 11 (4), 133 (1961); (translated from Fiz. Metal

i Metalloved., 11 (4), 628 (1961)).

[49] Taylor, R. E., and Finch, R. A., U.S. AEC NAA-SR-6034 (1961).

[50] Chekhovskoi, V. Ya., Inzh.-fiz. Zh . Akad. Nauk. Belorussk. SSR,

5 (6), 43 (1962).

[51] Kirillin, V. A., Sheindlin, A. E., and Chekhovskoi, V. Ya., Int. J.

Heat Mass Transfer, 5_, 1 (1962).

[52] Rudkin, R. L., Parker, W. J., and Jenkins, R. J., Measurements of

Thermal Properties of Metals at Elevated Temperatures, in Temperature, Its Measurement and Control in Science and Industry, Vol. Ill,

C. M. Herzfeld, Ed., Reinhold, New York, Part 2, p. 523 (1962).

[53] Schick, H. L., (Ed.) in Thermodynamics of Certain Refractory Compounds, Academic Press, New York, Vol. II, p. 161 (1966).

[54] Kirillin, V. A., Shiendlin, A. E., and Chekhovskoi, V. Ya . , Enthalpy

and Heat Capacity of Some Solid Materials at Extremely High Temperatures, in IUPAC High Temperature Technology, Proc . Int. Symp . High

Temp. Tech. held at Pacific Grove, CA, p. 471 (1963).

[55] Lowenthal, G. C, Aust. J. Phys.,16_ (1), 47 (1963).

[56] Conway, J. B., Hein, R. A., Fincel, R. M., Jr., and Losekamp, A. C,

G.E. Advanced Technology Series, 1964 Ann. Mtg. Metall. Soc. AIME,

Paper TM 64-2-8 (19 Feb. 1964).

[57] Kraftmakher, Ya. A., Soviet Physics-Solid State, 6_ (2), 396 (1964);

(translated from Fiz. Tverd. Tel ., 6_ (2), 503 (1964).

[58] Taylor, R. E., and Finch, R. A., J. Less-Common Metals, 6_, 283 (1964)

[59] Cezairliyan, A., A High-Speed (Millisecond) Method for the Simultaneous Measurement of Enthalpy, Specific Heat, and Resistivity of

Electrical Conductors at High Temperatures, in Advances in Thermophysical Properties at Extreme Temperatures and Pressures, p. 253,

ASME, New York, (1965) .

[60] Filippov, L. P., and Yurchak, R. P., High Temperature (USSR), 2 (6),

837 (1965); (translated from Teplofiz. Vys. Temp.. 2 (6), 901 (1965))

[61] JANAF Thermochemical Tables 2nd edition, NSRDS-NBS 37, June 1971,

for sale by Superintendent of Documents, Washington, DC.

[62] Kraftmakher, Ya. A., Rab. Fiz. Tverd. Tela., 1_, 37 (1967).

60
Chekhovskoi, V. Ya., and Petrov, V. A., High Temperature (USSR), (5 (4), 717 (1968); (translated from Teplofiz. Vys. Tern., 6_ (4), 75 2

(1968)).

Filippov, L. P., Arutyunov, A. V., Makarenko, I. N., Mardykin, L. N.

Trukhanova, L. N., and Khusainova, B. N., Tr. Vses. Nauch.-Tekh.

Konf. Termodin. Sb . Dokl. Sekts . "Termodin. Fazovykh Perekhodov,

Potoka Neobratimykh Protsessov" i "Teplofiz. Svoistva Veschestv."

3rd, p. 242 (1968, publ. 1969).

Khusainova, B. N., and Filippov, L. P., High Temperature (USSR),

6_ (5), 891 (1968); (translated from Teplofiz. Vys. Tem., 6_ (5),

929 (1968)).

Kirillin, V. A., Sheindlin, A. E., Chekhovskoi, V. Ya . , and

Petrov, V. A., Enthalpy and Heat Capacity of Molybdenum at Extremely

High Temperatures, in Proc. 4th Symp. on Thermophys. Prop.,

J. R. Moszynski (Ed.), ASME, New York, p. 54 (1968).

Kirillin, V. A., Sheindlin, A. E., Chekhovskoi, V. Ya., and

Petrov, V. A., Tr. Vses. Nauch.-Tekh. Konf. Termodin., Sb . Dokl.

Sekts. "Teplofiz. Svoistva Veshchestv" 3rd, p. 80 (1968, publ.

1969) .

Chekhovskoi, V. Ya., Sheindlin, A. E., and Berezin, B. Ya., High

Temp. -High Press., 2 (3), 301 (1970).

Makarenko, I. N., Trukhanova, L. N., and Filippov, L. P., High

Temperature (USSR), 8_ (2), 416 (1970); (translated from Teplofiz.

Vys. Temp.,j$ (2), 445 (1970)).

Sheindlin, A. E., Chekhovskoi, V. Ya., and Shpil'rain, E. E.,

High Temp. -High Press ., 2 (1), 1 (1970).

Touloukian, Y. S., and Buyco, E. H., Specific Heat: Metallic

Elements and Alloys, in Thermophysical Properties of Matter, The

TPRC Data Series, Touloukian, Y. S., and Ho, C. Y. (Eds.), IFI,

Plenum, New York (1970).

Berezin, B. Ya., Chekhovskoi, V. Ya., and Sheindlin, A. E., High

Temp. -High Press., 3 (3), 287 (1972).

Chekhovskoi, V. Ya., and Berezin, B. Ya., Inzh.-Fiz. Zh., 21_ (2),

309 (1971).

Dikhter, I. Ya., and Lebedev, S. V., High Temperature (USSR), 9_ (5),

845 (1971); (translated from Teplofiz. Vys. Temp.,9_ (5), 929 (1971))

Ishihara, S., and Douglas, T. B., National Bureau of Standards Report No. 10481, National Bureau of Standards, U.S. Department of

Commerce, (July 1, 1971).

61
[76] Oetting, F. L., and Navratil, J. D . , J. Chem. Eng. Data, 1_7 (2),

230 (1972)

.

[77] Bondarenko, V. P., Fomichev, E. N. , and Kandyba, V. V., High Temp.-

High Press., _5 (1), 5 (1973).

[78] Douglas, T. B., and Ditmars, D. A., National Bureau of Standards

Internal Report No. 73-280, National Bureau of Standards, U.S.

Department of Commerce, (January 1, 1973).

[79] Kraftmakher, Ya. A., High Temp. -High Press., 5_ (4), 433 (1973).

[80] Mebed, M. M. , Yurchak, R. P., and Filippov, L. P., High Temp.-

High Press., 5_ (3), 253 (1973).

[81] Chekhovskoi, V. Ya . , and Kalinchina, R. G., Russ . J. Phys . Chem.,

49 (3), 431 (1975); (translated from Zh. Fiz. Khim., 49^ (3), 740

(1975)).

[82] Fedorov, V. B., High Temperature (USSR), 13 (3), 608 (1975);

(translated from Teplofiz. Vys . Temp., 13 (3), 666 (1975)).

[83] Bean, C. P., DeBlois , R. W., and Nesbitt, L. B .

, J. App . Phys.,

30 (12), 1976 (1959).

[84] LePage, J., Bernalte, A., and Lindholm, D. A., Rev. Sci. Inst.,

39 (7), 1019 (1968).

[85] Hellenthal, W., and Uelhoff, W., Z. Angew. Phys., 21 (6), 535 (1966).

[86] Eastman, E. C, Williams, A. M., and Young, T. F., J. Am. Chem.

Soc, 46_, 1185 (1924).

[87] Van Voorhis, C. C, Phys. Rev., 30_, 318 (1927).

[88] Campbell, I. E., (Ed.), High Temperature Technology, John Wiley

and Sons, Inc., 1956.

[89] Hoch, M. , High Temp. -High Press., 1 (5), 531 (1969).

62
APPENDIX

Table Al

Calculation3

of estimated impurity levels in OSRM SRM-781

6.35-mm-O.D. molybdenum rod, specimen no. 12d

Element Impurity Level

Atomic contribution

to resistivity at 4

Total contribution

to resistivity at 4

mass % 3. toin % ufi" cm/at.

yfi 'cm

Fe 0.01 0.017 0.8 0.0136

Ni 0 .01 0 .016 0.8 0.0128

Co 0.01 0.016 0.8 0.0128

Al 0.01 0.036 0.3 0.0108

I = 0.0500

w 0.0586 0.0307

Ta 0.0579 0.0307

P, 7 n K 4.84

KRR - 2 7 3 K _ _ 55 g

C

p 4 R 0.05 + (0.3) -4x

Nb 0.0297 0.0307

Zr 0.0292 0.0307 x = 0.0307 at.%

T, = 0.216 mass %.

See text, section 2.1.C, for a description of the assumptions underlying this

calculation

^Value for Ni from reference [ 6 ]•

Values for Fe , Co, Al estimated.

Value for P 97 o of w from reference [7]. 2/3 K

This specimen number refers to table 3.

63
crH

I 4J PhO

CT.

•

4-) Po

4J

o

(B •aa

to

cw

w o

to O

a> e 6 to

' v EC EC

EC

l Eh

co

cj

cr cr O VD m cm

1

en co

co <ro

+

<r m

+ ; +

O 1—

I

in r~ O O

I I

00 00

<r Ono

1

cr r-~ o c

o

+

cr

CO C

¥¥

141 U-i cm -cr c

I

O CM in m

o o

cr c m vc CM CM

o <r

vD rH

in -cr

-a- <t

rH

>H

0) LO in C rH

•H

to Ul <r in in c cr. 0u

VC CM

in in

cr. co

u~> co o o

n co

cr co

rH O

c cr

LO LO

co cm CO 00

Eh «

1 2

01 O

ttj O

CD e

CO

Ed < <

CM

cr CMo

cr. en

r-~ co ¥¥ c

1

-JD rH

cm crc

1

i£ oc ¥¥

VC rH <T rH ?¥

CM <f c

1

en o

rH C

+ I ¥ ¥

co in

u~i CM c c

1 1

EC

I Eq

U

01c

•H

to

4-1 Co

t_>

>H

0)c

•H

CO

4-1 C

oo

r- rH VO CM O O cr cr

r- cm ui cr en en

CM CM

O "1

-a- vi- vo VO

en <t

rH VC

cr 1

m m

vc vo

CT v£> 00 rH

cr in 00 cm

-3- < en <t

in in in m co cc co co

vc cr

vo m

m in

cr c r- c

01 o

vo

en en

r-~ in

en en O cr

vo m

m m

vC vo m m

Eh M crin

en

CM

cc

cr

toa

co

cuu

cu H

cj

>H Ph

toC

>j

CU

4-1 EM

Et;

I Eh

EC

II EC

64
Table A3

Hemispherical total emittance of the SRM-781 molybdenum specimen

in the temperature range 1730 to 2760 K

Code

Symbol K c Code

Symbol

m

~TT~

E

B 1730 0 . 242 2655 0 318

1733 0 . 233 E 2658 0 316

B 1912 0.257 A 2663 0 308

A 2066 0.256 B 2671 0 308

B 2068 0.268 F 2673 0 316

A 2323 0.276 D 2 706 0 321

B 2344 0.278 D 2760 0 324

C 2655 0.310

Indicates the experiments from which the emittance data were derived

according to the following code:

A Specimen Dl, experiments 1, 3-5

B Specimen Dl, experiments 6- 10

C Specimen Dl, experiment 11

D Specimen Dl, experiments 12 -14

E Specimen D2, experiment 19

F Specimen D3, experiment 31

b

IPTS-68[13]

65
Table A4

Corrections for molybdenum (s) to convert enthalpy and heat-capacity data

between IPTS-48 and IPTS-68 temperature scales a

r

48 or T68

H

b8~

H

68 (V48-(C

p

) 68 r

48

° r T

68 ff48~ ^68

r—

( V48- ( V68

K J " mo 1 J-mol"''" •K-"'" K J-mol""1" J-mol

-

''' •K- ''"

300 -0.2 -0 .004 1550 + 57.2 +0 .071

350 - 0.2 -0 .006 1600 + 60.9 +0 .075

400 + 0.3 +0 .011 1650 + 64.7 +0 .078

450 + 0.8 +0 .012 1700 + 68.7 +0 .082

500 + 1.4 +0.010 1750 + 72.9 +0 .086

550 + 1.8 +0.006 1800 + 77.3 +0.090

600 + 2.0 +0.003 1850 + 81.9 +0.094

650 + 2.1 0 .000 1900 + 86.7 +0.099

700 + 2.0 -0 .001 1950 + 91.7 +0 .104

750 + 2.1 +0 .003 2000 i + 97.0 +0 .108

800 + 2.4 +0 .012 2050 +102 .6 +0 .114

850 + 3.4 +0 .029 2100 +108.4 +0 .119 + 5.4 +0 .054 2150 +114 .5 +0 1

950 + 9.2 +0 .078 2200 +120 .9 +fl 111

1000 +13.2 +0 .081 2250 +126 .7 1050 +17 .3 +0 .083 2300 +134 .6 +0 .144

1100 +21 .5 +0 086 2350 +142 .0 +0 .151

1150 +25 .

8

+0 .089 2400 +149 .7 +0 .158

1200 +30.3 +0.091 2450 +157.8 +0.166

1250 +35.0 +0.094 2500 +166.3 +0.177

1300 +39.8 +0.098 2550 +175.5 +0.190

1350 +44.2 +0.059 2600 +185.4 +0.206

1400 +47.3 +0.062 2650 +196.2 +0.225

1450 +50.4 +0.065 2700 +208.0 +0.248

1500 +53.7 +0.068 2750 +221.0 +0.274

2800

J

+235.5

1

+0.304

a Calculated from reference [12]

.

66
Table A5

Enthalpy relative to 273.15 K and heat capacity of SPM-781 molybdenum

computed from equations (8) and (7)

K

„„b C H

T 273.15

T

K

C°

r>r

TJ O TJO « — ~~ ft , „ _ ,_ T 273.15

,-l -1

J*mol -K

, -1

J-mol x J-mol -K

-,-1

J -mol

273.15 23.56 0.00 720 27.07 11472.

275 23.58 43.60 740 27.17 12014.

280 23.66 161.72 760 27.26 12558.

285 23.74 280.21 780 27.35 13104.

290 23.81 399.07 800 27.44 13652.

! 295 23.88 518.29 820 27.53 14202.

298.15 23.92 593.59 840 27.62 14754

300 23.95 637.87 860 27.71 15307. i 305 24.02 757 .80 880 27.80 15862. i 310 24.09 878.06 900 27.89 16419

1 315 24.15 998.66 920 27.98 16978.

320 24.22 1119 .6 940 28.08 17538.

325 24.28 1240 .8 960 28.17 18101. ' 330 24.34 1 36 2 .

980 28.27 18665

335 24 .40 1484 .2 1000 28 . 37 19232. '

340 24.46 1606.4 1020 28.47 19800.

345 24 .52 1728.8 1040 28.57 20370

350 24.58 1851.6 1060 28.68 20943

355 24.63 1974 .6 1080 28.78 21517.

360 24.69 2097.9 1100 28.90 22094.

370 24 . 79 2 345 3 1120 22673

373.15 24.82 2423.4 1140 29.12 23255.

380 24.89 2593.7 1160 29.24 23838.

390 24.99 2843.1 1180 29.36 24424.

400

i 25.08 309 3.4 1200 29.49 25013.

1 410 25.17 3344 .

1250 29.81 26495.

420 25.26 3596.9 1300 30.14 27994.

430 25.34 3849.8 1350 30.50 29510.

440 25.42 4103.6 1400 30.86 31044

450 25.50 4358.2

1 1450 31.25 32597.

67
Table A5 (Continued)

Enthalpy relative to 273.15 K and heat capacity of SRM-781 molybdenum

computed from equations (8) and (7)

_aIT

K

C

p V"ff 273.15

T

K .

C

Vt- T 273. 15 ( --1 -1

JmijoI -K

, -1

J-mol ,-1 .-1 J»mol - K

,-1 J-mol

460 1 25.57 4613.6 1500 31.65 34169.

470 25.64 j 4869.7 1550 32.07 35762.

480 j 25.72 5126.5 1600 32.50 37376.

490 25.78 5384.0 1650 32.95 39012.

j 500 25.85 5642.2

1

1700 33.42 40671.

! 510 ! 25.92 | 5901.0 1750 33.91 42354

.

! 520 1

1 25.98 6160.5 1800 34 .42 4406 2.

I 5 30 26.05 6420.6 1850 34 .94 45796

.

540 26.11 6681.4 1900 35 .49 47557

.

550 26.17 6942.8 1950 36.06 49346.

560 26 .23 7204.8 2000 36.65 51163.

570 26.29 7467.4 2050 37.26 53011

.

580 26.35 7730.6 2100 37.90 54890.

590 26.40 7994.3 2150 38.55 56801.

600 26.46 8258.7 2200 39 . 24 I 58746.

610 26.52 8523.5 2250 ,

i 39.94 60725.

620 26.57 8789.0 2300 ; 40.67 | 62740.

6 30 26 .62 9054.9 2350 ; 41.43 64793.

640 26.68 9321.4 2400 ; 4 2.21 66884.

v jyj QSRR j _J OO LH ?A c>n D7UIJ •

660 26.78 9856.0 2500 43.89 71188.

670 26.83 10124. 2550 44.84 73406.

680 26.88 10392. 2600 45.88 75673.

690 26.93 10661. 2650 47.05 77996.

700 26.98 10931.

1

1

2700 !

1 2750 | 2800

48.37

1 49.87 I 51.57 1

80381.

82836.

85371.

aIPTS-68 [131. ^Atomic weight = 95.94 [25].

* U. S. GOVERNMENT PRINTING OFFICE : 1 977 -- ?i* 0- 8^8/3 08

68
BS-114A trcev. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBS SP 260-55

2. Gov't Accession

No.

3. Recipient's Accession No.

. TITLE AND SUBTITLE standard Reference Materials:

ENTHALPY AND HEAT CAPACITY STANDARD REFERENCE MATERIAL:

MOLYBDENUM SRM 781, FROM 273 TO 2800 K

5 r n nl 1 r a f ir\n 1 )arp

September 1977

6. Performing Organization Code

. AUTHOR(S)

D. A. Ditmars, A. Cezairliyan, S. Ishihara, and T. B. Douglas

8. Performing Organ. Report No.

. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

iu. Kroject/ i ask/ work Unit INo.

11. Contract/Grant No.

2. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same as above

.

13. Type of Report & Period

Covered

Final

14. Sponsoring Agency Code

SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 77-608175

6. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

The relative enthalpy of NBS Standard Reference Material No. 781 (99.95 mass-percent

pure, polycrystalline molybdenum: a metallic, high-temperature enthalpy and heatcapacity standard) has been measured with two differently designed, receiving-type

calorimeters in the temperature ranges 273 to 1173 K and 1173 to 2100 K, respectively.

The smoothed enthalpy data derived from these measurements are believed to have an

inaccuracy not exceeding 0.6 percent at any temperature in these ranges. The heat

capacity of Standard Reference Material No. 781 has also been measured in the

temperature range 1500 to 2800 K using a millisecond - resolution pulse technique with

resistive self-heating. This technique measured, in addition, hemispherical total

emittance. In this highest temperature range, the smoothed heat-capacity data are believed to be in error by no more than 3 percent. A complete description of all the

NBS experimental techniques and a detailed analysis of all suspected sources of errors

are presented. Equations representing the smoothed NBS enthalpy and heat-capacity

data for SRM-781 molybdenum in the range 273.15 to 2800 K are presented along with

a table of these data calculated from the equations at selected temperatures. A

bibliography of all known publications on the enthalpy and heat capacity of molybdenum

has been compiled. The NBS-measured enthalpy and heat-capacity data for molybdenum

have been compared with those of all the principal investigators and compilers

reported in the literature.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Drop calorimetry; emittance; enthalpy; heat capacity;

high-speed measurements; high temperature; molybdenum; pulse calorimetry; standard

reference material; thermodynamic functions.

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