AFOSR SCIENTIFIC REPORT

AFOSR—TR—71 — 2584 D-& DIIMARS

NATBONAL BUREAU OF STANDARDS REPORT

10 481

INTERIM REPORT

ON THE THERMODYNAMICS

OF CHEMICAL SPECIES

IMPORTANT IN AEROSPACE TECHNOLOGY

(The previous reports in this series have the NBS

Report Nos. 6297, 6484, 6645, 6928, 7093, 7192,

7437, 7587, 7796, 8033, 8186, 8504, 8628, 8919,

9028, 9389, 9500, 9601, 9803, 9905, 10004, 10074,

and 10326.)

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

U. S. Air Force, Office of Scientific Research

Agreement No. AFOSR — ISSA— 70— 0002, Project No. 9750-01.

INTERIM REPORT ON THE THERMODYNAMICS OF CHEMICAL SPECIES IMPORTANT

IN AEROSPACE TECHNOLOGY

1 July 1971

Approved for Public Release; Distribution Unlimited
Qualified requestors may obtain additional copies from

the Defense Decumentation Center; all others should apply

to the Clearinghouse for Federal Scientific and Technical

Information.
NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT NBS REPORT

2320423 1 July 1971 10 481

3160401

3160404

3160405

3160426

INTERIM REPORT

ON THE THERMODYNAMICS

OF CHEMICAL SPECIES

IMPORTANT IN AEROSPACE TECHNOLOGY

(The previous reports in this series have the NBS

Report Nos. 6297, 6484, 6645, 6928, 7093, 7192,

7437, 7587, 7796, 8033, 8186, 8504, 8628, 8919,

9028, 9389, 9500, 9601, 9803, 9905, 10004, 10074,

and 10326.)

Reference: U. S. Air Force, Office of Scientific

Research, Agreement No. AFOSR — ISSA — 70— 0002,

Project No. 9750-01.

IMPORTANT NOTICE NATIONAL BUREAU OF ST

for use within the Government, and review. For this reason, th whole or in part, is not autho Bureau of Standards, Washingt

the Report has been speciticall)

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST) on October 9, 2015.

iss accounting documents intended

; subjected to additional evaluation

3 listing of this Report, either in

le Office of the Director, National by the Government agency for which

copies for its own use.

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

U. S. Air Force, Office of Scientific Research

Agreement No. AFOSR-ISSA-70-0002, Project No. 9750-01.

INTERIM REPORT ON THE THERMODYNAMICS OF CHEMICAL SPECIES IMPORTANT

IN AEROSPACE TECHNOLOGY

1 July 1971

Approved for Public Release; Distribution Unlimited
CONDITIONS OF REPRODUCTION

Reproduction, translation, publication, use and

disposal in whole or in part by or for the

United States Government is permitted.
FOREWORD

Structure, propulsion, and guidance of new or improved weapons

delivery systems are dependent in crucial areas of design on the

availability of accurate thermodynamic data. Data on high- temperature

materials, new rocket propellant ingredients, and combustion products

(including exhaust ions) are, in many cases, lacking or unreliable.

This broad integrated research program at the National Bureau of Standards

supplies new or more reliable thermodynamic properties essential in several

major phases of current propulsion development and application. Measured

are compounds of those several chemical elements important in efficient

propulsion fuels; those substances most affecting ion concentrations in

such advanced propulsion concepts as ion propulsion; and the transition

and other refractory metals (and their pertinent compounds) which may be

suitable as construction materials for rocket motors, rocket nozzles, and nose cones that will be durable under extreme conditions of high temperature and corrosive environment. The properties determined extend in

temperature up to 6000 degrees Kelvin. The principal research activities

are experimental, and involve developing new measurement techniques and

apparatus, as well as measuring heats of reaction, of fusion, and of

vaporization; specific heats; equilibria involving gases; several thermophysical properties in fast processes at very high temperatures; spectra

of the infrared, matrix-isolation, microwave, and electronic types; and mass spectra. Some of these techniques, by relating thermodynamic properties to molecular or crystal structures, make it possible to tabulate

reliably these properties over far wider ranges of temperature and pressure

than those actually employed in the basic investigations.

ABSTRACT

The NBS program is presently devoted to reliable measurements of the

thermodynamic and other thermophysical properties of refractory metals and

their Aerospace- important compounds. This report presents in detail recent

results and critical analyses of several experimental investigations com- pleted or in progress, literature surveys, and new measurement-method

developments. All experimental values obtained are compared thoroughly with

the previously published results. The subjects may be enumerated under three

broad categories. (1) Properties of metals — Using a subsecond pulseheating technique, the heat capacity, electrical resistivity, and hemispherical total and normal spectral emittances were measured for tungsten

(2000-3600 K) and niobium (1500 - 2700 K) , with estimated inaccuracies of

2%-3% (heat capacity), 0.5%-l% (electrical resistivity), and 3% (the

emittances). Using a similar fast technique, preliminary work gave for

tungsten a melting point of 3692 K (IPTS-1968) , with an estimated uncertainty

of 15 K. The enthalpy of molybdenum, measured by drop-type calorimetry

1170-2100 K, agreesclosely for drawn- annealed and zone-refined samples,

with an estimated uncertainty generally within 1% for the derived heat

capacity. The measured emissivities of tungsten, molybdenum, tantalum,

i
and niobium were found to be higher than those predicted by a classical

theoretical relation to electrical resistivity (at 2000 K by amounts

rangirgfrom 10% for Nb to over 50% for W, but by progressively less at

higher temperatures). (2) Properties of compounds — MoF^ was prepared,

with a cryoscopically indicated purity of 99.85 mol %. After developing

a technique for preventing its decomposition, preliminary values for its

vapor pressure and heat of vaporization have been obtained by the transpiration method. To measure its heat of formation by oxidation to MoF^,

the heat of solution of MoF^ was undertaken, and preliminary results

indicate that the published value is far in error (besides disagreeing

by 14 kcal/mole from the published fluorine-combustion value) . Using

double-boiler Knudsen cells to suppress the polymer bands, the infrared

spectrum of NbF,. (matrix-isolated and some gas-phase) was observed, and

was interpreted to yield the six infrared-active fundamental frequencies

of the monomer molecule, assuming it to have symmetry. The known

composition and thermal properties, as well as sample-characterization

techniques, of the systems Mo-C, Ta-C, and Nb-B are reviewed, and criteria

for samples suitable for accurate drop calorimetry are discussed as background to measurements in progress. (3) New measurement techniques —

A high-speed (millisecond) method of measuring the thermal expansion of

electrical conductors at high temperatures was developed, and tests on platinum (300-700 K) show agreement with steady-state data well within

the estimated 5% uncertainty of the new method. Refinements being con- sidered are enumerated. A rotating attenuator for the generation of

subsecond-duration sawtooth-shape radiance pulses is described; the

observed radiance variation scatters by the order of 0.5% from the calculated values. Various optical methods (primarily photoelectric and photographic) for measuring transient high temperatures with millisecond- and

microsecond-order time resolution are critically reviewed. The advantages

and limitations of the various methods are discussed, and estimates of the

uncertainties given. Applications to solids above 1500 K are emphasized,

such as in measuring their various thermophysical properties and in determining surface temperatures and temperature gradients in ram-jet combustion

and ablating materials. Short-time (millisecond) fluctuations of the

temperature of a graphite arc were measured (at about 3800 K) , and were

found to be 3 to 4 K, being comparable to those reported over a period of

seconds using a slower pyrometer.

I'V Ru/zJGjfyfi—

Charles W. Beckett

ii
TABLE OF CONTENTS

Page

Foreword i

Abstract i

Chap . 1 . HIGH-SPEED (SUBSECOND) MEASUREMENT OF HEAT CAPACITY

,

ELECTRICAL RESISTIVITY, AND THERMAL RADIATION PROPERTIES

OF TUNGSTEN IN THE RANGE 2000 TO 3600 K

(by A. Cezairliyan and J. L. McClure) 1

Abstract ........

1. Introduction

2. Measurements

Fig. 1. Photomicrographs of the tungsten

specimen

Table 1. Impurities in tungsten specimen. . . 3. Experimental Results

3.1 Heat Capacity

Table 2. Heat capacity, electrical resistivity, hemispherical total and

normal spectral emittances of

tungsten

3.2 Electrical Resistivity

3.3 Hemispherical Total Emittance

3.4 Normal Spectral Emittance

4. Estimate of Errors

Discussion . Table 3. Tungsten heat capacity difference

(previous literature values minus

present-work values) in percent . . Fig

.

2. Heat capacity of tungsten reported

in the literature

Table 4. Tungsten electrical resistivity

difference (previous literature

values minus present-work) in percent

Fig

.

3. Electrical resistivity of tungsten

reported in the literature

Fig. 4. Hemispherical total emittance of

tungsten reported in the literature

Fig. 5. Normal spectral emittance of tungsten at A = 650 nm reported in the

literature

Table 5. Electrical resistivity of tungsten

at 293 K

Table 6

.

Excess heat capacity Ac in equation (5) and estimated vacancy con- tribution to heat capacity of tungsten

1

2

2

4

6

7

7

8

9

9

9

10

10

12

13

14

15

16

17

18

20

iii
TABLE OF CONTENTS (Continued)

Fig. 6. Heat capacity of tungsten

according to equation (6)

6 . References .

Fage

22

23

Chap. 2. PRELIMINARY RESULTS ON THE MEASUREMENT OF MELTING

POINT OF TUNGSTEN BY A PULSE HEATING METHOD

(by Ared Cezairliyan) 26

Abstract 26

1. Introduction 26

2. Results 27

3. Discussion 28

Table 1. Melting point of tungsten reported

in the literature 29

4. References 31

Chap. 3. HIGH-SPEED (SUBSECOND) MEASUREMENT OF HEAT CAPACITY,

ELECTRICAL RESISTIVITY , AND THERMAL RADIATION PROPERTIES

OF NIOBIUM IN THE RANGE 1500 TO 2700 K

(by Ared Cezairliyan) 33

Abstract 33

1. Introduction 34

2. Measurements 34

Fig. 1. Photomicrographs of the niobium

specimen 36

3. Experimental Results 37

Table 1. Impurities in niobium specimen. . . 38

Table 2. Heat capacity, electrical resistivity, hemispherical total emittance and normal spectral emittance

of niobium 39

3.1 Heat Capacity 40

3.2 Electrical Resistivity 40

3.3 Hemispherical Total Emittance 41

3.4 Normal Spectral Emittance ......... 41

4. Estimate of Errors 42

5. Discussion 42

Table 3. Niobium heat capacity difference

(previous literature minus presentwork values) in percent 44

Fig. 2. Heat capacity of niobium reported

in the literature 45

Table 4. Niobium electrical resistivity difference (previous literature minus

present-work values) in percent . . 46

IV
TABLE OF CONTENTS (Continued)

Page

Fig. 3. Electrical resistivity of niobium

reported in the literature 47

Fig. 4. Hemispherical total emittance of niobium reported in the literature. ... 48

Fig. 5. Normal spectral emittance of niobium

at X = 650 nm reported in the literature 49

Acknowledgement 51

Fig. 6. Heat capacity of niobium according to

equation (6) 52

6. References 53

Chap . 4 . DEPARTURE OF EMITTANCE-RESISTIVITY RELATION FROM

THEORETICAL PREDICTIONS FOR REFRACTORY METALS AT HIGH

TEMPERATURES

(by Ared Cezairliyan) 55

Fig. 1. Variation of the ratio of measured

emittance to computed emittance as a function of temperature for niobium,

molybdenum, tantalum, and tungsten . . 57

References 58

Chap . 5 . THE RELATIVE ENTHALPY AND HEAT CAPACITY OF MOLYBDENUM

METAL FROM 1170 TO 2100 K

(by Shigeru Ishihara and Thomas B. Douglas) 59

Abstract 59

I. Introduction 59

II. Samples 60

Qualitative Spectrochemical Analyses 60

Spark-Source Mass Spectrometry 61

Electronic Characterization. .... 61

Sample Annealing Prior to Enthalpy Measurements. 61

Table 1A. Qualitative spectrochemical

analyses of the molybdenum

samples, in weight % 62

Table IB. Mass-spectrometric analyses of a representative specimen of

Samples A and B 63

III. Calorimetric Apparatus and Method 64

IV. Enthalpy Data and Empirical Equations for Relative

Enthalpy and Heat Capacity of Molybdenum 66

Table 2. Individual enthalpy measurements

on molybdenum 68

Table 3A. Heat capacity and enthalpy of mo- lybdenum (in joules) 70

v
TABLE OF CONTENTS (Continued)

Page

Table 3B . Heat capacity and enthalpy of

molybdenum (in calories) 71

Table 3C . Corrections for molybdenum to con- vert to IPTS-48 and IPTS -68 scales . 72

V. Comparison with Previous Investigators and Compilers. 73

VI. Discussion of Errors 73

Table 4. Outline of reported measurements of

the enthalpy or heat capacity of

molybdenum metal above 1000 K. ... 74

Fig. 1. Comparison of molybdenum %-H29 g 15 values of various investigators.'. . 75

Fig. 2. Comparison of molybdenum heatcapacity values of various investigators 76

Table 5. Percentage deviation of the values

of enthalpy and heat capacity of

molybdenum adopted by various com- pilers from those of the present

work (Eq 1) .77

(1) Effects of Sample Impurities 78

(2) Effects of Temperature Errors 79

VII. Acknowledgements 80

VIII. References 81

Chap . 6 . THE HEAT OF FORMATION OF MoF (£) BY SOLUTION CALORIMETRY; ANALYSIS OF PRELIMINARY EXPERIMENTS

(by R. L. Nut tall, K. L. Churney, and M. V. Kilday) ... 84

Introduction 84

Reaction Scheme of Solution Experiments 86

Experimental Procedure . 89

Analysis of Results 90

(A) Heat of Solution of NaF(c) 90

(B) Heat of Solution of MoO„(c) 90

(C) Heat of Solution of MoF^(£) ,92

References 95

Chap . 7 . PROVISIONAL RESULTS ON THE PREPARATION, MELTING, AND

VAPORIZATION OF MoF

(by Ralph F. Krause, Jr.). 97

Abstract 97

Literature Survey 97

Table 1. Chemical analyses of some molybdenum

fluorides 98

Table 2. Estimate of the change in enthalpy of

Eqs 1 and 2, using the data of Cady

and Hargreaves. . 100

vi
TABLE OF CONTENTS (Continued)

Page

Preparation 101

Melting and Purity 103

Table 3. Observed melting data on samples of

MoF^ and MoF^ 104

Vaporization by Entrainment 105

Table 4. Preliminary results of vaporizing a sample of MoF by entrainment 106

References 108

Chap. 8. THE INFRARED SPECTRUM OF MATRIX ISOLATED NbF . (by Nicolo Acquista and Stanley Abramowitz) „ 110

Abstract 110

Introduction Ill

Experimental ........ 112

Experimental Results 113

Fig. 1. The gas phase infrared spectrum of

NbF

5

114

Fig. 2. The infrared spectrum of matrix isolated NbF

5

115

Fig. 3. Infrared spectra of matrix isolated

NbF

5

116

Conclusion ..... 117

Table I. Observed bands and vibrational assignment for NbF,. 118

References 119

Chap . 9 . SURVEY OF THE SYSTEMS Mo-C , Ta-C AND Nb-B WITH EMPHASIS

ON COMPOUNDS SUITABLE FOR ENTHALPY MEASUREMENT BY DROP

CALORIMETRY, INCLUDING A LITERATURE SURVEY OF ENTHALPY

AND HEAT CAPACITY DATA ON SELECTED COMPOUNDS FROM THESE

SYSTEMS

(by David A. Ditmars) 120

I. Introduction 120

II. Stable Phases Suitable for Calorimetric Measurement 120

A. Phase Diagrams — General Features. . . . 120

Fig. 1. Phase diagram of the system

Mo-C (ref. [1]) 121

Fig. 2. Phase diagram of the system

Ta-C (ref. [1]) 122

Fig. 3. Phase diagram of the system

Nb-B (ref. [1]) 123

Vll
TABLE OF CONTENTS (Continued)

Page

B. Methods of Synthesis and Sample Characterization 125

1. Synthesis 125

2. Sample Characterization 126

III. Literature 126

A. General References 126

Table 1. Reported investigations of enthalpy

and heat capacity of solid Mo~C, TaC,

Ta C, NbB, and NbB 127

References. ..... 7 128

Chap . 10 . A HIGH-SPEED METHOD OF MEASURING THERMAL EXPANSION OF

ELECTRICAL CONDUCTORS

(by Ared Cezairliyan) 130

Fig. 1. Optics of the high-speed thermal

expansion measurement system. . . . 131

References 134

Chap. 11. ROTATING OPTICAL ATTENUATOR FOR THE GENERATION OF SUBSECOND DURATION SAWTOOTH SHAPE RADIANCE PULSES

(by Ared Cezairliyan) . ......... 135

Abstract ........... ... 135

1. Introduction 136

2. Method and Apparatus ..... 136

Fig. 1. Functional diagram of the optical

system for the generation of subsecond duration sawtooth shape

radiance pulses 137

Fig. 2. The attenuator disk and the diaphragm opening 139

3. Results 141

Fig. 3. Oscilloscope trace photographs of

linear and quadratic pulses .... 142

Table 1. Summary of experimental parameters

and results 143

4. Conclusion ...... 144

5. References 145

Chap. 12. OPTICAL METHODS OF MEASURING TRANSIENT HIGH TEMPERATURES

(by Ared Cezairliyan) 146

Abstract 146

viii
TABLE OF CONTENTS (Continued)

Page

1. Introduction 147

2. General Considerations 148

3. Photoelectric Methods . 150

Fig. 1. Optical system of the high-speed

pyrometer (Foley, ref. 8) . . . . 154

4. Photographic Methods 155

First Method (measurement and calibration at

different times) 157

Second Method (measurement and calibration

simultaneously) 158

5. Applications 159

Photographic 160

6. Discussion 160

References ....... 165

Chap. 13. SHORT-TIME (MILLISECOND) FLUCTUATIONS OF RADIANCE

TEMPERATURE OF GRAPHITE ARC

(by Ared Cezairliyan) 169

Fig. 1. Variation of radiance temperature

of graphite arc and tungsten lamp

as a function of time (effective

temperature, approximately

3800 K) 171

References 172

Chapter 1

HIGH-SPEED (SUBSECOND) MEASUREMENT OF HEAT CAPACITY,

ELECTRICAL RESISTIVITY, AND THERMAL RADIATION PROPERTIES OF

TUNGSTEN IN THE RANGE 2000 TO 3600 K

A. Cezairliyan and J. L. McClure

National Bureau of Standards

Washington, D.C. 20234

Abstract

Measurements of heat capacity, electrical resistivity,

hemispherical total and normal spectral emittances of tungsten

above 2000 K by a pulse heating technique are described. Duration

of an individual experiment, in which the specimen is heated from

room temperature to near its melting point is less than one second.

Temperature measurements are made with a photoelectric pyrometer.

Experimental quantities are recorded with a digital data acquisition

system, which has a full-scale signal resolution of one part in 8000.

Time resolution of the entire system is 0.4 ms. Results on the above

properties of tungsten in the range 2000 to 3600 K are reported and

are compared with those in the literature. Estimated inaccuracy of

measured properties in the above temperature range is: 2 to 3 percent

for heat capacity, 1 percent for electrical resistivity, 3 percent for

hemispherical total and normal spectral emittances.

1
1. Introduction

Tungsten has the highest melting point (above 3600 K) of any

known metal. Because of the difficulties involved in performing

accurate experiments by conventional techniques at temperatures above

approximately 2500 K, a high-speed method was developed to measure heat

capacity, electrical resistivity, hemispherical total emittance and

normal spectral emittance of electrical conductors. In this paper,

application of this technique to measurements on tungsten in the temperature range 2000 to 3600 K is described.

The method is based on rapid resistive self-heating of the specimen

from room temperature to near its melting point. During the short experiment, which lasts less than one second, current flowing through the

specimen, potential across the specimen and specimen temperature are

measured. Temperature measurements are made with a high-speed photoelectric pyrometer [1] . Recordings of experimental quantities are made

with a digital data acquisition system, which has a time resolution of

0.4 ms, and a full-scale signal resolution of one part in 8000. Details

regarding the construction and operation of the measurement system, and

other pertinent information, such as formulation of relations for properties etc., are given in earlier publications [2,3] in connection with

measurements on molybdenum and tantalum.

2. Measurements

The measurements were made in the temperature interval 1900 to

3600 K. To optimize the operation of the pyrometer, this temperature

interval was divided into four ranges: low, 1900 to 2200 K; medium,

2150 to 2500 K; high, 2450 to 2900 K; and very high, 2850 to 3600 K.

2
Two experiments were conducted in each range; and three additional

experiments were conducted in each of the first three ranges in which

the surface radiance of the specimen was measured. Before the start of

the experiments, the specimen was annealed by subjecting it to approximately 30 heating pulses (up to 3200 K)

.

The duration of the current pulses in the experiments ranged from

410 to 630 ms depending on the desired final temperature. The average

heating rate of the specimen was: 7100 K s

^ at 2000 K, 5600 K s

^ at

3000 K, and 3700 K s

^ at 3600 K. At these temperatures, radiative heat

losses from the specimen amounted to approximately 3, 12, and 27 per

cent of the input power, respectively. All of the experiments were

conducted with the specimen in a vacuum environment of approximately

-4

10 torr.

The data on voltage, current, and temperature were used to obtain

third degree polynomial functions for each quantity in terms of time,

which then provided the input information for the determination of

properties

.

The pyrometer was calibrated before and after the entire set of

experiments against a tungsten-filament standard lamp, which in turn

was calibrated against the NBS temperature standard. The digital

recording system, including the differential amplifiers, was also

calibrated before and after the entire set of experiments. The details

of the calibration procedures are given in an earlier publication {2],

3
OJ mm

FIGURE 1. Photomicrographs of the tungsten specimen before (upper photograph)

and after (lower photograph) the entire set of experiments.

4
The specimen was a tube fabricated from a tungsten rod by removing

the center portion by an electro-erosion technique. The outer surface

of the specimen was polished to reduce heat loss due to thermal radiation.

The nominal dimensions of the specimen were: length, 4 in. (101 mm);

outside diameter, 0.25 in. (6.3 mm); and wall thickness, 0.02 in. (0.5 mm).

Specimen characterization was made by the following methods:

photomicrography, spectrochemical analysis, and residual resistivity ratio.

Photomicrographs of the specimen (figure 1) indicate that considerable

grain growth took place as the result of pulse heating to high temperatures. A list of the nature and composition of impurities in the specimen,

at the end of the entire set of experiments as determined by spectrochemical

analysis'*", is given in table 1. The residual resistivity ratio of the

specimen (ratio of electrical resistivity at 273 K to that at 4 K)

}

measured before the experiments, was 41.

The "effective" mass of the specimen was calculated from the total

mass by the ratio of the geometric surface area between voltage probes

to total surface area. Length measurements at room temperature were

made with a micrometer microscope. The cross-sectional area of the

specimen was calculated from the mass, density, and geometry. Density

3 -3

of the tungsten specimen was measured at 293 K to be 19.23 x 10 kg m

3 -3

This compares favorably with a previously cited value of 19.3 x 10 kg m [4].

Spectrochemical analysis of the tungsten specimen was made by the

Lamp Metals and Components Department of the General Electric Company.

5
TABLE 1

Impurities in Tungsten Specimen

impurity

Composition, ppm

(by weight)

A1 5 B <2

Ca 15

Cr 5 Co <2

Cu 10

Fe 60

Mg <2

Mn <2

Mo 310

Nb <20

Ni <2

Pb <2

Si 5 Sn <2

Sr <2

Th <250

Ti 10

Zr 30

450 < Total < 740

6
3. Experimental Results

This section presents the results on the thermophysical properties

determined from the measured quantities. All values are based on the

1968 International Practical Temperature Scale [5], In all

computations, the geometrical quantities are based on their room

temperature (298 K) dimensions. The experimental results are

represented by polynomial functions in temperature which were obtained

by least squares approximation of the individual points. The final

values on properties at 100 degree temperature intervals computed

using the functions are presented in table 2.

3. 1. Heat Capacity

Heat capacity was computed from data taken during the heating

period. A correction for power loss due to thermal radiation was

made using the results on hemispherical total emittance. The function

for heat capacity (standard deviation = 0.7 percent) that is valid

in the temperature range 2000 to 3600 K is:

c = -25.71 + 6.331 x

10~ 2 T - 2.459 x 10

_5

T

2 + 3.638 x 10

_9

T

3 (1) P

where T is in K and c^ in J mol 3

K

3

. In the computations of the

heat capacity, the atomic weight of tungsten was taken as 183.85.

To determine the effect of thermal cycling on heat capacity

the results of four additional experiments covering the range 2000 to

3300 K were compared with those reported above. The average difference

between the two sets of results was less than 0.1 percent which is

smaller than the measurement resolution. This indicates that the

measurements were not sensitive to thermal cycling.

7
TABLE 2

Heat capacity, electrical resistivity, hemispherical

total and normal spectral emittances of tungsten.

Temp

.

K

c P

J mol-

^ K“1

a

P

10" 8

tan

a

£ E N,A

2000 31.65 56.22 0.318

b

0.379

2100 32.49 59.74 .321

b

.379

2200 33.29 63.25 .324 b

.379

2300 34.08 66.77 .326 .379

2400 34.89 70.28 .329 .379

2500 35.72 73.80 .332 .379

2600 36.61 77.31 .335 .379

2700 37.57 80.83 .338 .379

2800 38.63 84.34 .340 .379

2900 39.81 87.86 .343 .379

3000 41.14 91.37 . 346 .379

3100 42.62 94.89 .349

3200 44.29 98.40 .351

3300 46.17 101.92 .354

3400 48.27 105,43 .357

3500 50.63 108.95 —

3600 53.25 112.46

Based on ambient temperature (298 K) dimensions.

^Extrapolated from higher temperature results.

8
3. 2. Electrical Resistivity

The electrical resistivity of tungsten was determined from

the same experiments that were used to calculate the heat capacity.

The function for electrical resistivity (standard deviation = 0.4

percent) that is valid in the temperature range 2000 to 3600 K is:

p = -14.08 + 3.515 x 10“ 2 T (2)

_8

where T is in K and p in 10 flm. The results of thermal

cycling indicates an average difference of less than 0.5 percent

in electrical resistivity.

3.3. Hemispherical Total Emittance

Hemispherical total emittance was computed using data taken

during both heating and initial free cooling periods in the

experiments. The function for hemispherical total emittance (standard

deviation = 1 percent) that is valid in the temperature range 2300 to

3400 K is:

e = 0.2627 + 2.770 x

10~ 5 T (3)

where T is in K.

3.4. Normal Spectral Emittance

Normal spectral emittance was computed using data from three

sets of two experiments, one in which the pyrometer was aimed at the

surface of the specimen, and another in which it was aimed at the

blackbody hole in the specimen. The target on the surface was a narrow

flat ground along the specimen. The measurements were made at the

effective wavelength of the pyrometer interference filter (650 nm;

bandwidth 10 nm) . The function for normal spectral emittance (standard

deviation = 0.2 percent) that is valid in the temperature range 2000 to

9
3000 K is:

e , = 0.3804 - 5.060 x

10~ 7 T

n, A

where T is in K.

(4)

4 . Estimate of Errors

Estimates of errors in measured and computed quantities lead

to the following estimates of errors in the properties over the

temperature range 2000 to 3600 K.

Heat capacity: 2 percent at 2000 K, 3 percent at 3600 K.

Electrical resistivity: 1 percent

Hemispherical total emittance: 3 percent

Normal spectral emittance: 3 percent

Details regarding the estimates of errors and their combination

in high-speed experiments using the present measurement system are

given in a previous publication [2], Specific items in the error

analysis were recomputed whenever the present conditions differed

from those in the earlier publication.

5. Discussion

The heat capacity and electrical resistivity results of this

work are compared graphically with those in the literature in figures

2 and 3, respectively. Numerical comparisons are given in tables 3

and 4. It may be seen that present results agree favorably with most

others at 2000 K. Considerable disagreement in heat capacity exists

acc u f 3-c^

above 2500 K. This may be expected, since above this tempera ture^of

heat capacity measured by conventional methods decreases rapidly.

10
Estimates of errors in papers cited lead to an estimate of

inaccuracies in previously reported heat capacity and electrical

resistivity of approximately 5 to 15 and 1 to 5 percent, respectively,

in the temperature range considered. Measurements of the electrical

resistivity of tungsten corresponding to 293 K, as well as values

reported in the literature, are given in table 5.

The results for hemispherical total and normal spectral emittances

of this work and those in the literature are presented in figures 4

and 5, respectively. Because of the strong dependence of emittance

on surface conditions, considerable deviations exist in the results

of various investigators.

Heat capacity results at high temperatures are considerably

higher than the Dulong and Petit value of 3R. Some of this departure

is due to c - c and the electronic terms. However, they do not

P v account for the entire departure. Heat capacity above the Debye

temperature may be expressed by

c = A - + CT + Ac (5)

P t

2

where the constant term is 3R (24.943 J mol ^ K

"*") , the term in

-2

T is the first term in the expansion of the Debye function, the

term in T represents c - c and electronic contributions, and the

P v quantity Ac represents excess in measured heat capacity at high

temperatures, which is not accounted for by the first three terms.

4 -3

The coefficients B(7.72 x 10 ) and C(2.33 x 10 ) were obtained from

data on heat capacity at room and moderate temperatures (at 298.15 and

1000 K) given by Hultgren et al. [6].

11
ten

heat

capacity

difference

(previous

literature

values c

0)o

<uft

CO

033

rH

cfl >

r—

o&c

0)co

03

ft

033C

•Hg

0300c3H

3600 +17 -17 o m o • CM

<r Oh rH co + i o UO o • • • CM CO CM CO + i i o 00 i—i o • • • • o Oh o o CO i 1 1 1 X o CM t—1

00 o • • • • 0) 00 UO vO co o rH

3-i CM iH i i 1 i 3 i

cdu

a) o o o CM Oh

ft o • • • • g MO CM o rH

CD C\1 rH i i 1 + H I o Cn s—1

M0 MO 00 o • • • • • • • o Oh CM CO CM o o

CM 1 i i 1 i 1 + o CO co <r CO o • • • • • • • CM o o CM CM o o

CM + 1 1 i i 1 +

cd CO o MO CM M0 uO o o o • o t—1

co <—1 i—i i—1

rH CM + i 1 + i i i +

nO # O 03 T 1 i—1 c CO a- ft ft 3 3 ft ft ft J rH o o o no no o o o

<13 3 n t-l

h o o u

u

H

a ft nO T3 "O

g

g no no no

00 o rH co CO CO 00 00

cd 1—1

CO VO M0 vO vO MO MO

CD Oh Oh Oh Oh Oh Oh Oh Oh

>H 1—1

rH 1—1

iH iH 1—1 —l i—I

<4-1

(13 o i—1

CM CO 1/0 MO 00

rH i—1

rH rH rH iH rH »H rH >OX

rH

g CD X u

-i o 4-J o XI c CO cd cd

-J c o 1—1 • u

Cd 03 4-) • no rH i—1cd md CO C/D rH e (D cd X H o c cd cd M3 •H u X cd 4-J X 0) o 4-J u «H 03 C/D CD nO *-) (D CD (h M > c X rH N 3 oc cd nO C X cd no 4-J no H c C •H cd X c •H 0

•H

p cd i—1 g 4-J cd s cd

x CD i—1

4-J

C

O

H 00

X •H <4-1 (D c X 4-J

n CD o U cd s •H •H C/D o cd o •H u O 0) 03 CD s *“D X *4 X X X 1 3

iZ

Extrapolated

from

1873 K
HEAT

CAPACITY,

J

MOL'

1

1000 1500 2000 2500

TEMPERATURE, K

3000 3500

FIGURE 2 . Heat capacity of tungsten reported in the literature.

13
o-w

ft53H o CN o • VO <N CO + O ON o • • <r L/O rH co + + o in CN in o • • • <N LO r—4

CN

CO + + +

CO

CL) 01—1

cd> o (N 1—1 m o • • • •

Cl) o L/0 o 1—1

CN

u3u

cd ft

CO + + 1 + 3

0)

4-1 r> o ON NT CO <r

•H a) o 0 • • • i—1 3 CO <d* o r-H CH 3 CN + + 1 +

CO 4J 3 cd O 4-J J-J •h e 01 > 0) ft

Cl)u e o 00 i—1NT CN 3 3 Q) o • • • • ft 0) H NO o i—1

CN

ft CN] + + i 4-

ce in a

d) /-—s 3 ft! o vO 1—1 m ON

m

0) )-i o • • • • • M-4 O NT o i—i i—1 o M-4 £

•HT3 4-)

CN + 4- i 4- 4- £

ft a) •3 CO •h a) o r-> CN CO NO <N r>. > )-i o • • • • • • •h a. CN NT o i—1 o i—1 o 4-1 co co •H 3

C/D c

CN + + i 1 4- 4-

0) -H n e 3 1—1

00 ON r—1 CN i—i O • • • « • • ed o m o o o *—1 i—1 a CN 4- + i 1 4- 4- •H3

4-> O

0) 1—1

-i in vO NT r-H <r

(1) cd CN CN CO Nt vO vO

a) ON o> ON ON ON ON

a >-l i—i i—1 i—1

rH rH rH

0)

4-> (000s3 • H mh ON o CN i—1

CN CO

<u CN CO CN CN CN

ft

003 >

•H 3 o 3

43 o u •H

-1 4-1 co c 3 O 3 4-J »TD O u o cd 0) 3

cd s s ft

C

00 > • rl T3 "d U 3 c 3 TJ

CO cd cd cd c

0) cd > CD <D > 3 43 r3 o ft M 4-1 4-1 3 3 3

ft CO ft 3 3 cd (/)

0) co

O 4-1 £ 3 3 u 43 cd •H o O o CO tH 0)

pLl ‘"O PH o ft z
LUU 8-01 ‘A1IAI1SIS3U ~IVDIU103“I3

15

1000

1500

2000

2500

3000

3500

TEMPERATURE,

K
FORSYTHE

(1934)

ALLEN

(I960)

RUDKIN

(1962)

NEIMARK

(1968)

o o o

ro CM

d d d

30NV11IIAI3 “IV101 !VDId3HdSllAi3H

16

1500

2000

2500

3000

3500

TEMPERATURE,

K

FIGURE

4.

Hemispherical

total

emittance

of

tungsten

reported

in

the

literature.
(UJU 059 ID) 30NV11IIAI3 “IVU103dS "IVIAIdON

17

1000

1500

2000

2500

3000

3500

TEMPERATURE.

K

FIGURE

5.

Normal

spectral

emittance

of

tungsten

at X

=

650

nm

reported

in

the

literature.
TABLE 5

Electrical Resistivity of Tungsten at 293 K.

Investigator Ref

.

Year

Resistivity

10~ 8

ton

Forsythe and Worthing 19 1925 5.46

Jones 20 1926 5.49

Forsythe and Wa.tson 32 1934 5.50

White and Woods 31 1959 5 . 29 a

Tye 24 1961 5.45

Present Work 5.45

a ideal resistivity.

18
Using eq (5) and the heat capacity results of this work, the

quantity Ac was computed for temperatures above 2000 K. The results

are tabulated in table 6. The estimated uncertainty in the computed

Ac may be as high as 1 J mol K \ This was obtained from the

combined uncertainties in the coefficients in eq (5) and the measured

heat capacities.

Although the mechanisms of vacancy generation become important

at high temperatures, it was not possible to attribute the high

values entirely to vacancies. To demonstrate this, a crude estimate

of the contribution of vacancies to heat capacity was made using the

method described in a previous publication [2]. The reported values

for vacancy formation energy of tungsten are 3.3 eV [7] and 3.6 eV [8].

Results of quenching experiments on various refractory elements

{7,9] have indicated that vacancy concentrations are probably in

the range 0.01 to 0.1 percent at their melting points. Estimates

corresponding to a vacancy concentration of 0.1 percent at the melting

point and a vacancy formation energy of 3.3 eV are given in table 6.

The results indicate that vacancy contribution is small, less than

0.8 J mol ^ K ^ (upper limit) at 3600 K, and does not account for high

heat capacity values.

If the entire difference between measured and computed [using

eq (5)] heat capacities is attributed to vacancies, a value of 1.3 eV

for energy and 12 percent for concentration at the melting point are

obtained. Both of these values seem to be unrealistic for tungsten.

19
TABLE 6

Excess heat capacity Ac in equation (5) and

estimated vacancy contribution to heat

capacity of tungsten.

T

K

Ac

J mol-1 K

_1

cvac

J mol" 1 K

-1

2000 2.07 0.0005

2200 3.24 0.002

2400 4.37 0.009

2600 5.62 0.03

2800 7.18 0.06

3000 9.21 0.14

3200 11.90 0.26

3400 15.41 0.47

3600 19.93 0.79

20
To give a simple expression for the heat capacity of tungsten over

4 a wide temperature range, an empirical term in T for the quantity

Ac in eq (5) was substituted. The coefficient of this term was obtained

from the results of the present work in conjunction with the values given

by Hultgren et al. [6] at temperatures below 1000 K. Then, eq (5) for

the range 300 to 3600 K becomes

4

c = 24.943 -

7 ° 72

- + 2.33 x 10

_3

T + 1.18 x

10~ 13

T

4 (6)

v T

where T is in K and c^ in J mol ^ K \ Average deviation of the

individual points from the function over the temperature range

considered is 0.2 percent. Equation (6) is presented graphically in

figure 6.

The experimental results reported in this paper have further

substantiated the feasibility of accurate simultaneous measurement of

re so Cation

selected properties above 2000 K by a millisecond pulse method. The A

technique is particularly attractive at high temperatures where

conventional methods fail to give accurate results.

21
i_M ,nOlAI P ‘AllOVdVO 1V3H

w

pioM

Pm

22

1000

2000

3000

TEMPERATURE,

K
6 . References

[1] Foley, G. M., High-speed optical pyrometer, Rev. Sci. Instr. 41 , 827 (1970).

[2] Cezairliyan, A., M. S. Morse, H. A. Berman, and C. W. Beckett,

High-speed (subsecond) measurement of heat capacity, electrical

resistivity, and thermal radiation properties of molybdenum in

the range 1900 to 2800 K, J. Res. Nat. Bur. Stand. (U.S.) 74A

(Phys. and Chem.), 65 (1970).

[3] Cezairliyan, A., J. L. McClure, and C. W. Beckett, High-speed

(subsecond) measurement of heat capacity, electrical resistivity,

and thermal radiation properties of tantalum in the range 1900

to 3200 K, J. Res. Nat. Bur. Stand. (U.S.), to be published.

[4] Tietz, T. E. and J. W. Wilson, Behavior and properties of

refractory metals, Stanford University Press, California (1965),

p. 28.

[5] International Practical Temperature Scale of 1968, Metrologia _5, 35 (1969).

[6] Hultgren, R. , R. L. Orr, P. D. Anderson, and K. K. Kelly, Selected

Values of Thermodynamic Properties of Metals and Alloys, John Wiley,

New York (1963)

.

[7] Schultz, H., "Quenching of vacancies in tungsten," in Lattice

Defects in Quenched Metals, R. M. J. Cotterill, M. Doyama

,

J. J. Jackson and M. Meshi, eds . , Academic Press, New York (1965),

p. 761.

[8] Gripshover, R. J., M. Khoshnevisan, J. S. Zetts, and J. Bass, A

study of vacancies in tungsten wires quenched in superfluid

helium, Phil. Mag. 2_2, 757 (1970).

[9] Meakin, J. D., A. Lawley, and R. C. Koo, "Vacancy loops in quenched

molybdenum," in Lattice Defects in Quenched Metals, R. M. J.

Cotterill, M. Doyama, J. J. Jackson, and M. Meshi, eds., Academic

Press, New York (1965), p. 767.

[10] Worthing, A. G. , Atomic heats of tungsten and of carbon at

incandescent temperatures, Phys. Rev. 1_2, 199 CL918) .

[11] Jaeger, F. M. and E. Rosenbohm, Exact measurement of specific heat

of solid substances at high temperatures, III: Pd and W,

Proc. K. Ak. V. Wetensch. 33_ y 457 (1930) .

23
[ 12 ] Hoch, M. and H. L. Johnston, A high-temperatur e drop calorimeter,

the heat capacities of tantalum and tungsten between 1000 and

3000 K, J. Chem. Phys . 6^5, 855 (1961).

[13] Kirillin, V. A., A. E. Sheindlin, V. Ya. Chekhovskoi, and

V. A. Petrov, Thermodynamic properties of tungsten, Russ. J. Phys.

Chem. 37, 1212 (1963)

.

[14] Kraftmakher, Ya. A. and P. G. Strelkov, Energy of -formation of and

concentration of vacancies in tungsten, Solid State Physics (USSR) _4

,

1662 (1963).

[15] Lowenthal, G. C., The specific heat of metals between 1200 K and

2400 K, Australian J. Phys. 16_, 47 (1963).

[16] Hein, R. A. and P. N. Flagella, Enthalpy measurements of UO and

tungsten to 3260 K, General Electric Report GEMP-578, 1968.

[17] Leibowitz, L. , M. G. Chasanov and L. W. Mishler, The enthalpy of

solid tungsten from 2800 K to its melting point, Trans. Met. Soc

.

AIME 245 , 981 (1969) .

[18] West, E. D. and S. Ishihara, Enthalpy of tungsten. Private

communication

.

[19] Forsythe, W. E. and A. G. Worthing, The properties of tungsten and

the characteristics of tungsten lamps, Astrophy. J. 61 , 146 (1925).

[20] Jones, H. A., A temperature scale for tungsten, Phys. Rev. 28 , 202 (1926).

[21] Osborn, R. H., Thermal conductivities of tungsten and molybdenum

at incandescent temperatures, J. Opt. Soc. Am. _31, 428 (1941).

[22] Platunov, E. S. and V. B. Fedorov, Use of photographic pyrometry

in thermal studies. High Temp. _2, 568 (1964).

[23] Neimark, B. E. and L. K. Voronin, Thermal conductivity, specific

electrical resistivity, and total emissivity of refractory metals

at high temperatures. High Temperature 6^, 999 (1968).

[24] Tye, R. P., Preliminary measurements on the thermal and electrical

conductivities of molybdenum, niobium, tantalum, and tungsten,

J. Less-Common Metals _3, 13 (1961).

[25] Allen, R. D., L. F. Glasier, and P. L. Jordan, Spectral emissivity,

total emissivity, and thermal conductivity of molybdenum, tantalum,

and tungsten above 2300 K, J. Appl. Phys. 31 , 1382 (1960).

24
[26] Rudkin, R. L., W. J. Parker, and R. J. Jenkins, "Measurement of

the thermal properties of metals at elevated temperatures," in

Temperature Its Measurement and Control in Science and Industry,

C. M. Herzfeld, ed., Vol. Ill, part 2, p. 523, Reinhold, New

York, (1962).

[27] Worthing, A. G., The true temperature scale of tungsten and its

emissive power at incandescant temperatures, Phys . Rev. TO, 377 (1917).

[28] DeVos, J. C., A new determination of the emissivity of tungsten

ribbon, Physica 20_, 690 (1954) .

[29] Larrabee, R. D., Spectral emissivity of tungsten, J. Opt. Soc.

Am. 49_, 619 (1959) .

[30] Latyev, L. N., V. Ya.. Chekhovskoi , and E. N. Shestakov, Experimental

determination of emissive power of tungsten in the visible region

of the spectrum in the temperature range 1200 to 2600 K, High

Temperature 7_, 610 (1969) .

[31] White, G. K. and S. B. Woods, Electrical and thermal resistivity of

the transition elements at low temperatures, Phil. Trans. Royal

Soc. (London) 251, 273 (1959).

[32]

Forsythe, W. E. and E. M. Watson, Resistance and radiation of tungsten

as a function of temperature, J. Opt. Soc. Am. 2A_, 114 (1934).

25
Chapter 2

PRELIMINARY RESULTS ON THE

MEASUREMENT OF MELTING POINT OF

TUNGSTEN BY A PULSE HEATING METHOD

Ared Cezairliyan

National Bureau of Standards

Washington, D. C„ 20234

Abstract

A subsecond duration pulse heating method is used to measure

the melting point of tungsten. Preliminary work yields a value of

3692 K, with an estimated inaccuracy of 15 K.

1 . Introduction

Serious difficulties are encountered in the measurement of

melting point of substances at temperatures above 2500 K by conventional methods. Most of the problems inherent in these methods are

eliminated by using high-speed measurement techniques. Application

of a high-speed (pulse heating) technique to the accurate measurement

of the melting point of molybdenum is described in the literature [1]

.

In the present study, the same pulse heating technique is used

for the measurement of the melting point of tungsten. The specimen,

which is in tubular form, was heated in vacuum from room temperature

to its melting point in 0.7 s by a single heavy-current pulse. During

26
the pulse period, specimen temperature was measured with a high-speed

photoelectric pyrometer [2], which permits 1200 temperature evaluations

per second. The pyrometer’s target was a small hole fabricated in the

wall at the middle of the specimen to approximate blackbody conditions.

The recordings of temperature were made with a high-speed digital data

acquisition system [3] , which is capable of recording data with a fullscale signal resolution of approximately one part in 8000 and a time

resolution of 0.4 ms. Details regarding the construction and operational

characteristics of the entire measurement system are given elsewhere [3, 4].

2. Results

The tungsten specimen was a tube of the following nominal dimensions:

length, 4 in. (102 mm); outside diameter, 0 . 25 in. (6.3 mm); thickness,

0.02 in. (0.5 mm). The outer surface of the specimen was polished to

reduce heat loss due to thermal radiation. The specimen was 99.

9

+

percent

pure. Spectrochemical analysis indicated the presence of the following

impurities in ppm by weight: Mo, 310; Th, <250; Fe, 60; Zr, 30; Ca and

Nb, <20 each; Cu and Ti , 10 each; Al, Cr and Si, 5 each; B, Co, Mg, Mn,

Ni, Pb, Sn, Sr, <2 each. All measurements reported in this paper, unless

stated otherwise, are based on the International Practical Temperature

Scale of 1968 (IPTS-1968) [5].

Specimen temperature near and during the initial melting period was

measured. The plateau in temperature indicates the region of solid and

liquid equilibria. By averaging temperature points on the plateau, a

value of 3692 K was obtained for the melting point of tungsten with a

standard deviation (individual point) of 1.3 K.

27
Sources and estimates of errors in experiments similar to the one

conducted in this study are given in detail in other publications [1, 3].

Estimated inaccuracy in the melting point is 15 K.

3 . Discussion

As may be seen in Table 1, considerable differences exist in the

tungsten melting points reported in the literature. In order to have a

common ground for comparisons, all reported values were converted to

IPTS-1968. It is interesting to note that, in general, the reported

values increase chronologically. The measurements were performed either

before 1930 or after 1960. The melting points reported prior to 1915,

as was summarized by Langmuir [6], were lower than that of Langmuir by

as much as 50 to 500 K. Experimental difficulties, including pyrometry

problems, encountered in high temperature quasi steady-state measurements

might have been responsible for the large discrepancies. Another source

of the discrepancies could have been the differences in the purity of the

various tungsten specimens.

Probably, the most reliable measurement performed on the melting

point of tungsten before 1930 was that of Worthing [8] which is 22 K

below the present value; however, this difference is within the combined

uncertainties of the two results. The average value of the melting points

reported by three investigators [11, 15, 16] since 1960 is 3693 K; average

and maximum differences from this value being 7 K and 10 K, respectively.

The melting point obtained in this study is 1 K lower than the above

average

.

28
TABLE 1

Melting Point of Tungsten Reported in the Literature

Investigator Ref. Year T

Au

(K) c

2

(cm K)

Melting Point, K

as reported on IPTS-1968

Langmuir 6 1915 1335 1.439 3540 ± 30 3559

Luckey 7 1917 3623

Worthing 8 1917 1336 1.435 3675 ± 15 3670

Henning and Heuse 14 1923 1336 1.430 3643 3616

Pirani 9 1923 1336 1.430 3660 ± 60 3633

Forsythe and Worthing 10 1925 1336 1.433 3655 3641

Zalabak 15 1961 1336.15 1.438 3680 3687

Allen 11 1962 1336.15 1.438 3682 ± 20 3689

Rudy and Harmon 16 1966 1336.15 1.438 3696 3703

IPTS-1968* 5 1968 1337.58 1.4388 3660 3660

Present Work 1337.58 1.4388 3692 ± 15 3692

Recommended as secondary reference point on IPTS-1968.

29
The presence of impurities in a specimen alters (in general,

reduces) the melting point of the element. Based on the Raoul t-Van't

Hoff equation, the melting point depression for the tungsten specimen

(with total amount of impurities less than 0.1 percent) is estimated

to be less than 3 K. Also, under the present operating conditions,

it is very unlikely that the effect of superheating, if present at

all, is more than a fraction of a degree.

30
A. References

[1] Cezairliyan, A., M. S. Morse, and C. W. Beckett. Measurement of

melting point and electrical resistivity (above 2840 K) of

molybdenum by a pulse heating method. Rev. Int. Hautes Temper, et

Refract. 7, 382 (1970).

[2] Foley, G. M. High-speed optical pyrometer. Rev. Sci. Instr. 41,

827 (1970)

.

[3] Cezairliyan, A., M. S. Morse, H. A. Berman, and C. W. Beckett.

High-speed (subsecond) measurement of heat capacity, electrical

resistivity, and thermal radiation properties of molybdenum in the

range 1900 to 2800 K. J. Res. Nat. Bur. Stand. (U.S.) 74A (Phys. and

Chem.), 65 (1970).

[4] Cezairliyan, A. Design and operational characteristics of a highspeed (millisecond) system for the measurement of thermophysical

properties at high temperatures. J. Res. Nat. Bur. Stand. (U.S.)

75C (Eng. and Instr.), 7 (1971).

[5] International Practical Temperature Scale of 1968. Metrologia .5,

35 (1969).

[6] Langmuir, I. The melting point of tungsten. Phys. Rev. (j, 138 (1915).

[7] Luckey, G. P. The tungsten arc under pressure. Phys. Rev. _9, 129

(1917).

[8] Worthing, A. G. The true temperature scale of tungsten and its

emissive powers at incandescent temperatures. Phys. Rev. 10, 377

(1917).

31
[9]

Pirani, M. and H. Alterthum. A method of measuring the melting

points of metals having high melting points. Zeitschrift

Electrochemie 29 , 5 (1923).

[10] Forsythe, W. E. and A. G. Worthing. The properties of tungsten

and the characteristics of tungsten lamps. Astrophys. J. 61,

146 (1925).

[11] Allen, R. D. Techniques for melting point determination on an

electrically heated refractory metal. Nature 193 , 769 (1962).

[12] Jones, H. A. A temperature scale for tungsten. Phys . Rev. 28 ,

202 (1926).

[13] Ubbelohde, A. R. Melting and crystal structure (Clarendon Press,

Oxford, 1965),

[14] Henning, F. and W. Heuse. Melting points of platinum and tungsten.

Zeit. Phys ik 16, 63 (1923).

[15] Zalabak, C. R. NASA Tech. Note, TND-761, 1961.

[16] Rudy, E. and D. P. Harmon. AFML-TR-65-2, Part I, Vol. VI^Air Force

Materials Laboratory Research and Technology Division, Dayton, Ohio,

(1966)

.

32
Chapter 3

HIGH-SPEED (SUBSECOND) MEASUREMENT OF HEAT CAPACITY,

ELECTRICAL RESISTIVITY, AND THERMAL RADIATION PROPERTIES OF

NIOBIUM IN THE RANGE 1500 TO 2700 K

Ared Cezairliyan

National Bureau of Standards

Washington, D. C. 20234

Measurements of heat capacity, electrical resistivity, hemispherical total emittance, and normal spectra emittance of niobium

in the temperature range 1500 to 2700 K by a subsecond duration

pulse heating technique are described. Results on the above

properties are reported and are compared with those in the literature.

A sharp increase in heat capacity above 2000 K was observed. Electrical

resistivity showed a negative departure from linearity in the curve

of electrical resistivity against temperature. Estimated inaccuracy

of measured properties is: 2 percent for heat capacity, 0.5 percent

for electrical resistivity, and 3 percent for hemispherical total and

normal spectral emittances.

33
1. Introduction

Because of the difficulties involved in performing accurate experiments at high temperatures by conventional techniques, a high-speed

method was developed to measure heat capacity, electrical resistivity,

hemispherical total emittance, and normal spectral emittance of electrical

conductors. In this paper, application of this technique to measurements

on niobium in the temperature range 1500 to 2700 K is described.

The method is based on rapid resistive self-heating of the specimen

from room temperature to near its melting point. During the short

experiment, which lasts less than one second, current flowing through

the specimen, potential across the specimen and specimen temperature

are measured. The experimental quantities are recorded with a digital

recording system, which has a time resolution of 0.4 ms, and a full-scale

signal resolution of one part in 8000. Details regarding the construction

and operation of the measurement system, the methods of measuring experimental quantities, and other pertinent information, such as formulation

of relations for properties, etc. are given in earlier publications

[1, 2]

1

.

2. Measurements

Measurements were made on two specimens designated as niobium-1

and niobium-2. Each specimen was a tube of the following nominal

dimensions; length, 4 in. (101 mm); outside diameter, 0.25 in. (6.3 mm);

$ &o[<2. and wall thickness, 0.02 in. (0.5 mm), fabricated in the wall at the

A

middle of the specimen approximated blackbody conditions for the highspeed photoelectric pyrometer [3].

Figures in brackets indicate the literature references at the

end of this paper.

34
The measurements were made in the temperature interval 1500 to

2700 K. To optimize the operation of the pyrometer, this temperature

interval was divided into six ranges: I, 1500 to 1650 K; II, 1600 to

1800 K; III, 1750 to 1950 K; IV, 1900 to 2200 K; V, 2100 to 2550 K;

VI, 2400 to 2700 K.

In each of the first five temperature ranges, two experiments

were conducted on niobium-1 and one on niobium-2; in the last range,

one experiment was conducted on each specimen. A total of three

additional experiments in the ranges II, III, and IV were performed

on niobium-1 in which the surface radiance of the specimen was measured.

Before the start of the experiments, each specimen was annealed

by subjecting it to 30 heating pulses (up to 2400 K) . All the experiments were conducted with the specimens in a vacuum environment of

-4

approximately 10 torr.

To optimize the operation of the measurement system, heating rate

of the specimens was varied depending on the desired temperature range

by adjusting the value of the resistance in series with the specimen.

Duration of the current pulses in the experiments ranged from 390 to

450 ms; and the average heating rate of the specimens was approximately

5200 Ks *. Radiative heat losses from the specimens amounted to approximately 1 percent at 1500 K, 3 percent at 2000 K, and 10 percent at 2700 K

of the input power.

Characterization of one of the specimens (niobium-1) was made by

the following methods: photomicrography, spectrochemical analysis, and

residual resistivity ratio. Photomicrographs of the specimen, shown in

35
FIGURE 1. Photomicrographs of the niobium specimen before (upper photograph)

and after (lower photograph) the entire set of experiments.

36
figure 1, indicate that considerable grain growth took place as the

result of pulse heating to high temperatures. A list of the nature

and composition of impurities in the specimen, at the end of the

entire set of experiments as determined by spectrochemical analysis,

is given in table 1. The residual resistivity ratio (ratio of electrical

resistivity at 273 K to the residual resistivity) of the specimen,

measured before the experiments, was 11.

The data on voltage, current, and temperature were used to obtain

third degree polynomial functions for each quantity in terms of time,

which then provided the input information for the determination of

properties

.

3. Experimental Results

This section presents the thermophysical properties determined

from the measured quantities. All values are based on the I9£>8 International Practical Temperature Scale [4]. In all computations, the

geometrical quantities are based on their room temperature (298 K)

dimensions. The experimental results are represented by polynomial

functions in temperature obtained by least squares approximation of

the individual points. The final values on properties at 100 degree

temperature intervals computed using the functions are presented in

table 2.

37
TABLE 1

Impurities in Niobium Specimen

Impurity Amount

ppm

Impurity Amount

ppm

A1 5 Mo 5

As <5 Ni <1

B <1 Pb <1

Bi <5 Sb <10

Ca <1 Si <5

Cd <5 Sn 3

Co <1 Ta 450

Cr <1 Te <5

Cu <1 Ti <1

Fe <3 V <1

Hf <50 W <100

Mg <1 Zn <10

Mn <1 Zr <5

470 < Total < 680

38
TABLE 2

Heat capacity, electrical resistivity, hemispherical

total emittance and normal spectral emittance of niobium

Temp . K

cEl -i

J mol K

0

Cl 1 00 O

i

—

1

a

e eN,A

1500 29.48 57.58

1600 30.11 60.41

1700 30.73 63.20 0.217 0.353

1800 31.35 65.96 0.230 0.352

1900 32.02 68.68 0.242 0.352

2000 32.75 71.37 0.254 0.351

2100 33.57 74.02 0.264 0.351

2200 34.53 76.63 0.274 0.351

2300 35.64 79.20 0.282 0.350

2400 36.94 81.74 0.290

2500 38.46 84.25 0.297

2600 40.23 86.71 0.303

2700 42.28 89.14

^ased on ambient temperature (298 K) dimensions.

39
3.1. Heat Capacity

Heat capacity was computed from data taken during the heating period.

A correction for power loss due to thermal radiation was made using the

results on hemispherical total emittance. The standard deviation of

the individual data points from a third degree polynomial function in

the range 1500 to 2700 K for each specimen is 0.7 percent for niobium-1

and 0.9 percent for niobium-2. The average absolute difference between

the results on two specimens is 0.7 percent. The function for heat

capacity (standard deviation = 0.8 percent) that represents the combined

results of the two specimens in the temperature interval 1500 to 2700 K

is

c = -3.395 + 4.855 x 10~ 2T - 2.531 x

10" 5 T

2 + 5.035 x 10

_9

T

3

(1) P

where T is in K and c^ is in J mol ^ K In the computations of heat

capacity, the atomic weight of niobium was taken as 92.91.

3.2 Electrical Resistivity

The electrical resistivity of niobium was determined from the same

experiments that were used to calculate heat capacity. The standard

deviation of the individual data points from a second degree polynomial

function in the range 1500 to 2700 K for each specimen is 0.2 percent

for both niobium-1 and niobium-2. The average absolute difference between

the results on two specimens is 0.5 percent. The function for electrical

resistivity (standard deviation = 0.3 percent) that represents the combined

results of the two specimens in the temperature interval 1500 to 2700 K

is

p = 10.74 + 3.396 x 10~ 2 T- 1.823 x 10” 6 T

2

(2)

is —8

where T is in K, and p in 10 ftm. In the computations of the specimen's

40
cross-sectional area, which is needed for the computations of electrical

3 -3

resistivity, the density of niobium was taken as 8.57 x 10 kg m [5].

The measurements, before pulse experiments, of the electrical resistivity

of the two niobium specimens at Z33 K with a Kelvin bridge were in agreement within 0.1 percent. Electrical resistivity of niobium at 293 K

_ g obtained by averaging the results of the two specimens is 15.9 x 10 flm.

3.3 Hemispherical Total Emittance

Hemispherical total emittance was computed for niobium-1 using

data taken during both heating and initial free cooling periods. The

function for hemispherical total emittance (standard deviation = 0.4

percent) that represents the results in the temperature range 1700 to

2650 K is

:

e = -0.144 + 2.88 x 10~ 4

T - 4.46 x

10~ 8

T

2 (3)

where T is in K.

3.4. Normal Spectral Emittance

Normal spectral emittance was computed for niobium-1 using data

from three sets of two experiments, one in which the pyrometer was

aimed at the surface of the specimen, and another in which it was aimed

at the blackbody hole in the specimen. The measurements were made at

the effective wavelength of the pyrometer interference filter (650 nm;

bandwidth 10 nm). The function for normal spectral emittance (standard

deviation = 0.6 percent) that represents the results in the temperature

range 1700 to 2300 K is:

c . = 0.361 - 4.77 x

10" 6

T (4) N,A

where T is in K.

41
4. Estimate of Errors

Estimates of errors in measured and computed quantities lead to

the following estimates of errors in the properties over the temperature

range 1500 to 2700 K: heat capacity, 2 percent; electrical resistivity,

0.5 percent; hemispherical total emittance, 3 percent; normal spectral

emittance, 3 percent. Details regarding the estimates of errors and

their combination in high-speed experiments using the present measurement system are given in a previous publication [2] . Specific items

in the error analysis were recomputed whenever the present conditions

differed from those in the earlier publication.

In all the earlier experiments with the present high-speed system,

the lowest temperature at which measurements were made was 1900 K. In

the present work, the measurements were extended down to 1500 K without

creating any significant uncertainties in temperature measurements.

The imprecision^ of temperature measurements was 0.7 K at 1500 K, and

0.5 K at 1900 K. The imprecision of voltage and current measurements

was less than 0.02 and 0.03 percent, respectively, over the entire

temperature range.

5. Discussion

The heat capacity and electrical resistivity results of this work

are compared graphically with those in the literature in figures 2 and

3, respectively. Numerical comparisons are given in tables 3 and 4.

Heat capacity results of this work are, in general, lower than those

of most other investigators, with the exception of Kraf tmacher [8].

'’Imprecision refers to the standard deviation of an individual point

as computed from the difference between measured value and that from

the smooth function obtained by the least squares method

.

42
Electrical resistivity results are in good agreement with those of others.

Estimates of errors in papers cited lead to an estimate of inaccuracies

in previously reported heat capacity and electrical resistivity of

approximately 5 to 10 and 1 to 3 percent, respectively.

The present result of the electrical resistivity of niobium

“8

corresponding to 293 K is 15.9 x 10 ftm; those reported in the recent

_ o _ o literature range from 14.6 x 10 ftm [13] to 16.9 x 10 Qm [12].

The results for hemispherical total emittance and normal spectral

emittance of this work and those in the literature are presented in

figures 4 and 5, respectively. Deviations in the results of various

investigators may largely be attributed to the differences in specimen

surface conditions.

Similar to the earlier results on molybdenum [2], tantalum [21],

and tungsten [22] obtained with the present measurement system, heat

capacity of niobium at high temperatures is considerably higher than

the Dulong and Petit value of 3R. Some of this departure is due to

c - c and the electronic terms. However, they do not account for

p v

the entire difference. Heat capacity above the Debye temperature may

be expressed by

c = A - ~~z + CT + Ac (5)

p T^

-1 -1 -2

where the constant term is 3R (24.943 J mol K ), the term in T is

the first term in the expansion of the Debye function, the term in T

represents c^ - c^ and electronic contributions, and the quantity Ac

43
Niobium

heat

capacity

difference

(previous

literature

minus

present

work

values)

in

percent

2700

m

LOl +

13.6 o o o CO o 6 • ® 40 1—1

CN

<N i *—1 t 1 + + O CN o O • * • O CO o co CN O

Pi CN + I r—1

rH + +

<u3 o LO Cl lO CN 3 o • • • •

4-) 1—1

CnJ CN o 00 3 CM + 1 1—1 + 3 +

0)Q*e o CO LO I 1 CN co

0) o O • * • • H CT\ 1—1 CO CO LO T 1 + + 1 + + O 00 1—1

<fr lO 1 1 o • • • 0 • T—1

CO CN 40 *—i + + 1 + + o 00 LO vO CN o • • • • O LO C4 CO CN 40 1—1 + + 1 1 + O & T 1 1—1 £ o 3 3 a. <x

4-J 3 TO TO o o

CD TO o o 3 3 a B 6 TO TO

}-i <3- CO CO 41 40

03 co lO lO lO NO

CL) cl ON CT\ CTl Ol

>4 r—i

rH 1 1 r~H « 1

4-1a) LD r>. 00 Cl o

Pi I—1

CO3

4-J CO3 3 • 0) rH

ai cu 3 u > tu o 3 4-J •u TO a) TO 3 c0

PI i—l 3

00 03 CO 3 3

-3 cd *H

u 3 U s fo rH

CO a) 3 4-J 3 rH

a) &o a> 4-1 S *H > a) & CCS 3 3 a 3 o u O M l“D hJ Pi cj Pi

44
o

o

in

CvJ

o

o

o

C\J

o

o

n

o

o

o

LU

ozZD

<

oc

LlJ CL

LU

h-

,_|OUJ r‘AH0VdV0 1V3H

45

FIGURE

2.

Heat

capacity

of

niobium

reported

in

the

literature.
Niobium

electrical

resistivity

difference

(previous

literature

minus

present

work

values)

in

percent

O o O • m ! 1 CN + o ao NO o • • CO CN o i—1

CN I + + o 00 pH I^> o e • •

ft pH Cs! o pH

<u CN i i +

!-i 3

4-5 cd

O

m N>

5-i o e ®

a) CTO CN

O -H

a. pH I 1 + H o CTO NO o • • • cn O s—1 i—l + I + o NO NO o o • • • m CO O rH i—1 + i -f

t-i NO i—1

NO CO

cd co NO NO NO

at cto cto CTO CTO sH pH ! 1 t 1 rH

M-l «—1

CN CO <t

at pH rH t—I i—1

Pi

G

•HGO • 5-i 5 1 o

cd >

-i o u 'CT U» at C

cd cd 00 •U • H G Xl Nd u G 5-i G

CO cd cd cd <U 6 rG g > *H at NO H G at at at H Pi H O a

46
90-

o

REIMANN

(1936)

TYE

(I960

a

GEBHARDT

(1966)

£

o

NEIMARK

(1968)

5^80-

PRESENT

WORK

o

o

O O

h- CD

_0I ‘A1IAI1SIS3U "lV3ld_L0313

o

Lf)

o

47

1000

1500

2000

2500

TEMPERATURE,

K
HEMISPHERICAL

TOTAL

EMITTANCE

FIGURE 4. Hemispherical total emittance of niobium reported in the literature.

48
-vO LO

m

ro

cr>

ro

CD

<J> — ro — > CD

C\J LlJ CT) v- ^

(D

LU —

OO

< ^

t- >

I- ID

CD or

CD O LU

cr cd

I- LU

lu cr

CL cl

X

X

LO O

ro ro O O

(WU 099 40 ) 30NV11I1A13 3Vai03dS IVIAIdON

49

1000

1500

2000

2500

TEMPERATURE,

K

FIGURE

5.

Normal

spectral

emittance

of

niobium

at X

=

650

nm

reported

in

the

literature.
represents excess in measured heat capacity at high temperatures, which

for

. . 4%

is not accounted/by the first three terms. The coefficients B(9.6 x 10 ) _ O and C (2. 9 x 10 ) were obtained from data on heat capacity at 200 K

and 1000 K given by Hultgren et al. [23].

Using eq (5) and the heat capacity results of this work, the quantity

Ac was computed for temperatures above 1500 K. The results for Ac in

J mol" 1K

_1

are: 0.2 at 1500 K, 2.0 at 2000 K, 6.3 at 2500 K, and 9.5

at 2700 K.

Although the mechanisms of vacancy generation become important at

high temperatures, it was not possible to attribute the high heat

capacity values entirely to vacancies. To demonstrate this, a crude

estimate of the contribution of vacancies to heat capacity was made

using the method described in a previous publication [2]. The results

indicate that vacancy contribution would be small, less than 0.05 J mol 1

K

at 2000 K and 0.5 J mol 1

K

1

at 2700 K, and would not account for the

high heat capacity values. If the entire difference between measured

and computed [using the first three terms in eq (5)

]

heat capacities is

attributed to vacancies, values of 1.3 eV for vacancy formation energy and

3.5 percent for vacancy concentration at the melting point are obtained.

Both of these values seem to be unrealistic for niobium.

To give a simple expression for the heat capacity of niobium over

a wide temperature range, an empirical term for the quantity Ac in eq (5)

was substituted. Trials indicated that a term in T~* describes the experi4 mental results better than a term in T . The coefficient of this term

was obtained from the results of the present work in conjunction with the

50
values given by Hultgren et al. [23] at temperatures below 1000 K. Then,

eq (5) for the range 300 to 2700 K becomes

4

cp = 24.343 - -9-

6

- yg

1- + 2.9 x

10“ 3

T + 6.4 x 10_17

T

5 (6)

[S -1 -1

where T is in K and c in J mol K . Average absolute deviation of the

individual points from the function over the temperature range considered

is 0.4 percent. Equation (6) is presented graphically in figure 6.

Earlier work on tantalum [21], which also belongs to Group V

^ indicated that the quantity Ac in eq (5) is best represented by a term in

T

3

. However, the results on molybdenum [2] and tungsten [22], which

belong to Group VI, indicated that the same quantity is best described

4

by a term in T . The significance of this is not apparent at this time.

Electrical resistivity of niobium, in the range of present measurements, showed a negative departure from linearity in the curve of

electrical resistivity against temperature. A similar trend was also

observed for tantalum [21].

Acknowledgement

The author expresses his gratitude to Dr. C. W. Beckett for his

continued interest and encouragement of research in high-speed methods

of measuring thermophysical properties. The contributions of Mr. M. S.

Morse in connection with electronic instrumentation are also greatly

appreciated

51
52

FIGURE

6.

Heat

capacity

of

niobium

according

to

equation

(6).
6 . References

[1] Cezairliyan, A. Design and operational characteristics of a highspeed (millisecond) system for the measurement of thermophysical

properties at high temperatures. J. Res. Nat. Bur. Stand. (U.S.) 75C

(Eng. and Instr), 7 (1971).

[2] Cezairliyan, A., M. S. Morse, H. A. Berman, and C. W. Beckett,

High-speed (subsecond) measurement of heat capacity, electrical

resistivity, and thermal radiation properties of molybdenum in

the range 1900 to 2800 K, J. Res. Nat. Bur. Stand. (U.S.) 74A

(Phys. and Chem.), 65 (1970).

[3] Foley, G. M. , High-speed optical pyrometer, Rev. Sci. Instr. 41 , 827 (1970)

[4] International Practical Temperature Scale of 1968, Metrologia _5,

35 (1969)

[5] Tietz, T. E. and J. W. Wilson, Behavior and properties of refractory

metals, Stanford University Press, California (1965), p. 28.

[6] Jaeger, F. M., and W. A. Veenstra. The exact measurement of the

specific heats of solid substances at high temperatures, VI, the

specific heats of vanadium, niobium, tantalum, and molybdenum.

Rec. Trav. Chim. _53, 677 (1934).

[7] Lowenthal, G. C., The specific heat of metals between 1200 K and

2400 K, Australian J. Phys. 16 , 47 (1963).

[8] Kraftmakher, Ya. A., Vacancy formation in niobium. Solid State

(USSR) , _5, 696 (1963) .

[9] Conway, J. B., and R. A. Hein, "Enthalpy Measurements of solid

materials to 2400 C by means of a drop Technique" in Advances

in Thermophysical properties at extreme temperatures and pressures,

S. Gratch, ed . (ASME, New York, 1965), p. 131.

[10] Kirillin, V. A., A. E. Sheindlin, V. Ya. Chekhovskoi, and I. A.

Zhukova, Experimental determination of the enthalpy of niobium

in the temperature range 600 to 2600 K, High Temperature, _3, 357 (1965) .

[11] Reimann, A. L., Some high-temperature properties of niobium,

Phil. Mag. 22 , 34 (1936)

[12] Tye, R. P., Preliminary measurements on the thermal and electrical

conductivities of molybdenum, niobium, tantalum, and tungsten,

J. Less-Common Metals, _3, 13 (1961).

53
[ 13 ]

II II Gebhardt, E., W. Durrschnabel , and G. Horz, J. Nucl. Mat. 18 , 119 (1966).

[14] Neimark, B. E., and L. K. Voronin, Thermal conductivity, specific

electrical resistivity, and total emissivity of refractory metals

at high temperatures, High Temperature, _6 , 999 (1968).

[15] Cost, J. R., Emissivities of niobium and niobium-nitrogen solids

solutions, Trans. Metall. Soc. AIME 224 , 634 (1962).

[16] Petrov, V. A., V. Ya. Chekhovskoi, and A. E. Sheindlin, Experimental

determination of the degree of blackness of niobium at temperatures

of 1200 to 2500 K, High Temperature, _1 , 416 (1963) .

[17] Gordon, A. R., and G. F. Muchnik, Determination of the emissivity

of niobium as a function of the roughness of the surface, High

Temperature, _2, 505 (1964).

II II [18] Horz, G., W. Durrschnabel, and E. Gebhardt, Hemispherical total

emittance of niobium, J. Nucl. Mat. 17, 277 (1965).

[19] Whitney, L. V., The temperature scales of columbium, thorium,

rhodium and molybdenum at 0.667 y , Phys. Rev. _48, 458 (1935).

[20] Khrustalev, B. A., I. P. Kolchenogova , and A. M. Rakov, Spectral

coefficients of tantalum, molybdenum and niobium radiation,

High Temperature, _1 , 13 (1963).

[21] Cezairliyan, A., J. L. McClure, and C. W. Beckett, High-speed

(subsecond) measurement of heat capacity, electrical resistivity,

and thermal radiation properties of tantalum in the range 1900

to 3200 K, J. Res. Nat. Bur. Stand. (U.S.) 75A (Phys. and Chem.)

1 (1971).

[22] Cezairliyan, A., and J. L. McClure, High-speed (subsecond) measurement of heat capacity, electrical resistivity, and thermal radiation

properties of tungsten in the range 2000 to 3600 K, J. Res. Nat.

Bur. Stand. (U.S.), 75A (Phys. and Chem.), in press.

[23] Hultgren, R. s R. L. Orr, P. D. Anderson, and K. K. Kelly, Selected

Values of Thermodynamic Properties of Metals and Alloys, John Wiley,

New York (1963)

.

54
Chapter 4

DEPARTURE OF EMITTANCE - RESISTIVITY RELATION

FROM THEORETICAL PREDICTIONS FOR

REFRACTORY METALS AT HIGH TEMPERATURES

Ared Cezairliyart

National Bureau of Standards

Washington, D.C. 20234

Based on the free electron theory of metals and Maxwell's

electromagnetic theory of radiation, a relation between thermal

radiation emitted by a metal and its electrical resistivity was

obtained by Aschkinass [1] . This was further modified and refined

by other investigators [2,3]- The general relation expressing

hemispherical total emittance, e , as a function of electrical

resistivity, p, isn

e = E (-D

1+1

C (pT/c 2 ) ±/2

(1)

i=l

where T is temperature in K, c 2 is the second radiation constant and

C_^ are constants obtained in the derivation. For simplicity, e will

be referred to as emittance.

Different investigators have used different number of terms

(ranging from one to four) in the above equation. Equation (1) for

n = 4, given by Davisson and Weeks [3], is

e = 0.8992(pT/c 2 ) 1/2 - 0.9047(pT/c 2 ) + 1 . 149 (pT/c 2 ) 3 / 2 - 1 . 245 (pT/c 2 ) 2 (2)

55
In this study the validity of Eq. (2) is checked using the results

on four refractory metals, niobium, molybdenum, tantalum, and tungsten

above 2000 K. Emittance and electrical resistivity were measured

simultaneously by a transient technique. This technique is based on

resistive self-heating of the specimen, by the passage of high currents

through it, from room temperature to near its melting point in less

than one second, and measuring the pertinent experimental quantities

(voltage, current, and temperature) with millisecond resolution. Data

taken during the heating period and the initial cooling period following

the heating period are used to determine emittance as well as electrical

resistivity. The details on the measurements are given in other

publications [4, 5, 6, 7].

Computed emittances, using C 2 = 1.4388 cm K in Eq . (2), in terms

of measured resistivities were compared with experimentally obtained

emittances. Emittance and electrical resistivity values were corrected

for dimensions at the specimen temperature using thermal expansion

results on niobium [8,9], molybdenum [8,9,10,11], tantalum [10,12], and

tungsten [12,13]. The results on the refractory metals are shown in

Fig. 1 in terms of the quantity e /e, where e and e are measured and

m m

computed emittances, respectively. It may be seen that, in general, the

difference between experimental and theoretical results decreases with

increasing temperature.

56
TUNGSTEN

57

2000

2500

3000

3500

TEMPERATURE,

K

Figure

1.

Variation

of

the

ratio

of

measured

emittance

(e

)

to

computed

emittance

(e)

as
References

1. Aschkinass, E., Ann. d. Phys . 1_7, 960 (1905).

2. Foote, P. D., Bull. Nat. Bur. Stand. (U.S.) 11, 607 (1915).

3. Davisson, C., and J. R. Weeks, J. Opt. Soc. Am. _8, 581 (1924).

4. Cezairliyan, A., J. Res. Nat. Bur. Stand. (U.S.), 75A (Phys. and

Chem. ) , in press

.

5. Cezairliyan, A., M. S. Morse, H. A. Berman, and C. W. Beckett,

J. Res. Nat. Bur. Stand. (U.S.) 74A (Phys. and Chem.), 65 (1970).

6. Cezairliyan, A., J. L. McClure, and C. W. Beckett, J. Res. Nat.

Bur. Stand. (U.S.), 75A (Phys. and Chem.), 1 (1971).

7. Cezairliyan, A., and J. L. McClure, J. Res. Nat. Bur. Stand. (U.S.),

75A (Phys. and Chem), 283 (1971).

8. Edwards, J. W., R. Speiser, and H. L. Johnston, J. Appl. Phys. 22 ,

424 (1951)

.

9. Amonenko, V. M., P. N. V'yugov, and V. S. Gumenyuk, High Temp. _2,

22 (1964).

10. Worthing, A. G., Phys. Rev. _28, 190 (1926).

11. Rasor, N. S., and J. D. McClelland, J. Phys. Chem. Solids, 15 ,

17 (1960).

12. V'yugov, P. N., and V. S. Gumenyuk, High Temp. _3, 879 (1965).

13. Forsythe, W. E. s and A. G. Worthing, Astrophy. J. 6JL, 146 (1925).

58
Chapter 5

THE RELATIVE ENTHALPY AND HEAT CAPACITY OF MOLYBDENUM

METAL FROM 1170 TO 2100 K

By

Shigeru Ishihara and Thomas B. Douglas

Abstract

The enthalpy of two samples of molybdenum metal at least 99.8%

pure (one triply zone-refined) was recently measured relative to 298 K

at eleven temperatures from 1170 to 2100 K using a precise droppingtype method, and showed on simple smoothing a standard deviation of

about 0.2%. Check measurements on synthetic sapphire (standard-sample

Al^O^) were made at 1170 and 1700 K, and agreed excellently with earlier

precise NBS data. The smoothed enthalpy and corresponding heat-capacity

values for molybdenum are compared with the results of 17 previously

published sets of results in the same temperature range. Subsequent

planned measurements on this metal will complete the data for the whole

temperature range 273 K to approximately 2500 K. Errors are estimated.

I . Introduction

The recent experimental results on molybdenum metal reported in

this chapter for the first time were obtained as part of an NBS-sponsored

program and primarily for the purpose of establishing suitable samples

of this metal as a high- temperature heat-capacity standard. These results

are included in this report because they are of equal importance in the

AFOSR-sponsored program currently devoted to thermodynamic research on

the high-melting-point metals and their Aerospace-important compounds:

molybdenum metal is a key material in this class, but many of its

previously published heat capacities disagree seriously at the higher

temperatures

The relative enthalpy of pure A^O^ (as a standard reference material)

was recently measured at the Bureau from 273 to 2250 K [1]-*-. Two widely

different dropping-type apparatuses were used over the respective temperature ranges 273 - 1173 K and 1173 - 2250 K. The results show almost perfect

continuity at 1173 K (as well as at 273 K with earlier precise NBS adiabaticNumbers in brackets denote literature references at the end of this

chapter

59
calorimetry results from 15 to 380 K on a comparable sample) , with

estimated accuracies of enthalpy (relative to room temperature) of

±0.1 and ±0.2% in these two respective higher temperature ranges.

As recognized by many people, a metallic standard also is desirable;

molybdenum was chosen because of its high melting point (2890 K)

,

freedom from transitions, and availability in high purity. The measurements over the range 1170 - 2100 K have been completed, and are reported

here. After the results on molybdenum to still higher temperatures (up

to approximately 2500 K) have been obtained, a comparison will be available with those (1900 - 2800 K) by a widely different method, a precise

millisecond pulse-heating method developed at NBS in the AFOSR-sponsored

program [21]

.

The enthalpy or heat capacity of molybdenum has been measured by

many other workers (by several, to within 100 K of the melting point),

and later in this chapter we compare 17 sets of these results with ours. Although some workers have made no claim to even moderately good accuracy,

the wide disagreements among the others on molybdenum (by as much as a factor of 1.5 for the heat capacity at 2500 K ! [ 21 ] ) are not easy to explain

or rationalize. In an effort to achieve a much higher order of reliability

of our results, we have paid particular attention to what are probably the

most serious sources of error in such measurements (sample- temperature

measurement, and sensitivity of the enthalpy and heat capacity of this

metal to low-atomic-weight impurities) . Details relevant to these sources

of error are discussed in later sections of the chapter.

II . Samples

The enthalpy measurements were made on rods of three different

samples of molybdenum—subsequently distinguished as A, B and C—-of

two different types. Samples A and B were really different specimens

of the same sample, one previously drawn and annealed, and presently

stocked by the Office of Standard Reference Materials of the Bureau.

Sample C was 3-pass electron-beam zone-refined polycrys talline material

machined to 0.35" diameter and obtained from Materials Research Corporation, of Orangeburg, N.Y., who classified it as of "grade 1" and stated

a purity of 99.992%. Details of analyzing and treating the three samples

prior to the enthalpy measurements are as follows.

Qualitative Spectrochemical Analyses -- All three samples were

analyzed separately, and the results are given in Table 1A. (In the case

of Sample C, the purest sample, special care was taken to remove all sur- face contamination, consume the sample completely in the arc excitation,

and use a high-purity reference sample of molybdenum.) This technique

omits the important nonmetals, but indicated a total metallic impurity of

less than 0.02% for Samples A and B, and a still smaller figure for

Sample C which is consistent with the supplier's claimed purity stated

above

.

60
Spark-Source Mass Spectrometry — Two rods from the lot from which

Samples A and B were taken were first etched in nitric acid, washed in

distilled water, then boiled in distilled water to clean the surface.

These specimens were then presparked to identify and remove any remaining

surface contamination. The mass-spectra metric results are given in

Table IB. Note the near-completeness of the coverage of elements, and

particularly the low levels of those low-atomic-weight elements analyzed

for (to which the enthalpy and heat capacity of molybdenun^ as calculated

from the data, are particularly sensitive, as discussed in Section V).

This analytical technique showed a total impurity of 0.02% by weight of

the elements detected, and set a total upper limit of (an additional)

0.02% by weight to the elements (except F, Ne, Na, and Ti) partially

masked by major interference.

Electronic Characterization -- This technique was applied to specimens

typical of Samples A and B only. The specimens were cleaned with ethyl

alcohol, then heavily electroetched in an electrolyte of sulfuric acid

and methyl alcohol to remove surface contamination. For this technique

adequate prior annealing of the specimens was important. Annealing for

one hour at 1000°C (slow cool) proved inadequate, but the adopted con- ditions (two anneals, the second for two hours at 1200°C with slow cooling) was judged sufficient. The resistance ratio (273 K to 4 K) was then

found to be 70. This ratio was interpreted assuming the residual resistance (at 4 K) to be due to equal atomic concentrations of the likely

metallic contaminants W, Ta, Nb , and Zr; on this hypothetical basis

the total impurity was calculated to be 0.2 weight % (0.1 atomic %)

Note that these levels of impurity far exceed those found by the spectrochemical and mass-spectrometric analyses detailed above. The cause of

the disagreement is not known.

Sample Annealing Prior to Enthalpy Measurements — After etching

with HNO^ , then with HC1 , with subsequent treatment with boiling water.

Sample A was annealed for two hours at 1200°C in 10 cm pressure of argon.

(After this etching, the surface was found to discolor in moist air but

without detectable weight gain; nevertheless, moisture was excluded thereafter as a precaution.) Sample B was not deliberately annealed, although

the first enthalpy measurement on it was made only after it had been held

in the furnace at about 1425°C for about 40 minutes, and these conditions

may have effected its annealing; at least, a repetition of this heating

did not change its enthalpy detectably (see Table 2) . Sample C was neither

etched nor annealed; it had not been subjected to mechanical stress since

its zone refinement, so that annealing was believed unnecessary.

An inspection of the data (Table 2, Section IV) will show that despite

the apparent greater purity of Sample C, Sample A was chosen as the principal one. There were several reasons for this decision. Since the primary

aim was to establish calorimetric values for an easily accessible standard

material, an important factor was that the molybdenum represented by Samples

A and B is more readily available and less costly than the zone-refined

61
Table 1A

Qualitative spectro chemical analyses of the molybdenum samples,

in weight %a

Element

Sample A

(1/8" rod)

Sample B

(1/4" rod)

Sample C

(triple- zone-refined

1/2" rod)

(weight %) (weight %) (weight %)

A1 .001 - .01 .001 - .01 _?

Ca <.001 <.001 <.0001

Cu <.001 <.001 <.0001

Fe .001 - .01 .001 - .01 <.0001

Mg <.001 <.001 <.0001

Mo >10 >10 major constituent

Si <.001 <.001 <.001

W - - _?

“Ag, As,

La, Mn,

Th, Tl,

{ - xn tion of

Au, B, Ba, Be, Bi, Cd , Ce, Co, Cr, Ga, Ge, Hf , Hg, In

Na, Nb, Ni, Os, P, Pb , Pd, Pt, Rh, Ru, Sb , Sc, Sn, Sr

U, V, W, Y, Zn, and Zr also were analyzed for but not

the above table means the same.) The estimated limit

an alkali metal is 0.005%.

Ir, K,

Ta, Te,

detected

of detec

62
Table IB

Mass-spectrometric analysis of a representative specimen

of Samples A and B, in ppm by weight^

Elements Measured Elements Showing Interference

Element ppm Element ppm Element ppm Element ppm

Ag 1 Sb 0.5 Ar <20 N <10

A1 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 Cl < 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

H and He were not analyzed for, and interference was complete for F,

Ne, Na, and Ti. In addition to the elements listed in the table, the

following were reported as not detected and to be considered as present

below stated amounts (all less than 1 ppm each; 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, f, Yb, and Zr.

63
(Sample C) . (The only disadvantage of Sample B over A was its more

compact shape, requiring longer times to reach temperature equilibrium

in the calorimetric apparatus.) Additional facts weighing against the

choice of Sample C are that it is believed to be less homogeneous in

impurities, and also its characterization thus far is much less complete,

as indicated earlier in this section.

Ill . Calorimetric Apparatus and Method

The apparatus used for the present work is essentially the same as the one used for earlier work and is described in ref. [32]. Materials

studied with this high temperature enthalpy apparatus include graphite [32]

,

aluminum oxide [33], tungsten [34], beryllium aluminate (BeO 'A^C^) [35] , pyrolytic graphite [36], and SRM 720 synthetic sapphire (AI 2 O 3 ) [1].

This "drop" type apparatus consists of four major parts: one, an induction heating furnace to heat the specimen to the desired temperature;

two, an automatic optical pyrometer to measure and control the temperature

of the furnace and sample; three, an adiabatic receiving type calorimeter

to measure the heat transfer from an encapsulated sample; and four, a semi-automatic lifting device to uniformly accelerate and decelerate the

capsule suspended on a tungsten wire.

A capsule (empty or containing a specimen) at the furnace temperature

is lifted into the calorimeter at a uniform acceleration of 9.1 meter/sec ^ with an elapsed time of around 600 milliseconds. The shutter and shields

are closed in the same way for each lift. The rise in the calorimeter

temperature is measured with an absolute copper resistance thermometer

which has been compared with a NBS calibrated platinum resistance

thermometer. Knowing the heat equivalent of the calorimeter enables

us to determine the enthalpy change of the capsule and contents. One

experimental point consists of enthalpy measurements of two lifts, one

on an empty capsule and another on the same capsule with a molybdenum

sample. The difference is the enthalpy change of the molybdenum specimen

after applying a small correction for the change in final calorimeter

temperatures near 298.15 K. This is true if the temperature of the

capsule, radiation losses, flight time, and shutter and shield closures

are the same for both lifts during the 0.1 second interval the capsule

is in the cold zone at the time of the transfer.

The induction heated furnace is powered by a 7-1/2 kilowatt oscillator operating at 385 kH with a water cooled copper working coil in a shape of a solenoid with shorter spacings near the ends to decrease the

gradient of the induction field near the furnace core, where the capsule

hangs during the heating operation. One-half centimeter from the bottom

of the capsule is a diaphragm with an eighth inch hole through which the

automatic optical pyrometer sights in the bottom of the capsule for

temperature measurement and control. Placed on the axis of the working

64
coil and along the center of the quartz tube is a hollow graphite

susceptor which couples with field and serves as the heating element.

Concentric layers of carbon black, 25 my particle size, and fine silicon

carbide powder are used for thermal insulation inside the quartz tube

because they do not appreciably couple with the working coil up to

2300 K. After thoroughly degassing the furnace parts by heating to

2800 K, the furnace is operated in a 1 cm 3 /sec flow of argon at 10 cm pressure

An exploratory graphite probe the size of our capsule was used to

measure the axial temperature gradient along the graphite core. This

showed that the temperature along the axis is uniform to ±2-1/2 K for

20 centimeters from the bottom of the capsule at 2300 K after two hours

furnace warm-up time. With sufficient warm-up time the temperature

variation was found to be too small to determine with a visual pyrometer.

This test plus other experimental tests--including variation of flight

time, capsule material, sample size, suspension wire size, and pyrometer

target, e.g. sighting on the diaphragm, with no change in test results

give us confidence that the temperature at the capsule bottom is the same as the temperature of the specimen, as well as we can determine.

The automatic optical pyrometer developed by Leeds and Northrup

Company and used in our work is an instrument of high precision and

sensitivity for measuring the brightness temperature of objects or substances between 1175 and 2800 K. A fast response photomultiplier

alternately sees the target image and a filament image of an internally

mounted standard lamp and automatically adjusts the reference lamp

until the photomultiplier output level for both is the same. The

apparatus has been modified many times to incorporate the many improvements that have been made on the instrument later. It requires a target

size of somewhat less than one-eighth inch diameter at a distance of

twenty inches and a means to measure the output current of the standard

reference lamp. This instrument has been periodically calibrated by

the radiation pyrometry section of NBS . The uncertainty of this instrument is now estimated 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 an important parameter in this enthalpy

apparatus, 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 is optically

clean.

The adiabatic calorimeter used for this work was designed and

developed by E. D. West in 1962 and the final modification was made in

late 1966. Its heat equivalent is around 2900 joules per degree K and

operates in the range 25 to 65°C. The apparatus has been repeatedly

checked (8 times since the last modification) by electrical calibration

and the standard deviation of the accumulated calibration data points

65
from a smoothed curve representation is estimated to be ±0.004% for a temperature interval of five degrees. The electrical energy supplied

to the calorimeter for calibration is determined by the voltage, current,

and heating interval on a heater element in the calorimeter, and is

corrected for the leak rate which is small and almost constant. All

instruments used in absolute measurements of EMF, resistance, time, and

temperature have been periodically calibrated through the services

available here at the NBS

.

Briefly, the adiabatic calorimeter consists of two concentric

cylinders, one made of nickel and the other of copper, in contact with

each other with a ring 45 mm diameter and 8 mm thick. This introduces

a time constant of about five minutes and reduces the temperature control

problems associated with the surrounding adiabatic shield with moderate

or high rate of heating. Surrounding the adiabatic shield is a guard

jacket controlled at temperatures slightly below the temperature of the

adiabatic shield. The leak rate is thus kept small and almost constant

throughout the temperature range of the calorimeter. The absolute copper

thermometer and differential thermometers, also copper, are wound around

the copper cylinder and epoxied on for good thermal contact.

The lifting device used in this work is an operational amplifier

designed to generate a signal to uniformly accelerate the hot capsule

from the furnace to the calorimeter. This is accomplished by electronic

double integration of a constant voltage source. Thus, the tension in

the wire is smooth and the time of flight is constant for a given setting.

A solid state interval timer is used to monitor the flight time of the

capsule and the time intervals do not vary by more than ±2 milliseconds

out of 600.

IV. Enthalpy Data and Empirical Equations for Relative

Enthalpy and Heat Capacity of Molybdenum

A chronological sequence of random furnace temperatures has been

determined by the table of random numbers selected by a computer. This

method was employed so as not to introduce a bias to the measurements due

to the changing condition of furnace insulation or the gradual change in

the automatic optical pyrometer. A day’s run usually consists of four

lifts, two empty and two filled with molybdenum sample. The last lift

usually duplicates the first lift of the day, thus the agreement of the

results is an indication that the warm up time of the furnace was sufficient to settle the gradients along the furnace core. There is usually

a small but insignificant difference in the results between the two lifts

and this small correction, nevertheless, has been applied as a drift

correction and has somewhat improved the precision of the enthalpy data.

The weight of Sample A was constant to ±.06 mg below 2000 K, which

is about the limit of the balance detection. An observed increase of

0.30 mg (.004%) at 2000 K and 0.40 mg (.005%) at 2100 K was too small

to apply a correction. (The assumption was made that the pickup is due to

66
carbon from the susceptor.) Samples B and C, which were not subjected

to these high temperatures, did not change weight.

A small correction for the difference in the final calorimeter

temperature from the reference temperature, 298.15 K, is necessary. The

difference for the 2100 K run amounted to a maximum of 17-1/2 K and 2%

of the net heat measured for that furnace temperature. These corrections

were applied using the heat capacity evaluations from references [30, 37,

38] and are believed to be accurate to at least 5%, thus contributing an error to the corrected enthalpy of the sample no greater than 0.1%.

The results of the enthalpy measurements on molybdenum are tabulated in table 2. Each data point represents the result of two lifts, one on the empty capsule and another on a filled capsule. The empty

capsule represents 54.4%, 54.2%, and 54.3% of the gross heat measured

for the molybdenum filled capsule at 1175, 1600, and 2100 K respectively.

The capsule itself was machined from a molybdenum rod claimed to be of

99.95% purity.

Two convenient empirical equations (each with only 4 or 5 disposable

constants) have been selected to represent the enthalpy data relative to

298.15 K. The enthalpy values obtained from either equation differ from

each other by less than 0.03% throughout the observed temperature range

(well within the precision of our measurements) . Values of heat capacities derived from either equation will differ by less than 0.25% up

through 1900 K. At 2000 K and 2100 K the difference is 0.39% and

0.86% respectively.

H

T

“ H

298.15

= A + BT + CT

2 + D exp (-E/T) , j/M (1)

for 1175 < T < 2100, K

where

A = -6.18063 (10

3

)

B = 21.6641

C = 3.24129 (10

-3

)

D = 1590 (10

3

)

E = 16,000

The coefficients A, B, C, and D were determined by the least squares

relative fit method for a selected value of E = 16,000. The sum of the

squares of the relative deviations for values of E = 10,000 to E = 22,000

is essentially the same, hence E = 16,000 is taken to be "typical" of the

sets of equation that can be used.

67
Table 2

Individual enthalpy measurements on molybdenum

Temperature T

Date of run

(all dn 1971) Sample

Heat from sample

to calorimeter at

298. 15K (observed)

TJ TT T 298.15

(observed) 3

Deviation

from

Eq (1)

(IPTS-68, K) (joules) (j oules/mole) (%)

1 1 7A /. J.

r May 3 A 2021.15 23635 +0.08

±± /U . H

4 3 C 3431.71 23585 - .14

r- 10 A 2090.62 24447 + .00

1198.6 i 10 A 2089.30 24431 - .06

r

7 A 2346.46 27439 - .01

i onn i y

7 A 2347.79 27454 + .05

1299.1 S June 4 A 2342.19 27470 + .11

4 B 2348.05 27457 + . 06

1 9QQ 6 ^ April 7 A 2610.01 30522 + .05

7 A 2609.50 30516 + .03

r 29 A 2874.85 33617 + .01

1499.0 < 29 A 2876.27 33634 + .06

i June 1 B 2864.41 33592 - .06

1601 6 2r April 5 A 3151.20 36850 - .15

L 5 A 3149.64 36832 - .20

r 2 A 3422.29 40021 - .24

• 1 «L

2 C 5823.24 40021 - .24

1 6QQ 9 < r May 24 B 3427.65 40201 + .20

1077 • Z N 24 B 3424.81 40168 + .12

1 ROO 7 v —

5 A 3732.22 43643 + .19

lOUU • / \ 5 A 3732'. 76 43649 + .21

1 £QQ A «f April 22 A 4020.16 47010 - .13

-L 077 o 0

L 22 C 6828.85 46988 - .06

onm 9 <

r* 9 A 4334.30 50684 - .01

ZUU J. « 4 l

9 A 4337.44 50721 + .06

910? A <r May 19 A 4657.48 54463 - .04

i L 19 A 4657.67 54465 - .03

^o: 1 mole = 95,94 g; density = 10.2 g/cm^. The sample mass was redetermined

in each run.

68
The second equation is as follows, and is in a form often more

convenient for computations not using a computer.

Hr ~ H

2g8 15 = F (T - 298.15) + (G/2) (T

2 - 298. 15

2

) +

(H/3) (T

3- 298. 15

3

), j/M (2)

for 1175 < T < 2100, K

where,

F = 25.4998

G = -2.13386 (10“ 4

)

H = 2.88650 (10“ 6

)

The estimated standard deviation of the observed points for both

equations (1) and (2) is 0.13%. No attempt has been made to join

smoothly the ends of the equations (1) and (2) at 1175 nor at 2100 K

with results reported by previous investigators. The spread in observed

points by various investigators as shown in figures 1 and 2 shows that

more accurate data are needed both from room temperature to 1175 K and

also to higher temperatures (above 2100 K)

As an overall check on the apparatus, one measurement of H - ^298 15

an(^ ° ne ^1702 2 ~ ^298 15

were ma^e on a SRM-720 sample

of synthetic sapphire after most of the measurements of Table 2 had been

completed. The values obtained were 99,841.5 and 169,454 j/mole, respectively. The former value differs by 0.01% from a determination made on

this material by another more precise method [1, 39]. The latter value

differs by 0.06% from previous determinations using our apparatus [1].

All furnace temperature is based on the International Practical

Temperature Scale of 1968. Table 3C was prepared so that the readers 5 if they wish, can readily convert our values to the basis of the IPTS-48

scale, on which scale the preponderance of the investigators have reported

their work on molybdenum.

69
Table 3A

Heat capacity and enthalpy of molybdenuma

T

(IPTS-1968 , K)

C°

P (Joules /mole-K )

i_r 0 ij o T 298.15

(Joules/mole )

1173.15 29.29 23697

1200 29.47 24486

1250 29.81 25968

1300 30.16 27468

1337.58 30.42 28606

1350 30.52 28984

1400 30.88 30519

1450 31.26 32073

1500 31.65 33646

1550 32.06 35238

1600 32.49 36852

1650 32.93 38487

1700 33.40 40146

1750 33.90 41828

1800 34.42 43536

1850 34.96 45270

1900 35.53 47032

1950 36.13 48824

2000 36.76 50646

2050 37.42 52500

2100 38.11 54389

a

l mole = 95.94 grams [31]

H

298 15

~ H

273 15

= joules/mole [30]

This table was calculated from Eq Cl)

70
Table 3B

Heat capacity and enthalpy of molybdenuni

T

(IPTS-1968, K)

C°

P (Cal/Mole-K)

O H° — H

T 298.15

(Cal/Mole)

1173.15 7.00 5664

1200 7.04 5852

1250 7.13 6207

1300 7.21 6565

1337.58 7.27 6837

1350 7.29 6927

1400 7.38 7294

1450 7.47 7666

1500 7.56 8041

1550 7.66 8422

1600 7.76 8808

1650 7.87 9199

1700 7.98 9595

1750 8.10 9997

1800 8.23 10405

1850 8.36 10820

1900 8.49 11241

1950 8.64 11669

2000 8.79 12105

2050 8.94 12548

2100 9.11 12999

^1 cal = 4.1840 joules

1 mole = 95.9^ grams [31]

H° - H° = 142 cal/mole [30]

298.15 273.15

This table is identical to Table 3A but in calorie units.

71
Table 3C

Corrections for molybdenum to convert to IPTS-48

and IPTS-68 scales. (See ref. [24])

Temp

IPTS-68 or 48

(K)

C Delta p

( V48 " ((V68

(j oules/mole-K)

Delta H

®48 - (H) 68

(joules/mole)

1100 0.086 21.4

1150 .089 25.8

1200 .092 30.3

1250 .095 35.0

1300 .098 39.8

1350 .059 44.3

1400 .062 47.3

1450 .065 50.4

1500 .069 53.7

1550 .072 57.2

1600 .076 60.8

1650 .080 64.6

1700 .085 68.6

1750 .089 72.8

1800 .095 77.3

1850 .100 81.9

1900 .106 86.8

1950 .113 91.9

2000 .119 97.3

2050 .127 103.0

2100 .134 109.0

72
V . Comparison with Previous Investigators and Compilers

The high practical importance of the high-temperature thermal properties

of molybdenum metal is reflected in the large number of experimenters who

have reported measurements of its enthalpy or heat capacity. Table 4

summarizes, in approximately chronological order, all these investigations

that we have found who report values in the temperature range of the present

work (1170 - 2100 K) . Most of this work employed either drop-type calorimetry (which measures relative enthalpy directly) or pulse-heating calorimetry

(which measures the heat capacity) . An exception is the work of Lowenthal,

which used a.c. heating of the sample, and derived the heat capacity from

its observed temperature fluctuations.

Figures 1 and 2 show a graphical comparison of our values with those

of the earlier investigators. In Fig. 1 the base line represents our smooth

values of enthalpy relative to 298.15 K as given by Eq (1) (Section IV), and

the points represent the percentage deviations from this base of the

individual unsmoothed values, including ours (all adjusted to 298.15 K

whenever necessary) . (Curves are given only in those cases where only

smoothed values were reported.) Figure 2 shows total heat capacity vs temperature; the solid curve represents our smoothed values as given by

the derivative of Eq (1), and the points are unsmoothed values, including

ours. When the measurements were of enthalpy, the plotted values are simply

AH/ AT from the unsmoothed enthalpies for pairs of successive temperatures

(the curvature corrections are negligible in this case), with the following

exception. The enthalpy values at relatively close temperatures were first

averaged so as to make each interval AT as close to 100 K as practical, in

order to afford a fairer comparison of precision from one investigator to ano ther

Figure 1 shows that the enthalpies of most of the other observers are generally lower than ours. The closer balance between positive and negative

deviations of heat capacity (Fig. 2) is due partly to the fact that this

graph, unlike Fig. 1, includes those observers who did not measure enthalpy

but only heat capacity. In Fig. 2 the majority of points lie within ±5% of our

curve, and almost all lie within ±10%. The deviations from our results of

the smoothed values of enthalpy and heat capacity adopted by three sets of

well-known recent compilers are shown in Table 5. Since these adopted

values are based on much of the work (except the more recent) represented

in Figs. 1 and 2, they reflect some of the same trends. Nevertheless,

Figs. 1 and 2 are actually more revealing: they show graphically the wide

spread among some individual observers, and at the same time they suggest

that in some cases poor agreement is largely attributable to poor precision.

VI. Discussion of Errors

The relatively good precision of cur enthalpy measurements is shown in

the last column of Table 2 and in Fig. 1, and the small degree to which

the precision limits the reliability of our results (including our claim

73
Cn pHO3P

cdup

cd3P3o

<r

0)

IdH

tn P PP O

cd o P o 4-1 I—I g

0) 3> 3 o P P 4-i cd

4-1 r-H o cd 3 3

1-1 3 3 P 3 p cd tn 3 tH B o p3 4-4 P o 3oP

cu

1-4

4-1o

<DG

•r-4 rHp3o

>N /—N TJ p 4-1 tn /-s /-"N P #

cu 3 o • p S • CD Cu 3 s p p •H oa o CJ a) 3 3 p 3 3 CJ 3 a p O B cd 3 'w' P CM 4-» 3 CJ CX 3 0) CX O V S'? •H 3 o • CU p o b B £-? O 6s? o 3 3 3 P 3 CO s—/

-H LO 3 • <t 1—1 3 3 4-J 0) 3 p • P p V +1 CX 44 O 4-J 3

CO V-P cu CO &-? CM

O 3 a 3 3 3

<u B^S cu LO 1 3 P ••

A •H 3 ex

B rH

CO 3 3 o co rH CX 3 3 to 0 •H 3 •H

p

p

V 00 +1 • 3 4-J

O o 6s? 3 'w' 4-J s

1-1 cd < o #\ ' ' 3 3 3 O

p 3 cd

cd 1 | > m | • • j 3 3 1 3 o 3 1 1 1 3 >N 3 3 i i 3 1 • CO 1 • O Cn Co 3 ! 3 • 3 1 1 i P 4-J § p o o M • p 3 P P O o 3 3 •H 3 rO

cu 3 s pp 3 3 •H •H CX

O 3 3 O 4-J

p 3 P 3 3 3 CJ 3 Cu ex * 3 3 •H

4-) 3 p

p o < 1 3 3 • • • CJ 3 3 & 3 3 o 3 p o 3 0 P CX CX P P P Td 3 O B 3 3 o >-, P °H 1—1 B p 3 B B 3 O 3 0» S'? 3 °rH •H P E CX 1 3 4-J •H H P O P p m 4-J PI

CO 3 O P 3 3 <r 3 3 • 3 3 S'? CJ P 3 Bi OO 1 3 3 B S'? B CM B B 1—1 < 1 P m 00 n -3 o 3 O “H LO CM A H •H 1 P •H o 6-? •H P CJ CM o cx p o O 4J p p m § > • CO p c c 3 1—1 o £ 3 cn • • 3 CO 3 • 3 3 o 1 o W <d c CO 3 w o o w V w w o co 1 1 V CM cn P'W' CO CO CO ON CO CM 00 O o CM o O m m 00 ON o CM

cu Oi 1^

m CM 00 ONO o NO NO

O 1—1

CM CO NO o o

60 00 NO co NO CO CO CO CO o 00 CO rH o NO 00 00 00 1—1 3 ! 1 1—1 t 1 CM 1—1 p CM CM t—1

CM CN rH CM CN CM CN CM CNj CM

cd NO P i 1 1 1 1 1 1 1 1 CN 1 i i 1 i 1 i 1 1 1 CO LO CO CO NO O O CM o o O 00 CO o O

P. t'- NO r^. 00 o o o o o in o o m 00 NO

m ON o e Csl LO OnI rH CO CO f—1

co ON t—i

CN CO

m CM CM o ON i—I

<U \—1 1—1 »—i

rH rH 1 1 i—1

CN i—1

rH

H *\ CO 00 00 00 00 3 00 3 3 3 3 o 00 3

•H

H •H •HH 3 °H

p

p 4-J 4-1

p •H

p

p 3 3 cd 3 cd

p 3 o (X CX Cl, cx CX p 3 3 Cu ex 3 3 rH 3 Cu cu CX 3 p P o O O o O o 1 P P O o P 1 P rH 3 1 o o o P o p 14 l-i 3 3 3 3 I 3 3 I •rl P II 3 3 3 3 3

cu

Q P P P P p 3 3 P P 3 3 u

QQ

Q

Q S CO co 3 3 3 • CO 1 1 rH t 1 1 1 O o rH 3 3 3 3 • 3 P P P P-, H 3 P

i-i 00 <1- CM NO NOO

O t 1 ? 1

fi rH CN CN CO 00 00

O rH «—1

cd CO co LO LO LO LO NO NO NO NO NO NO NO NO NO NO NO NO

cu ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON

>4 1 1 1 1 rH1 1 1 1—1 1—1 1—1 1—1 l—1 1 1 1 1 r-H 1 1 1—1

rH 1—1 1 1 1 1 1—1 < 1 rH rHp3

cu

O

u i i P £ 1—1 i 1 1 1 1 00 1—1 i 1 1—1 1 1 1 ) 1

1 1 i i 3

<u 1 1 | , r 1 f ) 1—1

r—*l 1—iCN o 1 1 Csl COm CN 00 ON o rH 3

1-4 CM COm NO CO rH »—i 1—1

rH 1—1 ! 1 i—1

CM rH CM CN CM 3 | J i i i i 1 1 1 1 I 1 i i i i <r\ i NO 1 1 1 i 1 1 1 3—1 1 1—i 1 1 3

44 ON < 1 °H

CU 1 1 1 1 p

Pi

H > p o • 3

cd 3 • 3 3 • 3

14 3 3 P «—1 3 1 1 P 4-J ! 1 3 P • • • 3 3 00

CO CO 1 1 r-4 1 1 rH P i—1 P P 3 3 c 4-J 3 3 3 o • • 3 P 3 O

CU 3 P cj 3 ' 1 3 1 1 1 1 n-3 3 P

CO • 3 3 d) CJ P P *H • 3 3 P 3

l3 14 > > u3 3 3 O 3 3 PH rH 3 •H •H 3 o cd P 3 P 3 P rH P p p p <-3 nO T) 3 3 3 •-a 3 3 3 3 3 3 3 p p O i-3 •H > P P •H > > i—1 3 £ cu 3 3 3 P 3 »—1 3 3 3 3 P tn P O O 3 3

<d CU 3 *H 3 3 Td 3 cd i—1 3 o a

H 3 3 rH P P •H P p 00 OO HH xi p i—i O B •ri 3 i—1 I 1 i—1 3 §

•H P P 3 •H 3 CU 3 3) p O 3 CO P 3 N to O p > 3 3 3 3 N p

:3 3 3 3 o 3 °H cd 3 •H 3 3 O 3 O

O •H P P 3 3

Es H> H) P p

p P4 pi

p P H P Pi P CJ CJ CJ CJ

W

74
10.0

1X31 Nl 3AdH0 Ad“IVHlN3 Q3H100VMS lAIOUd N0I1VIA3Q !N30d3d

o

o

CM

oo

O'

CM

00

CO

cr>

CO

LiJ CC3

<tIT

UJ

Q.5

lx)

SC

I sc

G

G co TC i-i js o

>> w

r-H G

O 00 6 -rl u

4-1 CO O <0§H

COD

O

Go

cou

G

CU >H B U

G

M

3

00

•H

o

oCM

O

o

75
oo

CMoooo

cnoo

oooo

r-oo

COoo

inooO

roO

CMOO

CD

COi CD

UJ

cr3s

LlI

4-1o

co<u3

r-HCS>

•Ha

Cfl §*

CJI 4-1 to

a) rC3 • a) m

T3 t-l jo o

>,

w

iH cfl 00 S-H

4-1 CO o a) a c O -H

CO •H a; m 3

ccJ o

P4 *rl Bou

CM

OJ>43

00

•H

76
Percentage

deviation

of

the

values

of

enthalpy

and

heat

capacity

of

molybdenum

adopted

by

various

compilers

from

those

of

the

present

work

(Eq

1)

77
that Eq (1) or (2) suitably represents the data) can be readily judged.

As usual, the estimation of systematic errors is difficult, but in view

of the main purpose of the work stated in the Introduction — to arrive

at definitive values — an attempt should be made. We can do so more

completely after the measurements on molybdenum are made in the adjoining

temperature ranges 273 - 1170 K and 2100 - 2500 K, and after the samples

have been finally analyzed and the most critical instruments recalibrated.

Meanwhile, the following error analysis considers the contribution of all

important presently known sources of error to our measurements.

In the present type of measurements, the sample-mass determination

and energy measurement (the calorimetry, and accounting for the heat lost

by the sample during its transfer to the calorimeter) are of course

fundamental, and capable of introducing serious error. However, in our work these errors are believed to be relatively negligible, and we limit

ourselves to considering the two sources of error in enthalpy measurement

at high temperatures believed to be predominant — (1) the effects of the

sample impurities, and (2) the errors in measuring the average temperature

of the sample in the furnace.

(1) Effects of sample impurities — Impurities (if not adequately

corrected for) may introduce error in two ways: (a) by making the sample

one or more phases whose average heat capacity per unit mass differs from

that of the pure nominal material (molybdenum), and (b) by generating phase

changes with appreciable latent heats. The simplest way to estimate the

order of magnitude of the error from (a) is to make the roughly valid

assumption that all the impurity elements have the same atomic heat capacities as molybdenum, so that if one were to replace all the impurities atom

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

roughly the percentage change in both enthalpy and heat capacity. The effect

on this basis is illustrated by the use of the comprehensive Table IB: the

"elements measured" indicate a net error of +0.02%, and the upper limits

of the "elements showing interference", an additional +0.03%, or a total error of +0.05%. (Hydrogen, which was not analyzed for, could produce the

greatest error: e.g., 0.01% by weight in molybdenum would produce an error

of the order of +1%. It is believed likely, however, that hydrogen was at

a much lower level.) As noted in Section II, the "electronic characterization" of Samples A and B was interpreted as indicating an order of magnitude

greater impurity level (0.2% by weight) than did the other two analytical

techniques, but the impurities and their amounts postulated in this interpretation (see Section II) would on the above basis introduce a total error

of only +0.01%, owing to their high atomic weights.

Some impurities are capable of introducing much greater error of

Type (b) (latent heats of extraneous phase changes), whose magnitude cannot

really be estimated without specific knowledge as to what the phase changes

are. It seems likely, however, that for a substance like molybdenum which

when pure is believed to undergo no transitions, samples with as little

impurities as ours would display phase heterogeneity in only very narrow

78
temperature ranges, with no thermal effects (except those of Type (a)

discussed above) at other temperatures. By representing our smoothed

data by a strictly monotonic function [Eq (1) or (2)], any such "transistory"

effect should have been essentially eliminated.

We conclude from the above that, the errors introduced into our

enthalpies and heat capacities of molybdenum by the impurities were many

times smaller than those caused by temperature errors (see below)

(2) Effects of temperature errors — If the systematic error in

measuring the average temperature of the sample in the furnace, and its

variation with temperature, could be determined reliably, the corresponding

effects on the calculated values of enthalpy and heat capacity could then

be evaluated straightforwardly.

An approximation often made is that the error (expressed in K — i.e.,

°K) in pyrometrically determined temperatures such as those of our data

is approximately proportional to the square of the absolute temperature.

The estimated pyrometric uncertainties listed in Section III approximately

obey that temperature dependence, and interpolate to an uncertainty of 2.5 K

at 2300 K. To this should 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, we made with

simplifying assumptions a rough calculation which 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 a total error of 3K at 2300 K,

and of the same sign and proportional to the square of the temperature at

other temperatures, the smoothed results of our measurements (as given by

Eq (2), e.g.) indicate a corresponding error in the HT - ^93 ^5 varying

from 0.1% at 1200 K to 0.15% at 2000 K, and an error in varying from

0.15% at 1200 K to 0.3% at 2000 K. (Some additional error in Cp near the

ends of the temperature range investigated results when, as here, C is

determined by differentiation of an empirical function representing^ the

measured enthalpy.)

Some of the error in using a pyrometer may be a function of the

pyrometer current. Hence, when in proceeding to successively higher temperatures a point is reached where a stronger filter (calibrated) is interposed and the adjusted pyrometer then abruptly drops to a much lower current,

it is worthwhile to examine a regularly varying property to see whether a discontinuity in the measured values appears at that temperature. Our first

such occurrence was between 1500 and 1600 K; however, the apparent discontinuity in our unsmoothed values for the enthalpy of molybdenum appears to

be no greater than 0.1% if indeed it is outside the precision (see Fig. 1).

(Our second such occurrence was between 2000 and 2100 K; but because of the

marked curvature of the heat capacity of molybdenum in that temperature

region and our lack of data at more than one temperature using the stronger

filter, any search for an enthalpy discontinuity in that case would be

unreliable .

79
As stated in Section IV, the enthalpy of standard-sample aluminum

oxide was measured once at 1170 K and once at 1700 K near the end of

the present series of measurements on molybdenum. The agreement with

the highly consistent earlier results (to 0.05% or better) is evidence

that the pyrometry did not appreciably deteriorate during the measurements on molybdenum.

To summarize, we have no evidence thus far to believe that the errors

in the smoothed values of enthalpy and heat capacity of molybdenum reported

in this chapter are likely to exceed 0.5 and 1%, respectively, up to about

2000 K.

Although the error in sample- temperature measurements certainly seems

to be the most serious one in measurements of this kind, and it is safe

to guess that many investigators have seriously underestimated their

systematic temperature errors, one is justified in wondering whether a substantial part of the large disagreement among the many investigators

of the enthalpy and heat capacity of molybdenum is due to a real difference

between some samples of the pure annealed metal. Our data on molybdenum

include an enthalpy measurement on a sample with a very different history

(Sample C, triple- zone-refined) at each of the temperatures 1170, 1699,

and 1900 K. The agreement within 0.2% between Samples A and C at these

three temperatures is some evidence, however circumstantial, that the

massive annealed metal has reproducible enthalpies and heat capacities.

Several investigators have fitted their data for the enthalpy and

heat capacity of molybdenum at high temperatures with the inclusion of

a simple exponential term whose argument can be interpreted as the energy

of some reversible process in the metal (e.g., vacancy formation and

migration, but so far not satisfactorily identified — see, e.g., Ref.

[21]). Without pretending to throw any light on this interesting subject, we merely point out that our precise data (though not extending above

2100 K yet) were fit almost equally well by values of the constant E

in Eq (1) varying from 0.9 to 1.9 eV. This -range encompasses most of

the values arrived at by others, and our arbitrary choice of 1.4 eV

in Eq (1) (equivalent to E = 16,000 K) thus has no quantitative physical

significance

.

VII. Acknowledgements

The following professional staff of the National Bureau of Standards

made substantial contributions to the work reported in this chapter. With

the help of one of us (S.I.), E. D. West (NBS, Boulder) earlier designed

and constructed the calorimetric apparatus. R. E. Michaelis (Office of

Standard Reference Materials) furnished Samples A and B, and coordinated

their various characterizations. The spectrochemical analyses were performed

80
by Virginia C. Stewart (Samples A and B) and Martha M. Darr (Sample C)

the mass spectrometry, by C. W. Mueller and P. 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 D. A. Ditmars and M. L. Reilly provided a computer

code and many of the bibliographic sources.

VIII. References

[1] Certificate of Standard Reference Material 720, Synthetic Sapphire

(AI 2 O 3 ), Office of Standard Reference Materials, National Bureau of

Standards, Washington, D. C. 20234 (Aug. 26, 1970).

[2] F. Wust, A. Meuthen, and R. Durrer, Forsch. Gebiete Ingenieurw. 204 , 1-59 (1918).

[3] F. M. Jaeger and W. A. Veenstra, Rec. Trav. Chim. _53, 677-687 (1934).

{4J F. M. Jaeger and W. A. Veenstra, Proc. Acad. Sci. Amsterdam 37 , 61-76 (1934).

[5] T. A. Redfield and J. H. Hill, U. S. Atomic Energy Comm.; ORNL-1087,

1-9 (1951).

[ 6

]

, C. F. Lucks and H. W. Deem, WADC Tech. Rept. 55-496, 43 (1956).

[7] C. W. Kothen, Dissertation, Ohio State Univ. , Columbus, 0. (1952).

[ 8 ] I. B. Fieldhouse, J. C. Hedge, J. I. Lang, A. N. Takata, and T. E.

Waterman, WADC Tech. Rept. 55-495 (1956).

[9] V. A. Kirillin, A. E. Sheindlin, and V. Ya. Chekhovskoi, Dokl. Akad.

Nauk. SSSR 139 , 645-647 (1961) (English transl. pp . 557-559).

[10] V. A. Kirillin, A. E. Sheindlin, and V. Ya. Chekhovskoi, Int. J.

Heat, Mass Transfer _5, 1-9 (1962).

[11] L. S. Lazareva, P. B. Kantor, and V. V. Kandyba, Fiz. Met. i Mettalov

11, 628-629 (1961) (English: Phys . Metals and Metallog. 11 , 133-134 (1961).

[12] N. S. Rasor and J. D. McClelland, J. Phys. Chem. Solids _15, 17-26 (1960).

[13] M. J. Pool, R. W. Sullivan, and C. E. Lundin, Quarterly Status Rept.

No. 9, Contract AF 19 (604)-7222, U. of Denver, Denver Research Inst.,

Denver, Colo. (1962).

[14] G. W. Lehman, WADD Tech. Rept. 60-581 (I960) (19 pp)

81
[15] G. C. Lowenthal, Aust. J. Phys . 16^ 47-67 (1963).

[16] R. E. Taylor and R. A. Finch, Atomics International NAA-SR-6034

(1961) (32 pp).

[17] R. L. Rudkin, W. J. Parker, and R. J. Jenkins, Temp. Meas . Control

Sci. Ind., Vol 3, part 2, 523-534 (1962).

[18] V. A. Kirillin, A. E. Sheindlin, V. Ya. Chekhovsky, and V. A. Petrov,

ASME, Proc. 4th Symp . Thermophys . Prop., pp. 54-57, U. of Md.,

College Park, Md. ( J . R. Moszynski, ed.) (1968).

[19] A. E. Sheindlin, V. Ya. Chekhovskoi, and E. E. Shpil'rain, High

Temp. -High Press. _2, 1-15 (1970).

[20] V. Ya. Chekhovskoi, A. E. Sheindlin, and B. Ya. Berezin, High Temp.-

High Press. _2, 301-307 (1970).

[21] A. Cezairliyan, M. S. Morse, H. A. Berman, and C. W. Beckett, J.

Research NBS _74A, 65-92 (1970).

[22] J. B. Conway, R. A. Hein, R. M. Fincel, Jr., and A. C. Losekamp,

Rept. TM 64-2-8, General Electric Co., NSP (1964).

[23] M. Hoch, High Temp. -High Press. 1, 531-542 (1969).

[24] T. B. Douglas, J. Research NBS 73A, 451-470 (1969).

[25] R. Hultgren, R. L. Orr, P. D. Anderson, and K. K. Kelley, "Selected

Values of Thermodynamic Properties of Metals and Alloys," Univ. of

Calif., Berkeley, Calif, (table for Mo: March 1965).

[26] K. K. Kelley, U. S. Bur. Mines Bull. 584, p. 125 (1960).

[27] JANAF Thermo chemical Tables (table for Mo: Dec. 31, 1966).

[28] R. E. Taylor and R. A. Finch, J. Less-Common Metals 6_, 283-294 (1964).

[29] V. Ya. Chekhovski and V. A. Petrov, Teplofiz. Vysokikh. Temperatur _6

,

752 (1968).

[30] M. L. Reilly and G. T. Furukawa, "Critical Analysis of the Heat

Capacity Data of the Literature and Evaluation of Thermodynamic

Properties of Cr, Mo, and W from 0 to 300 K," NSRDS-NBS (to be

published)

.

[31] Chemical and Engineering News, p. 43 (Nov. 26, 1961).

82
[32] D. C. Ginnings, "Precision Measurement and Calibration on Heat,"

NBS special publication 300 , j5 , 220 (1970).

[33] NBS Report 9028, U. S. Air Force Order No. OAR 65-8, 71 (Jan, 1966).

[34] NBS Report 9803, U. S. Air Force, OSR Order No. ISSA-67-6, 80

(Jan, 1968).

[35] NBS Report 9601, U. S. Air Force Order No. ISSA-67-6, 55 (July, 1967)

[36] NBS Technical Note 494, ARPA-NBS Program, p. 18 (Sept., 1969).

[37] K. F. Starret and W. E. Wallace, J. Am. Chem. Soc. J30, 3176 (1958).

[38] G. T. Furukawa, private communication.

[39] D. A. Ditmars and T. B. Douglas, J. Res. NBS 75A , 5 (Sept. -Oct. 1971)

83
Chapter 6

THE HEAT OF FORMATION OF MoF

6

(j&) BY

SOLUTION CALORIMETRY; ANALYSIS OF PRELIMINARY EXPERIMENTS

R. L. Nuttall, K. L. Churney, M. V. Kilday

Introduction

This laboratory is currently engaged in a program to determine

the heats of formation of the lower fluorides (and the oxy-f luorides)

of molybdenum. Since it was deemed unlikely that the compound currently of interest, MoF^(c), could be formed in reasonable quantities

by direct reaction of F

2 ^) Mo(c), two other reaction schemes

are being used which involve either MoF^(g) or MoF^(j2.). The first,

the method of choice, is the reaction of MoF^(c) with F£(g) to form

MoF^(g). Because the available quantity of MoF^(c) and the heat of

reaction — ^ were expected to be small, a second, more sensitive,

scheme was deemed necessary either as a check or as an alternative

route. The method selected was the heat of solution of MoF^(i,) in

base and MoF^(c) in base containing an oxidant based on the apparent

success of this method with MoCl^(c) [3], for example. Both methods

require an accurate value for the heat of formation of MoF^(i) or

MoF^(g). Unfortunately, the heat of formation of MoF^(g) derived by

1 / -24 ± 15 kcal per mol MoF^(c) based on an estimated heat of

formation of MoF^(c) [1] and the heat of formation of

MoF

6 (g) [2].

84
solution calorimetry differs from that determined by direct combination of the elements.

Settle et al [2] obtained -372.35 ± 0.22 kcal/mol for the

reaction

Mo (c) + 3F

2 (g) = MoF6 (g) (1)

by burning molybdenum sheet suspended on a nickel rod in 14-15 atm

of F

2 (g) in a nickel combustion bomb. Correction for unburned

molybdenum (< 4$ of initial sample weight) could be made unambiguously

and accurately. While the corrections for the formation of MoF^(c)

(typically 0.10 ± 0.05$ of molybdenum burned) , NiF

2 (c) formed due

to corrosion, and impurities in the original sample were somewhat

uncertain, all made relatively small contributions to the resulting

value of AH° [MoF^(g)] (0.003$, 0.059$, and 0.087$ on the average,

respectively). Recalculation of the latter two corrections using

newer selected values for heats of formation (see [2,4]) yielded a

value of -372.29 kcal [5] for reaction (1).

The only other determination of the heat of formation of MoF^(i,)

was made by Myers and Brady [6] by measuring the heats of solution

of MoF^(i-) and Mo0

2 (c) in 0.531 N aqueous NaOH and of NaF(c) in

0.531 N aqueous NaOH containing molybdate. These authors calculated

their results according to the reaction scheme given by eq (2)

MoF, (j£) + 8NaOH(soln) = Na oMo0. (soln) + 6NaF(c) + 4Ho 0(soln) (2) b Z 4 Z to obtain -388.6 ± 4 kcal for the heat of formation of MoF^(i-). Recalculation of their results using newer selected values [2,4] of the

heat of formation [NaOH • 515H

2

0] (soln), Mo0

2

(c), and NaF(c) yields

-1

a value of -393.2 kcal mol . Using the selected value of

85
6.66 kcal/mol for the heat of vaporization of MoF^(i-) [5] (based

on the measurements of Ruff and Ascher [7], Cady and Hargreaves [8],

and Osborne et al [9]), one obtains -386.6 ± 4 kcal for reaction (1).

The uncertainty in this result greatly exceeds any error due to the

failure of Myers and Brady to maintain rigid stoichiometry. The

result is 14.3 ± 4 kcal more negative than that obtained by Settle

et al

.

Because of this discrepancy and particularly because solution

calorimetry involving MoF^(j&) is also to be used to determine the

heat of formation of MoF (c)> it was considered necessary to repeat

5

the measurements of Myers and Brady. We considered it more likely

that the error lay in their work than in that of Settle et al.

In the following three sections an outline of the reaction

scheme for the solution experiments is given, a brief summary of

experimental method, and a short summary and discussion of results.

Reaction Scheme of Solution Experiments

The actual reaction scheme used by Myers and Brady involves

the following three reactions:

MoF

6

(jfc) + [ (8+x)NaOH + yHo 0] (soln) = (3)

[Na

2Mo04 + 6NaF + xNaOH + (4+y)H o 0] (soln)

Mo0

3

(c) + [ (2+x)NaOH Jr (3+y)H

2

0] (soln) =

[Na

2

Mo0

4 + xNaOH + (4+y)H

2

0] (soln)

(4)

6NaF (c) + [Na

2

Mo0

4 + xNaOH + (4+y)Ho 0] (soln) =

[Na

2Mo0

4 + 6NaF + xNaOH + (4+y)H

20] (soln)

( 5 )

86
If rigid stoichiometry is maintained so the value of x and y are the

same for all reactions, one obtains for the sum of reactions (3) -

(4) - (5):

MoF

6 (jO + [ (8+x)NaOH + yH

2 0] (soln) = (6)

Mo0

3

(c) + 6NaF(c) + [ (2+x)NaOH + (3+y)H

20] (soln)

Reaction (6) can be simplified by adding reactions (7) and (8) to

give (9)

6NaF(c) = 6NaF(aq) (7)

[ (2+x)NaOH + (3+y)H

20] (soln) + 6NaOH(aq) =

3H

2 0(je) + [ (8+x)NaOH + yH

20] (soln) (8)

MoF

6 U) + 60H

_ (aq) = Mo0

3

(c) + 6F

_ (aq) + 3H

20(A) (9)

Thus, the heat of reaction (9), AH

g

, is given by

AH

g

= AH

6 + AH

? + AH

g

where AHg is determined experimentally and is equal to

AH. “ AH, - AH. - AH,

6 3 4 5

O The heat of formation of MoFg(jJ), AH^[MoFg (f,) ] , would then be

given by the heats of formation of the other species in reaction

(9) and AH

g

;

AH°[MoF

6 U)] s AH°[Mo0

3

(c)] + 3AH°[H

20(jO] + 6AH°[F“(aq)]

- 6AH° [ 0H~ (aq) ] - AH

g

Apart from experimental uncertainties, the uncertainty in the

assumed value for heat of formation of F (aq) will cause the

87
largest systematic error in the heat of formation of MoF^(f.).

The advantage of carrying out reactions (3) through (5) with

rigid stoichometry is that it eliminates any need for non-existent

heat of dilution data for basic molybdate solutions with and

without fluoride. Further, the correction terms, AH., and AHQ ,

added to AHg are small and unambiguous. The value selected by

Parker [10] for AH^/6, is +0.218 ± 0.010 kcal/mol. '(The selection

was based upon very few experimental measurements of the integral

heat of solution and estimated of heats of dilution). The value

of AHg when y

» 3 is given by

AHg 6 1- (l+x/2 ) y

<(> L

(y) + 3(3+x)L

2 (y)

y

where i (y) and L 9 (y) are the relative apparent molal enthalpy and

relative partial molal enthalpy of solute, respectively, of

[NaOH + yH

2 0](soln). The maximum value of AHg/6 when y > 100

(molality less than 1.5) and x « y is 0.112 kcal mol ^

.

Neither the experiments carried out by Brady and Myers nor

our preliminary work comply with the rigid stoichiometry required

to write reaction (6). Further, intercomparison of our preliminary

work with that of Myers and Brady and other workers is more informative if done on reactions (3) through (5) separately. Thus, we will

consider the heat of reactions (3) through (5) individually. Reactions

(3) and (4) will be corrected, if possible, by estimates for dilution

effects to yield the corresponding heats of reaction at infinite

for

dilution reactions (3a) and (4a), respectively.

MoFg(jJ) + 8NaOH(aq) = Na^MoO^Caq) + 6NaF(aq) + 4H

2

O(j0) (3a)

88
Mo0 (4a)

3

(c) + 2NaOH(aq) = Na

9MoC>4

(aq) +

Comparison of our limited work (single experiment) and the experiment

of Myers and Brady for reactions similar to reaction (5) are compared

to the selected value of AH^ to shed light on the difference in

dilution heat effects of basic molybdate solutions with and without

fluoride

Experimental Procedure

For the preliminary experiments described here CP grade MoO^

and NaF were used without further purification. The MoF^ was purchased

from Ozark-Mohoning Company and was purified by trap-to-trap distillation in an all-metal system. The MoF^ was then transferred by

distillation into Kel-F (polychlorotrifluoroethylene) bulbs for

introduction into the calorimeter. These bulbs were made from 1/2-inch

lengths of 3/8-inch I.D. tubing by sealing on end, windows of 0.005-inch

film and a 1/8- inch tube sidearm* The bulbs were filled through the

sidearm which was then sealed off.

The calorimeter is a precise adiabatic calorimeter which has been

described previously [11], [12]. The interior of the calorimeter

vessel is all platinum. For the MoF^(i-) solution experiments, the

sample holder was replaced by a Monel holder for the Kel-F bulbs. A

Monel cutter was used to cut out the end windows for starting the

solution reaction.

The energy equivalent of the calorimeter was determined using

electrical heating before and again after each solution experiment.

89
Analysis of Results

A) Heat of Solution of NaF(c)

We have carried out a single experiment corresponding to the

reaction

6NaF(c) + [ 10.21Na

2

Mo0

4 + 1250NaOH + 109,700H20] = soln

for which we obtain AH(25.0C) = +1.33 kcal. Myers and Brady [6]

studied the approximate reaction

6NaF(c) + [1.921Na

2

Mo0

4 + 40.7NaOH + 22,930H2

0] = soln

for which they obtained AH(25.0C) +0.54 kcal. The selected value

for AHy [10], is +1.308 ± 0.06 kcal. Because of the larger ratios of

moles of NaOH and Na

2MoO^ to moles NaF(c) in our experiment than in

Myers and Brady, one would expect our result to be in closer agreement

with AH^»

B) Heat of solution of MoQ

2 (c)

Three experiments were carried out for the heat of solution of

Mo0

2

(c) according to reaction (3) at an average temperature of 24.9 C

which are summarized below along with the results of Myers and Brady (M. B.)

Normality Moles NaOH Moles H

2 0 -AH.

4

Run of NaOH Moles MoO^ Moles NaOH (kcal)

1 0.706 50.8 78.7 18.69

2 0.706 120.1 78.7 18.56

3 0.643 124.4 86.4 18.69

18 . 65±0. 08

M.B

.

0.1075 24.9 515 17.6

The value for AH^

a of reaction (4a) based on Parker's selection [2]

18.80 kcal/mol

.

This value is based on the heats of solution of

90
Graham and Hepler [13] of the same number of moles of MoO^(c) and

Na^oO^Cc) in 0.531 N NaOH and Na^MoO^Cc) in very dilute base and

water and the work of Koehler et al [14] who studied the following

reaction by solution calorimetry.

Mo0

3

(c) + 2NaCl(c) + 26.462H

20(£) = Na

2Mo04

(c) + 2(HCl • 1731 H

20)

Recalculation of both results in accordance with newer selected aux- values

iliary data yields^ for the heat of formation of MoO^Cc) minus that of

Na

2

Mo0

4

(c) of -172.72 ± 0.07 kcal and -172.98 ± 0.11 kcal from Graham

et al and Koehler et al, respectively. Parker selected [5] a value of

-172.81 kcal/mol to which we assign an uncertainty of ±0.12 kcal. Use

of the value of of Na^oO^Cc) of -2.4 kcal selected by Hepler et al

[13] and selected values of the heat of formation of NaOH(aq) and

H

20 (j&) yields the value selected for AH.^.

Recalculation of the results of Graham and Hepler for the heat of

solution of Na

2Mo04

(c) in very dilute base water or assuming that

for Na

2

Mo0

4

(aq) is the same as for Na

2

S0

4 (aq) yielded a value of

AH° - -2.41 ± 0.05 (av. dev.) kcal. Use of this value and the pairs

of experiments reported by Grahams et al [13] for MoQ

3

(c) and Na

2

Mo0

4

(c)

yielded a separate check of Parker's selection as well as a correction

to infinite dilution for the heat of solution of Mo0

3

(c) as shown below

Moles NaOH Moles H

2

0 AH

3

Corr. to °° AH03a

Run Moles MoO^Cc) Moles Mo0

3

(c) kcal kcal kcal

1 111.2 104.5 -18.52 -0.50 -19.02

2 205.2 104.5 -18.70 -0.21 -18.91

3 247.7 52.23 -18.75 -0.22 -18.97

4 160.4 104.5 -18.69 -0.31 -19.00

5 192.2 104.5 -18.66 -0.15 -18.81

The sum of columns 4^ the observed value, and 5,

91

the dilution correction.
The average AH.^ '*' S “18.94 ± 0.07 (av. dev.) kcal with an estimated

uncertainty of ±0.15 kcal as compared with -18.81 kcal selected by

Parker (which has a comparable uncertainty). Comparison of this table

with our preliminary results suggest the heat of dilution to infinite

dilution is of the order of -0.2 kcal to yield an estimated value from

our results of -18.85 ± 0.15 kcal for reaction (3a). It seems apparent

that the result obtained by Myers and Brady is too positive particularly if it is compared with the results of Koehler et al [14] for

the heat of solution of MoO^(c) in a solution of the approximate

composition 18[NaOH • 278^0] of -18.450 ± 0.030 kcal.

C) Heat of Solution of MoF^.(j0)

Three measurements of the heats of solution of MoF^(j0) were

carried out for reaction (3) at 24.69 ± 0.05 C , one at 25.55 C, and

another at 29.62 C as summarized below for reaction (3) along with results of Myers and Brady (M.B.).

Normality Moles NaOH Moles ^0 Temperature -AH

3

Run of NaOH Moles MoF^(jJ) Moles NaOH (C) (kcal)

1 .643 162.0 86.4 29.62 165.1

2 .643 172.8 86.4 24.67 168.0

3 .643 203.4 86.4 24.63 170.7

4 .643 120.2 86.4 24.78 168.2

5 .706 88.9 78.7 25.55 171.8

M.B

.

.531 513 515 25.0 154.7

The value for AH,,^ of reaction (3a) based on the selected values [2,4]

of heats of formation is -170.05 kcal. The heat of formation of

92
MoO^"(aq) is based on comments in section B and the heat of formation

of MoO^c) selected by Parker [5] of -178.08 kcal to which we assign

an uncertainty of 0.08 kcal. The latter value is based on the work of

Staskiewicz et al [15] (-177.99 ± 0.10 kcal) and Mah [16] (178.15

± 0.11 kcal) rather than the earlier work of Delepine [17] (-167 kcal),

Mixter [18] (-185 kcal). Moose and Parr [19] (-175.6 kcal) or Neumann

et al [20] (-180.4 kcal). The selected value for the heat of formation of MoF^(f.) is the recalculated value of the results of Settle et al [1].

The selected value for the heat of formation of F (aq)

[4], -79.50 kcal, has been the subject of considerable controversy.

A brief summary of the problem as of 1969 is given by Armstrong [21]

and in 1971 by Vanderzee and Rodenburg [22]. The latter determined a -1

value of -14.72 ± 0.10 kcal mol for the reaction at 25 C.

HF(g, ideal) = H+(aq) + F (aq) (10)

This value supports the value selected by Parker [10] of -14.70

kcal/mol. Recently, Smith et al [23] determined a value of -7.691 ±

0.030 kcal mol ^ for the reaction at 25 C

HFU) = H

+

(aq) + F~(aq) (11)

Using the value of 7.231 ± 0.025 kcal mol ^ for the heat of vaporization of HF(j0) to HF(g, ideal) in its standard state determined by

Vanderzee and Rodenburg [24], one obtains from the previous work of

Vanderzee and Rodenburg on reaction (10) an alternative value for

reaction (11) of -7.49 ± 0.10 kcal mol Recently, Settle et al [25]

have completed a study of the heat of formation of HF(j£) for which

* Recalculated

93
they obtain -72.57 ± 0.09 kcal mol . In conjunction with the two

more recent values for the heat of reaction (11 ) ^ this yields

values for the heat of formation of F (aq) of -80.26 ± 0.09 kcal mol ^

(Smith et al) and -8CL06 ± 0.14 kcal mol ^ (Vanderzee and Rodenburg).

The corresponding value of AH„ for these values of the heat of

formation of F (aq) would be -174.61 kcal and -173.41 kcal, respectively.

Estimating the dilution correction that must be added to our experimental values of AH^ to obtain AH^

a to be at most of the order of

-1 kcal, it appears that our preliminary results are not consistent

with the more recent determinations of the heat of formation of F (aq)

.

Nevertheless, our results do support a conclusion that the value for

AH^ determined by Myers and Brady is far too positive.

94
References

[1] Settle, J. L., Feder, M., Hubbard, W. N., J. Phys . Chem.

5, 1337 (1961).

[2] Wagman, D. D., Evans, W. H., Parker, V. B., Halow, I.,

Bailey, S. M., Schumm, R. H., Nat. Bur. Std. (U.S.) Tech Note

270-4 (1969).

[3] Shchukarev, S. A., Vasil 'kova, I. V., Sharupin, R. N.,

Vestnik Leningrad Univ. JL4, No. 4, Ser. Fiz. i Khim., No. 1,

73-77 (1959).

[4] Wagman, D. D., Evans, W. H., Parker, V. B., Halow, I.,

Bailey, S. M., Schumm, R. H., Nat. Bur. Std. (U.S.) Tech. Note

270-3 (1968).

[5] Parker, V. B., Private Communication, Nat. Bur. Std. (U.S.),

See Ref . [ 2]

[6] Myers, 0. E., Brady, A. P., J. Phys. Chem. 64, 591 (1960).

[7] Ruff, 0., Ascher, E., Z. Anorg. Chem. 196 , 413 (1931).

[8] Cady, G. H., Hargreaves, G. B., J. Chem. Soc. 1563 (1961).

[9] Osborne, D. W., Schreiner, F., Malm, J. G., Selig, H.,

Rochester, L., J. Chem. Phys. 44, 2802 (1966).

[10] Parker, V. P., Thermal Properties of Aqueous Uni-valent

Electrolytes. National Standard Reference Data Series-NBS 2.

U. S. Govt. Printing Office; Washington, D. C. 1965.

[11] Kilday, M. V., Prosen, E. J., NBS Rept. 8306 (1964).

[12] Kilday, M. V., Prosen, E. J., Wagman, D. D., NBS Rept. 10004

(1969).

[13] Graham, R. L., Hepler, L. C., J. Amer. Chem. Soc. 7

_ 8 , 4846 (1956).

95
[14] Koehler, M. F.j Pankratz, L. B.j Barany, R. $ U. S. Bur. Mines

Rept. Invest. 5973 (13p) 1962.

[15] Staskiewicz, B. A.j Tucker, J. R.j Snyder, P. E.-# J. Amer

.

Chem. Soc. 7_7, 2987 (1955).

[16] Mah, A. D., J. Phys. Chem. _61, 1573 (1957).

[17] Delepine, M., Bull. Soc. Chim. 29, 1166 (1903).

[18] Mixter, W. G., Amer. J. Sci. 2_9, 488 (1910).

[19] Moose, J. E.> Parr, S. W.', J. Amer. Chem. Soc. 4F>, 2656 (1924)

[20] Neumann, B .5 Kroger, C.j Kunz, H.$ Z. anorg. und Allgem. Chem.

218 , 379 (1934).

[21] Armstrong, G. T., AFOSR Scientific Report AFOSR 69-2154 TR,

NBS Report 10074, July 1 (1969).

[22] Vanderzee, C. E.", Rodenburg, W. W.* J. Chem. Thermodynamics

3, 267 (1971).

[23] Smith, P. Nj Johnson, G. K.J Hubbard, W. N .5 Private Communica

tion, Argonne Nat. Lab.^ March 1970.

[24] Vanderzee, C. E .5 Rodenburg, W. W.* J. Chem. Thermodynamics

2, 461 (1970).

[25] Settle, J. L, Hubbard, Johnson, G. K. ; Greenberg, E. ; Private

Communica tior^ Argonne Nat. Lab., July 1970.

96
Chapter 7

PROVISIONAL RESULTS ON THE PREPARATION, MELTING,

AND VAPORIZATION OF MoF

5

Ralph F. Krause, Jr.

Abstract

A sample of MoF was prepared from the reaction of MoF^

vapor with powdered Mo near 150°C, purified by simple vacuum

distillation near 90°C, and collected as a viscous goldenyellow liquid which crystallized after a few days. A temperature-time melting curve of the light yellow solid gave a freezing-point- lowering of 0.22 kelvin, which was estimated

to correspond to a cryoscopic impurity of 0.15 mol %, and a melting point for the pure substance of 45.67°C, which is

much lower than a published value of 67°C. Several entrainment measurements on the sample at 60 and 90°C showed that

the partial pressure of MoF^ vapor, if assumed monomeric,

was 26 to 34% of a direct vapor pressure measurement, the

only published work, and that the vapor contained from 7 to

24 mol % MoF^, whose presence indicates disproportionation

of the sample. The entrainment value of the MoF^ pressure

decreased with subsequent flows which corresponds to a buildup in the liquid sample of a soluble impurity such as MoF^.

Deliberate enhancement of the carrier gas with MoF^ vapor

restored a maximum value which is in line with a sample of zero impurity. Composition of the gaseous and condensed

phases are still in doubt and further analyses are needed.

Since there is evidence that the sample reacts somewhat with

pyrex, future plans involve vaporization in monel.

Literature Survey

The fluorides of molybdenum have been a part of some recent reviews.

Ferguson'*' has discussed the chemistry of the anhydrous halides and oxyhalides of chromium, molybdenum, and tungsten. Canterford, Colton, and

2 O’Donnell have attempted to systematize the physical and chemical

properties of the hexa- and pentafluorides of the second and third row transition elements.

97
Although molybdenum can have in theory a valency from 0 to 6 and the

hexa-, penta-, tetra-, and trifluorides have been reported in the literature, only the thermodynamic properties of the hexafluoride have been wellcharacterized. Several investigators, the most recent of which are Claassen,

3

Goodman, Holloway, and Selig have measured both the infrared and Raman

4

spectra of MoF^(g). Osborne, Schreiner, Malm, Selig, and Rochester have

measured the low- temperature heat capacity, triple point, heat of fusion,

vapor pressure, and heat of vaporization. Using fluorine bomb calorimetry,

Settle, Feder, and Hubbard^ have measured the heat of formation of- MoF.

.

o In contrast, work6^7 on MoF,. has just begun. Fifty years after the

original preparation of MoF^, Peacock was the first to prepare MoF,. by

reacting F_(g) with Mo(CO), at -75°C. The product was heated to 170°C;

Z b

the yellow distillate of MoF,. and the green residue of MoF^ were identified

by chemical analysis as shown in Table 1. Using this preparation, Cady

Table 1

Chemical Analyses of Some Molybdenum Fluorides

Comp ! d Investigator Ref . %Mo % F

MoF„ Emeleus & Gutmann 12 62.2 36.1

3 62.8 35.7

LaValle et. al. 14 62.9

Theoretical (62.73) (37.27)

MoF Peacock 7 56.3 43.2

4 Theoretical (55.80) (44.20)

MoF Peaco ck 7 49.9 50.5

D Edward et. al

.

10 50.4

Ouellette et. al

.

11 50.19

Churney (this work) 17 50 . 14

a 50 . 47

a 50 . 37

a 50.45

3

Theoretical (50.25) (49.75)

m°f

6 Churney (this work) 17 45.79

45.79

45.91

Theoretical (45.70) (54.30)

MoOF.

4

Theoretical (51.05) (40.44)

MoOF

3 Theoretical (56.79) (33.74)

These values involve a blank correction based on the high results

of presumedly pure MoF^

.

98
and Hargreaves measured directly the vapor pressure of MoF,_(£) from

70 to 160° C with a pyrex diaphragm gauge as a null device; they also

reported the disproportionation of MoF,. at 165°C to form MoF^ and

involatile MoF, , for whose identity no analytical results were given.

^ 9

Also reporting no analytical results, O'Donnell and Stewart combined

MoF^ and PF^ in a glass vacuum system fitted with brass valves and

found the only products to be MoF and PF . Edwards, Peacock, and

10

b b

Small reported yet another method of preparation and the crystalline

structure of MoF^ . The passed sublimed MoF^ over Mo powder in a nickel

tube at 300 - 400°C and purified the product by trap-to-trap distillation

at 65°C in a glass vacuum system. Finally, Ouellette, Ratcliffe, and

Sharp^ modified this last method by heating a metal reaction vessel

to 60°C and determined the infrared and Raman spectra of crystalline

and liquid MoF,,.

The purity of MoF,. from the above preparations is open to question.

On the basis of a chemical analysis for Mo alone, an observed value of

0.2% greater than theoretical for MoF,. as shown in Table 1 could possibly

be an indication for as much as 25 mol % MoOF^ in the sample. In a related example the evidence for purity and crystalline structure of MoF„

12

J

is conflicting. Emeleus and Gutmann prepared a non-hygroscopic dark13 pink powder on heating the tribromide in HF; then Gutmann and Jack

determined a cubic ReO„-type structure by x-ray powder diffraction. Later

. J 14

LaValle, Steele, Wilkinson, and Yakel reduced MoF,. with Mo powder and

found their tan product to have the rhombohedral VF^-type structure. Yet

both samples were believed to be MoF^ as Table 1 indicates.

If disproportionation of MoF,. were to occur in addition to simple

vaporization as shown by eqs 1 and 2,

MoF,. (c) -* MoF

5 (g) ( 1 )

( 2 ) 8

2MoF c (c) -> MoF. (c) + MoF, (g)

O H O another interpretation of Cady and Hargreaves' vapor pressure data^,

which they represented as

log P(torr) = 8.58 - 2772/T(K) (3)

99
should be that

P - Pjl + P

2 (4)

in which is the partial pressure of MoF^(g) in eq 1 and P

^ is the

partial pressure of MoF^(g) in eq 2. Eqs 1 and 2 represent a binary

system that is univariant. If MoF^ is soluble in liquid MoF^, either

the case in which the concentration of MoF^ is near zero or perhaps

Raoult's law could be applied. The terms P^ and P^ are related to the

thermodynamic properties of eqs 1 and 2 respectively by

P. = exp [A S?/R - A Hf/RT] (5)

l l l

The inverse temperature derivative of eq 4 leads to

-R[dP/d(l/T)] = AH°P

1 +AH°P2 (6)

If we let T^ be 383 K, which comes from the average inverse temperature of

Cady and Hargreaves’ data, and assume values of A S ° and A S°, values of

P./P, A H°, and A H° may be generated from eqs 4, 5, and 6. Using the

_ i _ 25 estimation methods of Kubaschewski and Evans , values of A S ° and A S

at 383 K were taken as 30.7 and 15.5 eu respectively; however, since the

most uncertain estimate is the entropy of MoF^(c) at 298 K, this served

as a convenient parameter for the calculation by an iterative method of

the results shown in Table 2. Here it seems plausible indeed that appreciTable 2 Estimate of the Change in Enthalpy of Eqs 1 and 2,

Using the Data of Cady and Hargreaves (ref 8)

S° (eu)

MoF (c)

v<wVo

A H°

kcal

A H°

kcal

298 K 383 K 383 K 383 K

35 40 15.9 10.5

36

b

51 15.3 9.9

37

b

61 14.8 9.3

38 70 14.3 8.8

39 79 13.9 8.2

40 87 13.4 7.7

Q

Assumed values of A S° and A S° which are related to

to S^_ in this table were used along with eqs 4, 5 and

6. Subscripts refer to eqs 1 and 2.

This corresponds to values of A S° and A S° as and 15.5 eu, respectively. See text.

30.7

100
able disproportionation occurs along with simple vaporization over the

temperature range of Cady and Hargreaves' vapor pressure data.

Preparation

A sample of MoF^ was prepared from the reaction of triple-distilled

MoF^ vapor with powdered Mo in a previously evacuated monel tube near

150°C. In order to remove any possible HF, vapor from the commercial

source of MoF, was treated with a column of NaF, which was prepared by

o heating NaHF^ to 350°C in a helium flow (eventually discharged through

soda-lime) . More volatile impurities like F^ were removed by pumping

on the first distillate of MoF^ which was held in a dry-ice slurry.

As the reader will see later, the cryoscopic impurity of a sample of

MoF^ which was similarly treated was 0.031 mol %. The commercial

supplier of the powdered Mo (200 mesh) had reduced it in hydrogen and

assayed it at 99.90%; a general spectrographic analysis is currently

underway. Stainless-steel valves with teflon-packed stem and seat

connected the reaction tube to the source of MoF, and to a series of

6

three previously evacuated and baked pyrex U- tubes. After a few minutes

of reaction a batch of about 1 g of product was condensed at room temperature in the first pyrex tube while the excess MoF^ was withdrawn over

a period of several hours to a liquid nitrogen trap in the brass and

copper vacuum system (10 torr) . When a few batches of the viscous

golden-yellow liquid had accumulated, it was purified by simple vacuum- distillation near 90°C. The distillate was collected in the second

U-tube and allowed to drain into another vessel for subsequent analysis

while the third tube was kept in a dry-ice slurry. The remaining residue,

which was about 5% of the original, became brownish-yellow.

Since purification of MoF^ seemed difficult, reliance on the purity

of reactants was tempting. Both MoF,. and MoF^ are very reactive with

moisture. When a sample of MoF,. was accidentally exposed to moist air,

its surface turned green; this leads one to question the nature of

Peacock's^ green MoF^ . On one occasion the series of three pyrex U- tubes

exploded in the fume hood after it had been detached from the vacuum

101
system. Thereafter any fluoride sample was disposed of by drawing over

it a large quantity of water with an aspirator. If a pyrex tube under vacuum is not baked in a Bunsen flame beforehand, its surface turns blue

and is etched on exposure to these fluorides. Although MoF^ appeared to

be stable for many days in a properly prepared pyrex tube at room temperature, white needle-like crystals which melt near 95°C have been observed

to form in pyrex which was kept near 100 °C. Sealing pyrex previously

10

exposed to MoFj. turned the glass bluish-black. Edwards et . al . 8

believed the most likely impurity to be MoOF^ which Cady and Hargreaves

found to have at 100°C a vapor pressure about 2.5 times that of their

16 MoF^ measurement. Using a common derivation for simple batch distillation of an ideal binary solution, one finds that an initial fraction of

distillate which contains about 65 mol % of the original mixture must

be discarded to reduce the more volatile component in the residue from

0.5 mol % to 0.1 mol %. Clearly fractional distillation would be more

appropriate than the trap-to-trap process used by Edwards eit. al. In

this work this impurity was hopefully reduced by discarding the first

two batches from the reaction tube because the surface of powdered Mo

seemed a likely source of oxygen.

17 Churney analyzed a weighed sample of MoF^ which was prepared as above and sealed under vacuum in a pyrex vessel with a break seal. The

sample was dissolved in water, made alkaline with 2N KOH, and oxidized

to Mo (VI) by aqueous hydrogen peroxide. Using the 8-hy droxyquinoline

18 x gravimetric method , he determined % Mo which as shown in Table 1

involves a blank correction. He checked his method by several analyses

of presumedly pure MoF^, which was also supplied in a pyrex ampoule.

The average deviation above theoretical of % Mo in the MoF^ served as the blank correction. The high results are explicable on the basis of

entrapped silica in the fine fritted glass crucibles. Since analysis

of Mo above is ambiguous, plans are afoot to determine F by a null-point

19 potentiometric method

102
Melting and Purity

The melting point is a most important physical property from the

standpoint of identification and purity of a given compound. Taylor

20 and Rossini have described a method for determining, from appropriate

temperature-time melting curves, the melting point T^ of a given substance, and within certain wide limits, the melting point T^ of that

substance for zero impurity. This method applies to a liquid-soluble

and solid-insoluble impurity and assumes that its mol fraction N

g in

the sample is small in which case

N = (T - T ) A S°/RT

o m mm (7)

Since samples of MoF c and MoF^ were of necessity small and had to be

handled in a vacuum system, a miniature melting point tube was constructed

of three concentric pyrex tubes (of diameters 4, 8, and 28 mm). The

smallest tube held a chromel-alumel thermocouple, the sample was sealed

in the middle tube, and the third tube was evacuated and submerged in a stirred water bath which was controlled constant to 0.005 kelvin during

an experiment. The 1.7 ml sample (11 cm long and 1 mm wall) required

several days to crystallize. Since stirring was not possible, the

impurity was assumed to diffuse uniformly in the liquid phase during the

30 to 60 min. of melting. The rate of melting was constant to the extent

that the difference between the bath temperature T and the sample temperature was from 20 to 40 times greater than the melting range; so the

melting curve was assumed as a rectangular hyperbola upon three selected

ooints of which a geometrical construction yielded T and T . These points m o were selected from that portion of the melting curve which extended over

1/4 to 1/2 of the material melted and satisfied a test for the assumed

nature of the curve such that (z-z ) / (T-T ), in which z is the time and

r r —

z^_ is an arbitrary reference, appeared linear with (z-z^) The results of

melting MoF, are shown in Table 3 and agree very well with the calorimetric

6

4 value of Osborne et . al . . The last line was believed to give a better

value than the two preceding because a copper core the length of the sample

served as the thermocouple junction.

103
Table 3

Observed Melting Data on Samples of MoF

5

and MoF,

6

Sample

3 Investigator Ref

Bath

temp

.

°C

Sampleb

mp

°C

mp

lowering

kelvin

Cryoscopic

impurity

mol %

MoF c Peacock 7 64

D Cady & Hargreaves 8 67

This work 49.4 46.4

49.35 45.51 0.16 o.u

c 48.42 45.45 0.22 0 .15°

MoF. Osborne et. al

.

4 17.58 0.00516 0.0032

D This work 15.62 17.43 0.18 0.11

19.68 17.35 0.18 0.11

19.63 17.55 0.050 0.031

^ines 4 and 5 refer to the same sample; similarly lines 7 and 8 refer

to another. The sample holder for lines 5 and 9 used a copper core

the length of the sample.

The mp for zero impurity is the sum of columns 5 and 6.

QThese values are based on an estimated heat of fusion of 1400 cal per MoF,,.

The results of MoF were quite surprising compared to those of the

7 g

^ other investigators *

. An error that is possibly related to lack of

stirring is shown in Table 3. The experiment of line 4 which required

15.6 min. to melt half the sample indicated a lower (T -T ) than that of

o m

line 5 which required 28.0 min., but the former was without a copper core. The error of some solid solution is suspected because MoF,. has a small heat

of fusion, which will be discussed later. To explain the large discrepancy,

however, one may wonder if MoF^ can form a metastable solid as sulfur does.

Another explanation is that an eutectic is formed as Meyer, Oosterom, and

21

Van Oeveren offered in an analogous case. They found a eutectic of

NbCl^-NbOCl^CS .6 mol %) which melted 3.5 kelvin below pure NbCl,. and mixtures

with NbOCl^ greater than 5.6 mol % whose mp were observed greatly increased.

An estimate of the entropy of fusion is required to calculate from eq 7 the cryoscopic impurity of MoF^ . The fraction of sample melted is expressed

as

f = (T - T ) / (T - T) (8)

o m o

104
and the heat balance during melting may be approximated as

k (T - T)dt = n( A H°)df + CdT (9)

b m

in which _k is the heat transfer constant, ii is the moles of sample, and

C is the heat capacity of sample and container. The ratio k/

was evaluated

by integrating eq 9 for the special case of f = 1. Differentiating eq 8,

substituting in eq 9, and integrating the result by partial fractions gives

A H^. Using an estimated value of and points from the melting curve

of the experiment in line 5 of Table 3, gave an estimate of 1400 cal/mol

for A H° (MoF )

m 5

The heat transfer coefficient k was evaluated independently from a consideration of the heat transfer characteristics of the mp tube.

Longitudinal heat conduction from the bath to the sample was estimated

by integrating

d

2T/dx2 = m(T - T, ) (10)

b

in which m is a constant, and was found as 10% of the radiant heat transfer

from the isothermal bath to the enclosed sample holder. Their sum was 10%

greater than that observed from the melting curve. Perhaps the major con- tribution to this difference is an error in the assumed value of Finally

the temperature difference between the thermocouple junction and the sample

was estimated, by integrating an expression similar to eq 10, as 0.015 kelvin.

Vaporization by Entrainment

The details of an entrainment measurement similar to what was performed

22

here was described in an earlier paper . In general a flow of helium, which

was dried in a molecular sieve to about 1.5 ppm, was passed over a sample of

MoF in a pyrex vapor cell at a given temperature, which was provided by

a stirred oil bath controlled constant to 0.005 kelvin. The sample distillate was condensed by a dry -ice slurry downstream and weighed in a sealed

pyrex tube, and the quantity of carrier gas was measured in a tank. Saturation of the carrier gas was closely approximated by using the guidelines

105
of Merten and Bell for an appropriate geometry of the vapor cell and

flow of the gas mixture. An empirical test for saturation, however, has

yet to be made.

The preliminary results of the entrainment measurements are shown

in Table 4. The partial pressure of MoF,. was calculated from eq 11 as

if the vapor were monomeric.

P. = (n./n ..

)

1 1 total 7 total (ID

Table 4

Preliminary Results of Vaporizing a Sample of MoF,.

by Entrainment

Exp t

.

a

T

K

Gas

Flow

ml/ sec

w(MoF ) distillate ,mgP (MoF,.

)

of sample

torr

P(MoF

6

) of sample

torr

P (MoF .

)

added 6 ° torr

N (MoF.

)

0

mol %

1 333.0 0.799 88.7 0.468 0.151 24

2 1.008 251.7 0.459 b

3 0.650 156.0 0.442 0.065 13

4 362.8 1.172 501.0 b 0.4479

5 1.173 422.9 2.883 0.4476 13

6 1.271 477.0 2.755 0.207 7

7 333.0 1.037 191.6 0.465 0.087 15.8

8 362.8 0.814 297.7 3.010 0.509 14.5

The series 1, 2, and 3 and the series 5 and 6 give the results of

successive flows without altering the sample between runs. On the other

hand the sample was pre- treated before runs 1, 4, 5, 7, and 8 with MoF^.

after which any excess was evacuated.

b These condensates were accidentally destroyed before weighing.

Here the carrier gas was deliberately enhanced with MoF^ before reaching

the sample.

Experiments 1 through 6 indicate that MoF,. vaporizes simply and dispropoxtionates . Before each experiment the sample at room temperature was connected

to the vacuum system for several hours with no visible transfer of MoF;..

At the conclusion of a flow the distillate of MoF;. was warmed to room tern- perature while connected to the vacuum system and any MoF, was added to that

106
condensed further downstream by liquid nitrogen. These distillates were

identified roughly by their physical properties. In the series (1, 2,

and 3) and the series (5 and 6) successive flows of helium were passed

over the sample which was not altered between runs by a treatment with

MoF^ vapor. The liquid residue appeared darker brownish-yellow as the

observed partial pressure of MoF^ decreased; this corresponds to an increase of a soluble impurity such as MoF^ . Upon treating this dark

residue with MoF^ vapor, after which any excess was evacuated at room temperature, the residue was transformed to a light yellow crystal

again.

The last two experiments in Table 4 involve a flow of helium which

was deliberately enhanced with MoF^, vapor. This vapor was generated by

a constant temperature bath, in which methanol was circulated through

an external dry ice slurry and which was controlled to 0.01 kelvin for

more than 5 hours at -65°C . The partial pressure of MoF,. was calculated

4

6

from the data of Osborne _et. al. At the end of these runs the residue

continued to remain light yellow. The partial pressure of MoF. was found

as 26 to 34% of Cady and Hargreaves' direct pressure measurement . Tentative values of A H° and A S° of eq 1 at 348 K were calculated

by eq 5 and the pressure data of experiments 7 and 8 as 15.0^ kcal and

30.

4^ eu, respectively. Cady and Hargreaves' pressure data of eq 3 gives

A H° and AS 0 of eq 1 at 383 K as 12.68 kcal and 26.1 eu respectively.

Since there is some evidence that MoF_ and MoF. react somewhat with

5 6

pyrex, future plans involve entrainment measurements in monel.

107
References

[1] J. E. Fergusson, "Halide Chemistry of Chromium, Molybdenum, and

Tungsten," Halogen Chemistry , vol 3, V. Gutmann (editor), Academic

Press, London, 1967, p. 227.

[2] J. H. Canterford, R. Colton, and T. A. O'Donnell, Rev. Pure and

Appl. Chem., 17, 123 (1967).

[3] H. H. Claassen, G. L. Goodman, J. H. Holloway, and H. Selig,

J. Chem. Phys . , _53, 341 (1970).

[4] D. W. Osborne, F. Schreiner, J. G. Malm, H. Selig, and L. Rochester,

J. Chem. Phys., 4_4, 2802 (1966).

[5] J. L. Settle, H. M. Feder, and W. N. Hubbard, J. Phys. Chem., 65 , 1337 (1961).

[6] 0. Ruff and F. Eisner, Chem, Ber., 40, 2926 (1907).

[7] R. D. Peacock, Proc. Chem. Soc., 59 (1957).

[8] G. H. Cady and G. B. Hargreaves, J. Chem. Soc., 1568 (1961).

[9] T. A. O'Donnell and D. F. Stewart, J. Inorg. Nucl. Chem., 24 , 309 (1962).

[10] A. J. Edwards, R. D. Peacock, and R. W. H. Small, J. Chem. Soc.,

4486 (1962).

[11]

T. J. Ouellette, C. T. Ratcliffe, and D. W. A. Sharp, J. Chem. Soc.,

2351 (1969).

[12] H. J . Emeleus and V. Gutmann, J. Chem. Soc., 2979 (1949).

[13] V. Gutmann and K. H. Jack, Acta Cryst. 4-, 244 (1951)

.

[14] D. E. LaValle

,

R. M. Steele, M. K. Wilkinson, and H. L. Yakel, Jr.,

J. Amer. Chem. Soc .

,

82, 2433 (1960).

[15]

0. Kubaschewski and E. Evans, Metallurgical Thermochemistry , Pergamon Press, New York, 1958, pp . 180-197.

[16] Chemical Engineers' Handbook , J. H. Perry (editor), McGraw-Hill

Book Co., New York, 1950, p. 580.

[17] K. L. Churney, private communication, Aug. 1971.

108
[18] A. I. Vogel, Quantitative Inorganic Analysis , John Wiley and

Sons, Inc., New York, 1961, pp . 506-508.

[19] T. A. O'Donnell and D. F. Stewart, Anal. Chem., J33, 337 (1961).

[20] W. J. Taylor and F. D. Rossini, J. Res. Nat. Bur. Stand., 32 , 197 (1944).

[21] G. Meyer, J. F. Oosterom, and W. J. Van Oeveren, Rec. Trav. Chim.

Pays-Bas, 80, 502 (1961).

[22] R. F. Krause, Jr. and T. B. Douglas, J. Phys . Chem., _72, 475 (1968).

[23] U. Merten and W. E. Bell, "The Transpiration Method," The Characterization of High-Temperature Vapors , J. L. Margrave (editor), John

Wiley & Sons, New York, 1967, pp . 91-114.

109
Chapter 8

THE INFRARED SPECTRUM OF MATRIX ISOLATED NbF,_

Nicolo Acquista and Stanley Abramowitz

National Bureau of Standards

Washington, D. C. 20234

The infrared spectra of matrix isolated NbFs as well as some gas

phase spectra have been observed. These spectra have been obtained using

double boiler Knudsen cells. Interpretation of the spectra to yield the

six infrared active frequencies of a C 4 V monomeric structure for NbFs

is advanced.

This research was sponsored by the Air Force Office of Scientific

Research, United States Air Force under AFOSR-ISSA-69-001

.

110
The study of the spectra of the MF 5 molecules have shown these

molecules to have either a D3^ (trigonal bipyramid) or structure.

In several instances structures are different for the gaseous liquid

and solid phases. Furthermore, for the group VA fluorides, PF5 and

ASF5 have D

3^ symmetry and SbFs has C4V symmetry. This seems to indicate

that the barrier to internal rotation may be low leading to an equilibrium

between D3^ and C4 V structures. Indeed, for VF5 there exists some evidence for such an interpretation of the observed infrared and Raman

spectra. There are also polymers in the vapors of some of these species

including a tetramer of C4V symmetry. The x-ray diffraction patterns of

NbF 5 , TaFs, SbF 5 , etc. have been interpreted on the assumption of a tetrameric C4V structural unit for the crystalline species. We have

investigated the infrared spectra of the matrix isolated vapors above solid

NbF 5. By employing double boiler techniques we have been able to obtain

the spectra of the matrix isolated monomer.

There is no complete infrared spectrum of NbFs. Blanchard [ 1 ] studied

gaseous NbF 5 in the infrared region using NaCl and KBr optics at several

temperatures up to 142 °C and observed three strong bands above 500 cm

-1

. On the basis of his temperature studies he assigned the bands to fundamental

of monomeric NbFs. In order to make a partial vibrational assignment he

assumed NbF 5 gas to have a trigonal bipyramidal structure (03^). Other

pentahalides of the 5 th group are known to have this symmetry [ 2 ]. The

vibrational representation of an XY 5 , D 3 ^ molecule is 2 a^ ' + 2a2 M + 3 e

1 + e"

with the a2" and e’ modes infrared active and the a^ *

e' and e" modes

Raman active. For a C4V molecule the vibrational representation is 3a 1 +

2bi + b2 + 3e2 (a^ and e infrared active; a^ , b^ , b2 and e Raman active).

Using the observed vibration rotation band contours Blanchard assigned the

infrared bands at 740 , 688 and 510 cm

-1

to v^(a2") and V4(a2 M

) respectively

The Raman spectrum of liquid NbF 5 was observed at several temperatures

by Selig et al [ 3 ]. They concluded in contrast to VF5 that there was no evidence for polymerization in the liquid. The observed spectral intensity

changes with temperature in liquid VF5 were interpreted as indicating the

presence of polymer, while the absence of these changer, in the Raman spectrum

of liquid NbF 5 to the absence of polymer.

The Raman spectrum of liquid NbFs as verY simple, consisting of 4 strong

lines and 3 weak features. The bands observed at 767 and 683 cm

-1 are highly

polarized relative to the others. These lines are assigned to v^Cai’) and

^2

(

a l

1 ) respectively. The other strong features at 253 and 226 cm

-1 and the

weaker features were unpolarized. The selection rules for D 3 ^ point group

call for six Raman active bands of which two should be polarized. As a complete infrared spectrum was lacking, the other lines were not assigned.

Selig et al considered the observed infrared band at 688 cm

- -1 assigned to

V3(a2 M

) by Blanchard as an accidental coincidence.

Ill
Beattie et al [4] observed the Raman and infrared spectra of the

liquid and solid NbF5

. Their conclusions, different from Selig, were that

a cis-fluorine bridged tetrameric structure exists in the liquid and solid

phases. They also carried out force field calculations for this species in

condensed phases. These calculations show the expected distribution of

vibrational frequencies for this cis-f luorine-bridged tetrameric NbF 5 unit.

Many coincidences of the observed vibrational features were predicted for

this symmetry of the molecule.

Electron diffraction data [5] show NbF5 vapor at 300 K consists of

tetramers as in the solid, while at 475 K the vapor is mostly monomer with

D 3 ^ symmetry.

The electric deflection technique [6] has also been applied to NbFs

vapor at 310 K. The conclusions from these experiments were that NbF 5 vapor behaves as a non-polar molecule and that a large concentration of

monomer is present.

In view of the lack of a complete infrared spectrum and the uncertainty

in its vibrational assignment, it appeared worthwhile to reinvestigate

NbF 5

. In particular it was felt that the matrix isolation technique could

be useful for observation of the infrared spectrum of monomeric NbF 5

.

Experimental

In the present work, the electron beam furnace, an Air-Products

Cryotip operated at liquid hydrogen temperature and a Perkin-Elmer infrared

spectrophotometer operated from 4000-50 cm 1 were used [7]. Stainless

steel Knudsen single and double oven crucibles with one mm orifices were

employed. The double oven cell consisted of two identical crucibles

separated by a thin walled stainless steel tubing of 1/16" diameter. It was possible to change the distance between the crucibles. Our furnace

conditions allowed the direct heating of the upper crucible; the lower was heated by conduction through the thin walled stainless steel connecting

tubing. The larger the separation of the two crucibles the greater the

temperature difference between the upper and lower crucibles. The use of

stainless steel for the double oven with its relatively low thermal conductivity allowed temperature differences as great as 100°C to be maintained

when the two crucibles were separated by 1.5 inches. The temperature of

both crucibles was measured with a W 3% Re vs. W 25% Re thermocouple.

The NbF 5 , obtained from commercial sources, was used after prolonged

outgassing. During deposition the lower crucible was maintained at 25-30°C

to give NbF 5 a vapor pressure in the range of 0.001 to 0.005 torr~ [8]. The

flow of argon, the matrix gas used in all the experiments, was in range of

10 to 20 mmoles/hour. Estimates of the M/R in general are difficult to

make. For a single boiler with knowledge of flow rates, the Knudsen formula

112
and the geometry of the system an estimate can be made. When a double

boiler is used, the M/R is still more uncertain. If, for our system we estimate the M/R ratio to be about 500-1000 for a single boiler experiment,

the ratio in the double boiler will be considerably greater. Nevertheless,

most spectra were obtained in 30 minutes to one hour.

The gas phase spectrum of NbFs was observed using a 10 cm gas cell

having a monel body. Csl windows were demountably attached through

Viton 0 rings. This cell was heated to about 80°C in order to obtain a spectrum in the 400-800 cm 1 region. (Unfortunately, we were not able to

observe a spectrum using a one meter cell because of the low vapor pressure

of NbFs at room temperature coupled with the inconvenience of heating such

a cell.) The NbF 5 reacts with the Csl windows. This reaction proceeds

at a rate such that about 10-15 minutes is available to obtain a spectrum

of gaseous NbFs. The spectra were calibrated by using absorption line of

atmospheric water, ammonia, and CO 2 . The bands were measured to ± 1 cm

-1

.

Experimental Results

The gas phase spectrum of NbF 5 is shown in Figure 1. This spectrum

was run on a 112 G equipped with a 40 1/mm grating and a suitable interference

filter. From the observed contour of the doublet at 745.2 and 732.8 cm

-1 we conclude that these are two different bands and are not as Blanchard

concluded due to one vibration. Our conclusion was reached by considering

the contours expected for various j constants using the B values calculated

from the interatomic distances given by Romanov and Spiridanov [5]. The

contour expected for a P-R separation of 12.4 cm

-1 does not conform to the one observed [9]. Therefore, one concludes that there are three strong

features in the Nb-F stretching region (745.2, 732.8 and 689.7) which are assignable to the three infrared stretching modes of a C 4 V molecule (2a^ + e)

The band which occurs at 513 cm

-1 in an argon matrix was also observed in

the gas phase. Unfortunately, the pressures needed for the observation of

the far infrared spectrum required temperatures too high for our cell. At

these high temperatues the NbF 5 reacted too rapidly with the Csl windows.

The infrared spectrum of NbFs vapors isolated in Ar matrices at liquid

hydrogen temperatures is shown in Figures 2 and 3. This spectrum has two

regions of strong and one of weak absorption. Bands appear at 740, 729,

686 and 513 cm

-1 in Figure 2. The spectra in this region remained essentially

the same whether single or double boiler effusion cells were used. The

effusion temperature for the single oven was set to about 300 K. When the

double oven was used, the lower crucible temperature was set to 300 K while

the upper crucible temperature reached a temperature of about 400 K. At this

temperature one should expect effusing vapor to contain a large proportion of monomer.

113
114

The

Gas

Phase

Infrared

Spectrum

of

NbF5

.

The

band

at

667

cm

-1

is

due

to

atmospheric

CO2

.
115

The

Infrared

Spectrum

of

Matrix

Isolated

NbFs.
ABSORPTION

273 261 242 223 192 154

CM'l

Figure 3

Infrared Spectra of Matrix Isolated NbF 5

. 116
The gas phase infrared results shown in Figure 1 agree quite well

with the matrix data. The matrix data support the conclusions that we

are observing monomer in the temperature range of 370 to 410 K. Both sets

of data are listed in Table I with our assignment of these bands. The

above observation that the double boiler experiment in which monomer

prevails yields essentially the same spectrum as the single boiler does

not appear unusual. These high frequency vibrations which are assigned

to the stretching modes are less likely to be perturbed when the monomer

is condensed into polymers than the low frequency bands.

Figure 3 curve (a) shows the far infrared spectrum of NbF 5 in an argon

matrix at liquid hydrogen temperatures from 300 to 130 cm

-1

. The NbFs

effused from a single boiler crucible at a temperature of 325 K. At this

temperature the vapor consists primarily of polymer. The multiplicity of

bands is an indication of thei^ presence in the matrix. Bands occur at

271, 242, 222, 194 and 158 cm

-

. Curve (b) shows the same region of the

spectrum when double boiler effusion is used. Here the double oven consisted of two crucibles separated by 1.5 inch. The temperature of lower

crucible was 315 K, the upper 400 K. The character of the spectrum has

changed. At 400 K the vapor is primarily monomeric. All the bands have

been reduced in intensity and a new band appears at 261 cm

-1

. The double

oven effect is evident here. The polymer bands are still present but

considerably weakened. Diffusion experiments in this region showed a disappearance of 261 cm

-1 and a broadening, and slight increase of bands

at 222 and 242 cm

-1

.

A final double oven experiment was performed in which the 261 cm

-1

band was more intense than the polymer (curve c) bands. When this had

been accomplished, the far infrared was examined to about 50 cm

-1

. An

absorption band was observed at 103 cm

-1

. This band was detected only

when the monomer band was present. On the basis of the double oven and

diffusion experiments both the bands were assigned to monomeric NbF 5

. These

results are summarized in Table I, together with a proposed vibrational

assignment. In the table are included the Raman bands found in the liquid

by Selig et al

Conclusion

The monomeric spectrum of NbF 5 has been observed and all six infrared

active fundamentals have been assigned on the assumption of C 4 V symmetry.

The double oven experiments proved very effective in separating the monomer

from the polymer bands. The assignment of this molecule is complete

except for the Raman active b^ and b£ species. One would expect V 4 (b^) and

V 5 (bi) to have frequencies of about 500 and 275 cm

-1 respectively while

Vg(b 2 ) is expected to have a frequency of about 300 cm

-1

. The fundamental

frequencies assigned in this study are consistent with those of SbFg [ 10 ],

BrFs, CIF 5 and IF 5 [11]. Unfortunately, for all these species no infrared

spectra have been observed below 200 cm

-1

. The lowest frequency of VF 5 [12],

ASF 5 [13] and PF 5 [14,15] appear at 109, 138 and 179 cm

-1 respectively.

This is consistent with the observation of 103 cm

-1 for the lowest frequency

of NbF 5

.

117
Table I

Observed Bands and Vibrational Assignment for NbFs

. a Matrix Gas

a Seligj Liquid^ Assignment

767

739.9 745.2 Vi (a)

729.3 732.8

726

V 7 (e)

685.5 689.7

683

v2 (a)

513.0 497 v 3 (a)

271

315

261

253

Vs (e)

242

226

polymer

222 polymer

194 polymer

158

136

polymer

103 v 9 (e)

this study

Reference 3

118
References

1. S. Blanchard, J. Chim. Phys . (1965), 919.

2. K. Nakamoto, Infrared Spectra of Inorganic and Coordination

Compounds (John Wiley and Sons, Inc., New York, N. Y. , 1970).

3. H. Selig, A. Reis and E. L. Gasner, J. Inorg. and Nucl. Chem. 30 , 2087 (1968).

4. I. R. Beattie, K. M. S. Livingston, G. A. Ozin and D. J. Reynolds,

J. Chem. Soc. (London) (A1969) , 958.

5. G. V. Romanov and V. P. Spiridanov, Vestn. Mosk. Univ. Khim. 23 , 761 (1968).

6. T. R. Dyke, A. A. Muenter, W. Klemperer and W. E. Falconer, J. Chem. Phys. 53, 3382 (1970).

7. S. Abramowitz, N. Acquista and I. W. Levin, J. Res. NBS 72A , 487

(1968)

8. J. H. Junken, R. L. Fauen, Jr., E. J. Barber and H. A. Beinhardt,

J. Am. Chem. Soc. _74_> 3464 (1952).

9. R. V. Valentine, Ph.D. Thesis, Purdue University, 1957.

10. A. L. K. Aljibury and R. L. Redington, J. Chem. Phys. 5_2, 453 (1970).

11. G. M. Begun, W. H. Fletcher and D. F. Smith, J. Chem. Phys. 42 , 2236 (1965).

12. H. Selig, J. H. Holloway, J. Tyson and H. H. Claasen^J. Chem.

Phys. 53, 2559 (1970).

13. L. C. Hoskin and R. C. Lord, J. Chem. Phys. 4^6, 2402 (1967).

14. I. W. Levin, J. Chem. Phys. _5(3, 1031 (1969).

15. I. W. Levin, J. Mol. Spectroscopy _33, 61 (1970).

119
Chapter 9

SURVEY OF THE SYSTEMS Mo-C, Ta-C and Nb-B WITH EMPHASIS ON

COMPOUNDS SUITABLE FOR ENTHALPY MEASUREMENT BY DROP CALORIMETRY,

INCLUDING A LITERATURE SURVEY OF ENTHALPY AND HEAT CAPACITY DATA

ON SELECTED COMPOUNDS FROM THESE SYSTEMS

David A. Ditmars

I. Introduction

Refractory metal carbides and borides, because of their extremely

high melting points (some as high as 4000 K) and because of the

stability of certain compounds of this class at elevated temperatures,

are attractive prospects for construction materials in very-hightemperature applications. Thermodynamic data on well-characterized

compounds of this class should be of use not only in design calculations but also in predicting the behavior of refractory metals themselves when exposed to corrosive environments. As part of the

continuing NBS effort to improve or augment the thermal data on these

carbides and borides, the literature has been surveyed for heat

capacity and enthalpy investigations of stable compounds chosen from

the systems Mo-C, Ta-C and Nb-B. In addition, efforts have been made

to obtain compounds belonging to these systems, suitable for precise

high-temperature enthalpy measurements. The results have given

valuable insight into the difficulty of synthesizing refractory

carbides and borides and in their adequate characterization.

II. Stable Phases Suitable for Calorimetric Measurement

A. Phase Diagrams --General Features

The phase diagrams for the refractory carbides and borides of

this study are shown in figures 1, 2 and 3. These represent the

latest information available on these systems and resulted from an extended experimental investigation [l] a which employed x-ray,

metallographic, DTA and standard chemical analytical techniques.

3 Figures in brackets indicate literature references listed at the end

of this chapter.

120
TEMPERATURE

Figure 1. Phase diagram of the system Mo-C (ref.[l}).

121
TEMPERATURE

Figure 2. Phase diagram of the system Ta-C (ref .[!]).

122
Figure 3. Phase diagram of the system Nb»B (ref «[1 j)

123
The general features exhibited by all these systems which are especially pertinent to the present study are the formation of hightemperature phases unstable at lower temperatures (particularly in

the Mo-C system) and the existence of solid phases stable over a wide

range of temperatures extending to room temperature but with a variable

range of homogeneity. These latter solid phases exist within the

speckeled areas in the phase diagrams.

Since the enthalpy measurements planned on these systems will be

carried out with drop-type calorimeters (one, isothermal; one, adiabatic)

in which the samples are suddenly quenched to the ice point from a temperature as high as 1173 K (isothermal calorimeter) or to room

temperature from a temperature as high as 2600 K (adiabatic calorimeter),

the study has been initiated with those compounds stable over these

temperature ranges or with at most one polymorphic transition. With

these guidelines in mind the following compounds were selected as potential candidates for study: M02C, TaC, Ta£C, NbB, NbB2, Nb3B2 and

Nb3B4» Note again that these are conventional formulae corresponding

to compounds of ideal stoichiometry whereas in reality, both the metal

and non-metal sublattices show a considerable tolerance for vacancies,

giving rise to a continuous series of defect compounds [6]. For

instance (see fig. 1), at 2000°C, the structure identified with

can exist with any carbon concentration from ~ 30 to ~ 34 atomic percent.

Two of the difficulties which seriously limit the value of much

of the existing thermal data on these compounds is that previous

investigators have in many cases not recognized the importance of

establishing the stoichiometry of the compounds they investigated,

nor (in the case of M02C) the considerable effect of this upon a recently identified order-disorder transition in this compound. ^ The

value of the thermal data to be obtained in this program will be further

enhanced by the investigation of two or more compositions of some of

the compounds. This will hopefully allow interpolation of the thermal

properties of other compositions. The existence of variable and narrow

According to both Storms [4] and Rudy [2], M02C, upon cooling to room

temperature from above 1700 K, undergoes a transition from the

(disordered) 3 phase to the (ordered) a phase. Furthermore, there

exist critical cooling rates for this compound, dependent upon the

carbon content, which if exceeded could result in "frozen-in" disorder. These same investigators have indicated that both the sample

carbon content of the M02C samples chosen for measurement in this

program and the known cooling rates within the existing drop calorimetric apparatuses are such as to minimize the risk of the sample

being in a non-equilibrium state within the calorimeters.

124
homogeneity ranges (especially in the system Nb-B) indicates that

considerable difficulty can be expected in achieving high phase-purity

for some of these compounds. This proved to be the case in one commercially available sample of "NbB" which x-ray analysis showed

to be only 75 percent NbB with the remainder NbB2, Nb3B2 and an unknown

fourth phase. Therefore, in selecting compounds for enthalpy measurements, priority has been given to those compounds having the widest

homogeneity ranges (M02C, TaC and NbB2)

B. Methods of Synthesis and Sample Characterization

1. Synthesis

The synthesis of any one of these compounds can be a considerable problem in itself and involves a good measure of "trial

and error". It is in general not possible to purchase these compounds

"off the shelf" if one desires to obtain material of a chemical and

phase purity adequate for meaningful thermodynamic investigations.

Also, it is usually not possible to produce these carbides and borides

by blindly heating mixtures containing the correct stoichiometric

proportions of the metal and non-metal components, and assuming that

the desired compound alone will result [2]. This is so, partly because

the temperatures required to melt or react these substances (mostly in excess of 1500 K) are sufficiently high that selective vaporization of one of the components can alter the composition significantly, leading

sometimes to the formation of undesired phases [2].

The favored method for synthesis of these compounds is by

powder metallurgy. Arc-melting has also apparently been used successfully. In the former technique, high-purity powders of the elements

involved are thoroughly mixed (sometimes with an excess of one or the

other) with an organic binder and cold-pressed into pellets. The

binder is driven off as the pellet is heated—-usually to above 1500 K

to homogenize it. In the case of the Ta-C compounds, the pellet must

then be reground and the powder heated to 1800 K several times [3],

X-ray patterns are customarily taken between each regrinding and heating

to establish when the material has reached the desired phase purity.

In the case of M02C, adjustment of this compound to a composition which will be stable and phase-pure at all temperatures

down to room temperature can be achieved by taking advantage of the

fact that M02C vaporizes congruently near MoCQ^g[4], The sample is

fabricated in nearly these proportions by the powder technique referred

to above and then heated for several hours at 2400 K, driving off any

excess component as well as dissolved oxygen.

125
2 . Sample Characterization

Whereas the techniques of synthesis may vary with each of the

compounds referred to above , the same methods of analysis are useful for

all of them for proper characterization. Standard analytical techniques

(mass spectrographic analysis, atomic absorption spectroscopy) can be

employed to indicate the amounts of trace elements present. In addition,

a separate analysis for oxygen is desirable. However, because of the

high likelihood of phase impurities in these compounds, a "wet" chemical

analysis for the major components will not suffice to complete the

sample characterization. A number of techniques have been applied by

workers to establish the phase purity of their samples; among them,

nuclear magnetic resonance, x-ray diffraction, neutron diffraction,

microscopic metal lographic analysis and a combination of the last

method with electron microprobe analysis. The first three methods

cannot be considered as definitive methods if one is concerned with

phases present in amounts below a few atomic percent,. Metal lographic

examination is the most useful technique here and it is claimed [2]

that properly applied, it can quantitatively detect as little as 0.1

percent of a foreign solid phase.

III. Literature

A. General References

The most valuable general references dealing with the chemistry,

thermodynamics and phase behavior of refractory carbides and borides

have been found to be the monographs of Storms [5] and Hausner and

Bowman [6], the extensive report series of Rudy and co-workers [7,8,

9,10,11,12] and the compendia of Schik [13], Hansen [14], Elliot [15]

and Shunk [16].

A search of the literature has been made for reported enthalpy

and specific heat data on the carbides and borides of interest to this

program. In addition to consulting the general references listed

above. Chemical Abstracts were covered through July 1971; Ceramic

Abstracts, through December 1970 and the Bulletin(s) of Thermodynamics

and Thermochemistry, through No. 13 (1970) . The results of this search

are tabulated in table 1.

126
Table 1

Reported Investigations of Enthalpy and Heat Capacity

of solid Mo

2 C, TaC, Ta

2 C, NbB, and NbB

2

Compound Year Enthalpy Heat: Capacity c 298 15Ref.

Range Range

-1 -1

K K cal, mol ,K

Mo-C 1964 533-2200 [19]

z 1966 52-296 15.73 ± .09 [17]

1966 406-1403 [17]

1968 21-300 15.74 ± .03 [18]

TaC 1940 55-295 10.11 ± 0.08 [20]

1962 538-2761 [23]

1963 1296-2843 [21]

1963 1300-2100 [22]

1965 476-1113 [24]

1966 405-1700 [17]

1967 324-985 [25]

1968 1205-2163 [26]

1968 1.5-18 [27]

Ta

2

C 1968 1.5-18 [27]

NbB 1969 1.5-18 [28]

NbB

2 1962 468-1102 [29]

1963 5-350 8.91 ± .01 [30]

1966 0.6-2.

[31]

127
References

[1] Rudy, E., AFML-TR-65-2, Part V, 1969.

[2] Rudy, E., private communication, March 1971.

[3] Bowman, A., private communication, March 1971.

[4] Storms, E. K. , private communication, March 1971.

[5] Storms, E. K. , The Refractory Carbides, Academic Press, 1967.

[6] Hausner, H. H. , and Bowman, M. G., Fundamentals of Refractory

Compounds, Plenum Press, 1968.

[7] Rudy, E., Windisch, ST., and Chang, Y. A., AFML-TR-65-2, Part I,

Vol. I, March 1965 (Mo-C system).

[8] Rudy, E., Windisch, ST., and Hoffman, J. R. , AFML-TR-65-2, Part I,

Vol. VI, January 1966 (Mo-C system).

[9] Rudy, E., Windisch, ST., Stoisick, A. J., and Hoffman, J. R.,

AFML-TR-65-2, Part I, Vol. XI, April 1967 (Mo-C system).

[10] Rudy, E., AFML-TR-65-2, Part V, 1969 (Mo-C, Ta-C, NbB systems).

[11] Rudy, E., and Harmon, D. P., AFML-TR-65-2, Part I, Vol. V,

January 1966 (Ta-C system)

.

[12] Rudy, E., and Windisch, ST., AFML-TR-65-2, Part I, Vol. X,

(May 1966) (Nb-B system).

[13] Schick, H. L., Thermodynamics of Certain Refractory Compounds,

Vols. I and II, Academic Press, 1966.

[14] Hansen, M. , Constitution of Binary Alloys, Second edition,

McGraw-Hill, 1958.

[15] Elliot, R. P., Constitution of Binary Alloys, First supplement,

McGraw-Hill, 1965.

[16] Shunk, F. A., Constitution of Binary Alloys, Second supplement,

McGraw-Hill, 1969.

128
[17] Pankratz, L. B., Weller, W. W. , and King, E. G., Bureau of Mines

Rept. Invest. 6861 (1966).

[18] Paukov, I. E., Strelkov, P. G., and Filatkina, V. S., Russ. J. Phys. Chem. 42 (11), 1576 (1968).

[19] Southern Research Institute, ASD-TDR-62-765 (1963).

[20] Kelley, K. K. , J. Am. Chem. Soc. 62, 818 (1940).

[21] Levinson, L. S., J. Chem. Phys. 39 (6), 1550 (1963).

[22] McDonald, R. A., Getting, F. L. , and Prophet, H., Interagency

Chemical Rocket Propulsion Group, Working Group on Thermochemistry,

Proc. first meeting, N.Y. (1963). CPIA Pub. No. 44 (U) , p. 213

(Feb. 1964).

[23] Neel, D. S., Pears, C. D., and Oglesby, S., WADD-TR60-924

(Feb. 1962).

[24] Mezaki, R., Tilleux, E. W. , Jambois, T. F., and Mangrave, J. L.,

Proc. Third Symposium on Thermophysical Properties, Purdue Univ.,

Lafayette, Ind., p. 138 (1965).

[25] Chang, Y. A., Trans. AIME 239, 1685 (1967).

[26] Bolgar, A. S., Guseva, E. A., Gorbatyuk, V. A., and Fesenko, V. V.

Sov. Powd, Met. Metal Ceram., No. 4, 297 (1968).

[27] Toth, L. E., AFOSR-68-0265 (Feb. 1968).

[28] Tyan, Y. S., Toth, L. E., and Chang, Y. A., J. Phys. Chem. Solids

30, 785 (1969).

[29] Mezaki, R. Tilleux, E. W., Barnes, D. W., and Margrave, J. L.,

Int. At. Energy Agency, Proc. Symp. on Thermod. of Nucl. Mat.,

Vienna, p. 775 (1962).

[30] Westrum, E. F. Jr., and Clay, G. A., J. Phys. Chem. 67 , 2385

(1963).

[31] Ukei, K. , and Kanda, E., Sci. Rep. Res. Inst. Tohoku Univ. Ser. A,

Suppl . 18, 413 (1966).

129
Chapter 10

A HIGH-SPEED METHOD OF MEASURING

THERMAL EXPANSION OF ELECTRICAL CONDUCTORS

Ared Cezairliyan

National Bureau of Standards

Washington, D.C. 20234

To avoid the difficulties involved in conventional steady-state

methods of measuring thermal expansion of electrically conducting substances at temperatures above approximately 2000* K, a transient technique

is developed. In this technique, the specimen can be pulse heated from

room temperature to near its melting point in less than one second and

pertinent experimental quantities can be measured with a time resolution

of 0.4 ms and a full-scale signal resolution of one part in 8000.

The method is based on detecting the change in radiance coming from

a constant radiation source as a result of the expansion of the specimen

placed between the radiation source and a radiation detecting system.

Aperture stop of the optical system (Figure 1) is defined by a diaphragm

which has a rectangular opening (15.9 x 12.7 mm). The "effective" aperture of the system depends on the dimensions of the rectangular opening

and the area of the portion of the specimen in line with the opening. As

the specimen is pulse heated its dimensions increase which, in effect,

130
131

FIGURE

1.

Optics

of

the

high-speed

thermal

expansion

measurement

system.
reduce the "effective" aperture. To eliminate errors on final results

due to radiation emitted by the specimen, radiance from the source is

modulated at 600 Hz with a chopper. This allows the pyrometer to measure

alternately (1) radiances from the radiation source and the specimen

together, and (2) radiance from the specimen alone. Then, the difference

between the two radiances is proportional to the dimensions of the specie

men. Specimen radiance as seen by the pyrometer is minimized by placing

a shield, which is slightly narrower than the specimen, between the

specimen and the pyrometer.

This note describes the results of preliminary experiments designed

to demonstrate the feasibility of the method. They were performed in the

temperature range 300 to 700 K to allow the comparison of the results

with those obtained by well-established steady-state methods.

The specimen was a platinum strip with the following nominal dimensions: length = 90 mm, width = 11 mm, and thickness = 0.03 mm. It was

pulse heated by passing electric currents through it. During this time,

current flowing through the specimen and potential difference across the

mid-portion were measured. Potential leads were platinum wires (0.02 mm

in diameter) spot welded to the strip approximately 30 mm apart. In

addition, radiance from the radiation source attenuated by the expanding

specimen was measured with a high-speed photoelectric pyrometer [1].

Recordings of experimental quantities were made with a high-speed digital

data acquisition system [2]. Details of the electrical pulsing, control,

and measuring circuits were described in an earlier publication [2].

132
Specimen temperature during the pulse heating period was determined

from a knowledge of the resistance- temperature relationship for platinum [ 3 ]

The relation between variation of radiance with specimen expansion

was determined by calibrating the optical system under steady-state

conditions. This was accomplished by inserting obstructions of known

cross-section in the optical path. A total of five cylindrical obstructions, ranging from 0.025 to 0.25 mm in diameter, were used. The

results of radiance variation in terms of obstruction cross-section were

fitted to a linear function using the least squares method, which gave a

standard deviation of 0.06 percent.

Two pulse experiments were performed in which the platinum specimen

was heated from room temperature to 700 K in approximately 120 ms.

Thermal expansion results of each experiment were fitted to a third

degree polynomial function using the least squares method, which gave a

standard deviation of less than 0.1 percent. The results of the two

experiments are in agreement within 2 percent. The averages of the

results of the two experiments are approximately 3 percent lower than

the recommended values for thermal expansion of platinum given by Kirby

et al [4]Estimates of errors indicate that the present results are

accurate within 5 percent.

The results of preliminary experiments described above demonstrate

the feasibility of measuring thermal expansion of electrical conductors

by a transient technique. Because of the very short experiment duration,

this technique is particularly attractive for measurements at high

133
temperatures (above 2000 K) . Also, the fact that only the middle portion

of the specimen is used for the measurements, uncertainties due to axial

temperature gradients are greatly reduced.

At the present time, several refinements are being considered to

improve the accuracy of the measurements. These are summarized in the

following items:

a. to reduce the effective aperture—this will increase the

measurement sensitivity.

b. to use specimens which are of tubular shape—this will

eliminate uncertainties due to possible specimen misalignment

and movement providing better symmetry.

c. to measure specimen temperature directly with a high-speed

pyrometer

.

d. to investigate the possibility of using a laser as the

radiation source.

References

[1] Foley, G. M. , Rev. sci. Inst. 4_1, 827 (1970).

[2] Cezairliyan, A., M. S. Morse, H. A. Berman, and C. W. Beckett,

J. Res. Nat. Bur. Stand. (U.S.) 74A (Phys . and Chem.), 65 (1970).

[3] Evans, J.P., National Bureau of Standards, private communication.

[4] Kirby, R.K., T. A. Hahn, and B. D. Rothrock, "Thermal Expansion",

American Institute of Physics Handbook, third edition, to be

published

.

134
Chapter 11

ROTATING OPTICAL ATTENUATOR FOR THE GENERATION OF SUBSECOND DURATION

SAWTOOTH SHAPE RADIANCE PULSES

Ared Cezairliyan

National Bureau of Standards

Washington, D. C. Z0234

Abstract

A rotating attenuator for the generation of sub second duration

sawtooth shape radiance pulses is described. The attenuator disk

is in the form of a cam. The geometry of the opening of a diaphragm

used as the aperture stop determines the shape of the radiance pulses.

Radiance is determined from the measurements with a high-speed

photoelectric pyrometer. Recording of signals is made with a highspeed digital data acquisition system. The combined measuring and

recording systems have a full-scale signal resolution of approximately

one part in 8 000 and a time resolution of 0. 4 ms. Two different

diaphragms are used in this study yielding radiance pulses (20 to 150ms

long) with linear and quadratic rise. The standard deviation of the

experimental points from the pertinent functions describing the radiance

variation is less than 0. 5 percent.

135
1. Introduction

Considerable amount of work has been done to develop various

techniques to modulate radiance beams in the visible as well as in the

ultraviolet and infrared regions. Most of these techniques were confined

to generating either repetitive rectangular pulses, or short-duration

fast-ri se -time single pulses. A review of various methods for modulating radiance pulses was given by Jones [l]. Optical modulation

techniques in the infrared region were discussed by Hudson [z].

Increasing interest in research in transient techniques for the

measurement of properties of matter at high temperatures and related

studies have necessitated the development of programable optical attenuators. Such attenuators are needed in order to simulate (using steadystate radiance sources) the rapid heating or cooling of the specimen and

also to check dynamic characteristics of radiation detectors and of

high-speed temperature measurement systems in general.

2. Method and Apparatus

In this study an optical system, including a rotating optical attenuator

is described which is capable of generating repetitive sawtooth shape

(either linear or quadratic) radiance pulses, ranging from 20 ms to several

seconds in duration. The optical system is shown in figure 1. It consists

of a radiance source (tungsten filament lamp), a rotating disk (cam with

helical circumference), a special diaphragm, a high-speed pyrometer,

and other pertinent optical components. The lenses 01 and 02 shown in

figure 1 were 63 mm in diameter with f = 2. 5. The circumference of the

disk was machined in such a way that its radius r was proportional to

the angle from a fixed reference point according to the following relation

r = r 0 - kff (1)

136
DIAPHRAGM

137

FIGURE

1.

Functional

diagram

of

the

optical

system

for

the

generation

of

subsecond

duration

sawtooth

shape

radiance

pulses.
where r 0 is the maximum radius, a the angle, and k, the proportionalityconstant. The maximum and minimum radii of the disk were 7 in. (177. 8mm)

and 6 in. (152. 4 mm), respectively, yielding a maximum difference of

1 in. (25. 4 mm). The thickness of the disk was 0. 12 in. (3 mm).

The aperture stop of the optical system was defined by the circumference of the disk and the diaphragm placed in the collimated portion of

the beam. As the disk rotated, the effective cross-sectional area of

the beam changed, which, in turn, generated sawtooth shape pulses. The

shape of the diaphragm opening determined the shape of the radiance pulse.

For example, a rectangular opening as seen in figure 2 yields a pulse with

linear rise, a triangular opening gives a pulse with quadratic rise. Rotation

of the disk was synchronized with other measuring equipment with a signal

obtained from a radiation detector. The radiation detector PM (figure 1)

generated a signal each time a 0. 2 mm in diameter hole H (figure 2)

fabricated in the disk was in line with the detector and the light source L

(figure 1). Relative radiance of the source after attenuation was measured

with a high-speed photoelectric pyrometer [3] . The electrical signals

from the pyrometer were recorded with a high-speed digital data acquisition

system [4]. The combined measuring and recording system has a fullscale signal resolution of approximately one part in 8 000 and a time resolution of 0. 4 ms.

The photomultiplier in the pyrometer was alternately exposed to the

radiance from the tungsten filament lamp and to the radiance from a reference lamp. This scheme eliminated errors that result from photomultiplier fatigue, etc.

Pulse shape as a function of time for various diaphragm geometries

are derived in the following paragraphs.

Effective cross-sectional area of the light beam, when disk circumference is at point x on the diaphragm, may be expressed as

y dx (2)

138
47T

139

FIGURE

2.

The

attenuator

disk

and

the

diaphragm

opening.
where x = r 0 - r and y is the width (height) of the diaphragm at x

(figure 2).

For rectangular geometry, y

= constant = a, thus

A

x

= ax (3)

For triangular geometry, y

= bx, thus

Ajj. = bx 2

/ 2 (4)

When the disk rotates at constant speed, angle of rotation is proportional to time t

a = k't (5)

From Eq. (1) and the definition of x

x = r 0

- r = key (6)

Combination of Eqs. (5) and (6) yields

x = kk't (7)

Radiance L as seen by the pyrometer at a given instant is

L = k" A (8)

Combination of Eqs. (3), (4), (7), and (8) yields the following:

For rectangular geometry

/ L = Kt (9)

For triangular geometry

L = K't 2 (10)

where K and K' are combination of constants. Equations (9) and (10)

represent radiances which are linear and quadratic functions of time,

respectively.

140
3, Re satis

In order to assess the operational characteristics of the system,

experiments were performed using diaphragms of rectangular and

triangular openings. These experiments are summarized in the following

paragraphs.

Linear Radiance Pulses: A total of fifteen experiments were conducted at five different attenuator speeds yielding radiance pulses

(increasing linearly with time) in the range 20 to 150 ms. Additional

four experiments were performed with the direction of rotation of the

attenuator reversed. This scheme generated radiance pulses which

decreased linearly with time.

Quadratic Radiance Pulses: A total of four experiments were conducted at two different attenuator speeds. An additional experiment was

performed with the direction of rotation of the attenuator reversed.

Oscilloscope trace photographs of representative radiance pulses

are shown in figure 3. The radiances as detected by the high-speed

pyrometer and recorded with the digital data acquisition system were

fitted to linear and quadratic functions, depending on the pulse shape,

using the least squares method. The summary of the experimental

parameters and the results are given in table 1. It may be seen that

average standard deviation (individual point) of the results of both pulse

shapes is approximately 0. 6 percent corresponding to data covering a radiance ratio of over 10.

The above value for the standard deviation reflects departure from

ideal behavior which may be due to several factors,- such as random

noise in radiance samples and in the pyrometer operation, non-uniformity

in the lenses and in the optical alignment, non -uniformity in the attenuator

circumference, variation in the attenuator speed, etc. In order to separate

the contribution of the pyrometer and the random noise inherent in radiance

measurements from the attenuator and the associated optical system,

141
TIME

FIGURE

3.

Oscilloscope

trace

photographs

of

linear

(upper)

and

quadratic

(lower)

pulses.

Horizontal

scale:

10

ms

(upper),

20

ms

(lower)

per

major

divis

Vertical

scale:

arbitrary

units.

Dots

forming

the

long

horizontal

li
TABLE 1

Summary of Experimental Parameters and Results

em

Radiance

Variation

Direction

of

Radiance

Variation

Pulse

Length

(ms)

Number

of

Experiments

Number of

Points per

Experiment

Average

Radiance

Ratio

Average

Standard

Deviation

(*)

1 Linear Increasing 23 3 20 10. 3 0. 6

2 Linear Increasing 30 3 26 12. 1 0. 7

3 Linear Increasing 39 3 33 9. 0 0. 6

4 Linear Increasing 59 3 50 11. 8 0. 5

5 Linear Increasing 144 3 123 11. 3 0. 6

6 Linear Decreasing 23 1 20 10. 0 0. 7

7 Linear Decreasing 30 1 26 9. 5 0. 7

18 Linear Decreasing 39 1 33 10. 4 0. 6

1 Linear Decreasing 59 1 50 10. 6 0. 5

0 Quadratic Increasing 60 3 39 11. 0 0. 6

1 Quadratic Increasing 40 1 26 10. 1 0. 5

2 Quadratic Decreasing 60 1 39 11. 1 0. 6
two separate experiments were conducted under steady- state conditions.

In one of the experiments, the attenuator was positioned to provide the

maximum opening of the diaphragm as seen by the pyrometer. Then

the pyrometer response to the radiance source was recorded. The

standard deviation of the results was 0. 2 percent. A similar experiment

was performed with the attenuator positioned to provide radiance equivalent

to that of the lowest level used in the dynamic experiments. The standard

deviation of the results of the pyrometer output was 0. 8 percent. If one

assumes an approximately linear variation of randomness between the

two extremes, one arrives at a value of 0. 5 percent for the standard

deviation contributed by the pyrometer and radiance measurements in

general. Thus, if it is assumed that total standard deviation is the

square root of the sum of the squares of individual standard deviation, the

standard deviation corresponding to the non-uniformities of the attenuator

and the associated optical components becomes approximately 0. 3 percent.

In order to ascertain the fact that the value obtained for the standard

deviation was the result of random deviations in the data, the data on

radiance was also fitted to functions of one and two higher degrees than

the pertinent one. No improvement in the standard deviation was observed.

This indicated that there was no detectable systematic curvature imposed

on the proper function.

fi 4. Conclusion

The results of the experiments described above have shown the feasibility of generating subsecond duration pulses of prescribed shapes (linear

and quadratic) with a standard deviation of less than 0. 5 percent over a radiance ratio of 10. The method allows one to insert appropriate diaphragm

in the optical system to obtain radiance pulses of various shapes. For

example, in addition to linear and quadratic, it is possible to generate pulses

of cubic, exponential and other shapes.

144
The scheme of generating radiance pulses allows one to detect

the linearity of radiation detectors under dynamic conditions, and also

provides the experimenter with means of simulating high-speed heating

or cooling experiments.

5. References

1. Jones, O. C. , J. Sci. Instr. , 41, 653 (1964).

Z. Hudson, R. D. , Infrared System Engineering, Wiley,

New York (1969) p. Z35.

3. Foley, G. M. , Rev. Sci. Instr . , to be published (1970).

4. Cezairliyan, A. , M. S. Morse, H. A. Berman, and C. W.

Beckett, J. Res. Nat. Bur. Stand. (U. S. ), 74A (Phys.

and Chem. ) 65 (1970).

145
Chapter 12

OPTICAL METHODS OF MEASURING TRANSIENT HIGH TEMPERATURES

Ared Cezairliyan

National Bureau of Standards

Washington, D. C. 20234

Abstract

Various optical methods, primarily photoelectric and photographic,

of measuring transient high temperatures are described. Emphasis is

placed on techniques of measuring transient temperatures of solids

above approximately 1500 K with subsecond (upper millisecond to upper

microsecond) resolution. Advantages and limitations of the various

methods are discussed and estimates of uncertainties are given.

Application of the high-speed temperature measurement methods to

various fields of investigations, including determination of thermophysical properties, is presented.

146
1. Introduction

Increasing interest in high-speed studies of high- temperature

phenomena and the utilization of transient techniques for the measurement of properties at high temperatures has necessitated the development

of temperature measurement methods having high time resolution* Most

well-established steady-state temperature measuring devices, such as

thermocouples, resistance thermometers, conventional optical and automatic optical pyrometers, etc., are inadequate because of their relatively long response times. The definite advantages of non-contact

methods in high temperature measurements suggest the selection of

optical methods in developing high-speed high temperature measuring

systems

Although at present there is no commercially available instrument

for high-speed temperature measurements, several prototype instruments

have been developed in various laboratories for research purposes.

However, most of these instruments were built for specific practical

applications with little attention being given to the attainment of

high precision and accuracy. Preliminary research has shown the potential of optical methods as means for high-speed measurement of high

temperatures. Optical methods may be classified under the following

general categories: photoelectric, photographic, and spectroscopic.

Each method has certain advantages and the selection of an appropriate

method for high-speed temperature measurements depends upon the specific

application. Since the primary objective of this papei is to discuss

techniques of measuring transient temperatures of solids at high temperatures, emphasis is placed on the photoelectric and photographic methods;

147
the spectroscopic methods are used for temperature measurements in gases.

In view of the lack of accurate and versatile high-speed (millisecond

and microsecond resolution) pyrometers, certain criteria and possible

avenues for future research and development are also discussed in the

last section of the paper.

2. General Considerations

A basic requirement in all high-speed optical temperature measurements is the availability of sufficient number of photons within the

bandwidth of the detection system. Selection of a proper detection

system to meet this requirement depends on a number of factors. Among

these are: (1) level of temperature to be measured, (2) effective wavelength of radiance measurement, (3) spectral sensitivity of detectors,

(4) time resolution, (5) characteristics of existing calibration

facilities, and (6) special experimental requirements. Some of the

above items are interrelated in such a way that the proper selection of

a detection system must be based on optimization under a given set of

conditions

Calibration facilities for conventional pyrometry (visual or automatic) are developed for the red region in; the vicinity of 650 nm.

Therefore, it is advantageous to utilize this wavelength in high-speed

pyrometry as much as possible. This can be done successfully for temperatures up to approximately 5000 K. Above 5000 K it may be desirable

to shift the operation to shorter wavelengths because the peak of the

Planck radiation function moves toward shorter wavelengths with increasing temperature. The selection of the wavelength to correspond to the

peak in radiation at the average temperature of measurements provides

148
the detection system with the maximum number of photons. However, in

most cases the peak of the radiation function for a given temperature

does not correspond to the wavelength of the maximum response of the

detector. Therefore, an optimization becomes necessary.

The high-speed temperature measurement methods described in the

literature are based, in general, on the measurement or comparison of

radiance of the specimen with that of a known reference. The detection

systems used for the measurement or comparison of radiances are mainly

photoelectric or photographic.

If the unknown radiance source is not a blackbody, measurements

performed at one wavelength, in conjunction with a proper calibration,

yield brightness temperature. To obtain true temperature, a knowledge

of normal spectral emittance for the surface at the operating temperature is required. Accurate measurements of this property at high

temperatures are difficult and results reported in the literature

cannot be properly applied to a particular specimen due to strong

dependence of normal spectral emittance on surface conditions. To avoid

some of the above difficulties, a few investigators have developed

techniques in which radiance measurements are performed at more than one

wavelength. Such an approach eliminates, to a first approximation, a

knowledge of the absolute value of normal spectral emittance. However,

this method is wavelength sensitive, and thus its ultimate accuracy

depends on the accuracy with which effective wavelengths can be

determined

149
In steady-state temperature measurements, detectors are used

generally to match the radiance of the unknown with that of the reference. However, in high-speed measurements this approach cannot be used

because of time limitations. In the latter case, the unknown temperature is usually determined by the interpolation of the unknown radiance

from bracketing reference radiances. Accuracy of this approach depends,

among other factors, on the linearity of the detectors. Linearity of

photomultipliers is generally better than 1 percent over a radiance

range of 3 decades, which is sufficient for most measurements. If

properly exposed, processed, and interpreted, linearity of films may be

1 percent over a radiance range of 2 decades.

3 . Photoelectric Methods

In most photoelectric methods, the unknown radiance is detected

with a photocell or a photomultiplier corresponding to a bandwidth at

a certain effective wavelength. The resultant electrical signal is

recorded with an appropriate high-speed recording system.

The photocell or the photomultiplier is exposed to the unknown

radiance continuously during the transient experiment and its output is

recorded either with a high-speed chart recorder or an oscilloscope.

The system is calibrated under steady-state conditions before or after

an experiment by substituting a standard radiance source for the unkown.

This scheme has the disadvantage that it assumes stability and reproducibility of the detector between calibration and transient experiments.

Studies performed on photomultipliers indicate that this assumption is

not completely justified; thus, measurements based on the above technique

may be subject to considerable errors.

150
In the literature, a few investigators used this or similar techniques to measure temperatures in connection with either the studies of

temperature variations in transient events, or property measurements

utilizing transient techniques. These are summarized in the following

paragraphs

Use of a photomultiplier, in conjunction with proper optics and

electronics, to measure temperature fluctuations of incandescent surfaces was described by Dehn^. The time resolution was better than 1 ys.

Photomultiplier output was recorded with an oscilloscope. Reported

measurement inaccuracy was approximately 10 percent, with a sensitivity

of 2 R at 1100 K. The technique was used to measure temperature fluctuations of an oscillating magnetron.

The design of a photoelectric pyrometer intended for use in transient measurements of thermal properties at temperatures above 1300 K

2 was described by Rasor and McClelland . This instrument could measure

small temperature changes (6 K) with a response- time of less than 10 ms

during pulse heating of the specimen. A photomultiplier having a S-l

surface was used as a detector, and its output was recorded with an

oscillograph

In an attempt to measure specific heat by a transient technique

3

at temperatures above 1300 K, Cezairliyan used a photomultiplier

(S-20 surface) with associated optics and electronics. Signals were

recorded with an oscilloscope. The system measured radiance of the

specimen as it was heated at the rate of 6600 Ks

151
For the transient measurement of specific heat of metals at high

4

temperatures, Affortit and Lallement utilized a photomultiplier system,

in addition to thermocouples, to measure the temperature of a heating

specimen. Signals were recorded with an oscilloscope.

A high-speed ratio (multicolor) pyrometer, which operated on the

principle of measuring sequentially radiance at three different wavelengths (700, 800, and 900 nm) , was described by Hornbeck^. A single

detector was used for all selected wavelengths. Signals were recorded

with an oscilloscope. Reported measurement rate was over 1000 sets

per second.

Another version of a high-speed multicolor pyrometer was described

by Kottenstette . This pryometer also employed the method of measuring

unkown radiance at three different wavelengths ranging approximately

from 600 to 750 nm. A separate detector (silicon photovoltaic cell)

for each wavelength was used. Detector response time was 5 ys. Signals

were recorded with an oscilloscope. The pyrometer’s operating range

was from 1500 to 4000 K with a reported inaccuracy of 3 percent at

4000 K.

In some experiments, it is important to determine rapidly temperature distribution over the specimen. A pyrometer, utilizing a photomultiplier, was designed by Sims and Place^ that could measure temperature distribution over an incandescent surface. The scanning was

achieved by a rotating disk, which contained fifteen holes in the form

of a spiral. The duration of a complete scan was approximately 0.1 s.

Recording of signals was made with an oscilloscope. The reported

inaccuracy was 4 K at 1400 K.

152
All of the above were preliminary attempts to measure temperature

at high speeds by photoelectric methods. In all cases, the system was

calibrated either before or after the experiment under steady-state

conditions. This assumed that the behavior of the detectors and other

related components were not altered between the calibration and the

actual experiment. Since photomultipliers are highly unstable, the

g above approach cannot be used for accurate measurements . Foley

developed a laboratory prototype of a pyrometer that eliminated the

above uncertainties by incorporating a self-calibrating scheme during

the experiment. The pyrometer permitted 1200 evaluations of the specimen temperature per second. A schematic diagram of the optical system

of the pyrometer is shown in figure 1. An outline of the description

of the method and operational characteristics of the pyrometer is given

in the following paragraphs.

A chopper disk (shutter) in the pyrometer alternately passes

precisely timed samples of radiance from the specimen (unknown) and

from a reference source through an interference filter (wavelength

650 nm, bandwidth 10 nm) to a photomultiplier (S-20 surface) . The

reference source is a calibrated gas-filled tungsten lamp. Successive

exposures to the reference pass through a sequence of three different

calibrated optical attenuators, mounted on a rotating disk on the

chopper motor shaft, resulting in a staircase of reference exposures,

with approximately 50 percent attenuation between succeeding steps. The

target may be as small as 0.2 mm in diameter at a range of 100 mm.

153
REFERENCE

154

FIGURE

1.

Optical

system

of

the

high-speed

pyrometer

(Foley
During each exposure to the reference or unknown source, the photomultiplier current is integrated and recorded, together with other data

of experimental significance, by a digital data acquisition system

composed of a multiplexer, an analog- to-digital converter, a magnetic

core memory, and related control and interfacing equipment. At the end

of an experiment, information is retrieved via a teletypewriter and is

processed using a time-shared computer. The data acquisition system has

a full-scale signal resolution of one part in 8000, and a time resolution of approximately 0.4 ms. The pyrometer has also been connected

directly to a small dedicated computer to demonstrate temperature

measurement in real time.

Since the same photomultiplier and electronic components are used

to evaluate the radiance of the specimen and the reference on alternate

exposures, uncertainties resulting from fatigue, drift, external magnetic fields, etc. are negligible. Inaccuracy of temperature measurements with this pyrometer is estimated to be 4 K at 2000 K. At the same

temperature, sensitivity is approximately 0.5 K. This pyrometer is

the most accurate photoelectric instrument in existence at the present

time for transient temperature measurements above 1500 K with millisecond resolution.

4 . Photographic Methods

In photographic methods, the film takes the place of both the

detector and the recording system. The unknown radiance is determined

from the measurement of the density of the film exposed to the unknown

radiation corresponding to a bandwidth at a certain effective wavelength.

155
A discussion on the efficiency and other characteristics of radiation

9 detection by photographic films is given by Bird et al. .

Investigations of the possibility of using photographic techniques

for temperature measurements under steady-state conditions started in

the early thirties. These are summarized by Shramko^.

Applications of this technique to transient temperature measurements were initiated in the mid-forties. They were developed to study

temperature variations in transient or unstable phenomena associated

with combustion chambers, flames, ablation, property measurements, etc.

Almost all attempts to use photographic techniques for transient

temperature measurements were of a preliminary nature. Nevertheless,

they have shown the potential of such techniques in experiments of

short duration. A distinct advantage of photographic techniques over

others is that they are capable of giving temperature distribution

over the specimen surface at any given instant.

Photographic methods of transient temperature measurements are

based on photographing, at high speeds, either (1) the unknown alone,

or (2) the unknown and one or more reference radiance sources simultaneously. In the first method, film exposures have to be calibrated

after the experiment with known radiance sources. The second method is

far superior to the first since it reduces most of the calibration

uncertainties. In both cases, the unkown radiance is obtained by interpolating the exposure density between the two adjacent references.

Research activities along these lines since the mid-forties are

summarized in the following paragraphs.

156
First Method (measurement and calibration at different times)

Application of the photographic method to the measurement of liquid

steel temperatures using a 16-mm camera was described by Hail‘d. Half

of the film was marked off while the exposures were made on the steel

streams. The mask was then reversed and the film was run through the

camera four times in order to record the four images of a calibrated

tungsten strip lamp at four brightness temperatures on the other half

of the film. Thus, images of the unknown and references were placed

side by side on each frame of the film. Temperature of the unknown was

determined by the interpolation between two adjacent references.

Reported inaccuracy was 10 to 20 K at 1800 K.

A photographic pyrometer utilizing a 35-mm camera was described

12

by Londeree . Exposure time of each film was 1/6 s, and the measurements were made with a red filter. Film was calibrated with a tungsten

filament lamp and a set of absorbing filters of known transmission.

Reported inaccuracy of these temperature measurements was 5 K at 1800 K.

13

The photographic pyrometer described by Platunov and Fedorov

operated at an effective wavelength of 630 nm with a speed of 24 frames

per second.

14

Exton designed a photographic pyrometer for operation in the

range 1000 to 2000 K. A 35-mm framing camera was used, which had a

speed of 20 frames per second. The reported inaccuracy of temperature

measurements was approximately 2 to 3 percent.

157
Second Method (measurement and calibration simultaneously)

A photographic pyrometer capable of photographing simultaneously

15 an unknown source and four reference radiances is described by Male

References were four tungsten filament lamps placed next to each other.

They were viewed by the camera by means of a mirror located immediately

below the optical path to the unknown and mounted 45° to the optical

path to the camera lens. Temperature of the unknown was determined by

an interpolation of film exposure densities between references.

The construction of a similar apparatus ^also using four reference

radiances was described by Simmons and DeBell^. They used their photographic pyrometer to measure the temperature of rocket exhaust flames

by employing the two pathlength method. Radiance measurements were made

in a narrow bandwidth at 650 nm. The reported uncertainty in temperature measurements was 10 K in the range 1300 to 2300 K. Simmons and

DeBell^ later modified this technique to photograph the unknown at

three wavelengths. This reduced the uncertainties due to variations in

the normal spectral emittance of the unknown.

The methods summarized above had time resolutions ranging from

tens of milliseconds to seconds. Faster (microsecond resolution)

photographic temperature measurements in relation to shock, exploding

conductor, and plasma studies were also tried. Almost all the attempts

made to measure transient temperatures photographically were of an

exploratory or preliminary nature. At the present time, there is no

accurate and self-contained high-speed photographic pyrometer.

158
5 . Applications

High-speed temperature measurement techniques find applications in

transient experiments designed for the determination of selected thermophysical and related properties at high temperatures. Time-resolved

temperature measurements are also used in studying the behavior of rapid

events in complex systems, involving combustion, ablation, etc. In the

following paragraphs specific applications of high-speed photoelectric

and photographic temperature measurement techniques, as presented in

the literature, are summarized.

Photoelectric : Applications of various photoelectric temperature

measurement techniques in connection with the determination of selected

18 thermophysical properties are presented by Rasor and McClelland , 3 4 19 Cezairliyan , Affortit and Lallement , and Affortit . The accurate

g millisecond resolution pyrometer described by Foley was used to

measure specific heat, electrical resistivity, and thermal radiation

20 21 22 properties of molybdenum , tantalum , and tungsten from 1900 to

near their respective melting points. The same pyrometer was also used

23

to determine the melting point of molybdenum and to investigate the

behavior of normal spectral emittance of tantalum during the initial

24 6 melting period . The pyrometer described by Kottenstette was

developed in conjunction with a study of high-energy chemical reactions.

Changes in surface temperature of the cathode of an oscillating magnetron

and temperature rise on the surface of thermionic cathodes were measured

, n , 1,25 by Dehn

159
Photographic : Photographic techniquer have been applied particularly to cases where a knowledge of spacial temperature distribution is

of importance. The pyrometer described by Male^ was developed for

measurement of apparent surface temperature in a ram-jet combustion

chamber. Temperature of luminous rocket exhaust flames was measured by

16 26 Simmons and DeBell 5

. Surface temperature variations on ablative

27 materials were studied by Exton . Measurements of liquid steel temperature were performed by Hall^. Application of photographic temperature measurements to property determinations was described by Platunov

13 and Fedorov in connection with the measurement of thermal conductivity

of tungsten above 1800 K.

6 . Discussion

There are other possible optical methods of measuring transient

28

temperatures. Spectroscopic techniques'" have been useful in temperature measurements in hot gases and plasmas. However, most of the work

has been concentrated in steady-state type measurements. High-speed

bolometers with response times ranging from 50 ys to 0.1 ys have also

been developed and used in connection with measurements of the radiance

29 30

of nuclear fireballs and pulsed plasmas

In millisecond resolution experiments, the accuracy of photographic

methods is, in general, lower than that of photoelectric methods.

However, in faster experiments, photographic methods show great promise.

A considerable amount of research and developmental work on high-speed

photography and related techniques, ranging from millisecond to nanoJ , . . , . , , . 31,32,33,34 . . . .

second resolution, is reported m the literature . Application

of available technology on high-speed photography to temperature measure160
merits may result in the successful development of photographic pyrometers of microsecond resolution. Even after the development of accurate

electronic temperature measuring equipment with microsecond resolution,

photographic methods will continue to be exploited and will be useful in

detecting temperature non-uniformities and measuring temperature gradients in the specimen. However, because of the relative ease and operational advantages, electronic methods are likely to be more desirable

in most applications.

For the successful development of accurate high-speed temperature

measuring systems utilizing electronic techniques one of the following

two conditions has to be satisfied: (1) stable and reproducible radiation detectors, or (2) reliable high-speed radiation modulation.

Item (1) represents the case where the detector does not monitor

alternately the radiance from the unknown and a reference. This

requires the detector to be stable and reproducible between calibrations and high-speed experiments. It is also important that detector

behavior is invariant under transient electromagnetic fields, which are

generally present in high-speed experiments. Most of the sensitive

detectors operating in the visible range, such as photomultipliers, are

highly unstable photoelectrically , and in addition their output depends

on environmental conditions, such as electromagnetic fields, vibration,

etc. However, photomultipliers have been used because of their short

response time (nanoseconds) and acceptable quantum efficiency. A

35 detailed discussion on photomultipliers is given by Engstrom

161
Recent developments in the field of solid-state detectors show

considerable promise. They have submicrosecond response characteristics

However, no careful study has been made regarding their stability,

reproducibility and behavior under strong electromagnetic fields. Most

solid-state detectors have a maximum response in the near infrared and

infrared regions, which are not very desirable for very high temperature

work. Discussions on high-speed solid-state detectors may be found in

36 37 38 articles by Amsel and Zajde , Lucovsky and Emmons , DiDomenico et al

39

and Anderson and McMurtry

Given the condition of detector unstability, the alternative for

accurate temperature measurements is to devise techniques for the

detector to monitor alternately the radiance of the unknown and a reference. This scheme requires dependable radiation modulation methods.

Relatively simple motor-driven choppers can be used for modulation at

millisecond and even upper microsecond rates. However, there are no

compact and reliable optical radiation modulating devices operating at

lower microsecond rates. Reasonably reliable mechanical modulating

schemes with microsecond resolution (such as, rotating mirrors used in

high-speed cameras) are bulky, expensive, and are not easily adaptable

to the rest of the system. Devices which operate on electro-optic

phenomena are available, although at present their reproducibility is

not adequate for accurate temperature measurements. A review on

various methods of optical radiation modulation at high frequencies

40

(up to GHz) was given by Jones

162
In the design of high-speed pyrometers, it is important to optimize

the speed with respect to temperature. If approximately 0.2 s of exposure time is required to make temperature measurements (by photoelectric methods) at the gold point (1337.58 K) corresponding to an

effective wavelength of 650 nm, the following approximate exposure

times are computed to be needed to perform the measurements at higher

temperatures: 1000 ys at 2000 K, 1 ys at 5000 K, 0.1 ys at 10,000 K,

and 0.01 ys at 50,000 K. Of course by optimizing the effective wavelength as temperature is increased, the exposure times can be further

reduced

In photographic pyrometry, characteristics of films play an important role in the proper design and operation of the overall system.

Some of the items that have to be considered in connection with films

are: (1) wavelength dependence of film sensitivity, (2) the shape of

the film's "characteristic curve" that relates the film density to the

logarithm of exposure, (3) spacial non-uniformities on the film,

(4) processing the exposed film, (5) the degree of the failure of the

reciprocity law for the film.

An important item that needs to be considered in the design, and

operation of high-speed temperature measurement systems is the availability of reference radiance sources. At moderately high temperatures

(up to 1500 K) vacuum tungsten filament lamps are generally used, in

the range 1500 to 2500 K gas-filled lamps can be used. They are convenient to use, and their calibration usually stays within one degree

at 2000 K after operating for ten hours. For temperatures above 2500 K,

there are no reliable and well characterized radiance sources. The best

163
available source is the low-current graphite arc which yields a

brightness temperature of approximately 3800 K. The temperature level

is dependent on the composition of the graphite rods and the operating

conditions, such as current, electrode separation, and atmospheric

pressure.

Radiance temperature of the graphite arc and its relatively long41 time (seconds to minutes) variations were investigated by Chaney et al , 42 43 43 Null and Lozier , and Lee and Lewis . The most recent measurements

made with a photoelectric pyrometer having 1/6 s time constant gave 3 K

for the standard deviation of temperature fluctuations from the mean,

and up to 10 K for temperature variations over a period of 15 minutes.

44 Recently, Cezairliyan studied the short-time behavior of a graphite

arc with a high-speed (millisecond resolution) photoelectric pyrometer.

The standard deviation of radiance temperature fluctuations was found

to be in the range 3 to 4 K; maximum deviations as much as 10 K from

the mean were also observed.

Above 3800 K, lasers and high pressure arcs may become useful as

reference radiance sources. However, so far very little research has

been done regarding their radiance stability and reproducibility.

From the presentations in the earlier sections it may be seen that

high-speed temperature measuring techniques are in their infancy as

almost all approaches have been of a preliminary nature. However, continued interest in high temperature research and the possibilities of

both photoelectric and photographic techniques may lead to the development of accurate and versatile high-speed pyrometers for temperature

measurements in millisecond, microsecond, and even shorter times.

164
References

*"R. Dehn, Brit. J. Appl. Phys . _7, 144 (1956).

^N. S. Rasor and J. D. McClelland, Rev. Sci. Instr. _31, 595 (1960).

3

A. Cezairliyan, "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 (ASME,

New York, 1965), p. 253.

4

C. Affortit and R. Lallement, Rev. Int. Hautes Tempdr. et Rdfract. _5

19 (1968).

~*G. A. Hornbeck, "High-Speed Ratio Pyrometer" in Temperature Its

Measurement and Control in Science and Industry, C. M. Herzfeld, ed.

(Reinhold, New York, 1962), Vol 3, Part 2, p.425.

^J . P. Kottenstette, ISA Trans. 4^, 270 (1965) .

^R. B. Sims and J. A. Place, J. Sci. Instr. 31 , 293 (1954).

^G. M. Foley, Rev. Sci. Instr., _41, 827 (1970).

^G. R. Bird, R. C. Jones and A. E. Ames, Appl. Opt. _8, 2389 (1969).

l^Y. P. Shramko, High Temperature _5, 328 (1967) .

^J.A. Hall, The Photographic Journal 86B , 117 (1946).

^j. w. Londeree, J. Am. Ceram. Soc. _37, 354 (1954).

13

E. S. Platunov and V. B. Fedorov, High Temperature _2, 568 (1964).

l^R. J. Exton, ISA Trans. _4, 365 (1965).

165
15

16

17

18

19

20

D. W. Male, Rev. Sci. Instr. _22, 769 (1951).

F. S. Simmons and A. G. DeBell, J. Opt. Soc. Am. 4_8, 717 (1958).

F. S. Simmons and A. G. DeBell, J. Opt. Soc. Am. _4£, 735 (1959).

N. S. Rasor and J. D. McClelland, J. Phys . Chem. Solids _L5, 17 (1960)

C. Affortit, High Temp. -High Pres. 1_, 27 (1969).

A. Cezairliyan, M. S. Morse, H. A. Berman and C. W. Beckett, J. Res.

Nat. Bur. Stand. (U.S.) 74A (Phys. and Chem.), 65 (1970).

21

A. Cezairliyan, J. L. McClure and C. W. Beckett, J. Res. Nat. Bur.

Stand. (U.S.), 75A (Phys. and Chem.), 1 (1971).

22

A. Cezairliyan and J. L. McClure, J. Res. Nat. Bur. Stand. (U.S.),

Section A, to be published (1971)

23

A. Cezairliyan, M. S. Morse and C. W. Beckett, Rev. Int. Hautes

Temper, et Refract. 2_, 382 (1970).

24

25

26

27

28

29

A. Cezairliyan, High Temp-High Pres, to be published.

R. Dehn, Brit. J. Appl. Phys. _7, 210 (1956).

F. S. Simmons and A. G. DeBell, Aircraft Engineering 31 , 144 (1959).

R. J. Exton, AIAA Journal _7, 2262 (1969).

W. Lochte-Holtgreven, "Production and Measurement of High Temperatures",

in Reports on Progress in Physics (The Physical Society, London, 1958),

Vol . 21, p. 312.

H. E. Stubbs and R. G. Phillips, Rev. Sci. Instr. _31, 115 (1960).

166
M. Camac and R. M. Feinberg, Rev. Sci. Instr. _33, 964 (1962).

31

J. S. Courtney-Pratt, "A Review on the Methods of High-Speed

Photography" in Reports on Progress in Physics (The Physical

Society, London, 1957), Vol. 20, p. 379.

32

K. R. Coleman, "Ultra-High-Speed Photography" in Reports on Progress

in Physics (The Physical Society, London, 1963), Vol. 26, p. 269.

33

W. G. Hyzer, Engineering and Scientific High-Speed Photography

(The Macmillan Co., New York, 1963).

34Proceeding of the International Congress on High-Speed Photography.

A total of eight held until 1968. The last one: High-Speed Photography, eds. N. R. Nilsson and L. Hogberg (Wiley, New York, 1968).

35

R. W. Engstrom, "Photoelectric Devices", in Methods of Experimental

Physics, E. Bleuler and R. 0. Haxby, eds. (Academic Press, New York,

1964), Vol. 2, p. 743.

Or

G. Amsel and C. Zajde, Rev. Sci. Instr. _3f), 1538 (1964).

37

G. Lucovsky and R. B. Emmons, Appl. Opt., _4, 697 (1965).

38

M. DiDomenico, W. M. Sharpless and J. J. McNicol, Appl. Opt. _4, 677

(1965)

39

L. K. Anderson and B. J. McMurtry, Appl. Opt. _5, 1573 (1966).

40

0. C. Jones, J. Sci. Instr. _41, 653 (1964).

41

N . K. Chaney , V. C . Hamister and S . W . Glass , Trans . Electrochem.

Soc. 67, 107 (1935)

167
R. Null and W. W. Lozier, J. Opt. Soc. Am. _52, 1156 (1962)

43

R. D. Lee and E. Lewis, Appl. Opt. _5, 1858 (1966).

44

A. Cezairliyan, Appl. Opt., to be published (1971).

168
Chapter 13

SHORT-TIME (MILLISECOND) FLUCTUATIONS OF

RADIANCE TEMPERATURE OF GRAPHITE ARC

Ared Cezairliyan

National Bureau of Standards

Washington, D. C. 20234

Successful development of high-speed (millisecond and submillisecond resolution) photoelectric and photographic pyrometers

for very high temperature research requires stable high temperature

reference radiance sources. Low current graphite arcs are generally

12 3 considered as reference sources in the vicinity of 650 nm

* 3

. However, investigations regarding their radiance temperatures have

been made with relatively slow detecting and recording systems. The

3 fastest one had an electronic time constant of 1/6 s . The objective of this note is to investigate, with submillisecond

resolution, the behavior of the radiance temperature of graphite arcs. The positive and negative electrodes were spectroscopically pure

graphite rods (National Carbon grade SPK 1/4 inch and AGKS 1/8 inch,

respectively) . The negative electrode was inclined -120° with respect

to the positive. The radiance temperature of the crater of the positive

electrode along its axis was measured with a high-speed photoelectric

4 pyrometer which can make 1200 temperature determinations per second.

The effective wavelength of radiance measurements was 650 nm with a bandwidth of 10 nm. The pyrometer target was a circular area 0.2 mm

in diameter. A neutral density filter was placed between the pyrometer

\

and the graphite arc in oirder to reduce the radiance of graphite arc to

the level of the pyrometer reference, which was a gas-filled tungsten

filament lamp. The output of the pyrometer was recorded with a highspeed digital data acquisition system^, which has a full-scale signal

resolution of one part in 8000 and a time resolution of 0.4 ms.

169
A total of four experiments were performed at two locations on

two positive electrodes. The arc current was kept within 0.5 A of

the overload point. Each experiment, which was 150 ms in duration,

consisted of 180 temperature data points. A representative temperature

for each experiment was obtained by taking the average of these data.

The standard deviation of the averages was approximately 4 K.

The range of low and high temperatures for the four experiments

extended from 3799 K to 3808 K on the International Practical Temperature Scale of 1968^ (IPTS-68) . The average of the four experiments

was 3804 K. This compares favorably with the values 3806 ± 20 K, both

3 2 on IPTS-68, reported by Lee and Lewis , and Null and Lozier , respectively . In order to separate the contribution of the pyrometer operation

on the measured temperature fluctuations, a separate experiment was performed in which the graphite arc was replaced by a tungsten filament

lamp. The neutral density filter was removed and the current flowing

through the lamp was adjusted to give approximately the same pyrometer

output. The average of 180 temperature data points obtained under these

conditions was 2380 K with a standard deviation of 0.3 K. When this is

extrapolated to 3800 K an equivalent standard deviation of 0.7 K is

obtained, suggesting that the graphite arc has short-time (millisecond)

fluctuations amounting to approximately 3 to 4 K in standard deviation.

It is interesting to note that this is almost equal to the value 3 K,

3 reported by Lee and Lewis , for the standard deviation of radiance temperature fluctuation over a period of a few seconds measured with an electronic time constant of 1/6 s. Target size of the pyrometer used

by Lee and Lewis was essentially the same as that used in this work.

The results of typical graphite arc and tungsten lamp experiments

corresponding to approximately the same effective temperature (3800 K) are shown in figure 1. It may be seen that deviations of radiance

temperature from their mean for the graphite arc are random. The lack

of any cyclic pattern eliminates the possibility of the contribution

of improper current rectification on the results.

170
oro

O

OJ

O

171

TIME,

ARBITRARY

UNIT

FIGURE

1.

Variation

of

radiance

temperature

of

graphite

arc

and

tungsten

lamp

as

a

function

of

time.

Both

results

correspond

to

the

same

effective

temperature

of

approximately

3800

K.

For

simplicity

every

third

point

is

plotted.

1

time

unit

=

2.5

ms.
The high-speed pyrometer was calibrated against a tungsten filament standard lamp, which in turn was calibrated against the NBS

Temperature Standard. The estimated possible maximum error in temperature measurements at 3800 K is 10 K.

It may be concluded that short-time (millisecond) fluctuations

of the graphite arc are 3 to 4 K, which is comparable to the fluctuations obtained over a period of seconds with a slower pyrometer.

References

1. N. K. Chaney, V. C. Hamister, and S. W. Glass, Trans. Electrochem.

Soc. 67., 107 (1935) .

2. M. R. Null, and W. W. Lozier, J. Opt. Soc. Am. _52, 1156 (1962).

3. R. D. Lee, and E. Lewis, App. Opt. _5, 1858 (1966).

4. G. M. Foley, Rev. Sci. Instr. 4_1, 827 (1970).

5. A. Cezairliyan, M. S. Morse, H. A. Berman, and C. W. Beckett,

J. Res. Nat. Bur. Stand. (U.S.) 74A (Phys . and Chem.), 65 (1970).

6. International Practical Temperature Scale of 1968, Metrologia .5, 35 (1969).

172
UNCLASSIFIED

Security Classification JFM

DOCUMENT CONTROL DATA - R & D

(Security classification of title, body of abstract and indexing ann otation must be entere d when the overall report is classified

£

1. ORIGINATING ACTIVITY (Corporate author) NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D. C. 20234

2a. REPORT SECURITY CLASSIFICATION UNCLASSIFIED

26. GROUP

3. REPORT TITLE INTERIM REPORT ON THE THERMODYNAMICS OF CHEMICAL SPECIES IMPORTANT IN AEROSPACE

TECHNOLOGY

4. DESCRIPTIVE NOTES (Type oi report and inclusive dqtes) Scientific Interim

5. AUTHOR(S) (First name, middle initial, last name)

THOMAS B DOUGLAS CHARLES W BECKETT

6. REPORT DATE

1 July 1971

7a. TOTAL NO. OF PAGES 76. NO. OF REFS l&L 27 5 , 8a. CONTRACT OR GRANT NO. ISSA-70-0002

6. PROJECT NO. 9750-01

' 61102F

9a. ORIGINATOR'S REPORT NUM8ERISI NBS REPORT 10 481

96. OTHER REPORT NO(S) (Any other numbers that may be assigned

this report)AFOSR-TR- 7 1-2584

10. DISTRIBUTION STATEMENT

Approved for public release; distribution unlimited

11. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY AF Office of Scientific Research (NAE)

TECH, OTHER 1400 Wilson Boulevard

Arlington. Virginia 22209

13. ABSTRACT Detailed report of recent results and critical analyses of experimental measurement:

completed or in progress, literature surveys, and new measurement -method developments -for high-melting metals and their Aerospace-important compounds. (Numbers

in parentheses are temperature ranges or estimated general uncertainties.) Using

subsecond pulse heating technique, the heat capacity ( 2%-3%), electrical resistivity (0.5%-lYo), and hemispherical total and normal spectral emittances ( 3%) were

measured for tungsten (2000-3600K) and niobium (1500-2700K), including 3692K(±15K)

for the melting point of tungsten. Drop calorimetry gave the heat capacity (1%) of

molybdenum (1170-2100K) . Theoretical emissivity-resistance relation is only roughlj

obeyed. M0F5 prepared (cryoscopically, 99.85% pure), with preliminary vapor

pressures and heats of vaporization measured by transpiration (after developing a technique to suppress decomposition). Preliminary heats of solution of MoFft promise

resolving large discrepancy with the published fluorine-combustion value. Matrix

isolation and gas-phase infrared spectroscopy gave the six active frequencies of

NbF^ (assuming

,C4V

symmetry). Thorough review of the systems Mo-C, Ta-C, Nb-B,

with criteria for sample suitability for drop calorimetry. Millisecond method

measuring high -temperature thermal expansion ( 5%) of electrical conductors developed

and tested. Rotating attenuator for generating subsecond "sawtooth" radiance

pulses (0.54) is described. Various optical methods for measuring millisecond and

microsecond high temperatures are critically reviewed (solids above 1500K, as in

ramjet combustion and ablating materials). Millisecond fluctuations of 3 to 4K of

_the carbon-arc temperature (at about 3800K) were found comparable to those reported

for

DD FORM1 NOV 63 1473 for seconds intervals.

IINCTASSTFTFD

Security Classmcation
UNCLASSIFIED

Security Classification

14 . LINK A LINK B LINK C KEY WORDS ROLE WT ROLE WT role WT

THERMODYNAMIC PROPERTIES

HIGH-SPEED MEASUREMENTS

CRITICAL LITERATURE REVIEWS

HEAT CAPACITY

ELECTRICAL RESISTIVITY

THERMAL RADIATION PROPERTIES

MELTING POINTS OF ELECTRICAL CONDUCTORS

THERMOCHEMICAL CALORIMETRY

VAPORIZATION BY TRANSPIRATION

MATRIX -ISOLATION INFRARED SPECTROSCOPY

THERMAL EXPANSION OF ELECTRICAL CONDUCTORS

TUNGSTEN

NIOBIUM

MOLYBDENUM

MOLYBDENUM FLUORIDES

NIOBIUM PENTAFLUORI D

REFRACTORY -METAL CARBIDES AND BORIDES

CARBON -ARC TEMPERATURES

'

UNCLASSIFIED

Security Classification