NBS SPEC. PUBL. 260 "19

Standard Reference Materials:

ANALYSIS OF INTERLABORATORY MEASUREMENTS ON THE

VAPOR PRESSURE OF GOLD

(CERTIFICATION OF STANDARD REFERENCE MATERIAL 745)

U.S. Department of Commerce

dopy a. National Bureau of Standards

ybraiy, w

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1970 A111D3 DfiSbfiS
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards ' was established by an act of Congress March 3, 1901. Today,

in addition to serving as the Nation's central measurement laboratory, the Bureau is a principal

focal point in the Federal Government for assuring maximum application of the physical and

engineering sciences to the advancement of technology in industry and commerce. To this end

the Bureau conducts research and provides central national services in four broad program

areas. These are: (1) basic measurements and standards, (2) materials measurements and

standards, (3) technological measurements and standards, and (4) transfer of technology. The Bureau comprises the Institute for Basic Standards, the Institute for Materials Research, the

Institute for Applied Technology, the Center for Radiation Research, the Center for Computer

Sciences and Technology, and the Office for Information Programs. THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United

States of a complete and consistent system of physical measurement; coordinates that system with measurement systems of other nations; and furnishes essential services leading to accurate and

uniform physical measurements throughout the Nation's scientific community, industry, and commerce. The Institute consists of an Office of Measurement Services and the following technical

divisions:Applied Mathematics—Electricity—Metrology—Mechanics—Heat—Atomic and Molecular Physics—Radio Physics -—Radio Engineering -—Time and Frequency 2—Astrophysics -—Cryogenics.- THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research leading to im- proved methods of measurement standards, and data on the properties of well-characterized

materials needed by industry, commerce, educational institutions, and Government; develops, produces, and distributes standard reference materials; relates the physical and chemical properties of materials to their behavior and their interaction with their environments; and provides

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' Located at Moulder. Colorado 80302. Located at S2X6 Port Royal Koad. Springfield. Virginia 22151.
UNITED STATES DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

Standard Reference Materials:

Analysis of Interlaboratory Measurements on the

Vapor Pressure of Gold

(Certification of Standard Reference Material 745)

Robert C. Paule and John Mandel

Institute for Materials Research

National Bureau of Standards Washington, D.C. 20234

J.

1), S < National Bureau of Standards. Special Publication 260-19

Nat. Bur. Stand. (U.S.), Spec. Publ. 260-19, 21 pages (January 1970) CODEN: XNBSA

Issued January 1970

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 (Order by SD Catalog No. C 13.10: 260-19), Price 30 cents
JIGNAL BUREAU SEP 1 2 1970 me** °

l f 7©

Library of Congress Catalog Card Number: 70-603290
Contents

Page

1. Introduction 1 2. Treatment of data 2

3. Statistical analyses 4

4. Comparison of second and third law results 6

5. Footnotes and references 7

6. Appendix 8

Tables

1. Summary of experimental methods 2

2. List of experimental temperature-pressure data (Appendix) 10

3. Summary of second law results 3

4. Summary of third law results 4

Figures

Figures 1 to 5 (Appendix) 14 Figure 6 _ 6 Figure 7 6

in

Analysis of Interlaboratory Measurements on the Vapor Pressure of Gold

(Certification of Standard Reference Material 745)

Robert C. Paule and John Mandel

A detailed statistical analysis has been made of results obtained from a series of interlaboratory measurements on the vapor pressure of gold. The gold Standard Reference Material 745 which was

used for the measurements has been certified over the pressure range 10" 8 to 10" 3 atm. The temperature range corresponding to these pressures is 1300-2100 K. The gold heat of sublimation at 298 K

and the associated standard error were found to be 87,720±210 cal/mol (367,040±900 J/mol). Esti- mates of uncertainty have been calculated for the certified temperature-pressure values as well as for the uncertainties expected from a typical single laboratory's measurements. The statistical analysis has also been made for both the second and third law methods, and for the within- and betweenlaboratory components of error. Several notable differences in second and third law errors are observed. Key words: Components of error (within- and between-laboratories); gold; heats of sublimation (second and third law); interlaboratory measurements; standard errors; standard

reference materials; vapor pressure.

1. Introduction

This report is part of a program to establish five standard reference materials. The materials, Cd,

Ag, Au, Pt, and W, are being certified by the National Bureau of Standards for their vapor pressures

as a function of temperature. Certification covers the

10~8 to 10"3 atm range. For the complete series of

materials, the temperatures corresponding to the above pressures will range from 600 to 3000 K. Gold,

the first material to be certified, covers a temperature range from 1300 to 2100 K. The gold standard

reference material is now available for sale to the

public [l]. 1 Experience in high-temperature vapor-pressure measurements has shown that large systematic

errors in pressure of 30, 50, or even 100 percent are

not uncommon, even among experienced investi- gators. The vapor pressure standard reference

materials will allow workers in the field to detect such systematic errors and to evaluate the precision and accuracy of their measurements. The materials should be most useful for checking low vapor pres- sure measurement methods such as the Knudsen,

torque Knudsen, Langmuir, and mass spectrometric methods.

This report will give estimates of the uncertainty

of the certified terftperature-pressure values as well

as estimates of the uncertainties of a "typical"

single laboratory's measurements. These uncertainties summarize results obtained from inter- laboratory tests made in 1968 (see list of cooperative laboratories). The uncertainties represent

current practice and should not be considered fixed with respect to time and progress. We believe the

uncertainties will be reduced in the future through

the use of the vapor pressure standard reference

materials.

1 Figures in brackets indicate footnotes and references beginning on p. 7.

The results from the 1968 interlaboratory tests were used to obtain a composite heat of sublimation

for gold at 298 K. The certified temperature-pressure

values were then obtained by back-calculating through the third law equation T

^ A ^

G°T-H°2^ _R l n pj = A//sub298 (J)

using the composite AHsub2 »8 of 87,720 cal/mol [2] (367.040 J/mol) [3] and the referenced free energy

functions [4]. P is expressed in atmospheres. All temperatures for this report have been converted

to the 1968 International Practical Temperature

Scale (IPTS-68). The certified temperature-pressure

values as well as the corresponding l/T and log P

values are listed below.

T(K) P(atm) [3] (i/r)xio4 (K- 1 ) LoginPfatmp]

1300 9.92X10-9 7.692 -8.003

1338 (M.P.) 2.56 x 10 8 7.474 -7.592

1400 1.01 x lO" 7 7.143 -6.993

1500 7.36 x 10 7 6.667 -6.133

1600 4.14 X 10-" 6.250 -5.383

1700 1.90 X 10 * 5.882 -4.721

1800 7.25 x 10~ 5 5.556 -4.139

1900 2.42 x 10-> 5.263 -3.616

2000 7.07 x 10 ^ 5.000 -3.151

2100 1.87 X 10" 3 4.762 -2.727 A broad cross-section of measurement techniques were used by the cooperating laboratories in the

interlaboratory tests; the techniques included the Knudsen (weight loss and condensation methods),

torque Knudsen, and calibrated mass spectrometric methods. Summary information regarding the ex- perimental details for each laboratory are given

in table 1.

1
TABLE 1. Summary of Experimental Methods

Laboratory Method Temperature measurement technique Container material Effective orifice areaX 103

. cm2 Remarks

1 Knudsen using condensation plates Optical pyrometer with black-body hole W crucible with

graphite or AI2O3

insert cups

2.84. 11.59 In preliminary experi- ments Au wet and

crept excessively on Uro \Y/' Dare w ceu

2 Knudsen using condensation plates and x-ray fluorescence detection

Optical pyrometer with Mo cell 0.70, 2.15, 5.85 Au wet Mo and some

3 Knudsen

graphite

0.36, 2.60. 3.91

4 Knudsen Optical pyrometer with Pyrolytic graphite 3.21, 4.93

5 Knudsen plus Knudsen

eter

Optical pyrometer Carbon 1.53 First Knudsen results spectrometer

6 Knudsen Pt-13%Rh, Pt thermocouple ZTA graphite 62.4

7 Torque Knudsen Pt-13%Rh, Pt thermocouple ZTA graphite 8.5. 31.9, 55.7 Each curve's temperature measurements made

8 Torque Knudsen Pt-10%Rh, Pt and Pt- 30%Rh, Pt-6%Rh

thermocouples

Pyrolytic graphite 1.36, 9.40 Each curve's temperature measurements made

in one direction only

9 Knudsen cell in mass

spectrometer with

absolute weight cali- bration

Optical pyrometer look- ing at side of crucible

Ir crucible with A12 03 insert cup

4.7 Au2 also measured

10 Triple Knudsen cell in TOF mass spectrom- Hultgren Ag vapor

pressure values and Mann's cross sections

for calibration

Optical pyrometer with black-body hole W crucible 0.49

11 Double oven Knudsen

cell used for absolute Au calibration of TOF

mass spectrometer

Optical pyrometer sight- ing into orifice Graphite

2. Treatment of Data

The detailed temperature-pressure data from the

11 laboratories which measured the vapor pressure

of gold are given in table 2 (see sec. 6.3). Plots of the data are given in figures 1 through 5 of section 6.3. The solid fine in these figures represents the pooled

curve for all accepted data from all laboratories. A total of 41 sets of data (runs) with over 350 temperature-pressure points were available for consideration. Each temperature-pressure run has been used

to obtain both the second and third law heats of sublimation at 298 K. Equation (1) was used to calculate the individual third law AHsub2 9ts values corresponding to each temperature-pressure point and the average A//sub298 value was calculated for

each run. The evaporation coefficient for gold has been assumed to be unity. In agreement with this assumption, we observed no evidence of trend in third law heats with changing orifice area. The second law heat for each vapor pressure- temperature run was obtained by least-squares

fitting the A andfi constants in the equation: A (_

et-H°»» y

RlnP=A+ B

(2) where P is expressed in atmospheres. This calculational procedure is similar to the sigma method, and does not require the specification of a mean

effective temperature [5]. The slope B is the second

law heat of sublimation at 298 K. The intercept A

2
will be zero for the ideal case where the measured

pressures and the free energy functions are completely accurate. We have kept the intercept A in the least-squares equation to allow for possible

error. This second law procedure is very convenient

to use when the calculations, including the inter- polation of free energy functions, are made by computer. The OMNITAB computer language [6] was

used in this work. A summary of the second and

third law results is given in tables 3 and 4.

Table 3. Summary of Second Law Results

Lab No. Run No. No. of points Intercept A(see eq. 2) cal • mol -1

* deg -1

Slope B, 2d Law AHsub298 (see eq. 2) cal * mol -1 (see eq. 7) £ (see eq. 8) (see eq. 5)

1 1 11 -.744 89664 4.73 8510 .1904

2 12 -.957 90003 3.77 6570 2209

2 1 10 .698 87176 7.95 14190 .1364

2 9 .1039 4 6 - 2.809 92638 15^57 25820 .1224

3 1 11 1.080 85924 9.05 15580 .0771 2 10 1.906 84868 9.07 15390 .0690

3 8 - 1.640 90142 17.27 28060 .0993 4 1 10 -.531 89133 5.65 10480 .2288 7.20 .1650

3 9 -1.238 89815 6.11 11310 .1835

5 1 5 -.779 88508 7.31 11880 .0193

2 31 -.329 87758 2.59 4300 .1194

7 1 10 — .352 88464 11.41 17870 .0559

2 6 L833 85015 13^42 21220 !0196

3 6 1.392 85687 14.44 22740 .0409 4 12 -1.081 89500 11.61 18340 .0499

5 6 -.829 88911 11.57 17730 .0463 6 15 .868 86480 11.52 18100 .0304

7 7 -1.648 90212 13!41 22130 !0662 8 1 11 -.130 86862 4.95 7900 .0426

2 11 .128 86300 5.99 10090 .0547

3 9 — .302 87041 7 35 11450 .0392 4 10 -!l48 86927 5^28 8380 !0562

5 11 -.236 86931 6.07 10260 .0199

9 1 13 -1.409 87338 3.91 6170 .0706

2 14 -1.493 87702 3.69 5880 .1681 3 14 -3.368 91092 3.58 5710 .1275 4 14 -3.098 90977 3.62 5740 .1971 10 1 6 2.472 81981 13.61 22010 .1190

2 7 -5.184 98741 11.64 19990 .3271 3 10 4.746 77563 6.92 11080 .2544 4 17 .020 84593 5.66 9020 .2350

11 1 6 -6.594 98536 12.96 20850 .0538

2 5 -7.390 99568 19.61 30560 .3024

3 6 10.508 70700 12.48 20410 .2270 4 5 6.400 77335 30.62 49260 .1955

5 5 -.947 89209 12.80 20470 .3695

3
Table 4. Summary of Third Law Results

Lab No. Run No. No. of points 3d Law AHsub298 f3 cal • mol -1 (see eq. 10) (see eq. 9)

1 1 11 88316 .302 325.2

2 12 88320 .289 393.9

2 1 10 88425 .316 230.2

2 9 87626 .333 269.4

3 2 87747 J07 47!6

4 6 87975 .408 225.7

5 2 88120 .707 133.6

3 1 11 87786 .302 141.3

2 10 88108 .316 160.8

3 8 87477 .354 158.2

4 1 10 88142 .316 412.1

2 7 88566 .378 318.0

3 9 87514 .333 345^4

5 2 31 87208 .180 201.5

6 i 4 88068 .500 402.9

7 1 10 87912 .316 82.8

2 6 87917 .408 99.7

3 6 87882 .408 87.6

4 12 87791 .289 85.5

5 6 87638 .408 79! 1 6 15 87845 .258 55.8

7 7 87489 .378 128.6 8 1 11 86653 .302 61.0

2 11 86517 .302 89.3

3 9 86570 ^333 58!4 4 10 86691 .316 85.0

5 11 86531 .302 39.4

9 1 13 85097 .277 195.6

2 14 85304 ^267 322^4

3 14 85679 .267 461.2 4 14 86016 .267 492.8

10 1 6 85984 .408 215.1

2 7 39821 .378 613.3

3 10 85191 .316 552.5 4 17 84624 .243 363.1

11 1 6 87911 .408 373.2

2 5 88041 .447 501.1

3 6 87911 .408 695.5

4 5 87635 .447 323.9

5 5 87693 .447 507.9 3. Statistical Analyses

Two OMNITAB programs were written to perform

the statistical analyses, the ultimate purpose of which was to obtain overall weighted average values

of the second and third law heats of sublimation and estimates of the uncertainties. The first OMNITAB program performed least-squares fits for each run to obtain the second law heats and the average third law heats. The program also made a preliminary test to detect laboratories that exhibited excessive scatter of points about the fitted curves

(see sec. 6.1). The authors then examined the

results and made tentative decisions regarding the data to be excluded from the weighted averages

and the estimated uncertainties [7]. The second OMNITAB program was then run to determine (1) the weighted average values of the second and

third law heats of sublimation, (2) the uncertainties associated with the heats, and (3) the uncertainties expected for a typical in-control laboratory's meas- urements (see sec. 6.2). In the second OMNITAB

program the rejected data were not used for the

calculation of the weighted averages and standard

deviations, but were used in all other statistical

tests. This procedure avoids distorting the overall

results, but still allows for further evaluation of all of the data. The statistical analyses indicate the weighted

4
averages [8] and the associated standard deviations (standard errors) are as follows:

,4 =-0.26 ±0.25 cal - mol" 1

• deg" 1 5 = 2nd law A// sub2 »« = 88,140 ±500 cal - mol" 1 3rd law A//sub2 »8 = 87,720 ±210 cal - mol" 1

. The A coefficient is essentially zero which indicates the observed pressures and the free energy functions are in reasonable agreement. In the analyses

it is tacitly assumed that the errors in the free energy

functions are negligible. The second and third law

A// SU b2W8 are observed to be in good agreement. We

believe the third law A//sub298 value of 87,720±210

cal • mol" 1 (367.040 ± 900 J

• mol" 1

) [3] is to be pre- ferred since its standard error is smaller and since

the free energy functions for gold are believed

reliable. A laboratory measuring a single temperaturepressure curve may wish to compare its values with the weighted averages from this study. The

total expected variance required for this comparison

will be the sum of:

(1) the between-curve variance,

(2) the between-laboratory variance, and

(3) the variance of the weighted average. Assembling the numerical values corresponding

to these components of variance in the above order we obtain for the single curve case: V{A) =0.020/;2 +0.0 +0.063

F(2nd law) = 0.020/1 +0.59X 106 +0.24X 106

F(3rd law) = 0.070 X 106 + 0.340 x 106 + 0.046 X 106 where the f\ and /•> values may be calculated as indicated in section 6.1. The constants in these equations are based on pooled estimates of the variance components. By use of the variables, f\ and fz, allowance is made for the actual number of data points used and for the spread of 1/T values. The units of variance of the values are the squares

of the units of the values being evaluated (A, B, or 3rd law heat). The numerical values in the variance equations have been derived using energy units of

calories. The above formula giving the variance of the third law heat is based on the assumption that a laboratory makes at least five temperaturepressure measurements. For such a case, our analysis indicates the between-curve component of vari- ance is approximately a constant, 0.070. To illustrate the above equations for a "typical

single curve case," assume that a laboratory measures a single temperature-pressure curve taking 11 points, one every 25 K, over the temperature range

1600 to 1850 K. For this case the ft and ft values

are calculated to be 43.2 and 1.28 X 108

, respectively, and V(A) =0.864 +0 +0.063 = 0.927 V(2n& law) =2.56 X 106 +0.59X 106 +0.24X 10 6 = 3.39xl06 (3) F(3rd law) = 0.070 X 106 + 0.340 X 106 + 0.046 X 106 = 0.456 X 106 (4) The following limits, which are equal to twice the square root of the above variances, can be used for the estimation of maximum allowable differences between the single curve results obtained by the

typical laboratory and the weighted averages. Approximately 95 percent of the time, a result obtained by the above described typical laboratory should

fall within the following limits:

,4 = 0.26 ±1.93 cal - mol" 1 deg" 1 2nd law = 87,720 ±3700 cal - mol" 1 3rd law = 87,720 ±1350 cal - mol" 1

. Since the third law value is believed to be more

accurate, we have replaced the second law weighted

average by the third law weighted average, 87,720

cal • mol-1

. A laboratory wishing to evaluate its own results should calculate its own specific/i and/2 values for use in the above equations. An examination of the values of the individual components of variance for the typical single curve

case yields considerable information. For the second law case (eq 3) one can note that the betweencurve variance is relatively large compared to the

total variance (2.56/3.39). If a laboratory measures

(n — 1) additional temperature-pressure curves

the between-curve variance will be reduced to (2.56 X 106

)/rc. For the third law case (eq 4) it can

be observed that additional curves will not be partic- ularly helpful since a large fraction of the total variance for the third law case is due to the betweenlaboratory component of variance (0.340/0.456). By back calculating through the third law equation it is possible to determine approximate 95

percent limits for which the pressure-temperature

relationship is known. This has been done using both the uncertainty of the weighted average third law value and the uncertainty of the typical single curve third law value. The results are shown in figure 6. From the weighted average third law limits

it is seen that for a fixed temperature, the uncertainty in the associated pressure is approximately ± 13 percent, while for a fixed pressure, the uncertainty in the associated temperature is approxi- mately ± 9 K. The corresponding limits for the

typical single curve case are ±45 percent and ±30 K. The large uncertainty for the typical single curve case is primarily due to the large betweenlaboratory uncertainty.

363-394 O - 70 - 2
18 50 1800 1700 I600K

'0

6

l 1 L-, r—A- 1 r-J 1 5.4 5.6 5.8 6.0 6.2 6.4

(l/T) X I0+4

, K"

1 Figure 6. A single laboratory's evaluation of error may be

greatly underestimated if systematic betweenlaboratory errors are not considered. The diligent use of vapor pressure standard reference materials should help in the detection of elimination of such

systematic errors. 4. Comparison of Second and Third

Law Results

From the statistical analyses we have observed two fundamentally different situations for the ac- cepted second and third law results. Regarding the second law results, the between-curve but within laboratory variation was found to be no larger than

that expected from the average scatter of temperature-pressure points about the curves. Furthermore,

the second law case showed no (statistically) sig- nificant difference between the results from the

different laboratories. For the third law case, however, a significant difference was found for both the between-curve and the between-laboratory results.

It should be noted that the significant differences

for the third law tests are due to the smaller third law uncertainties rather than to a wider spread of the values. The third law uncertainties are signifi- cantly smaller than the second law uncertainties. Figure 7 summarizes the accepted second and third law results. List of Cooperating Laboratories

Aerospace Corporation, P. C. Marx, E. T. Chang,

and N. A. Gokcen

SECOND AND THIRD LAW &H z9e USED IN POOLED VALUES

i 90

" 89 x

< 88

2ND LOW lH 2 g 8 + 3RD LAW aH 2 g 8

D

13 a

+

+ D

|

+ a

+

1 Q a

a 0123456789 LABORATORY NUMBER

Figure 7. Air Force Materials Laboratory (MAMS), H. L. Gegel

Air Force Materials Laboratory (MAYT), G. L. Haury

Douglas Advanced Research Laboratories, D. L. Hildenbrand

Gulf General Atomic, Inc., H. G. Staley, P. Winchell, J. H. Norman, and D. A. Bafus Michigan State University, J. M. Haschke and H. A. Eick

National Bureau of Standards, E. R. Plante and

A. B. Sessoms

Philco-Ford Corporation, N. D. Potter Space Sciences, Inc., M. Farber, M. A. Frisch, and

H. C. Ko

Universita Degli Studi di Roma, V. Piacenta and

G. DeMaria

University of Pennsylvania, W. W. Worrell and A. Kulkarni

The authors are greatly indebted to the above

listed cooperating laboratories for their vapor pres- sure measurements. D. L. Hildenbrand of Douglas Advanced Research Laboratories, should be given

particular credit for the original impetus in the establishment of the vapor pressure standard refer- ence materials program. The authors also wish to acknowledge aid received from the following NBS

staff members. E. R. Plante has contributed freely

to discussions dealing with thermodynamic aspects

of the analysis, and J. J. Diamond has made an

extensive vapor pressure literature survey from his information "Data Center on the Vaporization of Inorganic Materials." W. S. Horton contributed to discussions dealing with statistical procedures and

F. L. McCrackin aided in the use of his computerized GRAPH routine. 6
5. Footnotes and References

fl] Standard reference material 745 may be ordered from the Office of Standard Reference Materials, National Bureau of Standards, Washington, D.C. 20234. This material is in the form of wire 1.4 mm (0.055 in) in diameter and 152 mm (6 in) long. The gold is homogeneous and 99.999 percent pure. The price for this material is $85 per unit; this includes a "Certificate of Analysis" containing

specific recommendations for usage as well as several statistical tests by which a laboratory may evaluate its results.

[2] This A//sub 2s« value is in good agreement with the values 87,500 and 87.300 cal/mol quoted by: Wagman, D. D., Evans, W. H., Parker, V. B., Halow, I., Bailey, S. M., and Schumn, R. H., Selected Values of Chemical Thermodynamic Properties, NBS Technical Note 270-4 (1969), and Hultgren, R., Orr, R. L., Anderson, P. D., and Kelley, K. K., Selected Values of Thermodynamic Properties of Metals and Alloys, pp 38-42, (June 1960), John Wiley & Sons, Inc., New York (1963).

[3] 1 calorie = 4. 1840 joules

1 atmosphere = 101,325 newtons • meters -2

.

Condensed phase a Gas phase b Temperature -H° Gt H°

T T

K, (IPTS-68) cal- mol -1 -deg -1 (J-mol-'-deg-'p] cal • mol-1

• deg~' (J-mol-'-deg-'p]

298.15 11.319 (47.359) 43.120 (180.414) 1200 15.352 (64.233) 46.304 (193.736) 1300 15.751 (65.902) 46.607 (195.004) 1338 (M.P.) 15.896 (66.509) 46.718 (195.468) 1400 16.236 (67.931) 46.894 (196.205) 1500 16.749 (70.078) 47.165 (197.338) 1600 17.233 (72.103) 47.426 (198.430) 1700 17.674 (73.948) 47.673 (199.464) 1800 18.117 (75.802) 47.910 (200.455) 1900 18.515 (77.467) 48.138 (201.409) 2000 18.913 (79.132) 48.356 (202.322) 2100 19.275 (80.647) 48.567 (203.204) 2200 19.636 (82.157) 48.768 (204.045)

a Converted to IPTS-68 from data of Tester, J. W., Feber, R. C, and Herrick, C. C, J. Chem. Eng. Data 13, 419-21

(July 1968). "From data of Hultgren, R., Orr, R. L., Anderson, P. D., and Kelley, K. K., Selected Values of Thermodynamic

Properties of metals and Alloys, pp 38-42 (June 1960), John Wiley & Sons, Inc., New York (1963).

[5] A) Horton, W. S., J. Res. Nat. Bur. Stand. (U.S.) 70A (Phys. and Chem.), No. 6, 533-9 (Nov.-Dec. 1966). B) Cubicciotti, D., J. Phys. Chem. 70, 2410-3 (1966).

[6] Hilsenrath, J., Ziegler, G. G., Messina, C. G., Walsh, P. J., and Herbold, R. J., OMNITAB, a Computer Program for Statistical and Numerical Analysis, Nat. Bur. Stand. (U.S.) Handb. 101, 256 pages, (March 1966).

[7] Preliminary examination of the data and the associated uncertainties for laboratories 9, 10, and 11 indicated that these laboratories deviated significantly from the consensus. An examination of the reports from the laboratories also indicated possible experimental

difficulties. The results from these laboratories were, therefore, not included in further poolings. Subsequent statistical examination

of these laboratories' data and associated uncertainties further indicated that these data should not be included in the pooled results.

[8] The results from eight cooperating laboratories with 27 curves and over 250 temperature-pressure points were used to determine

these weighted averages. The weighting procedure used, is given in section 6.2.

[9] A special pooling procedure for standard deviations was used throughout this study. An example of the pooling procedure is as follows:

pooled Sm = ——

i where the sum is over the i curves and ^4+ 3rk

and v,= number of degrees of freedom. For a normal distribution, this pooling procedure for standard deviations will give results comparable to those obtained by the usual procedure of pooling variances. This procedure, however, has the advantage of being less sensitive to distortion by outlier values. The authors wish to thank B. L. Joiner of the National Bureau of Standards for the derivation

of this pooling formula.

[10] Davies, O. L., Statistical Methods in Research and Production, pp. 97-99, Oliver and Boyd Publishers, London, England (1947).

[11] Mandel, J., The Statistical Analysis of Experimental Data, pp. 132-5, Interscience Publishers, New York (1964).

7
6. Appendix

This appendix gives additional details of the

statistical analyses which were necessary for the evaluation of the gold vapor pressure data. The

two-part statistical analysis has been made in terms

of two large OMNITAB programs. An outline of the two parts is as follows: 6.1.

C. The results for the second and third law least- square fits are given in tables 3 and 4.

2. The authors next examined all results in terms of

criteria A through F, listed below.

A. The chi-square test. Comparisons were made

of Snt values from all curves.

(1) A pooled Sfit was first calculated from the

individual Sm values from all curves [9]. (2) Each individual Sfi , was compared to the pooled Sfit using the approximate test:

1. The temperature-pressure data for each run were

given least-squares treatments described below

to obtain the second and third law values and the associated uncertainties. In all fits each data

point was given unit weight. A. For the second law equation, the least-squares model was Y=A+BX, where X=l/T. The

standard deviations of the coefficients (Sa and

S b) can be expressed in terms of the standard

deviation of the fit (Sfit ): Sa—/i • Sfit

(XV

1

(5)

(6)

(7)

(8)

and N= the number of data points. Thefi and

f-z values provide a convenient quantitative de- scription of the number and spread of the X(=l/T) values and have been used throughout the analyses. Since the OMNITAB least- squares fit program automatically gives the standard deviations for both the coefficients and the fit, the fi and f-z values were conveniently calculated using eqs (5) and (6). B. The third law equation was also treated by

least-squares. Here one obtains a single coeffi- cient, C (the average of the individual A//sub29R values), the standard deviation of the coefficient (Sr), and the standard deviation of the individ- ual A//sub2H8 values (Sfit ). For the third law

case, it can be shown that:

'here Sc=fz-Sm

1 V# of points

(9)

(10)

It can be noted that eq (9) has the same form as eqs (5) and (6). The same general computational

treatment was therefore used for both the second and third law results.

where x

2 is the 0.025 or the 0.975 percentile

of the chi-square distribution with v degrees

of freedom. A laboratory showing several curves for which the values of Sfit fell outside these two limits was noted for further

evaluation.

B. The between-curve (within-laboratory) differ- ences for both the second and third law results. C. The overall differences between the second and third law results. D. The overall differences for results from the

different laboratories. E. The possible drift of results with respect to time.

F. The laboratory's experimental procedures.

3. Based on the above considerations, the data from

laboratories 9, 10, and 11 were not used in further

calculations of averages and pooled standard

deviations. The results of laboratories 9, 10, and

11 were, however, compared to those of the other

laboratories in the second OMNITAB program.

This subsequent analysis confirmed the rejection decision. The variation of second law results for laboratories 10 and 11 was observed to be

especially large. The results of laboratory 9 were

not included because of combined minor diffi- culties in points C. E, and F above. The

fit values

for laboratories 7 and 8 were not used in further poolings since these laboratories did not randomly

vary their temperature during the measurement

of the temperature-pressure curves. As expected,

the Snt values for these laboratories were ab- normally small. All other values from laboratories

7 and 8 were, however, used in the further

calculations.

6.2.

1. In the second OMNITAB program, a comparison was made of runs within each laboratory. This comparison was made in terms of both the

intercept A and the slope B for the curve fitted to each run, and in terms of the average third law heat derived from each run. Using theF test, the variance of the A values between curves

within each laboratory was compared to the estimate of this variance derived from the pooled

8
Sfit . The B and the third law heat values were

similarly treated.

2. A comparison was made of laboratories with each other. First, a pooled value was obtained for the between curves (within laboratories) standard

deviation for each of the three parameters A, B, and third law heat; an average value (for each of the three parameters) was also computed. Then,

using Student's t test, the deviation of the average

value of each laboratory from the overall weighted

average was compared to the pooled standard

deviation between curves (within laboratories). In this way, detailed information was obtained on the variability between laboratories in terms

of the deviation of each individual laboratory from

the consensus value.

3. An analysis of variance was made [10J for each

of the three parameters,^, B, and third law heat, using the estimated values of these parameters

accepted after application of the first OMNITAB

program. The purpose of the analysis was to estimate the components of the within- and

between-laboratory variance.

4. Overall weighted average (A, B, and third law

heat) values and the associated variances were

determined. Since the laboratories did not submit

the same number of runs, the overall weighted

averages are dependent on the specific weighting procedure used. Statistically, a proper weighting procedure would be one that minimizes the vari- ance of the weighted average. The weighting

factors obtained by this procedure are functions

of the ratio of the between- to within-laboratory components of variance. Denoting the ratio for A

by p, it can be shown that laboratory i with re- curves has the weighting factor: ' ,'.',,„•

The value of p can be estimated from the results of the analysis of variance [10]. The weighted

average A will be:

where A, is the average A value for laboratory i. Using this procedure, the variance of A will be

smaller than for any other weighting procedure, and its approximate value will be:

, 2 \ _ "A" component of within-lab. variance [11]

The values for the B and the third law heat were

evaluated in an analogous manner using the p and rii values corresponding to these parameters. Two extreme cases for the weighting factor deserve special attention. For the situation where

the ratio, p, of the between- to within-laboratory components of variance is large with respect to unity, essentially equal weight is given to each

laboratory. For the situation where the ratio p is close to zero, each curve is given essentially equal weight. The p values for A, B, and the

third law heat which we obtained from the

analysis of variance are 0.0, 0.169, and 4.835,

respectively.

5. Finally, the components of variance were as- sembled from the analysis of variance to estimate

the uncertainties for the pooled and single curve

values.

9
6.3. Experimental Data Table 2. List of Experimental Temperature-Pressure Data

Lab 1, Run 1 Lab 1 . Run 2 Lab 2, Run 1 Lab 2, Run 2 Lab 2, Run 3

T, K P, ATM T, K P. ATM T, K P, ATM T, K P, ATM T, K P, ATM

1796.2 6.520 X 10- 1753.1 3.330 X 10-5 1680.0 1.110 X io- 1689.0 1.490 X 10- 1855.3 1.440 X 10-

1894.4 1.960 X 10- 1653.9 8.170 X 10-6 1724.0 1.960 X lO"5 1739.1 3.470 X 10- 1912.4 2.740 X 10-

1727.0 2.540 X 10- 1906.4 2.410 X 10- 1780.2 4.890 X 10- 1804.2 7.790 X lO"5 1840.3 1.130 X 10- 1694.0 1.680 X 10- 1821.2 7.310 X 10^ 1865.3 1.840 X 10-

1964.5 4.000 X 10- 1556.7 1.380 X 10-6 1871.3 1.410 X 10- 1900.4 2.470 X 10-

1705.0 1.760 X 10- 1847.3 1.040 X 10- 1900.4 1.960 X 10- 1927.5 3.530 X 10-

1998.6 6.040 X 10-* 1613.8 3.920 X 10^ 1860.3 1.240 X 10- 1845.3 1.420 X 10-

1924.4 2.790 X 10- 1972.5 5.510 X 10- 1793.2 5.610 X 10- 1774.1 3.870 X 10-s*

1635.9 5.880 X 10^ 1584.8 2.920 X 10-6 1747.1 3.260 X 10- 1673.9 1.270 X 10-* 1764.1 3.560 X 10-5 1935.5 3.010 X 10- 1703.0 1.780 X 10-5 1641.9 7.420 X 10-6 1677.0 9.150 X 10-6 1820.2 7.560 X 10-

1772.1 3.700 X 10-5

*This point discarded.

Lab 2. Run 4 Lab 2, Run 5 Lab 3, Run 1 Lab 3, Run 2 Lab 3, Run 3

T, K P. ATM T, K P, ATM T, K P, ATM T, K P, ATM T, K P, ATM

1690.0 1.440 X 10- 1712.0 2.060 X lO"5 1746.1 3.310 X 10-5 1686.0 1.350 X 10-5 1578.8 2.900 X 10-6 1727.0 2.800 X 10- 1776.1 4.650 X lO"5 1684.0 1.480 X 10-5 1729.1 2.450 X 10- 1629.9 7.000 X 10-6 1675.9 1.260 X 10- 1748.1 3.520 X 10-5 1631.9 6.600 X 10-6 1681.0 1.540 X 10-5 1651.9 9.180 X 10-6 1794.2 6.680 X 10-5 1686.0 1.360 X 10- 1591.8 3.800 X 10-6 1614.8 4.830 X 10-6 1785.2 5.620 X 10-5 1720.0 2.230 X 10- 1607.8 5.100 X 10-6 1599.8 3.450 X 10-6 1798.2 7.010 X 10- 1756.1 3.500 X 10-5 1659.9 1.150 X 10-5 1753.1 4.030 X 10"5 1803.2 6.500 X 10-5 1649.9 1.030 X lO"5 1707.0 1.990 X 10- 1735.1 2.780 X 10- 1604.8 5.200 X 10-6 1655.9 9.900 X 10-6 1659.9 1.020 X 10^

1673.9 1.370 X 10- 1591.8 3.300 X 10-6 1621.8 6.000 X 10-6

10
Table 2. List of Experimental Temperature-Pressure Data — Continued

Lab 4, Run 1 Lab 4, Run 2 Lab 4, Run 3 Lab 5, Run 2

T, K P. ATM

1736.1 3.749 X 10-5 1784 2 6.236 X io-5 1814 2 9.504 X 10-5 1772 1 5.780 X io-5 1759 1 4.841 X io-s 1719 0 2.903 X io-s 1662.9 1.230 X io-s 1635.9 7.725 X io-6 1583.8 3.740 X io-6 1536.7 1.811 X io-« 1502.6 9.439 X io-7 1453.5 3.597 X 10-7 1471.5 5.139 X 10-7 1523.6 1.270 X io-6 1581.8 3.732 X io-6 1630.9 7.429 X io-« 1663.9 1.439 X io-5 1707.0 2.618 X io-5 1738.1 4.236 X 10-5 1773.1 6.250 X io-5 1832.3 1.324 X io-1 1815.2 1.042 X io-* 1811.2 9.395 X 10-5 1786.2 7.584 X 10-5 1764.1 5.406 X io-5 1712.0 2.824 X 10-5 1681.0 1.636 X 10-5 1633.9 7.707 X io-6 1598.8 4.334 X io-* 1548.7 1.949 X io-6 1488.6 6.791 X io-7

T, K P, ATM T, K P, ATM T, K P, ATM

2022.6

1698.0

1758.1 1857.3

1951.5 1879.4

1785.2

1774.1 2010.6

1904.4

8.209

1.592 3.237

1.329 4.793

1.637 6.039

4.645

6.486

2.058

10^

IO"5 IO"5 10^

10^

io-4 io-5 io-5 10^

IO-4

1719.0

1883.4

1824.2 1912.4

1778.2

1957.5 2025.6

2.049

1.568 9.237

2.149 4.074

3.625

6.801

1719.0

1722.0

1866.3 1926.4

1820.2

1768.1 1915.4 2009.6

1973.5

2.316

2.895

1.566 3.934

9.684

4.816

3.408

7.816

5.934

1509.6

1563.7 1619.8

1667.9

1812.2

9.960 X IO 7 2.600 X 10-« 6.590 X 10-6 1.410 X IO"5 1.000 X io-*

Lab 6, Run 1 Lab 7, Run 1 Lab 7, Run Lab 7, Run 3 Lab 7, Run 4

T, K P, ATM T, K P, ATM T, K P, ATM T, K P, ATM T, K P, ATM

1323.2 1.780 X io-8 1499.6 7.024 X io-7 1506.6 8.129 X io-7 1506.6 8.160 X io-7 1534.7 1.386 X io-6 1323.7 1.600 X io-8 1506.6 7.365 X 10-7 1535.7 1.354 X 10-6 1536.7 1.400 X io-6 1564.7 2.309 X io-8 1325.2 1.320 X io-8 1541.7 1.442 X io-6 1585.8 3.063 X io-6 1568.7 2.295 X io-6 1584.8 3.210 X io-6 1325.7 1.790 X io-8 1544.7 1.534 X io-6 1605.8 4.279 X io-6 1597.8 3.704 X IO"6 1603.8 4.383 X io-6 1564.7 2.199 X IO"6 1627.9 5.852 X 10-" 1615.8 4.977 X io-6 1621.8 5.867 X io-« 1577.8 2.799 X io-6 1636.9 6.797 X 10^> 1632.9 6.626 X io-6 1630.9 6.795 X io-« 1599.8 3.844 X io-6 1501.6 6.961 X io-7 1602.8 4.117 X io-6 1540.7 1.460 X IO"6 1617.8 5.306 X io-6 1569.7 2.418 X io-11 1632.9 6.430 X io-« 1589.8 3.336 X io-* 1607.8 4.548 X io-6 1626.8 6.205 X IO"6

11
Table 2. List of Experimental Temperature-Pressure Data — Continued

Lab 7. Run 5 Lab 7. Run 6 Lab 7, Run 7 Lab 8. Run 1 Lab 8. Run 2

T. K P, ATM T. K P, ATM T. K P. ATM T. K P, ATM T, K p. ATM

1448.5 2.717 X 10-' 1591.8 3.564 X io-6 1569.7 2.578 X io-6 1444.5 3.480 X io-7 1555.7 2.980 X io-6 1488.6 6.068 X io-7 1603.8 4.195 X io-6 1643.9 8.478 X IO"6 1478.6 7.170 X io-7 1582.8 4.730 x io-6 1527.7 1.261 X io-6 1506.6 8.250 X io-7 1684.0 1.659 X 10~5 1510.1 1.280 x IO"6 1610.8 7.270 x io-« 1563.7 2.421 X io-6 1545.7 1.608 X io- 1710.0 2.404 X IO"5 1544.7 2.360 x lO^6 1642.9 1.176 X 10-

1582.8 3.238 X io-6 1564.7 2.239 X io-6 1606.8 4.892 X io-6 1575.7 3.950 x io-6 1665.9 1.635 x io-5 1600.8 4.249 X io-6 1584.8 3.076 X io-6 1655.9 1.129 X 10- 1605.8 6.450 X io-6 1692.0 2.342 x io-5 1604.8 4.206 x io-6 1690.0 1.758 X io- 1639.9 1.087 x IO-5 1719.0 3.380 X 10-

1614.8 4.920 X io-« 1673.9 1.785 X 10- 1746.1 5.000 X 10^

1604.8 4.275 X io-6 1702.0 2.663 X 10- 1772.1 7.154 x io-5 1611.8 4.898 X io-6 1725.5 3.692 X io- 1798.2 1.009 X 10^

1546.7 1.628 X io-6 1737.1 4.335 X 10- 1825.2 1.440 X io-» 1505.6 7.955 X io-7 1545.7 1.595 X io-6 1564.7 2.222 X io-6 1584.8 3.024 X io-»

Lab 8. Run 3 Lab 8. Run 4 Lab 8, Run 5 Lab 9. Run 1 Lab 9. Run 2

T. K. P, ATM T, K P. ATM T. K P, ATM T, K P. ATM T, K P. ATM

1448.4 3.900 X io-7 1439.5 3.140 X io-7 1562.7 3.270 X io-6 1615.8 1.140 X 10- 1738.1 7.260 X 10-

1480.6 7.600 X io-7 1483.6 7.780 X io-7 1589.8 5.020 X io-« 1528.7 2.850 X io-6 1631.9 1.520 X 10-

1508.5 1.272 X io-6 1515.6 1.370 X io-6 1618.8 8.150 X io-6 1397.4 2.180 X io-7 1518.6 2.140 X io-6 1542.2 2.320 X io-6 1548.2 2.440 X IO"6 1644.9 1.210 X 10- 1504.6 1.830 X io-6 1411.4 2.820 X io-7 1564.3 3.365 X io-6 1579.8 4.230 X io-6 1673.9 1.850 X 10- 1631.9 1.660 X 10- 1547.7 3.440 X io-6 1592.7 5.350 X io-« 1615.3 7.370 X io-6 1701.0 2.718 X 10- 1437.5 5.200 X 10-7 1651.9 1.900 X 10-

1621.8 8.446 X io-6 1654.4 1.398 X 10- 1727.0 3.894 X 10- 1764.1 1.050 X io-1 1708.0 4.550 X 10-

1654.9 1.386 X 10- 1684.0 2.013 X 10- 1754.1 5.587 X 10- 1604.8 1.060 X 10- 1597.8 7.260 X 10-6 1654.5 1.366 X 10- 1709.5 2.900 X 10- 1780.2 7.915 X 10- 1710.0 4.990 X 10- 1468.5 9.840 X io-7 1735.1 4.110 X 10- 1800.2 1.030 X 1572.7 5.930 X 10-6 1567.7 4.580 X io-6 1827.2 1.448 X io-* 1739.1 7.430 X 10- 1442.5 5.450 X io-7 1483.6 1.310 X 10-6 1666.9 2.640 X io-5 1687.0 3.470 X 10- 1754.1 9.490 X 10-

1785.2 1.250 X 10^

Au, Au2 Au2 Lab 9, Run 3 Lab 9, Run 4 Lab 9, Run 1 Lab 9. Run Lab 9, Run 3

T. K P, ATM T, K 9

P. ATM T. K P. ATM T, K P. ATM T, K P, ATM

1754.1 9.400 X 10- 1744.1 6.610 X 10- 1682.0 6.320 X io-8 1779.2 3.420 X io-7 1805.2 5.220 X io-7 1657.9 1.910 X 10- 1646.9 1.690 X 10- 1764.1 3.130 X io-7 1692.0 7.070 X io-8 1718.0 1.150 X io-7 1532.7 2.410 X io-6 1528.7 2.150 X io-6 1708.0 1.110 X io-7 1646.9 2.190 X io-8 1661.9 2.840 X io-8 1442.5 3.930 X io-7 1437.5 3.500 X io-7 1820.2 7.830 X io-7 1754.1 2.130 X io-7 1738.1 1.570 X io-7 1561.7 4.060 X io-6 1566.7 3.470 X io-6 1744.1 2.090 X io-7 1677.0 3.550 X io-8 1683.0 4.410 X IO"8 1677.0 2.710 X 10- 1677.0 2.500 X 10- 1795.2 5.120 X io-7 1728.1 9.270 X io-8 1780.2 2.980 X io-7 1738.1 6.860 X 10- 1733.1 4.930 X 10- 1656.9 4.020 X io-8 1805.2 5.820 X io-7 1826.2 7.360 X io-7 1622.8 1.250 X 10- 1621.8 9.080 X io-6 1508.6 1.440 X lO"6 1502.6 1.040 X io-6 1406.4 1.980 X io-7 1400.4 1.570 X io-7 1597.8 7.530 X io-« 1592.8 6.590 X io-6 1478.6 8.460 X io-7 1473.5 7.590 X io-7 1718.0 4.740 X io-5 1708.0 3.880 X 10-

1800.2 1.380 X io-1 1785.2 1.280 X io-»

12
Table 2. List of Experimental Temperature-Pressure Data — Continued

Au,

Lab 9, Run 4 Lab 10, Run 1 10, Run Lab 10, Run 3 Lab 10. Run 4

T, K P, ATM T. K P, ATM T, K P. ATM T, K P. ATM T, K P, ATM

1785 2 4 050 X io-7 1692.0 2.800 X IO-"' 1641.9 1.470 X 10-5 * 1717.0 3.700 X 10-5 1656.9 2.400 X io-5 9 110 X io-« 1651.9 1.470 X io-5 1792.2 4.800 X 10 s 1712.0 3.700 X 10-5 1707.0 4.800 X 10-5 2 560 X io-8 1631.9 1.210 X io-5 1792.2 4.200 X 10-> 1651.9 2.100 X io-5 1646.9 2.200 X io-5

1 7QO 1 X io-7 1571.7 5.000 X io-« 1757.1 1.980 X 10-5 1611.8 1.250 X io-5 1606.8 1.290 X IO-5 n 5 140 X io-8 1546.7 3.100 X io-* 1697.0 1.000 X 10- 1576.7 6.500 X io-6

' 1571.7 7.100 X io-6 177d 1' 2 710 X io-7 1621.8 9.400 X io-6 1656.9 5.400 X io-* 1536.7 3.700 X io-6 1541.7 4.300 X IO -*1 15.2 5 900 X io-7 1646.9 4.200 X io-« 1511.6 2.300 X io-« 1501.6 2.200 X io-6 1702.0 8.200 X io-* 1571.7 7.300 X io-6 1521.6 3.100 X io-6 1671.9 2.700 X 10-5 1606.8 1.400 X 10-5 1511.6 2.100 X IO

-" 1651.9 2.900 X IO -5 1727.0 7.100 X 10-5 1656.9 2.900 X 10-

1621.8 1.270 X 10-5 1571.7 6.100 X IO-6 1536.7 3.700 X io-6 1486.6 1.910 X io-* 1541.7 3.500 X io-6 1586.8 5.800 X 10 6

*This point discarded.

Lab 1 1 , Run 1 Lab 11, Run 2 Lab 1 1 , Run 3 Lab 1 1

, Run 4 Lab 1 1 , Run 5

T, K P, ATM T, K P, ATM T, K P. ATM T, K P, ATM T, K P, ATM

1536.7 1.150 X IO-6 1514.6 8.130 X IO"7 1555.7 2.660 X 10-6 1578.8 3.180 X 10-« 1513.6 7.880 X IO"7 1571.7 2.160 X IO-6 1539.7 1.040 X IO"6 1594.8 3.420 X IO"6 1585.8 3.350 X IO"6 1586.8 4.030 X 10-* 1584.8 2.950 X 10-6 1554.7 1.950 X IO-6 1634.9 7.160 X IO-6 1616.8 6.220 X IO"6 1596.8 4.610 X 10-« 1634.9 7.190 X 10-6 1567.7 2.420 X 10-« 1637.9 7.740 X 10-6 1625.8 6.410 X 10-* 1632.9 6.820 X 10-<; 1662.9 1.170 X IO"5 1622.8 6.030 X IO-6 1690.0 1.350 X IO- 1639.9 6.830 X 10-« 1682.0 1.320 X IO"5 1677.0 1.440 X IO-5 1714.0 1.670 X IO"5

13
GOLD DATA FROM LABORATORY NO. 1

GOLD DATA FROM LABORATORY NO. 2 -2.4-| ' ' ' ' ' ' 1 ' ' 1 1 1

1/T X 10+4 (K' 1 )

14
GOLD DRTR FROM LRBORRTORY NO. 3

GOLD ORTR FROM LRBORRTORY NO. 4 -2.4-. ' 1 1 1 ' ' 1 1 1 1 1

1/T X 10+4 (K- 1

)

15
GOLD DATA FROM LABORATORY NO. 5

16
GOLO OflTfl FROM LABORATORY NO. -3.6

-7.2-1 , , 1 , , , , , , , , , , , , , , 5.3 5.4 5-5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 1/T X 10+4 (IT 1

)

GOLD DATA FROM LRBORflTORY NO. 9 -3.6-1 1 1 1 ' ' 1 1 ' ' < 1

-7.2-1 , , , ,

, , , , , , , , , , , , , 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6-1 6.2 6.3 6.4 6-5 6.6 6.7 6.8 6-9 7.0 7.1 7.2 1/T X 10+4 (K" 1 ) Figure 4.

17
GOLD OflTq FROM LABORATORY NO. 10

IS

.$. GOVERNMENT PRINTING OFFICE : 1970 OL—363-394


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