NAT'L INST. OF STAND & TECH

NBSIR 73-280 ^dq^bi

NIST

PUBLICATIONS'

Thermodynamics of Chemical Species

Important to Rocket Technology

Physical Chemistry Division

Institute for Materials Research

National Bureau of Standards

Washington. D. C. 20234

1 January 1973

Final Report for Agreement No. AFOSR-ISSA-73-0001. Covering Period

July - December 1972

C^C^ ^ice of Scientific Research

/^O Boulevard

-CLS^ irginia 22209

NBSIR 73-280

THERMODYNAMICS OF CHEMICAL SPECIES

IMPORTANT TO ROCKET TECHNOLOGY

Various authors

Physical Chemistry Division

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

1 January 1973

Final Report for Agreement No. AFOSR-ISSA-73-0001, Covering Period

July - December 1972

Prepared for Air Force Office of Scientific Research

1400 Wilson Boulevard

Arlington, Virginia 22209

U. S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts. Director

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.

A 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 properties from 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. Additional

research activities of the program involve the critical review of published

chemical-thermodynamic (and some chemical-kinetic) data, and the generation

of new thermochemical tables important in current chemical-laser research.

i
Previous reports describing related work 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,

10326, 10481, and 10904.
ABSTRACT

This report (covering July -December 1972) and a subsequent

report (covering January-June 1973) constitute the Final Reports

on all past phases of the program except that measuring thermophysical properties by high-speed techniques, which will be continuing

The nature and scope of the subjects covered in the present report

may be inferred from the detailed Table of Contents to be found on

the following pages.

The relative enthalpy of high-purity molybdenum was accurately

measured over the temperature range 273-1173 and compared with

all competing published data. Thermodynamic functions are given for

273-2100 K after smooth- joining with the best published data below

273 K and earlier NBS measurements 1170-2100 K. The heat capacity

of a grade of graphite (AXM-5Q, Poco) was measured by a subsecondduration pulse-heating technique 1500-3000 K. The results agreed

to within 0,1% for two heating rates, and 0.6% for two different

specimens, the estimated inaccuracy of the smoothed values being 3%

or less.

Ideal-gas thermodynamic functions for MoF^(g) were computed and

are tabulated for the temperature range 0-6000 K. These are based on earlier NBS infrared and Raman spectra of M0F5, estimation of two

unobservable fundamentals, and the assumption of symmetry with the

Mo-F bond distance as in M0F5 . For deriving thermoaynamic properties

from combined transpiration and vapor-pressure data on a vapor such

as MoF^ that may be highly associated, three alternative treatments

are presented. One treatment is the c las sical- thermodynamic . The

other two assume an infinite number of associated gas species, and

numerical calculations illustrate the propagation of experimental errors.

The change in the normal spectral emittance (at 650 nm) of niobium

during melting was measured using subsecond-duration resistive heating.

Ten specimens deliberately varying in solid-state roughness from

0.1 to 0.95 \Jm were used. Upon melting, the radiance temperature dropped

by up to 35 K, and the emittance by up to 14% (the more so the greater

the solid roughness) . The radiance temperature of niobium was found to

be 2425 K (IPTS-68) a_t the melting point, with an average absolute deviation

of 0.6 K and a maximum deviation of 1.2 K using 12 specimens. This

temperature was found to show no dependence on the initial surface

conditions of the specimen.

Thomas B. Douglas U

Charles W. Beckett

TABLE OF CONTENTS

Page

Foreword i

Abstract iii

Chap. 1. MOLYBDENUM: ENTHALPY MEASUREMENTS 273-1173 K, AND

THERMODYNAMIC FUNCTIONS 273-2100 K

(by Thomas B. Douglas and David A. Ditraars) 1

Abstract 1 I. Introduction 2

II. Sample 3

Table 1. Mass spectroraetric analysis

of the molybdenum sample .... 5

III. Calorimetric Procedure and Enthalpy Data .... 6

Table 2. Enthalpy data for two empty

90 Pt-lO Rh containers 8

Table 3. Enthalpy data for the

molybdenum sample 9

IV. Thermodynamic Functions, 273.15-2100 K 10

Table 4. Thermodynamic functions for

molybdenum (in terms of

JOULES per mole) 14

Table 5. Thermodynamic functions for

molybdenum (in terms of

CALORIES per mole) 15

Fig. 1. Enthalpy compromise for the

two sets of NBS measurements . . 16

V. Comparison with Previous Investigators and

Compilers 17

Table 6. Outline of reported measurements

of the enthalpy or heat

capacity of molybdenum metal,

273-1200 K 18

Table 7. Corrections for molybdenum,

IPTS-48 to IPTS-68 ....... 20

Legend of Symbols for Figs. 2 & 3 21

Fig. 2. Comparison of H°-H°273? Mo,

various investigators 22

Fig. 3. Comparison of Cp, Mo,

various investigators 23

Table 8. Comparisons of H°-H293

and Cp for Mo in several

critical compilations 26

VI. References 27

Chap. 2. MEASUREMENT OF HEAT CAPACITY OF GRAPHITE IN THE

RANGE 1500 TO 3000 K BY A PULSE HEATING METHOD

(by Ared Cezairliyan) 31

Abstract 31

Introduction 32

v
TABLE OF CONTENTS (Continued)

Page

Method 32

Measurements 3^

Experimental Results 35

Table 1. Operational Characteristics

of the Measurement System

During the Experiments on Graphite-1 36

Table 2. Heat Capacity of Graphite

(AXM-5Q, Poco) 38

Fig. 1. Deviation of heat capacity

results for graphite-1 from

Equation (1) 39

Estimate of Errors 40

Fig. 2. Deviation of smoothed heat

capacity results for graphite-1

and graphite-2 from Equation

(1) 41

Discussion 43

Fig. 3. Heat capacity of various

graphites reported in the

literature 44

Acknowledgement 47

References 48

Chap. 3. THERMODYNAMIC FUNCTIONS FOR MoF

^ (g)

(by Thomas B. Douglas, Ralph F. Krause, Jr.,

Nicolo Acquista, and Stanley Abramowitz) 50

Molecular Constants Used for MoF5(g) 51

References 52

Table 1. Ideal-Gas Thermodynamic

Functions for Molybdenum

Pentafluoride Monomer (M0F5)

(in CALORIE energy units). . . 53

Table 2. Ideal-Gas Thermodynamic

Functions for Molybdenum

Pentaf luoride Monomer (MoF^)

(in JOULE energy units) ... 54

Chap, 4. ALTERNATIVE PROCEDURES IN INTERPRETING EQUILIBRIUM

DATA ON PARTIALLY ASSOCIATED VAPORS

(by Thomas B. Douglas and Ralph F. Krause, Jr.) .... 55

Abstract 55

I. A Classical -Thermodynamic Interpretation ... 56

II. Quasi -Chemical Interpretations 59

III. Preliminary: A Combination of Data

Yielding Ambiguous Thermodynamic

Solutions 59

vi
TABLE OF CONTENTS (Continued)

Page

112. Using Only Two Independent Data

for Each Temperature 62

113. Using Three Independent Data for

Each Temperature 65

Table 1. An example illustrating

errors in calculated values

resulting from experimental

errors in the input data ... 70

III. References 71

Chap. 5. CHANGE IN NORMAL SPECTRAL EKETTANCE (AT 650 nm)

OF NIOBIUM DURING MELTING AND ITS RELATION TO SURFACE

ROUGHNESS

(by Ared Cezairliyan) 73

Fig. 1. Variation of radiance temperature as a function of time

for a niobium specimen near

and at its melting point ... 75

Fig. 2. Difference in normal spectral

emittances of solid and

liquid niobium at the melting

point as a function of solid

surface roughness 76

Table 1. Summary of Experimental

Results for Radiance Temperature and Normal Spectral

Emittance (at 650 nm) of

Niobium at its Melting Point . 77

References 78

Chap. 6. RADIANCE TEMPERATURE OF" NIOBIUM AT ITS MELTING POINT

(by Ared Cezairliyan) 79

Abstract 79

1. Introduction 80

2. General Considerations 81

Fig. 1. Radiance temperature of pure

metals near and at their

melting points 82

3. Method 83

4. Measurements 83

Fig. 2. Oscilloscope trace photograph

of specimen radiance near and

at its melting point as measured

with the high-speed pyrometer . 85

5. Experimental Results 86

Fig. 3. Variation of radiance temperature of niobium as a function

of time near and at its melting

point 87

f vii
TABLE OF CONTENTS (Continued)

Page

Fig. 4. Radiance temperature at

the peak and at the

plateau for the niobium

specimens 88

Table 1. Summary of experiments for

the measurement of radiance

temperature of niobium during

melting 90

6. Estimate of Errors 91

Fig. 5. Radiance temperature of

niobium (with initially

"smooth" surface) at its

melting point 92

Fig. 6. Radiance temperature of niobium

(with initially "rough"

surface) at its melting point . 93

Fig. 7. Differences of radiance temperature of niobium at its melting

point for individual experiments 95

7. Discussion 96

8. References / 99

viii
chapter 1

MOLYBDENUM: ENTHALPY MEASUREMENTS 273-1173 K, AND

THERMODYNAMIC FUNCTIONS 273-2100 K

by Thomas B. Douglas and David A. Ditmars

Abstract

The enthalpy of a sample of molybdenum metal at least

99.87o pure was measured relative to 273 K at ten temperatures

up to 1173 K, using accurate drop-calorimetric apparatus. In

smoothing, the values were joined to recent enthalpy measurements on the metal by another NBS apparatus over the temperature

range 1170-2100 K (enthalpy discrepancy at 1170 K, 0.37o) and

to the results of published heat -capacity measurements below 273 K,

to yield thermodynamic functions over the range 273-2100 K. The

relative enthalpy and heat capacity over the range 273-1200 K are

compared with the results of 17 previously published results of

other investigators in the same temperature range.

1
I. Introduction

The National Bureau of Standards has for many years sponsored

the use of high-purity aluminum oxide as a high -temperature heatcapacity standard, and three years ago, on the basis of new NBS

measurements using two different accurate apparatuses covering the

respective temperature ranges 273.15-1173 K [29]^ and 1173-2250 K,

certified a standard sample of this material for this purpose over

the combined temperature range [32]. As a check on accuracy, it

is noteworthy that these two sets of results merged with but

negligible discrepancy not only with each other but with earlier

high-accuracy NBS adiabatic calorimetry on aluminum oxide both

above and below 273 K.

Subsequently, molybdenum was proposed as an alternative heatcapacity standard that can be obtained in high purity, is like

aluminum oxide free of transitions, has the advantages of a metallic

material, and has an even higher melting point (about 2890 K)

A special stock of this metal was procured, was characterized

in great detail, and, by use of the same two apparatuses, measurement of its relative enthalpy has now been completed from 273 to

2100 K. However, issuance of the certified standard sample of

molybdenum must await the completion of enthalpy measurements above

2100 K (perhaps to near the melting point using high-speed pulse

calorimetry as well). This is prudent because the future data above

''Numbers in brackets refer to literature references at the end of

this chapter.

2
2100 K can be expected to afford some refinement, however minor,

of the thermodynamic properties well below 2100 K.

These NBS -sponsored results above 1170 K were reported two

years ago [20], and those below 1170 K are being reported here for

the first time, because the properties of molybdenum are of equal

importance in Aerospace and other practical high-temperature

applications, in fact, the AFOSR-sponsored research program at NBS

has in recent years concentrated on the refractory transition

metals, particularly on molybdenum metal, molybdenum-containing

alloys, and molybdenum fluorides.

II . Sample

The earlier NBS work on molybdenum (above 1170 K) failed to

show any systematic difference in enthalpy between two samples of

widely different types (one zone-refined, and about ten times as

pure spectrochemically, but possibly less homogeneous, than the

other). The present measurements were on only one specimen, that

corresponding to Sample A of the earlier report [20]. That report

may be consulted for details of the very extensive characterization

of the sample. Important results are repeated below.

The sample from which the specimen for the present work (rods

of 1/8" diameter) was taken had been previously drawn and annealed.

3
The results of spark-source mass spectrometry on a

representative specimen are given in Table 1. (This analytical

technique is in general agreement with the results of a qualitative

spectrochemical analysis, summarized by footnotes to the table.)

Note the near completeness of the coverage of chemical elements

sought, and particularly the low levels of those low-atomic-weight

elements analyzed for (to which the enthalpy and heat capacity of

molybdenum, as calculated from the data, are particularly sensitive).

Unfortunately, hydrogen was not analyzed for, and 0.017o by weight

would be expected to make an error of the order of 1% if not corrected

for; but it seems likely that the high -temperature history of the

sample precluded the likelihood of more than a small fraction of

this amount. According to Table 1, the total impurity adds to

0.027o by weight of the elements analyzed for, with the possibility

of an upper limit of an additional 0.02% by weight of the elements

(except F, Ne, and Ti) partially masked by major interference.

The result of an additional test, the measurement of the

electrical-resistance ratio (R^.,^ >^/R/ rr) was interpreted as

2.7 J • K M- .

indicating a sample content of W, Ta, Nb, and Zr totaling 0.2

weight 7o. This far exceeds the levels of these elements shown

in Table 1, but if true should contribute an error of the order of

only 0.017o to the heat capacity, owing to the high atomic weights

invo Ived

4
Table 1

Spark-source mass-spectrometric analysis for impurities in a representative specimen of the molybdenum sample, in ppm by weight

Elements measured Elements showing interference

Element ppm Element ppm Element ppm Element ppm

<

Asd

Ca*^ Cr^

CuC

Feb

Gad

K

Mnd

pd

Rb

Sbd

1729

12

15

40

0.1

20

20.6

0.3

0.5

Si^

Wd

Znd

40

0.4

56

0.26

Ar

Aud

T^d Bad

C

Cdd

Cl

Cod

Cs

Ind

Ird

Li

Mg^

< 20 < 10

< 1 < 3 < 8 < 0.1 < 7 < 0.2 < 0.5 < 3 < 0.3 < 31

Nb^

Mi d INI

Pdd

Ptd

Re

Rhd

S Scd

Snd

Ta^

< 10 < 3

- Z.U < 30 < 6 < 6 < 4 < 1 < 0.2 < 1 < 0.3 < 30 < 25

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, If, Tm, U, Xe, Y, Yb, and Zr. H and He were not analyzed for.

Interference was complete for F, Ne, Na, and Ti ; of these, Na was not detected

by qualitative spectrochemical analysis, but the estimated detection limit

in this case is 50 ppm.

^10-100 ppm each by qualitative spectrochemical analysis,

c < 10 ppm each by qualitative spectrochemical analysis.

*^Not detected by qualitative spectrochemical analysis (generally, < 1 ppm).

5
Ill . Calorimetrlc Procedure and Enthalpy Data

The relative enthalpy of the molybdenum was measured by

drop calorimetry, which is described elsewhere in great detail

[28]. The specific details of apparatus and procedure were

identical in most respects with those described at length for

the recent NBS measurements on aluminum oxide [29] mentioned in

the Introduction (Section I) . The molybdenum specimen had a

mass of 20.8297 g (approximately 0.2 gram-atom), and was sealed

in a 90 Pt-10 Rh container together with helium at several torr

pressure. A Bunsen ice calorimeter measured the heat delivered

by the specimen and its container in cooling from the temperature

of the thermostated furnace to the ice-point (273.15 K) . The

presence of a long silver pipe around the sample (O.D. 2", I.D.I";

and with silver "guard" rings at its end) greatly reduces temperature

gradients in this apparatus, thus minimizing furnace-temperature

error, which is undoubtedly the most common source of instrument

error in most high-temperature drop calorimetry. The furnace

temperature was measured up to 773 K by a platinum resistance

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

thermocouples; all three were calibrated at NBS on IPTS-48, but

corrected [23] to the basis of the newer temperature scale (IPTS-68

[22]), on which all results in this chapter are based (since the

new scale more nearly approximates the corresponding thermodynamic

temperatures) . Both thermocouples were compared up to 773 K with

6
the thermometer in place in the furnace, and a slight adjustment

in their calibrations (0.1 K at and above 773 K) was made to avoid

a temperature discontinuity at 773 K.

Since it was not practical to separately measure the enthalpy

of the container actually used to hold the molybdenum, the required

empty-container enthalpies were derived from enthalpy measurements

on two entirely comparable containers in the aluminum-oxide work

[29]. For completeness , these are listed in Table 2. (In any

accurate drop calorimetry, including the present work, the empty

container is measured separately in order that the reproducible but

unknown heat lost during the drop cancel when the empty-container

measured heat is subtracted from that for the container-plus-sample,)

The smoothed empty-container "enthalpies" actually used are given

by Eq (1) of Reference [29] (in J, at Kelvin temperature T, IPTS-68):

"t'^273 15 " '^•529744(10"^)(T-273.15)^ + 8.068654(10"^) (T-273 . 15)^

4- 1. 901653 (T-273. 15) -34. 94647 (T-273. 15) /T (1)

The individual measurements on the container-plus-sample,

reduced to the basis of net relative enthalpy of the sample (see

table Footnote b^) are listed in Table 3 in the order in which they

were measured. (Actually, the measurements were made at temperatures

slightly different from those in the first column, with corrections

being made to the stated temperatures using published enthalpy data

[25, 26]. Since these temperature deviations did not exceed 1 K,

the uncertainties in these enthalpy corrections are far smaller than

the precision of the data.)

7
3 XI

1) w 0) C -u •d o

B o

6

CO

3

ON 0^ O ^

CN ON CO ro 00 <)•

-J- in in r~ O t-( in QO 00 <f On o o

c5n 00 o

in in

CM <)

--I o

+ + I I o o

+ +

I—I csj + +

o o

I I o o

+ ' o+

o o

+ +

o o

+ «

tn

0)B

CO

CM XIH

00O CNJ in in o o

<j- in

inON o in vo

CN CM

o <f

in <jON I—

I

in in ^ r- in <)

in in

ON ON

vO CM

in in

CTN 00

in ro o o

vO vD CO 0-)

On ro

r-l O

O ON

in in

COCO CM

00 00

)-l

4-1

t-1 0)eH

CO CO

CM

00

in

CO

00

CO

CM

CJN

CO

ON

CO

CMO

in

COo

in

00

CM

in

CO

0) tn XI0) 3 s: ON CO

CO

vX) I—

CM ON

in

vO 00

vo CM <}• CO CO

in <)- CO -—I vO CM CO O 00 in

in '-^ in CM o o

+ +

o o

+ • o o

+ +

o o

• +

O r-l

I I

.-I o

+ • O r-l + +

o o o o

+ + '

•

t3

<uu

3w

CO

CUB

vO CM o o

On C3N

Csl in ON CO CO

eg CNj

o

o

vo vO

CO <|-

.—I vO

ON 1^ in in

vo vo

C3N vO 00 >—

I

C3N in 00 CM

<!• <^ CO

in in m m

00 00 00 00

CO

CMH

3C

vO <7N CM vo

vO in

in in

CTN oO

ON o

vo

CO CO

in

CO CO O c:n vD in

in m

CO ON

vo vo

in in

3

4-1 u

01eH

CO

CMCO

On

in

CO

CO

CM

in

CO

in in m in in

1—1 r—

1

I—

1

1—1 r-H CO CO CO CO CO

CM 1^ CNJ CM

in in vo vO

8
Table 3

Enthalpy data for the molybdenum sample

^T~^273.15 (measured),

^ net for molybdenum sample

Measured minus smoothed

^ Temperature Based on Eq(3)^ Based on Table 4

K J mol'-"- J mol"-'- J mol"^

J

323.15 1 1187 Q 8.4

0.1

r 373.15 \ 2410.6 - 11.5

1.2

4 73 . i J + 5.9

J / J . ij /D4U .

+ 1.7

D / J . i J 5.5

773.15 1

12919.6

12910.5

+ 14.0

+ 4.9

873.15 15662.2 3.2

973.15 18470.6 0.7

1073.15 21314.2 - 6.7 - 11.5

1173.15 1

24228.7

24206.9

+ 15.9

- 5.9

- 11.2

- 33.0

International Practical Temperature Scale of 1968 [22].

^Each value in this column was obtained from the corresponding gross

measured heat by subs tracting, from the gross, the smoothed value for the

empty container (Eq (1)) and then scaling the remainder from the actual

sample mass, 20.8297 g, to the "mole" (atomic) weight of molybdenum,

95.94 g [241.

c Eq (3) represents a "best fit" to the data in Column 2.

*^Table 4 is based on Eq(3) below 1000 K, and on Eq(6) from 1000 to 1273.91 K.

9
The smoothing of the enthalpy data of Table 3, described

in the next section, resulted in the deviations listed in the

last two columns of the table.

IV. Thermodynamic Functions, 273.15-2100 K

The equations finally adopted to represent the thermodynamic

functions of molybdenum, as based on the combined NBS work, are

given later in this section as Eqs. (3)-(12), and were arrived

at in the following manner.

Choosing trial fitting functions consistent with the known

general shape of the C^CT) curve of molybdenum and similar

crystalline solids, the 14 values in the second column of Table 3

were used in the method of least squares to derive the coefficients

of several alternative temperature functions, each required to

2 vanish at T = 273.15 and containing terms in T, T , and one or

-1 -2 more of inT , T , and T . In addition, each such fitting was

done giving equal weighting alternatively to each enthalpy measurement and to each temperature, since the better choice is debatable.

Of the 14 fits tried, the "best" one had a standard deviation of

residues of 6.1 J mol . However, the next best fit (C7 = 6.6 J mol

was adopted because it proved to merge so well with the published

data below 273.15 K as to require no adjustment. This equation is

identical with Eq (3) (with proper choice of the constant term,

and application of the equation over the whole temperature range

273-1173 K).

10
The "published data below 273.15 K" referred to in the

preceding paragraph refers to an unpublished table of thermodynamic

functions for molybdenum over the temperature range 0-360 K,

prepared in 1968 by Reilly and Furukawa in an NSRDS program at the

National Bureau of Standards [30]. This table was generated after

critical examination of the published data then available, but

follows closely the precise low-temperature heat capacities (10-

273 K) of Clusius and Franzosini on 99.99% pure molybdenum [31].

The table, after adjustment from the IPTS-48 temperature scale to

the basis of IPTS-68 [23], gives the same value of heat capacity

as the derivative of Eq (3) at 278 K (but a 20% greater dC^/dT) .

The presently adopted equations for temperatures above 273.15 K

[Eqs. (3) -(5)] assume the following values (identical to those of

Reilly and Furukawa) at the ice-point: ^273 15

" ^0 ~ ^991 J

mol ^, and 82^2 15 ~ 26.52 J mol '''K ^.

The next step was to merge smoothly the equation representing

the present measurements [Eq (3)] with that representing the earlier

NBS measurements over 1170-2100 K, Eq (1) of Reference [20]. At

the common temperature, 1173 K, the latter equation gives a value

of H°-H^no greater by 78 J mol ^ (which could be interpreted as

equivalent to a temperature discrepancy of 2.6 K) . The two

equations were merged in the following manner: (T^, A, and B being

constants to be evaluated as below)

(a) Eqs. (3) -(5) were assumed to hold only up to 1000 K.

11
(b) For the temperature range 1000 K to T^, the relative

enthalpy was assumed to be represented by Eq (3) plus a tern

B(T-IOOO)^ J mol"-^.

(c) For the temperature range to 2100 K, the relative

enthalpy was assumed to be represented by Eq (1) of Reference

[20] minus a term A(2100-T) J mol"''".

(d) The three constants T^, B, and A were determined so as

to give continuity in enthalpy and heat capacity, not only at 1000 K

but also at T^, and in addition to give a value of enthalpy at

1170 K half as far from the original "273-1173 K" equation (Eq. (3)

of this work) as from the original "1170-2100 K" (Eq . (1) of

Reference [20]) (in recognition of the greater temperature

uncertainty in the latter work)

The above procedure led to the following values:

T^ = 1273.91 K; B = 0.000902 J mol'V"^; A = 0.05005 J mol"-''K"''" . (2)

With the additional requirement of continuity in the entropy at

1000 and 1273.91 K, the final equations for the relative enthalpy,

heat capacity, and absolute entropy of molybdenum based on the NBS

work then become [in terms of J mol ^ and T (K, IPTS-68), with

" i^n" = natural logarithm]:

(A) T = 273.15 to 1000 K

H°-H° = 25.79244 T + 1 . 73410(10"^)T^-862 .870 inT + 1657.1 (3)

C° = 25.79244 + 3 .46820(10"^)T-862 .870/T (4)

S° = 25.79244 InT + 3 .46820(10"-^)T + 862 .870/T-122 .282 (5)

12
(B) T = 1000 to 1273.91 K

H°-H° = 23.98844 T + 2 . 63610(10'^)T^-862 . 870 ^nT + 2559.1 (6)

Cp = 23.98844 + 5.27220(10 )T-862.870/T (7)

S° = 23.98844 /nT + 5 . 27220(10"-^)T + 862 . 870/T-lll . 624 (8)

(C) T = 1273.91 to 2100 K

H°-H° = 21.71415 T + 3 .24129(10'^)T^ + 1 .590(10^)exp(-16000/T)

-1700.8 (9)

C° = 21.71415 + 6.48258(10"-^)T + [ 2 .544(10^°) /T^ ]exp(-16000/T) (10)

P S° = 21.71415 ^nT + 6 .48258 ( 10"^)T

+ Q9.38ri + (16000/T) lexp(-16000/T) -96.232 (11)

Using Eqs. (3) -(11) and also the well-known thermodynamic equation

for the Gibbs-energy function,

-(G°-H°) = S°-[H°-H°)/T], (12)

the thermodynamic functions were computed and are given in Table

4. Table 5 is a replica of Table 4 except in terms of the defined

thermochemical calorie (= 4.1840 j)

The deviation plot of Fig. 1 shows the details of the compromise

in the enthalpy merging above 1000 K described above. Although

the heat-capacity function is continuous at all temperatures,

its temperature derivative (dC^/dT) increases abruptly by 35% at

1000 K and again by 20% at 1273.91 K according to Eqs. (4), (7),

and (10). It should, however, be pointed out that no evidence

exists that these discontinuities in dC /dT arise from the sample itself.

13
Table 4

Thermodynamic functions for molybdenum (in terns of JOULES per mole)

(International Practical Temperature Scale of 1968; 1 mole = 95.94 g)

T

K

H-Hq Cp S -(G -Hq)/T

J mol"^

L-, ^ J mol-J-K"^- T 1 J mol"^"^ J mol~^"l

273.15 3991 23 .58 26.52 11.91

275 4035 23.61 26.68 12.01

298.15 4585 23.93 28.60 13.22

300 4629 23.96 28.75 13.32

325 5232 24.26 30.68 14.58

350 5842 24.54 32.49 15.80

375 6459 24.79 34.19 16.97

400 7082 25.02 35.80 18.09

425 7710 25.24 37.32 19.18

450 8343 25.44 38.77 20.23

475 8982 25.62 40.15 21.24

500 9624 25 .80 41.47 22.22

525 10272 25.97 42.73 23.17

550 10923 26.13 43 .94 24.08

575 11578 26.29 45.11 24.97

600 12237 26.44 46.23 25.83

625 12900 26.58 47.31 26.67

650 13566 26.72 48.36 27.49

675 14236 26.86 49.37 28.28

700 14909 26.99 50.35 29.05

725 15585 27.12 51.30 29.80

750 16265 27.24 52.22 30.53

775 16947 27.37 53 .11 31.25

800 17633 27.49 53.98 31.94

850 19013 27.73 55.66 33.29

900 20405 27.96 57.25 34.58

950 21809 28.18 58.77 35.81

1000 23223 28.40 60.22 36.99

1050 24651 28.70 61.61 38.13

1100 26093 29.00 62.95 39.23

1150 27551 29.30 64.25 40.29

1200 29023 29.60 65.50 41.32

1250 30511 29.89 66.72 42.31

1300 32013 30.21 67.89 43.27

1350 33532 30.57 69.04 44.20

1400 35069 30.93 70.16 45.11

1450 36625 31.31 71.25 45.99

1500 38200 31.70 72.32 46.85

1550 39796 32.11 73.37 47.69

1600 41412 32.54 74.39 48.51

1650 43050 32.98 75.40 49.31

1700 44711 33 .45 76.39 50.09

1750 46396 33.95 77.37 50.86

1800 48106 34.47 78.33 51.61

1850 49843 35.01 79.28 52.34

1900 51607 35.58 80.22 53.06

1950 53401 36.18 81.16 53.77

2000 55226 36.81 82.08 54.47

2050 57083 37.47 83.00 55.15

2100 58974 38.16 83.91 55.83

14
Table 5 Thermodynamic functions for molybdenum (in terms of CALORIES per mole)

(International Practical Temperature Scale of 1968; 1 cal = 4.1840 J; 1 mole = 95.94 g)

„ "0 , ^ K cal mol cal mol K

- - _ 1 -1 - cal mol K

,-l--lcal mol K

273 . 15 953 .9 5 .636 6.339 2 .846

275 964.3 5.643 6.377 2 .870

298. 15 1095 .8 5.720 6.836 3 . 160

300 1106.4 5.726 6.871 3 .183

325 1250.5 5 .799 7.332 3 .485

350 1396.3 5 .865 7 . 765 3 .775

375 1543 .7 5 .925 8.171 4 .055

400 1692 .6 5 .981 8.556 4.324

425 1842.7 6.032 8.920 4 .584

450 1994 .

1

6.079 9.266 4.835

475 2146.7 6.124 9.596 5.077

500 2300,3 6. 167 9.911 5 .310

525 2455.0 6.207 10.213 5 .537

550 2610.6 6.245 10.503 5.756

575 2767 .2 6.283 10.781 5 .968

600 2924.7 6.318 11.049 6.175

625 3083.1 6.353 11.308 6.375

650 3242.4 6.386 11.558 6.569

675 3402.4 6.419 11.799 6.759

700 3563.3 6.450 12.033 6.943

725 3724.9 6.481 12.260 7.122

750 3887.3 6.511 12.480 7.297

775 4050.5 6.541 12.694 7.468

800 4214.4 6.570 12.902 7.634

850 4544.3 6.626 13 .302 7.956

900 4877 .0 6.681 13 .683 8.264

950 5212 .4 6.735 14.045 8.559

1000 5550.5 6.787 14.392 8.842

1050 5891 .

7

6.860 14.725 9.114

1100 6236.5 6.932 15.046 9.376

1150 6584 .

8

7 .003 15.356 9.630

1200 6936 .8 7.074 15.655 9.875

1250 7292 .

2

7 .143 15 .945 10.112

1300 7651.2 7.220 16.227 10.342

1350 8014 .3 7 .305 16.501 10.565

1400 8381 .

7

7 .393 16.768 10.782

1450 8753.6 7.483 17.029 10.992

1500 9130.

1

7.577 17 .285 11.198

1550 9511 .4 7 .675 17 .535 11.398

1600 9897 .

6

7.777 17 .780 11.594

1650 10289 .

1

7.884 18.021 11.785

1700 10686 .

1

7.996 18.258 11.972

1750 11088.8 8.114 18.491 12.155

1800 11497.5 8.237 18.722 12.334

1850 11912.6 8.368 18.949 12.510

1900 12334.4 8.504 19.174 12.682

1950 12763.2 8.648 19.397 12.852

2000 13199.3 8.798 19.618 13.018

2050 13643.2 8.956 19.837 13.182

2100 14095.1 9.120 20.055 13.343

15
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16
Such "unreal" discontinuities in higher derivatives as formulated

can sometimes be tolerated without doing serious injustice to

the known facts. For example, there are marked discontinuities

in the temperature derivative of the difference between temperatures

on the IPTS-48 and IPTS-68 scales at 904 and 1338 K (Ref. [23],

p. 466), and these discontinuities present small but real

ambiguities in correcting heat capacities from one temperature

scale to the other in the neighborhood of these two temperatures

In view of the high purity of the molybdenum sample as described

in Section II, it seems likely that the principal source of error

in the smoothed values of the present work (273-1173 K) is

inaccuracies in the measured temperatures of the sample in the

furnace. It was estimated that the error in relative enthalpy

^t'^273 P^°b^^ly varies from 0.5% or less at T = 373 to 0.1-0. 2%

at T = 1173, and that the error in heat capacity does not exceed

0.57. up to 1000 K.

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 6 summarizes, in approximately chronological

order, all these investigations found that report values in the

temperature range of the present work (273-1173 K) . These values

(except a few which were not readily available) were first converted

from the basis of IPTS-48 to IPTS-68 (unless the investigator

17
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18
defined his temperature scale in terms of recognized fixed points)

(See Table 7 for the magnitudes of these corrections.) The values

were then compared with those from the measurements reported here.

(For a similar comparison with the NBS work in the temperature

range 1170-2100 see Ref. [20].) The comparisons are shown

graphically in Figs. 2 and 3.

Figure 2 is a deviation plot of the enthalpy relative to

273.15 K. The base line represents Eqs. (3) and (6) (or Table 4

or 5), and the points represent the percentage deviations, from

this base, of unsmoothed values (including those of Table 3),

corrected to a base temperature of 273.15 K when necessary, using

Eq (3) . (Curves are given in those cases where only smoothed

values were reported, but no attempt was made to include in Fig. 2

the corresponding enthalpies of those investigators who measured

and reported only heat capacities.) In many cases "repeat"

individual measurements were reported over the same or nearly the

same temperature range, and in such cases only the average is plotted,

to simplify the graph.

Figure 3 shows total heat capacity vs. temperature. The

solid curve corresponds to Eqs. (4) and (7) (or Table 4). The

individual points are unsmoothed values, and some of them are from

investigators who measured heat capacity but not enthalpy. Other

points correspond to heat-capacity values calculated from unsmoothed

19
Table 7

Corrections for molybdenum to convert from the basis of

IPTS-48 to the basis of IPTS-68 (see ref. [23])

Temperature T ^ T 273^68"'^ t""273 ^48

K T r=l J mol

;

1 -irr-i

J mol

+ 0.2 + 0.004

400 -0.3 - 0.011

500 -1.3 - 0.010

600 - 2.1 - 0.003

700 -2.2 0.000

800 - 2.5 - 0.011

900 -5.3 - 0.054

1000 - 13 .

- 0.082

1100 - 21.5 - 0.086

1200 - 30.5 - 0.092

1300 - 39.8 - 0.098

1400 - 47.3 - 0.062

1500 - 53.7 - 0.069

1600 - 60.8 - 0.076

1700 - 68.6 - 0.085

1800 - 77.3 - 0.095

1900 - 86.8 - 0.106

2000 - 97.3 - 0.119

2100 - 109.0 - 0.134

20
LEGEND OF SYMBOLS FOR FIGURES 2 AND 3

NBS work (smoothed) [Eqs (3)-(ll) and Tables 4 & 5]

Kothen, 1957 (smoothed) [13]

Bronson & Chisholm, 1929 (smoothed) [7]

Taylor & Finch, 1961 (smoothed) [16]

Douglas and Dltmars,1973 [this report]

Bronson, Chisholm, & Dockerty, 1933 [8]

Lazareva et al., 1961 [18]

Cooper & Langstroth, 1929 [6]

Wust et al., 1918 [4]

Jaeger & Veenstra, 1934 [9]

Stucker, 1905 [3]

Defacqz & Gui chard, 1901 [2]

Ishihara & Douglas, 1971 [20]

Regnault, 1840 [1]

Redfield and Hill, 1951 [10]

Lehman, 1960 [14]

Lucks & Deem, 1956 [11]

Stern, 1928 [5]

Getting & Navratil, 1972 [21]

Kirillin et al., 1961 [17]

21
en

00

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00C

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O

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00

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22
3 I

30

29

28

27

26

25

24

23

22

21

20

19

-8-

300 400 500 600 700 800 900 1000 1100 1200

TEMPERATURE, K

Comparison of molybdenum heat-capacity values of various

investigators. [See neighboring page for legend of symbols.]

23
enthalpies at sucessive temperatures: Z^l/AT except when

was several hundred degrees. In this case the small curvature

corrections were applied (when appreciable) from the approximate

equation

C (at T ) = AH/AT - (1/24) (d^C /dT^), (13)

p m'^ '^p

2 9 where T is the middle of the temperature interval, and where d C / dT

m ^ P was calculated from Eq . (4) or (7). In plotting Cp values

thus derived from enthalpy data, an attempt was made to group an

observer's points and average them such that the intervals AT

were approximately 50 to 100 degs (as in the present measurements).

This leads to a fairer comparison of precision from one investigator

to another, since even good enthalpy precision would lead to. an

enormous scatter of Zl^H/Z^ values if AT were sufficiently small.

Figures 2 and 3 show that, aside from the earliest measurements,

most of the earlier investigators agree in this temperature range

with the present work to within 2 to 3% on relative enthalpy, and

to within 5% on heat capacity. For high temperatures the accuracy

of temperature measurement is always suspected as a major source

of error. But for lower temperatures (particularly those determined

by the ice and steam points), large deviations in the values

cast serious doubt on the calorimetry, and this is notably true

of the earliest measurements. Also to be questioned is the

purity of some of the molybdenum samples used, particularly since

small percentages of unsuspected impurities of low atomic weight

often lead to enthalpies and heat capacities that are too high

24
by several times the impurity percentage. In this connection

it might be mentioned that, in contrast to the very thorough

analysis of the NBS sample (Table 1) and the less comprehensive

analyses reported for many of the others, several investigators

merely reported that their samples were gifts and that they

"ought to be pure."

The deviations from the adopted results of this report

[Eqs (3) -(11), or Table 4 or 5 ] are listed in Table 8 for three

well-known critical compilations. These deviations reflect some

of the general trends noticeable in Figures 2 and 3, since the

compiled values necessarily depend on the literature available

up to several years ago.

25
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VI . References

[11 M. V. Regnault, Ann. chim. phys. [2] 73, 5 (1840).

[21 E. Defacqz and M. Guichard, Ann. chim. phys. [71 24,

139-144 (1901).

[31 N, Stucker, Sitzb. konig. Akad . Wlss., Wien, 114, 657 (1905).

[41 F. Wust, A. Meuthen, and R. Durrer, Forsch. Arb . Ver. deut.

Ing., No. 204 (1918).

[51 T. E. Stern, Phys. Rev. [2] 32, 298-301 (1928).

[61 D. Cooper and G. 0. Langstroth, Phys. Rev. 32, 243-248 (1929).

[7l H. L. Bronson and H. M. Chisholm, Proc . Nova Scotia Inst.

Sci. 17, 44-45 (1929) (cf. Chem. Abstr. 26, 4532-4533 (1932)).

[81 H. L. Bronson, H. M. Chisholm, and S. M. Dockerty, Can.

J. Research 8, 282-303 (1933).

[91 F. M. Jaeger and W. A. Veenstra: (a) Proc. Royal Acad.

Amsterdam 37, 61-66 (1934) (in Eng.); (b) Rec. Trav. Chim.

Pays-Bas 52, 677-687 (1934) (in Eng.).

[101 T. A. Redfield and J, H. Hill, Report ORNL-1087, Oak

Ridge National Laboratory, Oak Ridge, Tenn. (1951).

[Ill C. F. Lucks and H. W. Deem, WADC Tech. Report 55-496

(ASTIA Document AD 97185) (1956).

27
[12] I. B. Fieldhouse, J. C. Hedge, J. I. Lang, A. N.

Takata, and T. E. Waterman, WADC Tech. Report 55-495

(1956).

[131 C. W. Kothen, Diss. Abstr. 17_, 2842-2844 (1957).

[14] G. W. Lehman, WADD Tech. Report 60-581 (1960).

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

15, 17-26 (1960).

[16] R. E. Taylor and R. A. Finch, J. Less Common Metals 6_,

283-294 (1963) [cf. Report NAA-SR-6034 (Metals, Ceramics,

and Materials), Atomics International, Canoga Park, Calif.

(1961)].

[17] N. A. Kirillin, A. E. Sheindlin, and V. Y. Chekhovskoi : (a)

. Dokl. Akad. Nauk SSSR 139, 645-647 (1961); (b) Int. J.

t Heat Mass Transfer _5, 1-9 (1962) (in Eng.).

[18] L. S. Lazareva, P. B. Kantor, and V. V. Kandyba, Fiz. Met.

. i. Metal lov j_l, 628-629 (1961) (English: Phys. Metals

and Metallog. 11, 133-134 (1961)).

[19] M. J. Pool, R. W. Sullivan, and C. E. Lundlin, Quarterly

Status Rept, No. 9, contract AF 19(604) -7222, U. of

. Denver, Denver Research Inst., Denver, Colo. (1962).

[20] S. Ishihara and T. B. Douglas, NBS Report 10481 (AFOSR-TR71-2584), National Bureau of Standards, Washington, D. C.

(1971), pp. 59-83.

28
[21] F. L. Getting and J. D. Navratil, J. Chem. Eng. Data

17, 230-231 (1972).

[22] "The International Practical Temperature Scale of 1968",

Metrologia 5, 35 (1969).

[23] T. B. Douglas, J. Research Nat. Bur. Stand. (U. S.) 73A,

451-470 (1969).

[24] A. E. Cameron and E. Wichers, J. Am. Chem. Soc. 84, 4175

(1962).

[25] K. K. Kelley, U. S. Bur. Mines Bull. 584, p. 125 (1960)

(manuscript completed Nov. 1958).

[26] 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).

[27] JANAF Thermochemical Tables, 2nd ed . , Nat. Stand. Ref. Data

Series, Nat. Bur. Stand. (U. S.), 37, 1141 pages (1971)

(table for Mo(c): Dec. 1966).

[28] T. B. Douglas and E. G. King, "High Temperature Drop

Calorimetry, " Chapter 8 in "Experimental Thermodynamics,"

Vol. I (Buttervorths, London, 1968); also in "Precision

Measurement and Calibration (Heat)", D. C. Ginnings, Ed.,

Nat. Bur. Stand. (U. S.), Spec. Publ. 300, Vol. 6, 181-

219 (1970).

29
[29] D. A. Ditmars and T. B. Douglas, J. Research Nat. Bur.

Stand. (U. S.) 75A, 401-420 (1971).

[30] M. L. Reilly and G. T. Furukawa, National Bureau of Standards,

Washington, D. C, private communication.

[31] K. Clusius and P. Franzosini, Zeit. Naturforsch. 14a ,

99-105 (1959)

[32] Certificate: "Standard Reference Material 720, Synthetic

Sapphire (kl^O^) National Bureau of Standards, Washington,

D. C, 1970.

30
Chapter 2

MEASUREMENT OF HEAT CAPACITY OF

GRAPHITE IN THE RANGE 1500 TO 3000 K

BY A PULSE HEATING METHOD^

Ared Cezairliyan

National Bureau of Standards

Washington, D. C. 20234

ABSTRACT

Measurement of heat capacity of a grade of graphite (AXM-5Q,

Poco) in the temperature range from 1500 to 3000 K by a subsecond

duration pulse heating technique is described. The results for the

same specimen corresponding to two different heating rates are in

agreement within 0.17o. The results for two different specimens are

in agreement within 0.67o. The heat capacity of graphite in the

temperature range from 1500 to 3000 K is expressed by the following

function (standard deviation = 0.57c,):

c = 19.12 + 4.236 X lO"-^ T - 5.919 x lO"^ T^

P

where T is in K, and c^ is in J mol ^. The inaccuracy of reported

results is estimated to be not more than 37..

This work was supported in part by the U. S. Air Force Office of

Scientific Research.

31
INTRODUCTION

Considerable disagreements exist between the limited number

of experimental results for the heat capacity of graphite reported

in the literature above 1500 K. Most of the reported measurements

were performed on different grades of graphite, which complicate

their evaluation and pose the question whether the differences were

due to measurement errors or were indicative of the differences

in the graphite grades.

As an attempt to elucidate this, a program was initiated for

the systematic and accurate measurement of heat capacity of various

grades of graphite at high temperatures. The objective of this

paper is to present the results of the first phase, namely the measurement of heat capacity of a grade of graphite (AXM-5Q, Poco) in the

temperature range from 1500 to 3000 K. The measurements were performed utilizing a subsecond duration pulse heating technique.

METHOD

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

specimen from room temperature to high temperatures (above 1500 K)

in less than one second by the passage of electrical currents through

it; and on measuring, with millisecond resolution, experimental

quantities such as current through the specimen, potential drop across

the specimen, and specimen temperature.

32
Current through the specimen is detemined from the measurement

of the potential difference across the standard resistance placed

in series with the specimen. Potential difference across the middle

one third of the specimen is measured using spring-loaded, knife-edge

probes. Specimen temperature is measured at the rate of 1200 times

2 per second with a high-speed photoelectric pyrometer [1] . A

small hole in the wall at the middle of the tubular specimen provides

an approximation to blackbody conditions. The experimental quantities

are recorded with a digital data acquisition system, which has a

time resolution of 0.4 millisecond 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 [2, 3].

Figures in brackets indicate the literature references at the end

of this paper.

33
MEASUREMENTS

The measurements were performed on two tubular specimens,

designated as graphite-1 and graphite-2, which were fabricated from

3

the same graphite block . The nominal dimensions of the specimens

were: length, 76 mm; outside diameter, 6.3 mm; and wall thickness,

0.5 mm. The specimens were 99. 99"*" pure. Before the start of the

experiments, the specimens were annealed by subjecting them to

20 heating pulses (up to 2800 K) . The experiments were conducted

with the specimens in a vacuum environment of approximately 10

^

torr

To study possible effects that may be attributable to the

rate with which the specimen heats, two different heating rates,

designated as "fast" and "slow", were used in the experiments on

graphite-1. To optimize the operation of the high-speed pyrometer,

the temperature interval (1500 to 3000 K) was divided into six ranges

One experiment was performed in each range for each heating rate.

This yielded a total of 12 experiments for graphite-1. In the

case of graphite-2, only the "fast" heating rate was used and 4

experiments were performed to cover the range 1500 to 2200 K.

The graphite block (AXM-5Q, Poco) was furnished by the U. S. Air

Force Materials Laboratory, Wright-Patterson Air Force Base, Ohio.

34
To optimize the operation of the measurement system, the

heating rate of the specimen (in both "fast" and "slow" cases) was

varied depending on the desired temperature range by adjusting the

value of the resistance in series with the specimen. The operationa

characteristics of the measurement system, during the present

experiments such as current pulse length, specimen heating rate,

and heat loss from the specimen by thermal radiation, are summarized

in Table 1.

Optical checks performed on the experiment chamber window after

the pulse experiments ' did not indicate any graphite deposition.

Also, weight measurements before and after the entire set of pulse

experiments did not sViow any change in the specimen weight. However

trial experiments above 3000 K, indicated graphite evaporation both

in vacuum and in argon environment at atmospheric pressure, por

this reason, with the present system it was not possible to extend

the accurate measurements above 3000 K.

EXPERIMENTAL RESULTS

Heat capacity was determined from the experimental data on

current, voltage, and temperature obtained during the rapid heating

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

made based on data obtained during the initial radiative cooling

period following the heating period. The procedure for determining

properties from experimental data is given in an earlier publication

[31.

35
Table 1

Operational Characteristics of the Measurement System

During the Experiments on Graphite-1

Quant ity Heating Rate Temp

" Fast " Slow VIN. Current pulse length 210 280 1500

(ms) 280 510 3000

Specimen heating rate 6000 4400 1500

. (K s"b 6200 2700 3000

Radiative heat loss from 2 3 1500

specimen 7 10 2000

(7o of input power) 13 22 2500

26 45 3000

36
The heat capacity results obtained for the "fast" and "slow"

experiments were fitted separately to quadratic functions in temperature using the least squares method. Standard deviation of an

individual point from the smooth function is 0.5% and 0.4% for

the "fast" and "slow" experiments, respectively. The average absolute

difference between the heat capacity results of the "fast" and "slow"

experiments for graphite-1 over the range 1500 to 3000 K is 0.1%

with a maximum difference of 0.2%, Since this difference is

within the imprecision of the measurements, the final results for

graphite are obtained by combining the experimental results

corresponding to both heating rates for graphite-1. The function

for heat capacity (standard deviation = 0.5%) that represents the

results in the temperature range 1500 to 3000 K is:

c = 19.12 +4.236 x 10"^T-5.919 x 10"^T^ (1)

P

where T is in K, and c^ is in J mol ^. Heat capacity of graphite

computed using Equation (1) is given in Table 2. All the results

reported in this paper are based on the International Practical

Temperature Scale of 1968 [4].

Figure 1 shows the deviation of the experimental results of

graphite-1 corresponding to "fast" and "slow" heating rates from the

smooth function represented by Equation (1)

37
Table 2

Heat Capacity of Graphite (AXM-5Q, Poco)

T

(K)

cP

(J mol-lK-1)

i jUU 9 /. 1 A

1 Ann Z4 . Jo

L /UU 9/. C 1 24 .01

ioUU 24 . 83

iyuu 25 .03

^UUU 25 .22

L iUU 91; /.I 25 .4 i

9 C C "7 25 . 57

Z91J nnUvJ 2i) . / J

9Ann 9 ^ QQ 2 J . 00

9 i^inn 20 . U i

9fi 19 20 . iJ

2700 26.24

2800 26.34

2900 26.43

3000 26.50

38
o

ID O lO -

I lN3Dd3d *N0llVIA3a

39
The deviation of the smooth functions for the "fast" and

"slow" experiments for graphite-1 from the final combined function,

Equation (1), is presented in Figure 2. In the same figure, the

deviation of the results for graphite-2 from those of graphite-1 is

also shown. The average absolute difference between the heat

capacity results of graphite-2 and those of graphite-1 (combined)

is 0.6%, with a maximum difference of 0.77o.

ESTIMATE OF ERRORS

The details for estimating errors in measured and computed

quantities in high-speed experiments using the present measurement system are given in an earlier publication [3], In this paper,

the specific items in the error analysis were recomputed whenever

the present conditions differed from those in the earlier publication.

4 5 The imprecision in the measurements is 0.5%. The inaccuracy in

the results is estimated to be not more than 3%.

Because of the high value of hemispherical total emittance of

graphite, heat loss from the specimen due to thermal radiation

constitutes a substantial fraction of the input power, especially

at temperatures above 2500 K (Table 1). In the present work, the

uncertainty in measuring heat loss by thermal radiation is est imated

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.

^Inaccuracy refers to the estimated total error (random and systematic).

40
41
to be not more than 3%. To ensure the validity of this estimate,

experiments were performed utilizing two different heating rates.

At the highest temperature (3000 K), heat loss in the "fast" and

"slow" heating cases amounted to 26% and 45% of the input power,

respectively. This corresponds to a difference of approximately

207o in radiation loss. In this case, an error of 3% in the

measured heat loss would have amounted to a difference of approximately

0.67o in heat capacity obtained for the experiments corresponding

to the two heating rates. Yet, in the present work, this difference

is 0,1%. Therefore, in spite of the fact that heat loss by thermal

radiation constitutes a large fraction of the input power,

an accurate account of its magnitude has not affected the accuracy

of the heat capacity results.

42
DISCUSSION

Heat capacity results obtained for the two graphite specimens

under different experimental conditions were reproducible and

internally consistent. Electrical resistance measurements (with a

Kelvin bridge) before and after the pulse experiments were in agreement

within 0.1%, which indicates that no significant structural or

chemical changes had taken place in the specimen as the result of

its heating to high temperatures. It may be concluded that the

graphite specimens used in this work were stable under the present

operating conditions.

Only a limited number of experimental results for graphite

are available in the literature at temperatures above 1500 K. Since

most of them are for different grades of graphite, it is difficult

to have a common ground for comparison. As it may be seen in Figure

3, considerable differences exist between the results of various

investigators.

The results of the present work agrees best with those reported

by West and Ishihara [5] on grade CCH graphite. In the temperature

range from 1500 to 2000 K, the agreement is within 0.8%. However,

the difference increases with increasing temperature, amounting to

1.7% at 2600 K.

43
o

CD

CD

o

CD

h-• o o Lij cr < (D CD _J <

l_ 0^ 0} O X

C/) < < Q

- 3 f- I- 5 9 O LU UJ < ^

S cn (/:> cr 2:

N^: ^ o ^

I.I ^ <^ <^ m y 3 3 < y en Q.

,_>! jJOlAI r 'AllOVdVO 1V3H

44
The curve (in Figure 3) showing the results of Rasor and

McClelland [6] is an average, as given by the authors, representing

data on four grades of graphite (3474D, 7087, GBH, and GBE) . Actual

data have a scatter of approximately 5% about the smooth curve.

The difference between the results of Rasor and McClelland and those

of the present work is, on the average, approximately 3%.

Lucks et al. [7] have reported results for two grades of

graphite. The upper and lower curves (in Figure 3) represent the

results for the grades 7087 and GBH, respectively. The disagreement

between the results of Lucks et al, and Rasor and McClelland for

the same grades of graphite is more than 10%.

Over the overlapping temperature region (1500 to 1800 K), the

results for ATJ graphite reported by Fieldhouse et al. [8] agree,

within 3%, with those of the present work. However, the slope of

the curve representing the results of Fieldhouse et al. is considerably

greater than that of the present work.

In addition to the present measurements, the only other known

measurement on the same grade of graphite was performed by Binkele

[9]^ in the temperature range from 373 to 1273 K. Since there is no

overlapping region, it is difficult to report the differences in the

two results. However, from Figure 3 it may be seen that an

extrapolation of Binkele 's results to 1500 K is likely to yield a

value approximately TL lower than that of the present work.

The graphite (AXM-5Q, Poco) specimen used by Binkele was also

furnished by the U. S. Air Force Materials Laboratory.

45
The rather close agreement between the results of West and

Ishlhara [5] and those of the present work, which were obtained

on two different grades of graphite using two different measurement techniques, indicates that heat capacity of graphite may not

be very sensitive to differences in the grades, at least for some

of the grades. Therefore, the differences in the literature results

should not be entirely attributed to grade differences, as it

is likely that these differences might have been mostly due to

experimental errors. In addition, the state of the specimen (purity,

degree of graphitization and annealing) undoubt edly plays an

important role in the results. A final conclusion regarding heat

capacity of graphite can only be reached after performing

additional accurate measurements on other grades of graphite.

It may be seen that the heat capacity of graphite reaches the

Dulong and Petit value of 3R (24.943 J mol ''"K '') at approximately

1850 K, and continues to increase above that temperature.

The rate of change of heat capacity with temperature decreases

-3 -1 -2

from a value of 2.5 x 10 J mol K at 1500 K to a value of

-4 -1 -2

6.8 x 10 J mol K at 3000 K. This rather unusual trend for

heat capacity at high temperatures (above 1500 K) is due to the

high value of the Debye temperature (1550 K [10]) for graphite.

46
Future heat capacity measurements at temperatures above 3000 K

promise to yield information of practical and theoretical

significance. It is important to resolve the question whether heat

capacity of graphite reaches a constant value at temperatures above

approximately 3300 K, or increases sharply above this temperature,

as was reported by Rasor and McClelland [6].

In summary, the two potentially useful research areas in

connection with the heat capacity of graphite are:

(1) Investigations of the dependence of heat capacity on

graphite grades, and graphite stability from the viewpoint of

reproducibility of heat capacity measurements at temperatures below

3000 K.

(2) Accurate measurements in the range 3000 K to the

sublimation point of graphite. These measurements have to be

performed with the specimen in a pressurized environment to

suppress evaporation.

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 contribution

of Mr. M. S. Morse in connection with electronic instrumentation

is also greatly appreciated.

47
REFERENCES

Foley, G. M., "High-Speed Optical Pyrometer", Rev. Sci,

Instr . , Vol. 41, 1970, pp. 827-834.

Cezairliyan, A., "Design and Operational Characteristics

of a High-Speed (Millisecond) System for the Measurement

of Thermophysical Properties at High Temperatures",

J. Res. Nat. Bur. Stand. (U. S.), Vol. 75C (Eng. and Instr.),

1971, pp. 7-18.

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.) , Vol. 74A (Phys. and Chem.), 1970, pp. 65-92.

International Practical Temperature Scale of 1968,

Metrologia, Vol. 5, 1969, pp. 35-44.

West, E. D., and Ishihara, S., "A Calorimetric Determination

of the Enthalpy of Graphite from 1200 to 2600 K", Advances

in Thermophysical Properties at Extreme Temperatures and

Pressures

Am. Soc. Mech. Eng., New York, 1965, pp. 146-151.

Rasor, N. S., and McClelland, J. D., "Thermal Properties of

Graphite, Molybdenum, and Tantalum to Their Destruction

Temperatures", J. Phys. Chem. Solids, Vol. 15, 1960, pp. 17-26.

48
Lucks, C. F., Deem, H. W., and Wood, W. D., "Thermal

Properties of Six Glasses and Two Graphites", Am. Cer .

Soc. Bull .. Vol. 39, 1960, pp. 313-319.

Fieldhouse, I. B., Lang, J, I., and Blau, H. H.,

WADC TR 59-744, 1960, pp. 1-78, [AD 249 166].

Binkele, L., Private Communication, 1972.

Gschneidner, K. A., "Physical Properties and Interrelationships of Metallic and Semimetallic Elements", Solid State

Physics, F. Seitz, and D. Turnbull, eds.. Vol. 16, Academic

Press, New York, 1965, pp. 275-426.

49
ft

\ Chapter 3

THERMODYNAMIC FUNCTIONS FOR MoF^(g)

Thomas B. Douglas, Ralph F. Krause, Jr.,

Nicolo Acquista, and Stanley Abramowitz

. ' In last year's report two of us reported in detail the results of

infrared and Raman spectroscopic investigations of MoF^ [1]. The

structural and vibrational assignment of the molecule as stated there

were not entirely complete and unambiguous for the purpose of generating

a table of thermodynamic functions, but such an assignment of fundamentals

was provided later [2], and led to the table computed and reported in the

present chapter.

Ideal-gas thermodynamic functions for MoF^ gas (the monomer species)

over the temperature range 0 to 6000 K are given in Table 1 in terms of

the thermochemical calorie (=4.1840 J) as the unit of energy, and in the

format of the first five columns of the JANAF thermochemical tables [3].

(In "^2^2" the subscript refers to 298.15 K. The standard enthalpies and

Gibbs energies of formation are not included because a reliable value for

the heat of formation was not available, although it may be soon (Ref . [5J^

Chapters 5 and 6). Table 1 is repeated in Table 2 except with the joule

as the unit of energy.) The harmonic-oscillator rigid-rotor approximation

was used. .The space group and vibrational fundamentals assumed are those

referred to above [2]. The two fundamentals estimated but not observed

are bracketed below, according to the usual custom. The Mo-F bond distances

in the MoF molecule were assumed to be all the same, and to be equal to

50
the value found In an electron-diffraction study of MoF [4] and adopted

o In the JANAF table for that gas [3J. These tables for MoF^ assume a

single electronic state, and a multiplicity of 2 to account for the known

fact that MoF^ is electronically an "odd" molecule.

A collection of the molecular constants on which Tables 1 and 2 are

based is as follows. The symbols have the same meanings as in the JANAF

tables [3] .

MOLYBDENUM PENTAFLUORIDE (MoF^) (IDEAL GAS) GFW = 190.932

Point Group iD^j^J

^298.15 " ^^^'^^ gibbs/mol

Ground State Quantum Weight = [2]

Vibrational Frequencies and Degeneracies

-1 -1

759(1) 713(2)

738(1) 261(2)

683 (1) 112(2)

[500] (1) [200] (2)

Electronic Levels and Quantum Weights

-1

^'i cm g.

[2]

Bond Distance: Mo-F = [1.84] A

A A A AA AA

Bond Angles: [F -Mo-F = 120° F -Mo-F = 90° F -Mo-F = 180°]

* Equatorial **Axial

a = [6]

Product of the Moments of Inertia: I I„I^ = [4.478 x 10~ J g cm A D L

51
REFERENCES

N. Acqulsta and S. Abramowitz, AFOSR Scientific Report AFOSR-TR72-2004 (NBS Report 10904), National Bureau of Standards,

Washington, D. C. 20234, July 1972, Chapter 3 (pp. 49-63).

S. Abramowitz (Dec. 5, 1972).

JANAF Thermo chemical Tables, D. R. Stull and H. Prophet,

Project Directors, 2nd ed., NSRDS-NBS 37, U. S. Government

Printing Office, Washington, D. C. (June 1971).

G. M. Nazarian, Ph.D. Thesis, California Institute of Technology,

Pasadena, Calif. (1957).

Report NBSlR 73-281, National Bureau of Standards, Washington,

D. C. 20234 (AFOSR Agreement ISSA-73-0001) , 1 July 1973.

52
Table 1. Ideal-Gas Thermodynamic Functions for Molybdenum Pentafluorlde Monomer

(in CALORIE^ enerjty units

T

P -(G»-H°gg)/T " -»298

1 IT wax illUX . ^ <^ ii 1 m/^ 1 aX Ul\) JL

. noo .000 .000 00 -5 . 028

ion . onn 14. '"^0 62.230 10 1. gno -^.968

200.000 20. 31° 74 . 204 3 . 2 6 . 1"7

298. ISO 24 . 195 8"^. 170 8"^ . 170 .000

300.000 24.254 8'^.3?0 83. 17n . 045

400.000 D . ' -J -f on . f;«>A 84. 155 5.605

500.000 28.248 96.808 S'^'. 089 5.360

600 . 000 29.^00 ] 0^. 0 49 88.32"^ 8.2 35

29.825 106.600 qn" ' tic, 1 . c? 1 » 11 1 RQ

800 . 000 30.254 11':'. 612 ci?.87n 1 4. 194

yoo . ono 30 . 559, 114. lo(+ 1 "7 ^XiL 1000.000 30.733 117.426 97. 123 20.303

1100.000 30.951 120.368 90. 104 23.390

1200.000 31.082 123.067 100. 99n 26.492

1300.000 31 .184 125.559 1 02.786 2^.606

lUOO.OOO 31. 266 127 . 873 ] 04 .496 32 . 728

1500.000 31.333 130.0-^3 1 06. 127 35,858

1600 . 000 31.388 132.057 107.685 30,995

1 7no . nnn 31.434 13^.961 109. 176 4'' . 1 36

1800.000 31 .472 135. 71^9 110. 603 45.281

lyoo .000 31.505 137,14.62 111. y72 48 , 430

2000. ono 31 .533 139.078 1 13.287 51 ,582

2100.000 31.557 140.617 114.55? 54,736

2200 . 000 31.578 142. 0"6 1 1'=;.771 57,893

2300.000 31 .596 143.4^^0 1 16.9(+6 61 , 052

2400.000 1 1 0 , n 0 0 6'U21?

2500.000 31 .6?6 146. 196 1 19. 176 67 . 37u

2600 . 000 31.639 147. 3^,6 120.237 70 , 537

2700 .000 31.650 148.661 121. 264 7"^,709

2800.000 31.660 14^.712 122.259 76.867

2900 .ono 31 . 669 150,823 1 23.225 80 . 034

3000 . ono 31.677 151 .897 1 24. 163 83.201

3100.000 31.6«5 152.936 125.075 86. 36°

3200.000 31.692 15"^. 942 125.961 8°. 530

3300 . 000 31.698 154. oi7 126.824 90 .707

3400 . 000 31.703 X J J • 0 " J 127.664 95 . 877

3500.000 31.708 156.702 128.483 99, 048

3600.000 31.713 157.676 129.282 10'5.219

3700 .000 31.717 15". 545 130.061 105, 39]

3800.000 31.721 15^.391 130.822 100.563

3900 .ono 31 . 725 160.215 131 , 565 111 ,735

4000 . 000 31 .729 161.018 132.291 114. 908

4100.000 31 ."^32 161 .801 1 33 . 001 118.081

4200 . 000 31 .735 162.566 13-^.6'^6 121 .254

4300 .000 31.737 16'»i.3l3 1 34.376 124.428

4400 .000 31.740 16'i.043 135.042 127.601

'iSOO .000 31.742 164.7'^6 135.695 130.776

4600 . ono 1 ft5 ami 136.334 133. Q50

4700 .000 31.747 166.136 136.961 137. 124

4800 . 000 31.749 166,805 1 37.575 140

poa

4900 .000 31.751 167.459 1 "=^0 1 7Q 143, 474

5000 .000 31.752 160. ini 138.771 146. 64Q

OiUU.UUU 31 • i't4 168.730 1 3° .352 1 4^ . 825

5200.000 31.755 169.346 ] 30,92"^ 153.000

5300 . 000 31.757 169.9^1 1 40 .484 156. 176

5400 . ono 31.758 170.545 141.035 15Q.351

5500 . 000 31.760 171 .127 141 .577 16^.527

5600.000 31.761 171.700 142. 1 in 165.703

5700 .000 31 .762 172.252 142.634 168.880

5S00 . 000 ^1.763 172.81

143.149 17-^,056

5900 . 000 31.764 17-'.3'^7 143.657 175.232

6000 . 000 31.765 1^3. 8Q1 1 44. 156 178.409

1 cal = 4.1840 J

53
^^^1^ 2. Ideal-Gas Thennodynamlc Functions for Molvbden..,n PP.ntafluorlde MnnnmPr rM.ff (in JOULE energy units)

100

200

29fl 300

i+OO 500.

600.

700,

SOO,

900.

1000,

1100.

1200.

3 300.

1400.

1500,

1600,

1700.

1800 .

K.000

.000

.000

.150

.000

.000

.000

.000

.000

.000

.000

.000

.000

.000

,000

,000

.000

,000

,000

,000

J^ol2''"K~-'^ .000

61 .631

B5.015

101 .'34

101 .478

lll.'^61

1 1 8. 1<50 122. 171

124.7fl7

126.581

127. a57

128. "^^it 129.501

130.046

130.475

130.818

131.097

131.327

131.518

131.679

_ J mor-'-K"-'- .000

260.369

310.802

347.982

34P.609

37'5.3U8

405,0^5

426.973

446.015

462.802

477.789

4C»T .311

503. 6?1

514.914

525.340

535.023

544.058

552.526

560.494

568.016

J mol'-'-K""'-

426. 38Q

356.765

^47. 98?

71+7, q8U

355. 104

360 . 195

369.54^

379.137

388.567

397.

406.

414,

U22.

430.

437.

444.

450.

456.

462.

66^

36"^ 653

544

056

212

037

556

791

763

«*'-»298

kJ mol

-21 .037

-16.602

-Q.193

.000

. 188

lf^.897

22.425

34.458

46.815

59.388

75. 1 li+ 84.948

97.865

110.843

123.870

136.935

150.032

163. 153

176.296

1 8Q.456

1900.000

2000.000

2100.000

2200.000

2300.000

2400. 000

2500 . 000

2600.000

2700.000

2800.000

2900.000

3000.000

3100.000

3200.000

3300.000

3400 .000

3500 .000

3600.000

3700.000

3800.000

3900 .000

4000,000

t+100.000

4200.000

4300.000

4400.000

4500.000

U600 . 000

4700 . 000

4800 .000

4900.000

5000.000

5100.000

5200 . 000

5300.000

5400.000

5500.000

S600 . 000

5700.000

5800 .000

5900 .000

6000.000

131.815

131.932

132.0 33

132.121

132. 197

132.264

132.324

132.377

132.424

132.466

132.504

132.538

132.569

132.597

132.623

1^2.646

132.668

132.687

132.706

132.722

132.738

132.752

132.765

132.778

132.789

132.800

132.810

132.819

132.828

132.836

132.844

132.852

132.858

132.865

132.871

132. 877

132.882

132.887

1 32

132. 8Q7

132.901

132.906

575. 139

581.903

58". 343

594.4^^7

600.362

605. 9°0

611. 3°0

616. 5«1

621 .578

626. 3Q5

631 .044

63=^.5-^6 63^.883

644.092

648. 173

652.132

6=;5.978

65=". 715

663.351

666.890

670.338

673.699

676.9-'7

680.177

683.301

686.354

689.338

692.257

695. 1 14

697.91

700.6^0

703.334

705.964

708,544

71 1 .075

713.5^9

715. 9Q7

718. 3Q2

790. 7u4

723.055

72=^.357

72"^. 5^,1

468.492

473.994

479.287

484.385

48°. 301

494.047

498.633

50^.070

S07.368

511 .533

'=;15.574

52^.312

^^27.021

530.631

534.147

537.573

540.914

544. 174

^47.357

'^SO .i^67 553.506

556.477

55Q.384

562.230

56"=^. 017

S67.746

«=;7n.4?l

c;73. 044

575.616

•^78.140

S80 .617

583.049

585.438

'^87.785

590.091

592.358

594.587

596.780

598.937

601 .060

603. 150

202.631

21S.818

229.016

245.224

255.440

268.663

281 .8Ct3 29S.128

308.368

321 .612

334.861

340.113

361 .369

374.627

387.888

401 .151

414.417

427.685

440.955

454.226

467.499

480.773

494.040

507.327

520.605

533.884

547. 16"=^ 560.446

573. 72P

587.012

600.296

613.581

626.866

640.152

65'«.430

666.727

680.015

69-^.303

706.592

71-5.882

733.171

746.462

54
chapter 4

ALTERNATIVE PROCEDURES IN INTERPRETING EQUILIBRIUM DATA ON

PARTIALLY ASSOCIATED VAPORS

by Thomas B. Douglas and Ralph F. Krause, Jr.

Abstract

Alternative classical -thermodynamic and quasi-chemical treatments applicable to equilibrium data of various types on vapors

composed of many species representing various degrees of association

are discussed at some length. An example unexpectedly giving

ambiguous mathematical solutions is presented. A computation illustrates

the sensitivity of derived thermodynamic properties to errors in

the individual data.

As mentioned in the Introduction to a chapter of another report

[5], our earlier data for the vapor pressure of liquid MoF^, when

combined with our transpiration data on the same substance, had led

us to believe that the saturated vapor must contain (in the temperature

range of our measurements) numerous species in appreciable amounts

and representing different degrees of molecular association. . As

a result we examined and developed several alternative procedures

for deriving meaningful thermodynamic properties from a limited set

of data on such a vapor. While our most recent vapor-pressure data

for MoF^ suggest a much smaller degree of association [5] and hence

less urgency to use elaborate procedures of interpretation, we set

55
forth in this chapter the more significant aspects of this mathematical exploration in the belief that they may contribute helpfully

to dealing with other vapors that are actually associated in such

a complex way.

I . A Classical-Thermodynamic Interpretation

This type of approach applies rigorously to the case of two

or more molecular species in the vapor in major proportions (formally

evidenced by the fact that simple relations such as the ideal-gas

law do not or may not hold to a sufficient approximation), but

ignores the existence of all such species and treats the vapor as

a single substance. In the resulting equations, all extensive

quantities (V, volume; enthalpy; etc.) refer to a defined amount

of the substance or phase in question (unit mass could be selected,

but we shall choose instead a "mole" defined as a gram-formulaweight in terms of the monomer formula). These facts may seem too

elementary to mention, but are sometimes almost forgotten, so strong

is the present-day vogue of describing the properties of a vapor

in terms of those of its actual or supposed ideal components.

We limit ourselves here to a consideration of the three types

of measurements which we have undertaken on MoF^: (a) The true

vapor pressure ("A") at absolute temperature T; (b) the apparent

vapor pressure ("B") at T, from transpiration and assumption of the

ideal-gas law using the defined mole; and (c) the pressure of the

56
unsaturated vapor at T produced by heating vapor, at constant

volume, from a lower temperature t' where it was saturated. (The

unsaturated vapor is of course bivariant: T specifies its temperature, and T is equivalent to specifying its volume or density,

so that in principle the complete set [T, T] covers all possible

states of unsaturated vapor.)

Using V for the molar vapor volume and subscript "sat" for

saturated conditions of liquid-vapor equilibrium, we can then write

B = RT/V^^^. (2)

Since the gas is not ideal (experimentally, B > A), one cannot use

for conditions of vaporization equilibrium the Clausius-Clapeyron

equation, but may use its parent, the (exact) Clapeyron equation,

which is, omitting the usually negligible liquid volume,

(^?/^T) ^ = Zffl^'^P/TV. (3)

S 3- L

Substituting from Eqs. (1) and (2),

AH^'^P = (RT^/B) (dA/dT). (4)

Equation (4) gives the heat of vaporization to form a defined

mole of satu rated vapor. For the vapor in question, unlike an ideal

gas, the enthalpy and hence the heat of vaporization depend on the

pressure (or volume) of the vapor as well as on temperature, and this

57
variation can be expressed by the exact thermodynamic relation

(SH/^P)^ = V-T(?)V/?^T)p. (5)

From the mathematical identity for continuous functions

(^V/?^T)p = -(^P/^T)^/(?^P/^V)^ (6)

Eq . (5) becomes

(?^H/^P)^ = V + T (^P/^T)^/OP/BV)^. (7)

Application of Eq . (7) over a finite pressure (or volume) range at^

say^ temperature T requires enough data to allow integration of

the right-hand side from the saturated state to lower pressures.

These data would in principle be provided by experiments of Type

(c) mentioned above, with data for various temperature t' (up to

T), and also some variation in Temperature T to evaluate (r^P/I^T)^ .

Other thermodynamic properties could be similarly derived, but

will not be given.

In the subsequent sections of this chapter, procedures are

outlined for interpreting the data on the assumption that the vapor

behaves as a mixture of ideal-gas species whose properties admit of

some degree of quantitative discrimination. In contrast, the classicalthermodynamic approach may have the advantage of being less

presumptuous; on the other hand, it affords less scientific insight

into the molecular structure of the vapor (often useful in comparing

and correlating different chemical compounds of a series), and it

runs the risk that if the results are extrapolated to widely different

58
conditions, they may fail to reflect changing trends that occur

in the real system owing to the accentuation or suppression of

specific molecular species.

II . Quasi -Chemical Interpretations

The commonly used term "quasi -chemical" to describe a vapor

or' other fluid as a mixture of two or more molecular species in

chemical equilibrium seems like a wisely chosen one, particularly

when (as we do here) the species are assumed to behave ideally.

That the model is at least somewhat arbitrary is well illustrated

by the vigorous effort many decades ago to define the molecular

species of liquids in such a way that in terms of these species

their properties were those of "ideal" mixtures; but invariably

this led to inconsistencies traceable to treating two physically

adjacent "molecules" as a single molecule under some conditions

but as two separate molecules under other conditions. Nevertheless,

the model appears to be an excellent one for low-density vapors

(such as that of MoF^ in the temperature range of the present

investigation), and mass and absorption spectroscopy have

voluminously supported this idea in recent years.

II 1 . Preliminary; A Combination of Data Yielding

Ambiguous Thermodynamic Solutions

As is usually the case, the infrared and Raman spectroscopy

on MoF^ vapor [1] yielded some bands attributed to the monomer and

others attributed to associated molecules, but the vibrational modes

are much too complicated to allow identification of the different

59
species (except the monomer) or their properties with any

reliability. The mass -spec trometric behavior is, of course, far

simpler to interpret, and there have been two such investigations

of MoF^ vapor of which we are aware [2, 3], Collectively speaking,

these two mass-spectrometric researches detected in low-pressure

MoF^ vapors the four species (MoF^)^ with n = 1-4, and led at

stated temperatures to heats of the two reactions

(MoT^)^ = 2MoF^; (MoF^)^ = 3MoF^ (8)

and to species proportions which seemingly can be used with the

greatest cancellation of experimental error to express the (pressureindependent) equilibrium constants of two independent "isomolecular"

reactions which may be taken to be:

2(MoF^)2 = M0F5 + (MoF^)^; 2(KoF^)^ = (KoF^)^ + (MoF^)^. (9)

Our first serious attempt to develop a general interpretation

of the emerging assembly of data for MoF^ vapor was to assume only

these four species and to write a general computer program (actually,

two alternate programs were written independently) that would take

as input data from zero to three data (with accompanying temperatures,

which could all differ) of each of five types: (a), (b), and (c) of

Section I; heats of one or both reactions of Eq . (8); and equilibrium

constants for one or both reactions of Eq . (9). After assuming what

are sufficiently accurate "ACp" coefficients, each program was capable

of computing the remaining two constants in each ^nP-vs.-T equation

60
for the four vaporization reactions n MoF^(jJ) = (MoF^)^(g) . Thus

each program generated eight constants, and in a single run was

designed to use just eight data of the types enumerated (without

weighting or "least-squaring"). Our long-range purpose was to

evaluate a set of thermodynamic parameters which would reflect our

data and the mass -spec troscopic data with judicious weighting. Our

immediate goal was to be able to plan our future measurements with

least propagation of experimental error into the thermodynamic

parameters calculated from the data.

Each program was tested and found completely accurate. With

combinations of data for MoF^ (some very roughly estimated) as input, the

eight constants generated were shown beyond doubt to always reproduce

the input data exactly. Since the equations are non-linear, such

a program expands them linearly around an initial (approximate)

solution, and one might suppose that of the many real mathematical

solutions for any given data set, one can assume that only one solution

is physically possible (i.e., all partial pressures positive in this

case). This proved not to be true.' As verified by both programs,

a single data set was found to give two very substantially different

solutions depending on which of two initial solutions was used, but

not depending on which computer program was employed. We were thus

alerted to the fact that the data input for this type of program is

too general to guarantee a unique solution for the thermodynamic

properties of the different species. Solutions of such computations

should of course be examined for uniqueness before being accepted.

61
Numerical details of these computations are not given here

because, aside from the ambiguity just discussed, the input data

were too uncertain and subject to magnified error propagation as

illustrated later (Section II 3).

II 2 . Using Only Two Independent Data for Each Temperature

The mass-spectrographic data for MoF^ vapor [2, 3] indicate

proportions of species which are distinctly smaller the higher the

degree of association. But, of course, the proportions of the higher

species increase in a predictable way as one isothermal ly increases

the total pressure toward saturation, which is the state for most of

our data. In fact, the calculations outlined in the preceding section

led us to suspect at first that for saturated MoF^ vapor in the temperature range of our measurements the abundance does not fall off

enough in going from monomer to tetramer to justify neglecting all

still higher species (pentamer, hexamer, etc.). Accordingly, we decided

that a more realistic approach was to assume an infinite number of vapor

species (MoF^)^ (n = 1 to oo), but to assume enough reasonable relations

among the different species to leave undetermined a number of parameters

equal to the number of independent data used (this number differing

in this and the next section). This procedure will oversimplify the

relations among the higher species ; but since in many cases they are

minor. individually but appreciable collectively, this essentially

lumps them together in a plausible way instead of ignoring them entirely.

The procedure is highly analogous to our treatment of vaporization data

for the AiF^-AXCX^ system [4], where we undertook to assign the equivalent

of two thermodynamic parameters to each of 28 gas species on the basis

of a far smaller number of data.

62
A further modification of the approaches of this and the next

section, compared with the preceding section, is to treat the

data for each temperature independently, as this proves to afford

simpler criteria for ascertaining that a given set of data will

yield a unique solution for the thermodynamic parameters of the

vapor species

In line with the discussion above, we assumed the vapor to

be composed of ideal-gas species which in the case of MoF^ vapor

are (MoF^)^ with n varying from 1 to ^ , and we shall assume as

data at a given temperature the total vapor pressure A, and the

apparent vapor pressure B calculated from transpiration assuming

the monomer (m = 1) molecular weight. Using for the partial

pressure of Species n and remembering that the transpiration data

measure the available number of monomer units, we have (the

summation "E" extending over all values of n from 1 to <»)

^-P^ = A; (10)

SnP = B. (11) n

Now we assume a ratio ^ defined by

q = P ^ i/P • (12) n + 1 n

and to be determined from the data, to depend on temperature but not

n, with

0 < q < 1. (13)

using Eq. (12) to eliminate all P^^'s except Eqs. (10) and (11)

63
give

(1 + q + + ...)

(1 + 2q + 3q^ + ...)

P^/(l-q) = A;

: P^/(l-q)^ = B.

(14)

(15)

From Eqs. (14) and (15)

q = 1-(A/B); (16)

P^ = A^/B (17)

and in general

P„ = [A^/(B-A)] [(B-A)/B]". (18)

The values and temperature coefficients of the P 's determine values

for the equilibria and heats of the various vaporization and all-gas

reactions, using the usual thermodynamic relations.

It is clear from Eq . (18) that specific values of A and B

give a unique value for each P^ (and for every other thermodynamic .

parameter derived therefrom) . Furthermore, the sensitivity of each

P^ to experimental errors in A and B is not ordinarily great, and

can readily be determined from Eq . (18).

This simple treatment, unlike either type of data (A or B)

alone, promises to give a measure of the degree of saturated -vapor

association and its change with temperature, and the results would

be accurate if the saturated vapor were composed of just two ideal

species, and satisfactory if the vapor were mainly one species which

is only slightly associated or dissociated. However, we may examine

some of the consequences of the above treatment, and see whether

n

64
the available data are consistent with them. We immediately find

that Eq . (18) predicts unity at every temperature for the equilibrium

constant of every "isomolecular" all-gas reaction such as those of

Eq . (9) (Section II 1), and as a further consequence, a heat (or

AH) for such a reaction that is essentially zero. The available

mass-spectrographic data for MoF^ vapor [2, 3], even if only roughly

accurate, are at variance with these conclusions. The next section

suggests a reason why MoF^ vapor may behave anomalously in that sense,

and develops a modified treatment designed to overcome this objection

for substances of that type.

II 3 . Using Three Independent Data for Each Temperature

We again assume the infinite number of ideal-gas species

illustrated by (MoF^)^ with n from 1 to . As experimental data

we assume (all at absolute temperature T unless otherwise specified)

not only A and B [defined by Eqs. (10) and (11)] but also data

corresponding to one unsaturated state at T corresponding to Type

(c) described early in Section I. Limiting "P^^" to the saturated

vapor and using "p^^" for the unsaturated vapor, we define for vapor

at T that at the same volume was saturated at t'

2:p^ = D; (19)

(T/T')(i:nP^)^. = C. (20)

Four independent equations will be developed to use the data A, B,

C, and D.

65
In addition to the parameter P^, it is convenient to define

three additional parameters (R2, R^j and r^) as follows:

with possible ranges

^2^^1 " ^2

^n + 2/Pn = ^^3

0 < R^ < 1

0 < < ^

0 < rj^ < 1

Then for the saturated-vapor species pressures (relative to P^^)

we have an odd and an even series

n odd n even

1 P2/Pi =

Pj/Pj = R3 P4/P1 = R3

P5/P1 = R2

2

.3<'-)'^ Rj

!

V

(21)

(22)

(23)

(24)

(25)

(26)

(27)

(As special cases, if R^ = 0 we have only odd species; and if R2

= we have only even species.) The species partial pressures in

die unsaturated vapor can be obtained readily from the isothermal

66
invariance of an equilibrium constant--e .g .

Substitution for p^^ from Eq . (23) and for from Eqs. (27) gives

N /r, 2.(n-l)/2

n odd: P„n

= (Pir,)(R^r ) , 1 I 3 I I ^29)

n even: P„ = (RoPi'^i XRo^, ) 2^ VI ^^S^^l

The "odd" species (MoF^)^ (where n is odd) each have an odd

number of electrons, so that one electron (at least ) must be unpaired;

but each "even" species has an even number of electrons and one may

postulate the simplest case of no unpaired electrons. With few

3 exceptions , odd molecules show a decided tendency to associate,

presumably through a tendency to decrease the number of free electrons.

We may examine four general association reactions in the MoF^ system,

and formulate their equilibrium constants from Eqs. (27), as follows.

Reaction n A(no. of unpaired electrons)^

(MoF,) ,

4- (MoF,), = (MoF,)

5 n-2 5' 2 ^ [ ^ ) ^3/Vl 5 n ) even 0 /

(MoF.) , + (MoFJt = (MoF.) \ ^ ^ n /p 5 n-1 5 1 5 n ^ even -2 \ ^2 1

2 In this section (as not in Section II 2) ^ R2 , so as a

consequence the equilibrium constant (and Z^H) is allowed to reflect a

net change in the number of unpaired electrons. (Because of the latter,

we would expect an extra loss of entropy in the fourth reaction above,

but in its equilibrium constant this may be more than counterbalanced

at ordinary temperatures by an extra loss of energy.)

3 In a mass-spectrometric study [3] CrF^ was measured, but none of its

associated species was detected.

67
when the individual P 's are substituted from Eqs. (27) into

n

Eqs. (10) and (11) and the infinite series are replaced by their

closed-bracket equivalents, we get

(1 + R2)/(l-R3) = A;

Pj^ (1 + 2 R2 + R3)/(l-R3)^ = B.

(30)

(31)

Owing to the same volume at t' and T and the assumption of idealgas species, it can be shown that at T

Snp = C. (32)

On substituting for the p^'s from Eqs. (29) into Eqs. (19) and (32),

one obtains

Using data A, B, C, and D for a given temperature, Eqs. (30),

(31), (33), and (34) may be solved simultaneously for the parameters

P-j^, R2, R3, and r^, whose values substituted into Eqs. (27) and (29)

give the partial pressure of each species in the saturated and

unsaturated vapor, according to the present treatment.

Since these four equations are nonlinear in some of the parameters

to be solved for, there are of course multiple solutions mathematically,

and the solution accepted must of course indicate positive finite

partial pressures for all species. For such an acceptable solution,

the data must obey the relative order

^l^l (1 + R2rp/(1-R3r^^) = D; (33)

P^r^ (1 + 2R2r^ + R^r^^) /(l-R^r^^)^ = C. (34)

B > A > D; B > C. (35)

68
An attempt to prove generally that a data set obeying Eq . (35)

gives only one "acceptable" solution was unsuccessful, owing to the

simultaneous occurrence of several sign ambiguities in the equations

examined. However, by a series of arguments that will not be repeated

here, uniqueness of acceptable solution was proved for any data set

in the neighborhood of the "representative" set presently used as

an example.

A computer program was written to solve Eqs. (30), (31), (33),

and (34) simultaneously (using linear expansion and iteration). As

a specific example, the program was solved using a definite set of

values for the "data" A, B, C, and D. The solution was then repeated

four times, each time arbitrarily increasing one of the assumed data

by 17o. The specific original data set was chosen partly to approximate

preliminary experimental results for MoF^. The results (some truncated)

are given in Table 1, labeled for a vapor system (lest someone

be tempted to assume that they are trustworthy for (MoF^)^) . A

comparison of the results of the five computer solutions should,

however, provide some measure of the sensitivity to experimental errors

of the vapor-species properties when calculated for typical cases

as proposed in the present section. Furthermore, since the computer

cost is negligible, such a program is useful in planning future measurements whose errors would produce the least serious effects.

An examination of the lower part of Table 1 shows that (at least

in this example) a 1% error in a single datum leads to several percent

69
Table 1. An Example Illustrating the Errors in Calculated

Partial Pressures and Proportions of Gas Species

Resulting from Experimental Errors in the Input Data

[Equations (30), (31), (33), and (34) were used. The calculated

values are for temperature T. P^ applies to the saturated vapor, and

p to the unsaturated vapor. N = P /SP .] ^n ^ n n n

Original "Data" and Calculated Values (approximate)

T = 392 K C = 5.10 torr r^ = 0.70 N„ = 0.556

t' = 372 K D = 2.62 torr pj = 1.094 torr N3 = 0.049

A = 5.63 torr R2 = 2.86 p-^ = 0.766 torr = 0.139

B = 13.55 torr Ro = 0.25 N, = 0.194 N, + + N„ + N, = 0.938

J 1 1 2 3 4-

Percentage Changes in Calculated Parameters when One "Datum" is Assumed 1% Higher

Calculated

Parameter

R'

P4

Pi

Nl

N2

N3

N4

The Input "Datum" Assumed 1% Higher

9.5

4.7

0.6

4.2

4.9

8.7

0.03

4.8

5.1

3.9

9.6

1.0

0.6

B

- 6.2

+ 4.1

+ 0.2 + 3.4

- 3.0

7.6

0.9

3.6

3.4

3.0

7.6

+ 0.9

- 0.6

+ 12.6

- 2.5

+ 0.2

- 7.8

+ 3.8

- 10.1

+ 1.2

- 7.6

- 7.8

+ 3,

- 10.

+ 1,

+ 0,

D

- 13.0

+ 3.1

+ 0.3

+ 9.5

- 4.7

+ 12.9

- 1.8

+ 9.8

+ 9.5

- 4.7

+ 12.9

- 1.8

- 0.4

70
error in many of the more important parameters calculated. There

will actually be errors, of course, in all the data. To the extent

that these errors are random, the overall uncertainties will be

somewhat magnified. However, the errors in A and C are seen to

usually produce effects of opposite sign to those from errors

in B and D, and since all four data are pressure determinations, the

effects of systematic errors in pressure determination will tend

to cancel more or less. Nevertheless, Table 1 suggests that a singledatum accuracy to l7o or better is probably necessary to obtain

significant results by the procedure of this section, and that with

a much higher inaccuracy (say, 5%) the use of this many independent

measurements on the vapor would hardly be worthwhile. This would

clearly be even more pointedly true were one to attempt measurements

also on a second unsaturated vapor state (at the same temperature),

in the hope of getting still more detailed information on the vapor.

Ill . References

[1] N. Acquista and S. Abramowitz, AFOSR Scientific Report AFOSRTR-72-2004 (NBS Report 10904), National Bureau of Standards,

Washington, D. C. 20234, July 1972, Chapter 3 (pp. 49-63).

[2] C. F. Weaver and J. D. Redman, Section 11.6.3 of ORNL Report

4449, Oak Ridge, Tenn., Feb. 1970, p. 116.

[3] W. E. Falconer, Bell Research Laboratories, Murray Hill, N. J.,

private communication (Sept. 1972).

71
R. F. Krause, Jr., and T. B. Douglas, J. Phys. Chem.

72, 3444-3451 (1968).

T. B. Douglas and R. F. Krause, Jr., "The Vapor-Pressure

at 393 K of Liquid Molybdenum Pentaf luoride, MoF^, According

to Preliminary Static-Method Measurements," Chapter 6 of

Report NBSIR 73-281, National Bureau of Standards, Washington,

D. C. 20234 (AFOSR-ISSA-73-0001), 1 July 1973.

72
Chapter 5

CHANGE IN NORMAL SPECTRAL EMITTANCE (AT 650 nm)

OF NIOBIUM DURING MELTING AND

ITS RELATION TO SURFACE ROUGHNESS*

Ared Cezairliyan

National Bureau of Standards

Washington, D. C. 20234

The objective of this note is to report investigations on the

behavior of the normal spectral emittance (at 650 nm) of niobium

during melting. An attempt is made to relate the difference between

the emittances of solid and liquid niobium at the melting point to

the roughness of the solid surface.

The technique used for the measurements reported in this work

is based on resistive self-heating of the specimen from room temperature to its melting point in less than one second, and measuring

the specimen radiance temperature at the rate of 1200 times per

second with a high-speed photoelectric pyrometer. The interference

filter used for radiance temperature measurements had an effective

wavelength of 650 nm and a bandwith of 10 nm. The circular area

viewed by the pyrometer was 0.2 mm in diameter. The construction

and operation of the measurement system are described in earlier

publication$[ 1, 2]. The details of the experiments for radiance

temperature measurements on the niobium specimens are given in

another publication [3]. The niobium specimens (99.9**^ percent pure)

were in the form of strips with the following nominal dimensions:

*Thls work was supported in part by the U. S. Air Force Office of

Scientific Research.

73 J
length 75 mm; width, 6.3 mm; and thickness, 0.25 mm. The results

of radiance temperature measurements near and at the melting point

for a typical case flirc shown in Figure 1. The plateau corresponds

to melting of the specimen. The drop at the beginning of the

plateau corresponds to the change in the normal spectral emittance

of the specimen surface as it melts. An initial high radiance

temperature (peak of spike) indicates that normal spectral emittance

of the solid surface is higher than that of the liquid surface. The

normal spectral emittances corresponding to the plateau and the

peak of the spike were determined using the experimental data on

the respective radiance temperatures and the melting point of niobium,

2750 K J

, Different surface roughnesses were achieved by using

different grades of sand paper. The RMS surface roughness was easured with the stylus of the measuring equipment traversing aoraal

to the general direction of the grooves,

A summary of the experimental results is given in Table 1.

Emittance differences (corresponding to the radiance temperature

difference between the peak of the spike and the plateau) as a

function of specimen surface roughness ar^ shown in Figure 2. It

may be seen that the difference between the emittances of solid and

liquid surfaces at the melting point increases with increasing

surface roughness. The linear function in Figure 2 (obtained by the

least squares method and forced passage through the origin) is a

reasonably good representation of the general trend of the data. The

average absolute difference between the data points and the function

is 0.9 (in percentage emittance difference), which is within the

experimental uncertainties. The slope of the linear function is

0.177 Mm"^.

74
1 1 1 «4 1 1

•Jm 1 I* in ! 1 - •

•1

T. \\

1.•• -

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Table 1

Summary of Experimental Results for

Radiance Temperature and Normal Spectral

Emittance (at 650 nm) of

Niobium at its Melting Point

Specimen Roughness Radiance Temperature, K Emittance

Mm Feaic Plateau Dirt. (K) Peak Plateau Diff. (/o) 1 .38 2444.0 2424.0 20.0 .3650 .3387 7.76

2 .10 2429.7 2424.9 4.8 .3461 .3399 1.82

3 .10 2430.1 2425.6 4.5 .3466 .3408 1.70

4 .53 2456.5 2424.5 32.0 .3822 .3394 12.61

5 .95 2460.3 2425.2 35.1 .3876 .3403 13.90

6 .53 2452.3 2424.8 27.5 .3764 .3398 10.77

7 .10 2429.9 2425.9 4.0 .3463 .3412 1.49

8 .10 2428.9 2424.2 4.7 .3450 .3390 1.77

9 .10 2429.6 2425.2 4.4 .3459 .3403 1.65

10 .10 2429.7 2425.8 3.9 .3461 .3410 1.50

77
The fact that emittance difference approaches zero as the

roughness parameter approaches zero indicates that the primary

reason for the change in emittance during melting is the change

in surface conditions and not the change in the intrinsic properties

of the specimen. At this time, this may be said to apply to

niobium based on the .results of a limited number of experiments.

Additional work on other elements is necessary in order to generalize

the above conclusion.

References

[11 Cezairliyan, A., Morse, M. S., Berman, H. A., and Beckett,

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

65 (1970).

[2] Cezairliyan, A., J. Res. Nat. Bur. Stand. (U. S.), 75C

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

[31 Cezairliyan, A., J. Res. Nat. Bur. Stand. (U. S.), 77A

(Phys. and Chem.), 333 (1973).

[41 Cezairliyan, A High Temperatures - High Pressures,

453 U972).

78
chapter 6

RADIANCE TEMPERATURE OF NIOBIUM AT ITS MELTING POINT*

Ared Cezairliyan

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

Abstract

A subsecond duration pulse heating method is used to investigate

variations in the radiance temperature (at 650 nm) of niobium near

and at its melting point. Measurements were made on several specimens

with different surface conditions. The results do not indicate any

dependence of radiance temperature (at the melting point) on initial

surface conditions. The average radiance temperature (at 650 nm) at

the melting point for twelve different niobium specimens is 2425 K

on the International Practical Temperature Scale of 1968, with an

average absolute deviation of 0.6 K and a maximum deviation of 1.2 K.

*This work was supported in part by the Directorate of Aeromechanics

and Energetics of the U. S. Air Force Office of Scientific Research.

79
1. Introduction

In an earlier publication [1]''", the application of a millisecond

resolution pulse heating technique to the measurement of the melting

point of niobium was described. In the same publication, preliminary

results for the normal spectral emittance (at 650 nm) of two niobium

specimens at the melting point were also presented. Normal spectral

emittance was obtained from the measurements of the melting point

and the radiance temperature at the melting point.

In general, specimen radiance temperature at a given true temperature is not a reproducible quantity. Radiance temperature depends

on specimen surface conditions, thus it varies from specimen to specimen

(of the same substance) and it may even be different for the same

specimen at different times and under different environments.

However, the preliminary results of radiance temperature measurements for the two different specimens reported in the earlier study

[1] were within 1.5 K of each other at the melting point of niobium

(2750 K) . This has suggested the possibility that radiance temperature

(at the melting point) may be independent of surface conditions of the

solid specimen, thus it may be a reproducible quantity for pure

specimens of similar thermal history.

Figuresin brackets indicate the literature references at the end

of this paper.

80
The objective of this paper is to further investigate the

melting behavior of niobium and to report the results of recent

accurate measurements, utilizing a pulse heating technique, of the

radiance temperature of niobium near and at its melting point.

2. General Considerations

Melting of a pure metal is manifested by a plateau in the

temperature versus time curve as shown in figure 1 (Case 1) . Since

in the figure heating curve is represented by the specimen radiance

temperature, validity of the shape of the curve is based on the

assumption that normal spectral emittance of the metal does not

change during the solid-to-liquid transition. For real surfaces this

assumption is not satisfied, and it is likely that one obtains a

heating curve similar to the one shown in figure 1 (Case 2). The

iiro^ at the beginning of the plateau corresponds to the change

in normal spectral emittance of the metal surface as it melts. An

initial high radiance temperature (peak of spike) indicates that

normal spectral emittance of the solid surface is higher than that of

the liquid surface. This is likely to be the case, in general, since

solid surfaces, regardless of the degree of polish, depart from the

conditions of ideal smoothness.

81

3. Method

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

from room temperature to its melting point in less than one second

and measuring, with millisecond resolution^ the pertinent experimental

quantities. Specimen's radiance temperature was measured with a

high-speed photoelectric pyrometer [2], which permits 1200 evaluations

of specimen temperature per second. The radiance measurements were

performed at 650 nm which corresponds to the effective wavelength of

the pyrometer's interference filter. The bandwith of the filter was

10 nm. The circular area viewed by the pyrometer was 0.2 mm in diameter.

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

data acquisition system [3], which is capable of recording data at

the rate of 2400 per second with a full-scale signal resolution of

approximately one part in 8000, Details regarding the construction

and operational characteristics of the entire measurement system OLt^

given in an earlier publication [4].

4. Measurements

The niobium specimens were in the form of strips with the following

nominal dimensions: length, 75 mm; width, 6.3 mm; and thickness, 0.25 mm.

All of the specimens were from the same lot and were 99.9^ percent pure.

Manufacturer's analysis indicated the presence of the following impurities

in ppm by weight: Ta, 210; Hf and W, <100 each; Fe, Mo and Zr,

<50 each; M, Ca, Cr, Co, Cu, Mg, Mn, Ni, Pb, Si, Sn, Ti, V, <20 each;

Cd, <5; 0,42; N, 25; C, 14; H, 5.

83
A total of twelve experiments were performed on twelve different

specimens. Eight of the experiments were conducted on specimens with

surfaces in- "as received" conditions (smooth and shiny) . The

remaining four experiments were performed on specimens with three

different surface roughnesses, which were achieved by using different

grades of sand paper. The surface roughness of a typical "as received"

specimen was 0.10 Mm, and for the others it ranged from 0.38 to 0.95 \dm,

yielding a factor of approximately ten for the overall variation in

surface roughness.

In nine of the experiments the specimens were in a vacuum

environment of approximately 10 ^ torr, and in three of the experiments

the specimens were in an argon environment at approximately atmospheric

pressure.

The specimens were initially annealed by the manufacturer. Ten

of the experiments were performed without any additional heat treatment.

In two of the cases, the specimens were further annealed in the laboratory

before the experiments by subjecting them to 30 heating pulses (up

to 2400 K).

Different heating rates, ranging from 1000 K s"''' to 20,000 K s""*",

were used in the experiments. This corresponds to specimen heating

periods (from room temperature to the melting point) in the range from

40 ms to 800 ms . The magnitude of current pulses near the melting

point was in the range from 200 to 600 A. The high-speed pyrometer

was calibrated during the period between experiments 7 and 8 against

a tungsten filament standard lamp, which in turn was calibrated against

the NBS Temperature Standard.

84
85
A summary of the experimental procedure is given in table 1.

All measurements reported in this paper are based on the International

Practical Temperature Scale of 1968 [5].

5. Experimental Results

The radiance temperature of niobium at its melting point for the

twelve experiments (corresponding to twelve specimens) and other

pertinent results are given in table 1, Oscilloscope trace photographs of specimen radiance as measured with the high-speed pyrometer

for two typical experiments representing two specimens having

different initial surface conditions ("smooth" and "rough") are shown

in figure 2. Comparison of the traces in figures 1 and 2 verifies the

assumptions made regarding the shape of the traces in figure 1.

Figure 3 shows the variation of radiance temperature as a function

of time near and at the melting point for five typical experiments.

These experiments were selected to represent different specimen

surface and operational conditions. All the curves, with the exception

of "A", show spikes of varying magnitude. The specimen heating rate

in experiments corresponding to curves "B", "C", "D", and "E" were

four times slower than that of "A". Thus, the lack of a spike in

curve "A" may be attributed to the inability of the system's detecting

it. It is interesting to observe that, regardless of the, initial

surface and operational conditions, radiance temperature at the

melting plateau is approximately the same for all the specimens.

86
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the plateau for the niobium specimens.

88
The results of radiance temperature at the peak of the spike

as well as at the plateau for the twelve specimens are shown in

figure 4, It may be seen that the two fast experiments do not show

any peak for reasons discussed above. For the same "smooth" surface

conditions, the results of six experiments give approximately the

same value (within 1 K) for the peak temperature, which is 4.4 K

higher than the plateau temperature. Further changes in the heating

rate (slowing down) did not affect the results. The experiments on

specimens with initially rough surfaces yielded high peak temperatures,

however, the plateau temperatures were in good agreement (within 1 K)

with those of other specimens. The greatest difference between

peak and plateau temperatures, corresponding to the specimen with

the roughest surface, is 35 K.

A single value for the radiance temperature at the plateau for

each specimen was obtained by averaging the temperatures at the

plateau. The number of temperatures used for averaging ranged from

12 to 106 depending on the speed of the experiment and the behavior

of the specimen during melting. The standard deviation of an

individual temperature from the average was in the range from 0.3 to

0.6 K, with the exception of the very fast experiment which yielded

1.4 K. The details of the results for each experiment are given in

table 1. To determine the trend of measured temperatures at the

plateau, temperatures for each experiment were fitted to a linear

function in time using the least squares method. The slopes of the

linear functions (table 1) do not show any significant bias with

respect to direction. The maximum temperature difference between the

beginning and the end of the plateau (^corresponding to the slope in

the plateauywas in the range from 0.1 to 0.7 K. The standard deviation

89
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obtained by this procedure was the same as that obtained by direct

averaging of the temperatures.

The results of the radiance temperature at the plateau are

shown in figure 5 for two specimens having "smooth" surfaces representing two different heating rates (table 1) . The plateaus

do not show any anomalies and are horizontal from the beginning

to the end. However, the results are somewhat different in the

case of specimens having initially rough surfaces (figures 6).

Temperature instabilities are observed during the initial melting

period, which subside during the second half yielding a horizontal

plateau. The temperatures in the anomalous region are approximately

1 to 3 K above those at the stable plateau.

The average radiance temperature at the melting point for

the twelve specimens was 2424.9 K, with an average absolute

difference of 0.6 K and a maximum difference of 1.2 K. The results

are presented in figure 7. It may be concluded that the radiance

temperature (at 650 nm) of niobium at its melting point is 2425 K.

6. Estimate of Errors

The details of sources and estimates of errors in high-speed

experiments similar to those conducted in this study are given in

an earlier publication [3], Specific items in the error analysis

were recomputed whenever the present conditions differed from those

91

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In the earlier study. The imprecision of temperature measurements,

during heating as well as melting periods, is approximately 0.5 K

3 (table 1). Inaccuracy of temperature measurements near and at the

melting point of niobium is estimated to be not more than 7 K. The major

single source contributing to this inaccuracy is the uncertainty in

the calibration of the tungsten filament standard lamp (approximately

3 K at 2400 K) . The melting point depression due to the impurities

in the specimens is estimated to be not more than 2 K. It may be

concluded that the inaccuracy of measured radiance temperature of

niobium at its melting point is not more than 10 K.

It may be seen from table 1 that the imprecision of temperature

measurements during heating of the specimen (before reaching the

melting point) was approximately the same as that during the melting

period. This indicates that in the experiment the initial melting

phase progressed normally and that there were no undesirable effects

during melting of the specimen, such as vibration of the specimen,

instantaneous development of hot spots in the specimen, and random

changes in the specimen surface conditions.

Imprecision refers to the standard deviation of an individual temperature

as computed from the difference between the measured value and that

from the smooth function obtained by the least squares method.

"^Inaccuracy refers to the estimated total error (random and systematic).

54
0 4 8 12

EXPERIMENTS, IN CHRONOLOGICAL ORDER

FIGURE 7. Difference of radiance temperature (at the melting

point of niobium, at 650 nm) for individual experiments

from their average value of 2424.9 K (represented

by the "zero" line).
7. Discussion

The results of this study show that radiance temperature at the

melting point of niobium is reproducible and is independent of: (a)

the initial surface conditions of the specimen, (b) the environment

in which the specimen is heated, and (c) the heating rate of the

specimen.

The twelve experiments performed under different conditions

yielded an average value of 2424.9 K for the radiance temperature,

with an average absolute difference of 0.6 K and a maximum difference

of 1.2 K. The preliminary results on two niobium specimens reported

in an earlier publication [1] had yielded an average value of

2423.3 K, which is only 1.6 K below the present value.

Considering 2750 K for the melting point of niobium [1] and

2425 K for the radiance temperature at the melting point, a value

of 0.340 is obtained for the normal spectral emittance (at 650 nm)

at the melting point of niobium. Earlier measurement, utilizing

the same pulse heating system, on tubular niobium specimens in the

range 1700 to 2300 K showed a linear variation of normal spectral

emittance with temperature [6], Extrapolation of these results to

the melting point yields 0.348 for normal spectral emittance, which

is approximately 2 percent higher than the present value. Measurement of normal spectral emittance of niobium near its melting point

is reported in the literature to be 0.362 [7]; this is approximately

6 percent higher than the present value. In the case of solid surfaces departure, in varying degrees, from ideal surface conditions

may have been partially responsible for the high values.

^ 96
This may be demonstrated by considering the present results on

"rough" specimens. From table 1 (last column) it may be seen that

for the "rough" specimens a considerable difference exists between

the peak and plateau temperatures. This difference in temperature

corresponds to a difference in normal spectral emittance ranging from

7 to 14 percent for the four "rough" specimens. In the case of the

"smooth" specimens^ corresponding average difference in emittance

is approximately 2 percent. The above substentiate, both in

magnitude and in direction, the difference between present results

and those reported in the literature.

4

Radiance temperature (at 645 nm) liquid niobium at its melting A

point was measured recently using a lavitation calorimeter [8]. The

reported result of 2405 K is 20 K lower than the present value. No

satisfactory explanation has been found for this discrepancy.

It may be noted that, with the present system it was not possible

to follow the entire melting process because the specimen collapsed

and opened the main electrical circuit prior to the completion of

melting.

In conclusion, the results of this study have shown the constancy

and reproducibility of the radiance temperature of niobium at

its melting point. Compared to the difficulties encountered in the

construction and operation of blackbody cavities at temperatures

above 2000 K, the scheme of measuring radiance temperature at the

melting point of selected substances may be an easier, more

accurate, and in addition more practical approach for performing

secondary calibration on instruments and for conducting overall

97
on-the-spot checks on complicated measurement systems at high temperatures. This suggests the extension of investigations, similar

to those reported in this paper, to other refractory metals at

temperatures above 2500 K.

•'i .

98
8. References

Cezairliyan, A,, Measurement of melting point, normal spectral

emittance (at melting point), and electrical resistivity

(above 2650 K) of niobium by a pulse heating method, High

Temperatures -High Pressures, in press,

Foley, G. M., High-speed optical pyrometer. Rev. Sci. Instr.,

41, 827 (1970).

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).

Cezairliyan, A., Design and operational characteristics of a

high-speed (millisecond) system for the measurement of thermophysical properties at high temperatures. J. Res. Nat.

Bur. Stand. (U.S.), 75C (Eng. and Instr.), 7 (1971).

International Practical Temperature Scale of 1968, Metrologia,

5,35 (1969).

Cezairliyan, A., High-speed (subsecond) measurement of heat

capacity, electrical resistivity, and thermal radiation

properties of niobium in the range 1500 to 2700 K, J. Res.

Nat. Bur. Stand. (U.S.), 75A (Phys. and Chem.) ^ 565 (1971).

Pemsler, J. P., Thermodynamics of interaction of niobium and

tantalum with oxygen and nitrogen at temperatures near the

melting point, J. Electrochem. Soc, 108^ 744 (1961).

99
[8] Bonnell, D. W., J. A. Treverton, A. J. Valerga^and J. L.

Margrave, The emissivities of liquid metals at their

fusion temperatures, Proceedings of the Fifth Symposium

on Temperature, in press.

100

USCOMM-NBS-DC