National Bureau of Standards

Library, E-01 Admin. B!dg. FEB 1971 NBS SPECIAL PUBLICATION 260-21

Standard Reference Materials:

ANALYSIS OF INTERLABORATORY

MEASUREMENTS ON THE VAPOR PRESSURES

OF CADMIUM AND SILVER

UNITED STATES DEPARTMENT OF COMMERCE • Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

Standard Reference Materials:

Analysis of Interlaboratory Measurements on the

Vapor Pressures of Cadmium and Silver

(Certification of Standard Reference Materials 746 and 748)

Lj> S , National Bureau of Standards. Special Publication 260-21

Nat Bur. Stand. (U.S.). Spec. Publ. 260-21, 30 pages (Jan. 1971) CODEN: XNBSA

Issued January 1971

For sale by the Superintendenl of Documents, U.S. Government Prinlinp Office Washington. D.C. 20402 (Order by SD Catalog No. C 13.10:260-21), Price 35 cents

Robert C. Paule and John Mandei

Institute for Materials Research

National Bureau of Standards Washington, D.C. 20234

t.
Contents

Page

1. Introduction 1

2. Treatment of data 2

3. Statistical analyses 7

4. Discussion of silver second and third law results 9

5. Comparison of results from cadmium, silver, and gold 10

6. Footnotes and references 12

7. Appendix 14 Tables

1. Cadmium — Summary of experimental methods 2

2. Silver— Summary of experimental methods 3

3. Cadmium — List of experimental temperature-pressure data (Appendix) 16

4. Silver— List of experimental temperature-pressure data (Appendix) 19

5. Cadmium — Summary of second law results 4

6. Cadmium — Summary of third law results 5

7. Silver— Summary of second law results 6

8. Silver— Summary of third law results 7 Figures

Figures 1 to 3, Cadmium — Log P versus 1/7" Plots (Appendix) 22-24

Figures 4 to 8, Silver- Log P versus HT Plots (Appendix) 25-28

Figure 9, Cadmium — Accepted second and third law A//sub298 8

Figure 10, Silver — Accepted second and third law A//sub298 8

Library of Congress Catalog Card Number: 71-608659
Analysis of Interlaboratory Measurements on the

Vapor Pressures of Cadmium and Silver

(Certification of Standard Reference Materials 746 and 748)

Robert C. Paule and John Mandel

Detailed statistical analyses have been made of results obtained from a series of interlaboratory measurements on the vapor pressures of cadmium and silver. Standard Reference Materials 746 (cad- mium) and 748 (silver) which were used for the measurements have been certified over the respective pressure ranges 10-"-10-'' atm and 10-'--10"'' atm. The temperature ranges corresponding to these pressures are 350-594 K for cadmium and 800-1600 K for silver. The heats of sublimation at 298 K

and the associated two standard error hmits for cadmium and silver are 26660±150 cal/mol and

68010 ±300 cal/mol, respectively. Estimates 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 between-laboratory components of error. The uncertainty limits are observed

as functions of both the heat of sublimation and the temperature. Key words: Cadmium; components of error (within- and between-laboratory); heats of sublimation (second and third law); interlaboratory measurements; silver; standard errors; standard reference

materials; vapor pressure. 1. Introduction

This report is part of a continuing program to establish five new vapor pressure standard refer- ence materials. The materials, Cd, Ag, Au, Pt, and W, are being certified by the National Bureau of Standards for vapor pressures as a function of temperature. The certifications cover the 10" '^10^^ atm range; for the complete series of materials, the temperatures corresponding to these pressures will vary from 350 to 3000 K. Gold has previously been

certified over the temperature range 1300-2100 K

[1].' This report describes the current certification of cadmium (350-594 K), and of silver (800-1600 K)

[2].These vapor pressure standard reference materials will allow workers in the field to detect syste- matic errors and to quantitatively evaluate their

results. The materials should be most useful for checking low vapor pressure measurement methods, such as the Knudsen, torque Knudsen, Langmuir, and mass spectrometric methods. Experience in vapor pressure measurements, particularly at high temperatures, has shown that large systematic errors are common, even among experi- enced investigators. This report gives estimates of the uncertainties of the certified temperature-pressure values as well as estimates of the uncertainties

of a "typical" single laboratory's measurements. The current certification of cadmium and silver, when taken in conjunction with the prior certifica- tion of gold, gives an indication of the temperature dependence of the uncertainties of vapor pressure measurements. These uncertainties are statistical

in nature and reflect results for typical experienced

investigators. The use of vapor pressure standard

reference materials should aid in the detection and

eUmination of errors and should uhimately resuk in the decrease of the uncertainty hmits that are herein

reported.

' Figures in brackets indicate footnotes and references given on page 12.

Our results are based on interlaboratory tests (including NBS) made during 1968-9. A list of the cooperating laboratories is giveYi on page 11. The results from the interlaboratory tests were

used to obtain composite heats of subhmation

(^^sub298) for cadmium and for silver at 298 K. The certified temperature-pressure values were

then obtained by back-calculating through the third law equation r[A(-^^^)-/?lnP] = A//,.,.«s (1) These calculations used composite A/ysub298 of 26660 cal/mol (111550 J/mol) for cadmium, and 68010

cal/mol [3] (284550 J/mol) [4] for silver, along with

the referenced free energy functions [5]. P is ex- pressed in atmospheres. All temperatures for this report have been converted to the 1968 International Practical Temperature Scale (IPTS-68) [6]

.

The certified temperature-pressure values as well

as the corresponding IjT and log P values are hsted

below.

r(K) /'(atm) [4] (l/7'xlO"(K->) Log,oP(atm)[4] Cadmium

350 2.49 X 10-" 28.57 - 10.603 400 2.97 X 25.00 -8.528

450 1.20 X 10-' 22.22 -6.922

500 2.31 X 10-6 20.00 -5.637

550 2.56 X 10-^ 18.18 -4.592

594 (M.P.) 1.51X10-" 16.84 -3.820

Sil ver 800 1.35X 10-'2 12.500 -11.870

900 1.48 X 10 "' 11.111 -9.830

1000 6.28 X 10 " 10.000 -8.202

1100 1.33 X 10 ' 9.091 -6.875

1200 1.69X 10-« 8.333 -5.773

1235 (M.P.) 3.71 X 10-« 8.097 -5.431

1300 1.35 X 10-^ 7.692 -4.868

1400 7.80 X 10-^5 7.143 -4.108

1500 3.53 X 10-" 6.667 -3.452

1600 1.31 X lO--" 6.250 -2.881

1
Table 1. Cadmium —Summary of Experimental Methods

Laboratory Method

t' , , , 1 emperature measurement

technique

Temperature range, K

Container

material

Effective orifice area X 10^, cm^ Remarks

1 Mass spectro- metric, with Cd

calibrations

Pt-10% Rh, Pt thermocouple 413-590 Iridium 4.70 No cadmium dimer observed

(P < 5 X 10-" atm at 580 K). Temperature calibrations made using cadmium

melting-freezing point halts. Cadmium background was

i — f of primary cadmium

signal. 2 Knudsen weight

loss (runs 1-4); Torque Knudsen

(runs 5-7)

Pt-Rh, Pt thermocouple 423-690 Iron 7.48, 1.69, 124,

31.5, 14.5, 3.79, 67.0 for runs

1-7, respectively

A very wide range of orifice areas were used and an

effect of orifice area was

noted. This may indicate an effective non-unit evaporation coefficient for the cadmium sample. A slight oxide coating on the sample

could explain these results. 3 Mass spectro- metric, with Cd calibration

Chromel-Alumel

thermocouple 352-550 Spectroscopic grade

graphite

8.84 Cadmium dimer observed

to be less than 0.1% of monomer. Run temperature measurements made in one

temperature direction only,

i.e., temperatures were

decreased. Initial pressure

readings were low, presumably due to a slight oxide

coating. Heating sample 15 min. in vacuum at 460 K

ehminated this problem.

4 Knudsen weight Pt-10% Rh, Pt thermocouple 487-584 Alumina 2.65, 4.58 Orifices calibrated using

vaporization of lead. Used

Hultgren's data on lead (Nov.

1965). 5 Torque Knudsen Pt-13% Rh, Pt thermocouple 495-539 ZTA graphite 6.11, 12.84 Tempreature measurements made in one temperature

direction only, i.e., decreasing

temperatures.

6 Torque Knudsen Pt-10% Rh, Pt thermocouple 500-600 Beryllia 0.86 Automatic data recording used

by this laboratory to obtain hundreds of temperaturepressure data points. The re- sultant data were treated by

the cooperating laboratory and

third law AHsi,b298 were sub- mitted for use in this study. A broad cross section of measurement techniques was used by the cooperating laboratories; the tech- niques included the Knudsen (weight loss and con- densation methods), torque Knudsen, and cali- brated mass spectrometric methods. Temperatures

were measured using either thermocouples or

optical pyrometer. Summary information regarding

the experimental details for each laboratory is given in tables 1 and 2. 2. Treatment of Data

The detailed temperature-pressure data from the

six laboratories for cadmium, and from the nine

laboratories for silver, are given in tables 3 and 4

(see Appendix, section 7.3). Plots of the data for cadmium and for silver are given in figures 1 through

8 in section 7.3. The soUd lines in these figures represent the pooled curves for all accepted data from all laboratories. A total of 24 sets of cadmium

data (runs) with over 250 temperature-pressure

points, and a total of 27 sets of silver data with over 300 temperature-pressure points were available for consideration. Each temperature-pressure run has been used to obtain both the second and third law heats of sub- hmation at 298 K. Equation (1) was used to calculate the individual third law AH^uhiss values correspond-
Table 2. Silver— Summary of Experimental Methods

Laboratory MethodTemperature measurement

technique

Temperature range, KContainer

material

Effective orifice area X 10^, cm^ Remarks

1 Knudsen using condensation

plates

Optical pyrometer sighting

into blackbody

hole (runs 1 and

3); Pt-10% Rh,

Pt thermocouple

(runs 2 and 4)

1232-1584 Tantalum 4.05 Temperature calibrations made

using silver melting-freezing

point halts.

2 Mass spectro- metric, with Ag

calibrations

Chromel, Alumel

thermocouple 854-1284 Graphite 10.21 Temperature tended to be measured in one direction

only, i.e., decreasing

temperatures.

3 Knudsen weight

loss Optical pyrometersighting into blackbody holes

1373-1530 Graphite coated with

pyrolytic graphite

2.11, 3.72, 4.17 Significant difference noted in second and third law heats.

4 Knudsen weight

loss Pt-Rh, Pt thermocouple, plus

optical pyrometer as secondary temperature

recorder

1315-1584 Quartz 0.29, 0.80

5 Knudsen weight

loss Pt-10% Rh, Pt thermocouple 1256-1494 Alumina (run

1); stack- pole high

density graphite

(run 2)

4.58, 3.55 Orifice calibrated using vaporization of lead. Used Hultgren's data on lead (Nov. 1965).

6 Torque Knudsen Optical pyrometer

sighting into blackbody hole

1221-1433 Graphite 3.5, 1.6 Temperature measurements made in one temperature

direction only, i.e., decreasing

temperatures.

7 Torque Knudsen

(runs 1-6), Knudsen weight

loss (runs 7-8)

Pt-13% Rh, Pt thermocouple 1089-1209 ZTA graphite 6.12, 23.0 Temperature measurements made in one temperature

direction only, i.e., decreasing

temperatures.

8 Double cavity Knudsen cell used for absolute calibration of TOF mass

spectrometer

Optical pyrometer

sighting into

orifice

1143-1318 Graphite

9 Knudsen weight

loss Optical pyrometersighting onto bottom of cell and 0.77 emissivity correction made

1254-1434 AGSX graphite 2.45, 1.38 Temperature measurements made in one temperature

direction only, i.e., increasing temperatures.

ing to each temperature-pressure point and the average A//sub298 value was calculated for each run. Available information would indicate the evaporation coefficient for silver is unity. Cadmium, however, may have had evaporation-condensation coefficients less than unity [7]. Observations at NBS

have indicated a considerable bouncing of cad- mium vapors impinging on glass surfaces at room

temperatures. Furthermore, remarks listed in table 1

for cooperating laboratories 1, 2, and 3 indicate possible effective evaporation-condensation coefficients of less than unity. Since Knudsen cells with relatively small orifices were used in all ac- cepted experiments, we have not made corrections

for possible non-unit evaporation coefficients. The second law heat for each vapor pressure-temperature run was obtained by least-squares fitting the A and B constants in the equation: 3
i^l^--QLjiMyj^^^p=A^^ (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 [8, 9]. The slope is a second

law heat of sublimation at 298 K. The intercept A

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 accommodate possi- ble error. This second law procedure is very con- venient to use when the calculations, including the

interpolation of free energy functions, are made by

computer. The OMNITAB computer language

[10] was used in this work. Summaries of the second and third law results for cadmium and silver are given in tables 5 through 8.

Table 5. Cadmium —Summary of Second Law Results

Lab. Run Intercept A Slope B, 2nd Law /. /2 •5 fit No. No. No. of points (see eq 2) AA^sub298 (see eq 2) (see eq 4) (see eq 5) (see eq 3) cal-mol~'-deg~' cal-mol"'

J J 10 — 1 381 27158 3 24 1570 0 2387

2 8 -T176 27109 3!26 1580 !l511 3 8 -0.474 26817 3.37 1630 .1370 4 8 -1.119 27128 3.27 1610 .2501 5 8 -0.798 27130 3.23 1590 .2498 6 8 -.512 26922 3.17 1570 .2734

2 1 14 .180 26347 2.48 1250 .0916

2 TO -.628 26488 3.91 2030 .0682

3 16 2.247 26005 2.07 1010 .3027 4 8 2.886 25247 5.86 3170 .1035

3 1 25 2.758 25659 1.46 640 .2507 2 17 -0.204 27020 2.06 930 .3527 4 1 16 -.378 26840 4.72 2530 .0533

2 19 -.123 26734 5.01 2700 .0792

5 1 8 .300 26523 15.19 7970 .0212

2 6 -.084 26727 24.07 12640 .0131 3 8 -.794 27076 18.24 9370 .0074 4 6 -.383 26858 24.38 12410 .0063

2 5 12 4.302 24239 9.10 5080 .1434 6 10 4.434 23913 12.24 6980 .1835

7 15 6.000 23765 7.06 3680 .2687

4
Table 6. Cadmium — Summary of Third Law Results Lab No. Run No N0. 0 points /3 S'fit cal*niol~^ (see eq. 9) ^sec cq. o}

1 1 10 26480 0.316 136.6

2 8 26528 .354 102.8

3 8 26584 ^354 66.4 4 8 26568 .354 129.7

5 8 26729 ,354 121.9

6 8 26665 .354 121.3

2 1 14 26439 .267 45.5

2 10 26159 .316 44.4 6 10 26444 .316 119.1

3 1 25 26906 .200 192.4

2 17 26925 .243 156.7 4 1 16 26636 .250 29.7

2 19 26668 .229 43.1

5 1 8 26681 .354 10.9

2 6 26683 .408 6.3

3 8 26668 .354 9.2 4 6 26663 .408 4.6 6 1 > 100 26704 < .1 See Remark for

2 > 100 26722 < .1 Laboratory 6

3 > 100 26749 < .1 in table 1

2 3 16 27122 .250 192.4 4 8 26816 .354 114.4

5 12 26642 .289 109.9

7 15 26898 .258 176.3

5
Table 7. Silver— Summary of Second Law Results

Lab. Run

No. of points Intercept A Slope B, 2nd Law /, h Sfi, No. No. (see eq 2) A^^sub298 (see eq 2) (see eq 4) (see eq 5) (see eq 3) cal'mol~''deg"' cal*niol~^

1 1 12 -0.922 69361 3.95 5460 0.1531

2 11 — .585 68842 4.00 5480 1336

3 11 .245 67817 4.37 5980 J063

4 11 -.516 68981 4.95 6850 .0918

2 1 19 -2.432 69926 1.96 2070 .1456

2 28 -1.697 69080 1.56 1640 .2939 4 1 13 -1.733 70958 5.52 7940 .0573

2 12 -0.635 69412 5.82 8240 .0720

5 1 21 -.194 68562 4.10 5610 .0604

2 20 -.017 68295 4.92 6800 .0602

6 1 22 -.386 68678 5.41 7050 .0425

2 21 -.432 68723 4.88 6490 .0464

7 1 11 -.444 68155 15.05 17600 .0041

2 11 -.175 67840 13.97 16380 .0067

3 9 -.430 68246 16.94 19100 .0064

4 9 -.870 68705 19.61 22080 .0226

5 3 -.806 68647 91.36 104950 .0011 6 3 -.608 68444 76.33 87290 .0110

7 3 — .719 68588 91 36 104950 0232

8 3 -.592 68442 76.33 87290 .0126

3 J 10 — 3 730 73169 10 44 15150 1485

2 12 -2.560 71675 8' 48 12280 .1196

3 9 -3.095 72829 11.66 16860 .1384

8 1 8 1.973 65813 13.02 15690 .1112

2 5 16.483 47547 12.65 15900 .3319 9 1 5 -0.413 66865 9.92 13320 .41.36

6
Table 8. Silver-Summary of Third Law Results

Lab. No. Run No. No. of points 3d Law AWsubiss

cal-mol"' h

(see eq. 9) 5 'fit (see eq. 8)

1 1 12 68076 0.289 219.4

2 1

1

.302 185.7

3 11 6815.5 '302 137.3 4 11 68263 .302 121.4

2 1 19 67308 .229 328.6

2 28 67257 .189 390.2

3 1 10 .316 259.8

2 12 67963 ^289 206.9

3 9 68347 .333 229.2

4 1 13 68455 .277 154.5

2 12 68510 .289 105.5

5 1 21 68295 .218 80.4

2 20 68272 .224 79.5

6 1 22 68173 .213 55.7

2 21 68146 .218 66.9

7 1 11 67636 .302 11.9

2 11 67634 .302 8.8 3 9 67761 .333 12.0 4 9 67726 .333 29.5

5 3 67620 .577 7.2 6 3 67749 .577 11.0

7 3 .577 20.0

8 3 67764 ^577 12.0

8 1 8 68194 .3.54 142.2

2 6 68299 .408 835.8

9 1 5 66309 .447 480.7

1 69240 1.000

3. Statistical Analyses

The two OMNITAB programs written for the analyses of the gold (SRM 745) vapor pressure data were modified shghtly and were used in the current work. The ultimate purpose of these programs was to obtain overall weighted average values of the second and third law heats of sublimation and esti- mates 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. 7.1). The authors then examined the results and made

tentative decisions regarding the data to be excluded from the weighted averages and the esti- mated uncertainties [11]. The detailed criteria used

in making these tentative decisions are given in section 7.1. Summaries of the accepted second and third law results are presented in figures 9 and

10.The second OMNITAB program was next run

to determine (1) the weighted average values of the second and third law heats of sublimation, (2) the

uncertainties of the heats, and (3) the uncertainties expected for a typical in-control laboratory's meas- urements (see sec. 7.2). 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 avoided distorting the overall resuhs, but still allowed for further evaluation of

all of the data. 7
CfiDnlUI1--fiCCEPTE0 SECOND BNQ THIRD LAW oH, SILVER--f)CCEPTEC SECOND AND THIRD LAW <.H,,

urborbtory number Figure 10.

The statistical analyses for cadmium indicate the weighted average [12] and the two standard error

limits of the weighted averages to be as follows: ^ = 0.15 + 0.87 cal-mol-'-deg-i 5 = 2nd law A//sub2M8 = 26610 ±380 cal-mol-^ 3rd law A//sub 298 = 26660 ± 150 cal-mol"' The A coefficient is essentially zero which indicates the observed pressures and free energy functions

are reasonably concordant. In the analyses it is tacitly assumed that the errors in the free energy

functions are negligible. The second and third law

A//sub298 are observed to be in good agreement. We

beheve the third law Ai/sub298 of 26660 cal mol"'

to be the preferred value. A laboratory measuring a single temperaturepressure curve for cadmium 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 component of variance,

(2) the between-laboratory component of variance,

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

to the components of variance in the above order we

obtain for the single curve case: V{A) =1.08 +0.61 + 0.19 =1.88

V(2nd law) = ( 16.3 + 12.7 + 3.6) X 10-» = 32.6 X lO"" r{3rd law)=(0.7 +3.2 +0.6) X 10^= 4.5 XlO^ The numerical values in the above variance equations have been derived using energy units of

calories. The variance equations describe the typical

uncertainties in the measurement of a single cad- mium temperature-pressure curve. The equations

are a summary of results for all accepted cadmium

curves. The average temperature range for these curves is 120 K and the average number of points

is 13. The cadmium and silver data differ from the

gold data [1] in that the between-curve components

of variance are not realistically described by the products of the pooled standard deviations of fit (Sfit) and the f factors (/i,/2, and /s) which reflect the number and spread of \IT values (see eqs 4 through 9). Tables 5 through 8 show a general lack

of homogeneity of the Sfu valves. The variations of the between-curve (within-laboratory) A, B, and

third law values, however, are reasonably well behaved. The between-curve components of vari- ance were therefore directly obtained from the

analysis of variance [13] of the A, fi, and third law

values. The following limits for cadmium, which are equal to twice the square root of the above vari- ances, 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 single curve result obtained by the above

described typical laboratory should fall within the following limits: A =0.15 + 2.74 cal- mol-i • deg-i 2nd law A//sub 298 = 26660 + 1140 cal • mol"!

3rd law A//sub 298 = 26660 ± 420 cal • mol"'

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, 26660

cal • mol~^

8
For silver, the weighted averages [14] and the two standard error Hmits of the weighted averages

are as follows: ^=-0.79±0.58 cal • mol-> • deg-' fi-2nd law A//sub 29« = 68970 ± 570 cal-mol"'

3rd law A//sub2-.8 = 68010 ±300 cal • mol"' A comparison of the two standard error hmits with

the weighted averages indicates some inconsist- ency in the second and third law results, i.e., the uncertainty hmits do not quite allow an overlap of the second and third law heats. Furthermore, the value of the A coefficient cannot be assumed to be

zero. The individual second and third heats for each silver curve also indicate a consistent bias with

19 out of 20 accepted second law heats being higher than the corresponding third law heats (see tables 7 and 8). This problem has been examined in detail and it has been concluded that the higher second

law heats are a result of the basic temperaturepressure data obtained from the cooperating laboratories, and are not a result of the treatment of the

data. From a detailed analysis of possible error sources, it has been concluded that the silver second

law results are most hkely to be in error and that the

third law results are essentially correct. A more

detailed discussion of the problem is given in section 4. For the silver single curve comparison with the weighted averages, the respective components of variance are as follows: V{A ) = 0. 14 + 0.44 + 0.08 = 0.66 F(2nd law) = (25 + 40 +8) x lO"" = 73 x 10^ r(3rd law) = (1.6 + 15.0 + 2.2) X lO^ = 19 X 10* These single curve variances are a summary of

results for all accepted silver curves. The average temperature range for these curves is 240 K and the average number of points is 15. The following limits for silver, which are equal

to twice the square root of the above variances, can be used for the estimation of maximum allow- able differences between the single curve results obtained by the typical laboratory and the weighted

averages. Approximately 95 percent of the time, a single curve result obtained by the above described

typical laboratory should fall within these limits: A =- 0.79 ±1.63 cal -mol-i-deg-'

2nd law A//sub298 = 68010 ± 1700 cal • mol"'

3rd law A//,^,b ,98 ^ 68010 ± 870 cal • mol"'

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, 68010 cal-mol The larger single curve uncertainties

would, however, have easily overlapped the second and third law values. An examination of the above cadmium and silver values of the components of variance for the

typical single curve case is of considerable interest. For cadmium and silver, the between-laboratory components of variance are found to be an ap- preciable fraction of the total expected variance. Thus, a typical laboratory that measures (n — 1) additional temperature-pressure curves will reduce

only the between-curve variance by a factor of

1/n, and will not affect the large between-laboratory component of variance. Repetitive curve measurements within a single

typical laboratory will not greatly diminish the

overall uncertainties in the measured heats of sublimation. To paraphrase, we can say that a

typical laboratory's ability to reproduce its own

vapor pressure measurements exceeds its abiUty

to reproduce other laboratories' measurements.

This will be particularly true for measurements

of the third law heat of subhmation.

4. Discussion of Silver Second and

Third Law Results

Both the comparison of the standard error limits relative to the second and third law A//sub298 weighted averages, and the comparison of paired second and third law heats for individual pressure- temperature curves have indicated inconsistencies

in the silver data. A more severe rejection of indi- vidual second law results would decrease the in- consistencies. Additional rejections were not felt to be justified since one of our primary goals was to evaluate "typical" uncertainties of vapor pressure measurements made by experienced investigators. There is always a fundamental question of how much data to reject. For silver, it was felt that additional rejections would have unreahstically mini- mized the reported between-curve components of

variance. The differences in second and third law results are beheved to be due to the basic temperaturepressure data submitted by the cooperating laboratories. A detailed inspection has shown that the

calculational procedures and the OMNITAB computer programs have not artifically "synthesized"

the differences. The individual curve second and

third law heats are found to be in good agreement

with the results calculated by the cooperating laboratories. The cooperating laboratories results also showed the same trend of higher second law heats. To further check the calculational procedures and

programs, temperature-pressure data from eleven randomly selected literature reports on silver were

used to calculate second and third law heats. The

results showed no trends of high individual second

law heats. The overall average second and third law

heats were 67800 and 68000 cal • mol"', respectively. 9
Visits and discussions with several of the cooperating laboratories have not positively identified the source of the inconsistency. It appears most likely that the observed second law heats are too high and

that this is caused by systematic errors in the measurement of the sample temperatures.

It seems very unlikely that the third law heat can be 900 cal-mol"^ too low. For this to occur it would

be necessary that either (1) the free energy functions

are in error by 0.6 cal • mol^' • deg~\ or (2) the measured pressures were 35 percent too high, or (3) the measured temperatures were 20 K too low, or (4) some combination of factors (1), (2), and (3). It does

not seem reasonable that either the free energy

functions or the measured pressures can contain such large errors. Furthermore, the direct observation of melting-freezing point halts by laboratory 1 would seem to ehminate the possibility that the temperature scale was 20 K too low. Let us now consider trended errors that could

affect the second law heat by 900 cal - mol"^ By

trended errors we mean errors that either gradually increase or gradually decrease from one end of the measurement range to the other. Analysis of equation (2) shows that, for an average 240 K temperature

interval, the factors in the left hand side of the equation would have to have a trended error of about 0.1 cal • mol"^ • deg"^ Such a trended error in free energy functions is highly unlikely since extremely

large errors in heat capacity data would be required. A trended pressure error of 5 percent would be

equivalent to the 0.1 cal • mol^' • deg"^; such an

error is possible, but does not seem Hkely. The formation of a dimer or higher polymer, does

not appear to offer an explanation for a trended

pressure error. The Hterature [15, 16. 17] shows

the total polymer concentration to be less than

0.5 percent of the monomer at 1600 K, the highest temperature used by the cooperating laboratories. The most probable explanation of the 900

cal • mol"' difference in second and third law results would appear to be a trended error in the measure- ment of temperatures. A trended error of 4 K over

the 240 K interval, or 1 K out of 60 K, would be

required. At temperatures of 800-1600 K, gradients

of 5-15 K within a Knudsen cell are far from uncommon. A shift of temperature gradients within

the cell could account for an average trended temperature error of 4 K. The spectral and total emissivities of silver are both less than 0.1 [18]. This could help exaggerate temperature gradients

within the cell and could lead to temperature measurement errors and high second law heats. After consideration of all of the above factors, we favor the use of the third law A/^sub 'ss value of 68010 cal • mol-i.

5. Comparison of Results from

Cadmium, Silver, and Gold

A comparison of results for the cadmium, silver, and gold [1] standard reference materials allows

for a partial examination of vapor pressure uncertainties as a function of the temperature at which measurements are made. The future certifica- tion of platinum and tungsten should allow a further examination of temperature effects. A summary

of the currently available A//sub298 uncertainties is given below.

Material Average

temp.. K cal • mol"'

Two standard deviation limits of A//sub298 Weighted average Typical single curve 2nd law 3rd law 2nd law 3rd law Cadmium 500 26660 ±420 ±150 ±1140 ±380

Silver 1300 68010 ±870 ±300 ±1700 ±570

Gold 1700 87720 ±1350 ±420 ±3700 ±1000 As would be expected, the larger uncertainties in the second and third law heats are associated with

the higher temperature measurements. It can also be noted that the uncertainties are roughly proportional to the size of the heat of sublimation. The

uncertainties for the second law results are ap- preciably larger than for the third law results.

By virtue of equation (1), an uncertainty in A//sub298 Wil cause a corresponding uncertainty

in our knowledge of the relationship between temperature and pressure. The table below shows the temperature-log pressure uncertainties resulting from a change in ± two standard deviations in the

third law A//sub298. The uncertainties in temperature

Material Average

temp., K cal • mol"'

Two standard deviation limits corresponding to 3rd law A//sub:298 uncertainties Weighted average Typical si igle curve ^T or A log P ^T or A log P

Cadmium 500 26660 ±3 ±0.069 ±7 ±0.185

Silver 1300 68010 ±7 ±0.049 ±20 ±0.146

Gold 1700 87720 ±9 ±0.053 ±30 ±0.173 10
are calculated assuming a fixed pressure, and the

uncertainties in log pressure are calculated as- suming a fixed temperature.

Inspection of the above A log P values shows the values to be relatively independent of temperature. A consideration of the factors involved in the meas- urement of vapor pressure-temperature curves would seem to indicate the relative Constance of the A log P values may be due to the combined change

with temperature of (1) the uncertainties of temperature measurement and (2) the relative magnitudes

of the various heats of sublimation.

Finally, it should be reiterated that the large uncertainty of a typical single curve measurement is primarily due to the large between-laboratory uncertainty. A single laboratory's evaluation of error may be greatly underestimated if systematic be- tween-laboratory errors are not considered. The

diligent use of vapor pressure standard reference

materials should help in the detection of elimination

of such systematic errors.

List of Cooperating Laboratories for Cadmium

Bureau of Mines, A. Landsberg

Douglas Advanced Research Laboratories, D. L. Hildenbrand

Gulf General Atomic, Inc., H. G. Staley Los Alamos Scientific Laboratory, C. C. Herrick and R. C. Feber

Marquette University, T. C. Ehlert National Bureau of Standards, E. R. Plante and A. B. Sessoms

Sandia Corporation, D. A. Northrop

List of Cooperating Laboratories for Silver Aerospace Corporation, P. C. Marx. E. T. Chang,

and N. A. Gokcen

Air Force Materials Laboratory. G. L. Haury

Douglas Advanced Research Laboratories, D. L. Hildenbrand

Institut fiir Physikahsche Chemie der Universitat Wien (Austria), A. Neckel

Los Alamos Scientific Laboratory, C. C. Herrick and R. C. Feber

Marquette University, T. C. Ehlert National Bureau of Standards, E. R. Plante and A. B. Sessoms

National Chemical Laboratory (India), V. V. Dadape

Sandia Corporation, D. A. Northrop

Universita DegU Studi di Roma (Italy), V. Piacente and G. DeMaria

The authors are greatly indebted to the above

hsted cooperating laboratories for their vapor

pressure 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

reference materials. 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 literature survey of the vapor

pressure measurements on cadmium and silver. F. L. McCrackin has aided in the use of his computerized GRAPH routine.

11
6. Footnotes and References

[1] Paule, R. C, and Mandel, J.. Analysis of Interlaboratory Measurements on the Vapor Pressure of Gold, Nat. Bur. Stand. (U.S.), Spec. Publ. 260-19, 21 pages (Jan. 1970). ; [2] The cadmium (SRM 746), silver (SRM 748), and gold (SRM 745) may be ordered from the Office of Standard Reference Materials, National Bureau of Standards, Washington, D.C. 20234. The respective prices for SRM 746, 748, and 745 are 165, $75. and $85 .

j

per unit; this price includes a "Certificate of Analysis" containing specific recommendations for the material's usage as well as |, several statistical tests by which a laboratory may evaluate its results. All three materials are homogeneous and are in excess of jj 99.999 percent pure. The cadmium and silver are in the form of rods 0.25 in. in diameter and 2.5 in. long, while the gold is in the | form of wire 0.055 in. in diameter and 6 in long.

[3] These A//sub298 are in good agreement with the respective values 26770 and 68010 cal/mol, and 26720 and 67900 cal/mol quoted [ by: Wagman, D. D., Evans, W. H., Parker, V. P., Halow, I., Bailey, S. M., and Schumn, R. H., Selected Values of Chemical

| Thermodynamic Properties, Nat. Bur. Stand.(U.S.), Tech. Notes 270-3 (Cd-1968) and 270-4 (Ag-1969); and by Hultgren, R., ! Orr, R. L., and Kelley, K. K., loose-leaf supplement to Selected Values of Thermodynamic Properties of Metals and Alloys, University of California and Lawrence Radiation Laboratory, Berkeley, California (Cd reviewed Sept. 1966; Ag reviewed April

] 1968).

' [4] 1 calorie = 4.1840 Joules i 1 atmosphere = 101,325 newtons • meters"^.

Condensed phase ^ Gas phase'' ^298 G° -^298

Temperature T T

K, (IPTS-68) calmol"'-deg"' (J-mol-'-deg-i)[4] calmol"'-deg"' (J-mol->-deg-i)[4] CADMIUM

298.15 12.38 (51.80) 40.065 (167.632) 400 12.63 (52.84) 40.260 (168.448) 500 13.10 (54.81) 40.628 (169.988) 594 (M.P.) 13.61 (56.94) 41.011 (171.590) 600 13.67 (57.20) 41.040 (171.711) 700 14.58 (61.00) 41.453 (173.439) SILVER

298.15 10.169 (42.547) 41.320 (172.883) 600 11.378 (47.606) 42.295 (176.962) 700 11.899 (49.785) 42.708 (178.690) 800 12.408 (51.915) 43.107 (180.360) 900 12.898 (53.965) 43.487 (181.950) 1000 13.366 (55.923) 43.845 (183.447) 1100 13.815 (57.802) 44.184 (184.866) 1200 14.244 (59.597) 44.504 (186.205) 1235 (M.P.) 14.390 (60.208) 44.609 (186.644) 1300 14.767 (61.785) 44.807 (187.472) 1400 15.312 (64.065) 45.094 (188.673) 1500 15.822 (66.199) 45.366 (189.811) 1600 16.303 (68.212) 45.625 (190.895) 1700 16.755 (70.103) 45.871 (191.924)

''Converted to IPTS-68 using data of Hultgren, R., Orr, R. L., and Kelley, K. K., loose-leaf supplement to Selected Values of Thermodynamic Properties of Metals and Alloys (Cd-Sept. 1966; Ag-April 1968), and using data of Furukawa,

G. T., Saba, W. G., and ReiUy, M. L., NSRDS-NBS 18 (Ag-April 1968). The data were converted to IPTS-68 using equations

given by Douglas, T. B., J. Res. NBS, 73A, 451-69 (1969).

" From data of Hultgren, ibid.

[6] The International Practical Temperature Scale of 1968, Metrologia 5, 35-49 (1969). [7] Nesmeyanov, A. N., Khandomirova, N. A., Vilenskii, V. D., Birin, E. A., and Borisov, E. A., Rus. J. Phys. Chem. (Eng.), 34, 681-4

(1960). [8] Horton, W. S., J. Res. Nat. Bur. Stand. (U.S.), 70A (Phys. and Chem.), No. 6, 533-539 (Nov.-Dec. 1966).

[9] Cubicciotti, D., J. Phys. Chem. 70, 2410-3 (1966). [10] 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, 275 pages (Jan. 1968). [11] A preliminary examination of the cadmium data, as well as an examination of the reports from the laboratories have indicated the run 5, 6, and 7 second law results and the run 3, 4, 5, and 7 third law results from laboratory 2 should not be pooled with results from the other laboratories. The results from laboratory 2, however, are particularly valuable in supplying information regarding

usable limits for orifice areas (a < 1 X 10"^ cm-)

.

A preliminary examination of the silver data, as well as an examination of the uncertainties of the data, indicated that the second law results from laboratory 3 and the second and third law results from laboratories 8 and 9 should not be pooled with

the results from the other laboratories. A further discussion of results from the above laboratories is given in section 7.1. 12
I [12] The results from six cooperating laboratories with 21 curves and over 200 temperature-pressure points were used to determine

I these weighted averages. The weighting procedure used, is given in section 7.2. [13] Davies, O. L., Statistical Methods in Research and Production, pp. 134-6 (Hafner Publishing Company, New York, 1961). [14] The results from seven cooperating laboratories with 23 curves and over 250 temperature-pressure points were used to determine

these weighted averages.

[15] Ackerman, M., Stafford, F. E., and Drowart, J., J. Chem. Phys., 33, 1784-9 (1960). [16] Drowart, J., and Honig, R. E., J. Phys. Chem., 61, 980-5 (1957). [17] Schissel, P., J. Chem. Phys., 26, 1276-80 (1957).

I [18] Gubareff, G. G., Janssen, J. E., and Torborg, R. H., Thermal Radiation Properties Survey, second edition, pp. 153-61, (Minneapolisj Honeywell Regulator Company, Minneapolis, Minn., 1960).

j [19] A special pooling procedure for standard deviations was used throughout this study. An example of the pooling procedure is as

follows:

pooled Sfn=- IP:

where the sum is over the i curves and

a, =2.,. + ^2 + 31-

and i'i = 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.

;20] Mandel, J., and Paule, R. C, Anal. Chem., 42, 1194-7 (1970). 21] Mandel, J., The Statistical Analysis of Experimental Data, pp. 132-5 (Interscience Publishers, New York, 1964).

13
7. Appendix

This appendix gives additional details of the statis- tical analyses which were necessary for the evaluation of the cadmium and silver vapor pressure data. The two-part statistical analysis has been made in terms of two OMNITAB programs. An outUne of the two parts is as follows: 7.1

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 deviation of the fit (Snt) was obtained

using the OMNITAB "FIT" command. For the

least-squares fitting of the data points to a

straight line curve, r 2 iYi-Y,

N-2 (3) The standard deviations of the coefficients (Sa and Sb) can be expressed in terms of the stand-=- ard deviation of the fit (Sfit):

where

SA=fi-Snt

f2

1

(4)

(5)

(6)

(7)

The /i and f-z values provide a very convenient

quantitative description of the number and

spread of the X(= IjT) values. The /i and fo are independent of the measured F, values.

B. The third law equation was also treated by

least-squares. Here one obtains a single coefficient, C (the average of the individual ^^sub298 values), the standard deviation of the

coefficient (Sc), and the standard deviation of the individual A//sub298 values (S^jj). For the

third law case, it can be shown that:

where

1 V# of points

(8)

(9)

It can be noted that eq (8) has the same form

as eqs (4) and (5). The same general computational treatment was therefore used for both

the second and third law results. C. The cadmium and silver results for the second and third law least-square fits are given in tables 5 through 8. The authors next examined all results in terms

of criteria A through F, listed below.

A. The chi-square test. Comparisons were made

of Sfit values from all curves.

(1) A tentative pooled Sfit was first calculated from the individual Sfit values from all curves

[19].

(2) Each ijidividual Sfit was compared to the pooled Sfit using the approximate test:

where X' 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 out- side 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 for results from the

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

F. The laboratory's experimental procedures.

. Rejection of any laboratory's results was based

on consideration of criteria A through F. For cadmium, the run 5, 6, and 7 second law resuhs and the run 3, 4, 5, and 7 third law results of laboratory 2 were not used in further calculations of averages and pooled standard deviations. The

second law results for runs 5, 6, and 7 were not used due to the runs' small temperature intervals, and to minor difficulties in points B through

F. Laboratory 2 has made a total of seven runs

investigating the effect of orifice area (1.69 X 10"^

to 1.24x10"' cm-) and has contributed to our knowledge regarding the usable upper hmits for

orifice areas for cadmium. A consequence of this knowledge is that the cadmium third law results

for the large orifice runs could not be used in our pooled results. For silver, the results from laboratory 8 were

not used because of difficulties in criteria A, B, C, D, and F. The results from laboratory 9 were

not used because of problems in criteria A through

D. Some laboratories did not randomly vary their temperatures during the measurement of the temperature-pressure curves. The Sfit values for these laboratories tended to be abnormally small. For this reason, the Sfit values of laboratories 3 (run 1) and 5 for cadmium, and of laboratories 6 14
and 7 for silver, were not used in the pooled SfnAll other values from these laboratories were

used in the further calculations. 7.2

1. In the second OMNITAB program, a comparison was made of runs within each laboratory. This comparison was made in terms of both the inter- cept 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 the F test, the variance of the A values between curves within each laboratory was compared to the estjmate of

this variance derived from the pooled 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 [13] for each of the three parameters, A, B, and third law heat, using the estimated values of these parameters accepted after appHcation of the first OMNITAB

program. The ultimate purpose of the analysis was to estimate the components of the within- and the between-laboratory variance. An analysis

of variance indicated the between-laboratory components of variance to be significantly greater than zero. The calculation of components of vari- ance for this situation, where the number of curves is not the same for all laboratories, has been discussed elsewhere by the authors [20].

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 [20] that laboratory i with

n, curves has the weighting factor:

l + riip The value of p can be estimated from the results of the analysis of variance [20]. The weighted

average A will be:A^-

i 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: component of within-lab. variance [21] V{A) =

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 cadmium and silver p values for A,

B, and the third law heat which we obtained from

the analysis of variance are 0.568, 0.780, and

4.575, and 3.137, 1.590, and 9.546. 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.

15
7.3. Experimental Data

j

I Table 3. Cadmium — List of Experimental Temperature-Pressure Data \

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

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

525.0 LOlO X 10 -5 556.0 3.920 X 10-5 550.0 2.740 X 10-5 564.0 5.690 X 10-5 567.0 5.160 X 10-5 SOLO 2.830 X 10 6 475.0 5.780 X 10-" 475.0 5.780 X 10-' 487.0 1.060 X 10-« 493.0 1.220 X io-« 475.0 6.370 X 10 -7 418.0 1.400 X io-« 416.0 1.120 X 10-8 422.0 1.830 X 10-« 422.0 1.380 X 10-8 452.0 L590 X 10 -7 503.0 3.100 X io-« 500.0 2.700 X 10-" 508.0 4.630 X 10-« 511.0 .570 X io-« 413.0 8.640 X 10 -9 451.0 1.530 X 10-^ 457.0 1.840 X 10-' 457.0 2.160 X 10-' 461.0 2.030 X 10-' 55L0 3.120 X 10 -5 528.0 1.060 X 10-5 516.0 5.780 X 10-s 535.0 1.450 X 10-5 535.0 1.330 X 10-5 503.0 2.980 X 10 438.0 5.510 X 10-8 438.0 6.250 X 10-8 444.0 7.220 X 10-8 445.0 8.680 X 10-8 488.0 1.390 X 10 6 580.0 1.190 X 10-" 580.0 9.980 X 10-5 584.0 1.140 X 10-" 590.0 1.240 X 10-" 569.0 8.970 X 10 -5 432.0 4.890 X 10

Lab 1, Run 6 Lab 2, Run 1 Lab 2. Run 2 Lab 2, Run 3 Lab 2. Run 4

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

569.0 5.650 X 10-5 569.3 6.461 X 10-5 644.3 1.199 X 10-3 529.5 4.947 X 10-8 493.3 1.513 X 10-8 493.0 1.310 X io-« 535.3 1.658 X 10-5 614.1 4.763 X 10" 493.8 1.139 X 10-8 522.8 6.421 X 10-8 425.0 1.720 X 10-8 506.0 4.211 X io-« 584.6 1.737 X 10-" 464.9 2.395 X 10-' 551.1 2.237 X 10-5 510.0 4.390 X io-« 477.8 9.237 X 10-' 560.4 6.145 X 10-5 437.2 4.408 X 10-8 578.6 6.803 X 10-5 456.0 1.780 X 10-' 451.1 1.645 X 10-' 530.1 1.697 X 10-5 410.1 5.868 X io-» 507.2 3.447 X 10-8 539.0 1.670 X 10-5 464.5 3.882 X 10-' 504.1 4.934 X lo-** 398.0 1.658 X 10-" 537.1 1.355 X 10-5 440.0 7.150 X 10-8 423.1 2.500 X 10-8 450.9 2.184 X 10-' 426.1 1.129 X 10-8 566.0 4.224 X 10-5 589.0 1.280 X 10-" 435.3 5.355 X 10-8 477.8 1.099 X 10-8 454.5 9.961 X 10-8 592.8 1.092 X 10-" 490.0 1.750 X 10-8 491.9 2.355 X 10-" 482.5 6.092 X 10' 606.1 1.553 X 10-" 519.2 7.605 X 10-*^ 518.1 9.132 X 10-8 509.7 2.434 X 10-8 614.1 1.632 X 10-" 549.4 3.079 X 10-5 548.5 3.921 X 10-5 538.2 9.487 X 10-8 629.7 2.947 X 10-" 567.4 6.474 X 10-5 576.4 1.243 X 10-" 546.3 1.312 X 10-5 643.7 3.947 X 10-" 580.5 1.070 X 10-" 604.7 3.513 X 10-" 554.2 1.855 X 10-5 593.6 1.789 X 10" 628.4 7.500 X 10-" 561.9 2.526 X 10-5 605.4 2.039 X 10" 656.3 1.737 X 10-3 570.2 3.395 X 10-5 616.9 2.895 X 10-" 674.9 3.118 X 10-3 576.9 4.197 X 10-5 627.7 3.671 X 10-" 683.6 3.868 X 10-3 639.4 4.724 X 10-" 689.5 4.342 X 10-3

*Vapor pressure data above the melting point showed considerable deviations and were not used.

16
Table 3. Cadmium — List of Experimental Temperature-Pressure Daia — Continued

Lab 2, Rur 5 Lab 2, Run 6* Lab 2. Run 7 Lab 3, Run 1 Lab 3. Run 2

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

574.1 6.368 X 10-5 602.6 2.039 X lO"-" 531.3 6.276 X 10 6 559.9 2.712 X 10-5 441.7 3.948 X 10-8 559.9 3.868 X 10-5 593.2 1.579 X 10-" 542.5 1.316 X 10 5 552.5 1.875 X 10-5 449.9 7.347 X 10-8

553.1 2.895 X 10-5 581.9 1.036 X 10-" 537.4 9.908 X 10 6 551.0 1.852 X 10-5 469.8 2.584 X 10-' 541.4 2.053 X 10-5 569.0 7.355 X 10-5 524.0 5.816 X 10 6 536.9 1.008 X 10-5 491.4 9.404 X 10-' 532.3 1.213 X 10-5 557.4 3.724 X 10-5 508.6 2.829 X 10 6 520.3 4.320 X 10-" 482.1 9.847 X 10-' 542.8 2.105 X 10-5 550.7 3.447 X 10-5 495.8 2.224 X 10- 6 505.1 2.014 X 10-6 511.0 3.001 X 10-6 548.4 2.961 X 10-5 5.52.1 4.184 X 10-5 490.5 1.314 X 10- 6 504.7 1.962 X 10-6 511.3 3.076 X 10-6 565.4 4.618 X 10-5 562.4 5.632 X 10-5 495.0 1.671 X 10- 6 493.0 1.113 X 10-6 532.3 9.836 X 10-6 577.9 7.605 X 10-5 567.5 6.908 X 10-5 502.8 2.118 X 10- 6 484.5 6.066 X 10-' 546.1 1.893 X 10-5 586.6 1.072 X 10-^ 578.3 9.711 X 10-5 518.8 4.658 X 10- 6 473.4 3.463 X 10"' 550.0 2.143 X 10-5 582.3 9.487 X 10-5 593.2 1.724 X 10 526.8 7.487 X 10- 6 461.3 1.611 X 10-' 429.6 2.289 X 10-8 538.0 1.579 X 10-5 603.3 2.158 X IQ-" 523.4 5.868 X 10- 6 451.8 9.498 X IQ-S 429.0 2.175 X 10-8 612.1 2.829 X 10-" 538.3 1.270 X 10- 5 441.9 5.096 X IQ-S 416.3 8.229 X 10-9 544.2 1.632 X 10- 5 441.6 4.802 X 10-8 400.4 2.409 X 10-9 551.3 2.026 X 10- 5 430.1 2.310 X 10-8 389.0 7.021 X 10-10 419.9 1.563 X IQ-S 389.4 7.697 X 10-10 417.1 1.010 X 10-8 382.9 6.033 X 10-10 416.5 8.234 X 10-" 403.7 3.724 X 10-s 403.1 3.188 X 10-9 393.0 1.489 X 10-s 371.4 1.713 X 10-0 361.8 1.037 X io-» 362.2 1.181 X io-» 352.2 3.249 X 10-'

*Vapor pressure data above the melting point showed considerable deviations and were not used.

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

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

581.0 9.165 X 10-5 584.0 9.429 X 10-5 539.5 1.577 X 10 537.5 1.449 X 10-5 528.8 9.869 X 10 564.0 4.805 X 10-5 569.0 5.575 X 10-5 535.6 1.320 X 10 -5 533.2 1.174 X 10-5 524.2 7.884 X 10- 6 545.0 2.217 X 10-5 555.0 3.024 X 10-5 532.9 1.161 X 10 -5 529.9 1.005 X 10-5 520.7 6.613 X 10- 6 578.0 8.526 X 10-5 541.0 1.685 X 10-5 530.3 1.025 X 10 5 522.2 6.965 X 10-6 517.0 5.473 X 10- 6 555.0 3.369 X 10-5 527.0 8.723 X 10-6 527.2 8.865 X 10 517.7 5.597 X 10-6 513.2 4.511 X 10- 6 542.0 1.841 X 10-5 513.0 4.594 X 10-6 521.1 6.538 X 10 6 512.0 4.240 X 10-6 508.9 3.649 X 10- 528.0 9.574 X 10-6 578.0 8.561 X 10-5 514.6 4.918 X 10 502.9 2.666 X 10 -6 515.0 5.073 X 10-6 564.0 4.741 X 10-5 500.3 2.323 X 10- 6 497.8 2.019 X 10

501.0 2.421 X 10-6 549.0 2.538 X 10-5 487.0 1.188 X 10-6 536.0 1.393 X 10-5 500.0 2.311 X 10-6 537.0 1.428 X 10-5 514.0 4.643 X 10-6 523.0 6.984 X 10-6 529.0 9.791 X 10-6 509.0 3.496 X 10-6 545.0 2.122 X 10-5 494.0 1.684 X 10-6 557.0 3.650 X 10-5 513.0 4.518 X 10-6 571.0 6.335 X 10-5 528.0 9.397 X 10-6 559.0 3.771 X 10-5 543.0 1.943 X 10-5 572.0 6.812 X 10-5

17
Table 3. Cadmium — List of Experimental Temperature-Pressure Z)am — Continued

Lab 5, Run 4 Lab 6, Runs 1. 2, and 3t

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

52L1

516.1 511.6

506.9

503.1 495.2

6.777 X 10-f 5.307 X 10-'^ 4.199 X 10-« 3.319 X lO-'i 2.705 X 10-« 1.780 X lO-*^

tAutomatic data recording was used by this laboratory to obtain hundreds of temperature-pressure data points. The resultant data were

treated by the cooperating laboratory and only the third law AHjuwgs were practical to submit. The third law AHsub298 are Usted in table 6.

18
Table 4. Silver— List of Experimental Temperature-Pressure Data

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

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

1454.6 1.870 X 1336.3 2.630 X 10 1340.3 2.460 X 10 -5 1313.3 1.530 X 10~=* 1248.8 7.704 X io-« 1375.4 5.450 X 10-5 1258.1 5.320 X 10 -6 1496.7 3.330 X 10 4 1424.5 1.080 X 10-" 1228.0 5.012 X io-« 1393.5 7.060 X 1431.6 1.350 X 10 -4 1257.1 5.390 X 10 1518.8 4.230 X lo--* 1210.2 3.370 X io-« 1499.7 3.780 X 10"** 1367.4 4.110 X 10 5 1312.3 1.630 X 10 -5 1367.4 4.250 X 10-= 1232.2 5.166 X 10-6

1288.2 9 190 X 10-f> 1490.7 3 030 X 10 _^ 1370.4 4.300 X 10 .5 1251.1 4.170 X 10-" 1192.6 2.151 X 10-6

1344.3 3 180 X 20-5 1564.9 9 1 10 X 10 1434.6 1.240 X 10 -4 1467.7 2.050 X 10-" 1166.8 1.191 X 10-6 1584.9 1 090 X 10~^ 1232.1 3 740 X 10 -6 1404.5 8.430 X 10 .5 1344.3 2.850 X 10-5 1146.3 6.837 X 10-' 1423.5 1 160 X JQ—

*

1302.2 1 360 X 10 1469.7 2.110 X 10 -4 1500.7 3.280 X lo-* 1130.4 4.257 X lO-'' 1269.2 X 10~^ 1394.5 «U.OUU Ann A.Y 1546.8 6.380 X 10 -4 1401.5 7.700 X 10-5 1112.2 2.534 X 10-' 1323.3 1 890 X 10~^ 1.521.8 5 050 X 10 1242.1 4.370 X 10 -6 1439.6 1.280 X 10-1 1092.4 1.469 X IQ-' 1531.8 4.940 X 10-* 1283.2 9.720 X 10 1288.2 1.080 X 10 -5 1284.2 9.380 X 10-'5 1066.6 7.173 X 10-8

1242.1 3.660 X io-« 1044.6 3.670 X 10-8 1021.0 1.745 X 10-8 993.6 6.117 X 10-9 971.3 2.690 X lO-!* 947.9 1.200 X 10-^ 909.2 2.878 X 10-10 885.8 1.080 X 10-10 854.0 1.825 X 10-"

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

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

1072.6 1..369 X 10-' 1467.7 2.329 X 10-" 1515.8 4.816 X 10-" 1516.8 3.855 X 10-" 1336.3 2.130 X 10-5 1194.6 2.988 X 10-6 1431.6 1.474 X 10-" 1479.7 2.776 X 10-" 1462.6 1.855 X 10-" 1383.4 4.790 X 10-5

1193.1 3.015 X 10-6 1503.7 4.132 X 10-" 1451.6 1.895 X 10-" 1479.7 2.632 X 10-" 1376.4 4.260 X 10-5 1284.8 1.571 X lO-'-i 1463.6 2.408 X 10-" 1428.6 1.224 X 10-" 1430.6 1.118 X 10-" 1384.4 4.930 X 10-5 1258.0 8.829 X 10-6 1484.7 3.171 X 10-" 1400.5 6.842 X 10-5 1386.4 4.868 X 10-5 1424.5 9.390 X 10-5

1237.9 5.687 X 10-6 1433.6 1.329 X 10-" 1371.4 4.342 X 10-5 1399.5 6.316 X 10-5 1460.6 1.691 X 10-" 1207.4 2.619 X 10-6 1525.8 6.000 X 10-" 1530.8 5.816 X 10-" 1440.6 1.461 X 10-" 1492.7 2.788 X 10-" 1216.4 3.415 X 10-6 1400.5 8.816 X 10-5 1496.7 3.395 X 10-" 1495.7 3.132 X 10-" 1545.8 5.915 X 10-" 1225.7 3.910 X 10-6 1452.6 2.132 X 10-" 1472.7 2.421 X 10-" 1419.5 9.079 X 10-5 1584.9 1.024 X 10-3 1185.8 1.749 X 10-6 1373.4 4.474 X 10-5 1453.6 1.882 X 10-" 1518.8 4.204 X 10-" 1158.3 8.958 X 10-' 1411.5 9.474 X 10-5 1483.7 2.554 X 10-" 1139.7 5.382 X 10-' 1385.4 6.579 X 10-5 1425.5 1.054 X 10"

1118.4 2.941 X 10-' 1363.4 3.370 X 10-5 1098.6 1.722 X 10-' 1077.6 9.573 X 10-8 1053.8 4.896 X 10-8 1052.5 4.433 X 10-8 1029.7 2.066 X 10-8 1003.4 9.351 X 10-9 981.6 4..561 X lO-i* 959.3 1.786 X lO-s* 944.4 1.092 X lo-s 921.9 4.708 X 10-10 920.7 4.232 X 10-10 921.4 4.377 X 10-10 898.5 1.721 X 10-'" 877.5 7.171 X 10-"

856.2 3.346 X 10-"

19
Table 4. Silver— List of Experimental Temperature-Pressure Dam— Continued

Lab 4, Run 2 Lab 5, Run 1 Lab 5, Run 2 Lab 6. Run 1 Lab 6, Run 2

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

1334.3 1.970 X 10~5 1314.3 1.725 X 10-5 1432.6 1.151 X 10 "* 1387.5 6.056 X 10 5 1433.6 1.277 X 10-" 1371.4 4.060 X 10-^ 1328.3 2.039 X 10-5 1468.7 2.097 X 10 * 1381.4 5.447 X 10

I 1421.5 1.089 X 10-" 1348.4 2.610 X 10-5 1271.2 6.627 X 10-" 1440.6 1.378 X 10 '' 1362.4 3.983 X 10 1414.5 9.380 X 10-5 1385.4 5.050 X 10-5 1279.2 7.778 X 10-" 1286.2 9.961 X 10 1360.4 3.795 X 10 1407.5 8.456 X 10-5 1434.6 1.112 X 10-^ 1336.3 2.414 X 10-5 1309.3 1.438 X 10 1352.4 3.328 X 10 1399.5 7.784 X 10-5 1467.7 1.891 X 10"^ 1353.4 3.165 X 10-5 1328.3 2.071 X 10 1349.4 3.149 X 10 1384.4 5.485 X 10-5 1508.8 3.402 X 10-" 1328.3 2.027 X 10-5 1268.2 6.291 X 10 1344.3 2.899 X 10 1376.4 5.026 X 10-5 1553.9 6.176 X 10-* 1256.1 5.139 X lo-** 1399.5 6.606 X 10 1338.3 2.571 X 10 1362.4 4.057 X 10-5 1488.7 2.646 X io-« 1364.4 3.728 X 10-5 1380.4 4.998 X 10 1333.3 2.389 X 10 1352.4 3.305 X 10-5 1437.6 1.217 X 10-" 1376.4 4.684 X 10-5 1360.4 3.552 X 10 1327.3 2.129 X 10 1339.3 2.625 X 10-5 1396.5 6.650 X 10-5 1393.5 6.332 X 10-5 1340.3 2.575 X 10 1322.3 1.924 X 10 1333.3 2.394 X 10-5 1315.3 1.450 X 10-5 1403.5 7.311 X 10-5 1320.3 1.833 X 10- 1313.3 1.645 X 10 1326.3 2.085 X 10-5 1413.5 8.630 X 10-5 1494.7 2.976 X 10 -4 1304.2 1.356 X 10 1321.3 1.902 X 10-5 1422.5 9.955 X 10-5 1462.6 1.888 X 10 1295.2 1.173 X 10 -5 1311.3 1.656 X 10-5 1429.6 1.137 X 10-" 1437.6 1.304 X 10 4 1281.2 8.794 X 10 -6 1289.2 1.026 X 10-5 1437.6 1.266 X 10-" 1407.5 8.059 X 10 5 1275.2 7.766 X 10 1283.2 9.124 X 10-s 1447.6 1.503 X 10-" 1389.5 6.127 X 10 5 1260.1 6.098 X 10 1278.2 8.302 X 10-" 5.256 X 10-" 3.981 X 10- 5 4.615 X 10 -6 1269.2 6.953 X 10-" 1438.6 1.323 X 10" 1421.5 1.003 X 10- 1243.1 3.910 X 10 6 1256.1 5.238 X 10-" 1518.8 4.260 X 10-" 1438.6 1.339 X 10- 1229.1 3.007 X 10 1247.1 4.458 X 10-" 1480.7 2.547 X 10-" 1224.0

1221.0

2.813

2.478 X

X

10

10 1237.1 3.700 X 10-"

Lab 7, Run 1 Lab 7, Run 2 Lab 7. Run 3 Lab 7, Run 4 Lab 7. Run 5

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

1208.1 2.395 X 10 " 1209.1 2.446 X 10-" 1158.2 6.935 X 10-' 1153.7 6.331 X 10-' 1157.8 6.944 X 10-' 1203.3 2.144 X 10-" 1201.9 2.067 X 10-" 1152.0 5.901 X 10-' 1147.7 5.378 X 10-' 1148.6 5.494 X 10-' 1191.3 1.615 X 10-" 1195.1 1.769 X 10-" 1146.4 5.119 X 10-' 1142.5 4.692 X 10-' 1140.0 4.403 X 10-' 1184.1 1.364 X 10-" 1189.6 1.553 X 10-" 1139.5 4.290 X 10-' 1137.5 4.097 X 10-' 1177.5 1.164 X 10-" 1183.7 1.349 X 10 " 1130.9 3.419 X 10 ' 1126.8 3.189 X 10-' 1165.9 8.768 X 10-' 1176.0 1.119 X 10-" 1122.7 2.762 X 10-' 1118.6 2.536 X 10-' 1162.3 8.000 X 10-' 1171.9 1.012 X 10 " 1112.9 2.128 X 10-' 1110.9 2.025 X 10-' 1158.3 7.258 X 10-' 1159.3 7.445 X 10-' 1102.1 1.574 X 10-' 1104.1 1.665 X 10 ' 11.50.5 5.947 X 10-' 1151.0 6.028 X 10-' 1089.5 1.105 X 10-' 1096.3 1.356 X 10-' 1142.0 4.815 X 10-' 1140.9 4.674 X 10-' 1132.2 3.729 X 10 ' 1126.1 3.204 X 10-'

20
Table 4. Silver— List of Experimental Temperature-Pressure Daia — Continued

Lab 7, Run 6 Lab 7, Run 7 Lab 7, Run 8 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

1154.1 6.263 X 10-' M57.8 6.849 X 10-' 1154.1 6.224 X 10-' 1143.8 4.100 X 10-' 1206.0 1.990 X 10-" 1144.0 4.806 X 10-' 1148.6 5.347 X 10-' 1144.0 4.771 X 10-' 1180.9 1.090 X 10-« 1215.0 3.130 X 10-« 1132.9 3.626 X 10 ' 1140.0 4.345 X 10-' 1132.9 3.604 X 10-' 1189.0 1.180 X 10-« 1244.1 5.060 X lO-s 1209.0 1.970 X 10"^ 1279.2 7.960 X 10-" 1222.0 2.650 X 10-« 1291.2 8.530 X 10-«

1227.1 2.730 X lO-'' 1318.3 1.009 X 10-5 1229.1 2.730 X lO-'' 1254.1 5.140 X 10-"

Lab 9, Run 1 Lab 9, Run 2

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

1254.1 1.173 X 10--^ 1284.2 6.189 X 10-" 1314.3 2.709 X 10-^ 1354.4 8.601 X 10-5 1374.4 8.330 X 10-= 1434.6 2.588 X 10-"

21
CHDIIIUn DRTR FROfl LHBORHTORY NO. 1 -2.0 SOLID LINE REPRESENTS

POOLED RESULTS FROM ACCEPTED LHBORflTORIES

LflB 1 RUN 1 + RUN 2

« RUN 3

Y RUN 4 o RUN 5

M RUN 6

700 K 600 K 500 K 400 K 9.2

1 4 15 16 17 1 8 19 20 21 22 23 24 25 26

1/T X 10" (DEC K-M

-2 0- CROniUM DHTH FROn LRBORFITORY NO- 2 \ ++

+ SOLID LINE REPRESENTS

-2 8- POOLED RESULTS FROM ACCEPTED LABORATORIES

-3 6-

LflB 2 RUN 1 -4 4

- + RUN 2

« RUN 3

Y RUN 4 -5 2- w o RUN 5

« RUN 6 -6 0- l^^j z RUN 7

-6 8-

-7 6-

® \.

-8 4- 700 K 600 K 500 K _Q o IS 16 17 18 19 20 21 1/T X 10* (DEG K-' 25 26

22
23
CHDMIUM DHTR FROM LRBORPTORY NO- 5 -2. On > ' ' ' ' ' ' ' ^

1/T X 10* (DEG K-n

24
SILVER DRTH FROM LflBORfiTORY NO- 1 -2.9-|_ . . . . -. 1 . . . , . ,

SILVER DflTB FROn LfiBORHTORT NO. 2

7.0 7.3 7.6 7.9 8.2 8.S 8.8 9.1 9.4 9.7 10 .0 10 -3 10.6 10.9 1 1 .2 1 1. S 11.8 12.1 12.4 12.'' 1/T X 10< IDEG K-' ) Figure 4.

25
SILVER OBTB FROn LHBORflTORT NO. 3

SILVER DRTR FROM LRBORflTORT NO- 4 -2.9-r ' ' ' ' ' ' ' ' ' ' ' '

6.3 6.4 6.5 6.6 6.7 6.8 6.9 •'.0 7.1 7 .2 7 .3 7.4 7 .S 7.6 7 .7 7 .8 7.9 8.0 8 . 1 8.2

1/T X 10' (DEG K-'l

26
SILVER DHTR FROn LHBORBTORT NO. 5 -2.9

SILVER ORTH FROM LHBORHTORT NO. 6 -2.9t- ' ' ' ' ' ' ' ' ' '

Figure 6.

27
SILVER DflTB FROM LHBORRTORY NO. 7

1/T X 10* (DEC I

SILVER DflTB FROn LflBORflTORY NO- 8

Figure 7.

SILVER DflTH FROM LRBORRTORT NO. 9

6 .3 6 .4 6 .S 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7 .5 7 .6 7 .7 7 .8 7 .9 8 .0 8 . 1 8 .2 1/T X 10' IDEG K-'l

I Figure 8. 28

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