The thermodynamics and vaporization of thorium, hafnium, and zirconium

J. Chem. Thermodynamics 1972, 4, 521-532

The thermodynamics and vaporization thorium, hafnium, and zirconium” R. J. ACKERMANN

of

and E. G. RAUH

Chemistry Division, Argonne National Argonne, Illinois 60439, U.S.A.

Laboratory,

(Received 5 October 1971)

Thevapor pressures of liquidthorium,solidandliquid hafnium,andliquidzirconiumhave beendeterminedby a combinationof mass-effusion and mass-spectrometric techniques. Singlecrystaltungstencupswereusedascontainers.The substantial solubilityof tungsten in both liquid hafniumand zirconiummarkedlyextendsthe liquid rangeasa result of eutecticbehavior.Themeasured partialpressures correctedfor the respective solubilities via Raoult’slawthereforeyield the vapor pressures of the puremetalsoverrangesof temperature in whichthe liquidsare in part supercooled. The resultsderivedfor the puremetals are givenby the linearequationsin termsof the enthalpies and entropiesof vaporization: -(RT/ca&,, mol-l) In (p”(Th, l)/atm}= (1362OOflOOO)-(27.57&0.45)T/K, (2020to 2500K) ; -(RT/c& mol-I) In {p”(Hf, l)/atm} = (139300f llOO)-(28.85*0.39)T/K, (T> 2464 K); -(RT/cal,, mol-I) In {p”(Hf, s)/atm}= (145500&700)-(31.37+0.33)T/K, (1940to 2464K); -(RT/cal,, mol-I) In {p”(Zr, l)/atm} = (137OOO~llOO)-(29.93&0.37)T/K, (2134to 2550K). The measuredvapor pressures and enthalpiesare consistentwith the thermodynamic propertiesof the vaporandcondensed phases andyield the followingaveragevaluesfor the enthalpiesof sublimationat 298.15K: AH”(‘Ih) = (142.8&1.1)kcale,mol-I, AjY”(Hf) = (148.4&1.2)kcal,, mol-‘, andAH”(Zr) = (143.4%1.2)kc&, mol-‘.

1. Introduction Thorium is generally considered to be the first member of the 5f “actinide series” but its chemical behavior at high temperatures appears to parallel those of the Group IV transition metals, hafnium and zirconium, since all three atoms possess the same nd*(n+ 1)s’ ground state electronic configuration in the gas and all exhibit nearly unique stability of the +4 valence state in compounds. The vapor pressure, or more precisely the enthalpy of evaporation, of a metal is a direct measure of the metal-metal bond energy if the bonding electronic conhgurations are identical in the gas and metal phases. The enthalpies would make possible a quantitative examination of the problem. Furthermore, since reliable thermodynamic information is required for the study of these metal + oxygen systems now being undertaken by the authors, a critical examination of the published vapor pressures for these elements was made. LIWork performedunderthe auspices of the U.S. Atomic EnergyCommission.

522

R. J. ACKERMANN

AND

E. G. RAUH

The vapor pressures of solid thorium,“’ solid’2-4’ and liquid”’ hafnium, and solid@* ‘) and liquid’*’ zirconium have been measured by the Langmuir method. The results of Fedorov and Smirnov (‘) lead to a negative entropy of evaporation and have been discounted. Measurements of the vapor pressure of solid and liquid zirconium were obtained in a mass-spectrometric study of Zr + ZrB, + C.(‘) All these measurements show large random errors and, except for the results of Kibler, Lyon, Linevsky, and DeSantisc4’ and Koch and Anable, (*) large systematic errors as evidenced by the lack of consistency with the thermodynamic functions derived from heat capacities. Only Panish and Reifc3’ and Trulson and Goldstein(g’ included mass-spectrometric identification of the vapor species. Because of the discrepancies the vapor pressures of liquid thorium, solid and liquid hafnium, and liquid zirconium were remeasured with particular attention to the composition of the condensed and vapor phases.

2. Experimental methods and results A combination of mass effusion and mass-spectrometric methods was used. The partial pressures of thorium, hafnium, and zirconium over the liquid metals saturated with tungsten were determined at selected temperatures by the effusion method employing the apparatus and experimental techniques described previously.“” 11) In this method a known fraction of the effusate is collected on a target and the amount of condensate determined by activation or chemical analysis. The relation between the pressure p and the rate of collection is given by p = (m/at)(2xRT/M)“2((dZ

+ r2)/r2},

(1)

where m is the mass of the effusate collected on the target in time t, a is the area of the orifice, d is the orifice-to-collimator distance, and r is the radius of the collimator. Temperatures were measured by means of a disappearing-filament optical pyrometer and corrections were made for the transmissivity of the interposed window and prism. The pyrometer had been calibrated at the melting temperature of copper and the calibration extended to higher temperatures by means of rotating sectors.(12’ All temperatures were based on IPTS-68. (13) The targets were thin disks of Corning #7940 industrial grade silica which contains less than a few parts per million total impurities. The thorium and zirconium samples were taken from crystal bar material of high purity (99.95 mass per cent). The crystal bar hafnium contained about 2 mass per cent of zirconium, an impurity level considered negligible in view of the uncertainty in the measurement of a vapor pressure. Samples having masses of about 200 mg were contained in single crystal tungsten cups within tungsten effusion cells. Prior to the measurements the samples and cups were placed in the mass spectrometer source and heated until the monoxide ion currents had decreased to less than 2 per cent of the metal ion intensity; they were then transferred to the effusion apparatus and given a similar treatment. The masses of the thorium sublimates (about 1 ug) were determined by activation analysis, counting the gamma radiation of energy 313 keV from 233Pa resulting from neutron absorption by 323Th.t. The application 7 Throughout

this paper eV& 96487 J mol-‘;

calth =4.184 J; atm = 101.325 kPa.

VAPOR PRESSURES OF Th, Hf, AND Zr

523

of this method has been described previously. (rl) The hafnium targets (0.1 to 1 ug) were also assayed by activation analysis using the gamma radiation of energy 480 keV from ‘arHf. The zirconium sublimates (10 ug) were not amenable to activation analysis, and so were determined by calorimetric analysis via the alizarin-red-S complex.(r4’ The temperature dependences of the partial pressures were determined massspectrometrically. The Bendix model 12-101 time-of-flight mass spectrometer and the experimental techniques have been described elsewhere.(’ 5, An ionizing electron energy of 12 eV was used throughout to reduce the background of ions from the residual gases as much as possible. For each measured ion current Ii, the quantity log (IiT) was calculated for each value of T and each set of results was treated by the method of least squares. Samples were contained in single crystal tungsten cups within tungsten effusion cells and measurements were made after the samples had been deoxygenated in the manner already described. The melting temperatures of thorium, hafnium, and zirconium and the eutectic temperatures of the Th + W, Hf + W, and Zr + W alloys have been measured in this laboratory by a technique described in another publication.(‘6’ The results pertinent to this study are given in table 1. Also reported is a method for determining the solubility of tungsten in liquid metals. The measured solubilities of tungsten in hafnium and zirconium are given in table 2. The solubility of tungsten in thorium is relatively small and was found to vary nearly linearly from 1.5 moles per cent at 2000 K to 3 moIes per cent at 2500 K. TABLE

1. Melting temperatures 7’, of thorium, hafnium, and zirconium and the eutectic temperatures T, of the tungsten alloys Th+ W, Hf+ W, and Zr+ W (lB)

Th Hf Zr TABLE

TmIK

Z/K

2020 2464 2134

1968 2222 2008

2. Solubility of tungsten in hafnium and zirconium expressed as the mole fractions x(Hf) and x(Zr) of hafnium and zirconium (16) A.

B.

Solubility of tungsten in hafnium T/K x(Hf) 2229 0.824 2292 0.801 2407 0.757 2460 0.734 Solubility of tungsten in zirconium .u(Zr) T/K 2008 0.914 2008 0.900 2208 0.857 2312 0.820 2408 0.780

R. J. ACKERMANN

524

AND

E. G. RAUH

THE VAPOR PRESSURE OF THORIUM Initially the ThO+ ion intensity was about five times that of the Th+ but after 6 h at 2400 K had decreased by a factor of 250. The Th+ ion intensity was then measured at 16 temperatures in the range 2010 to 2460 K, and the results were fitted by the method of least squares to the linear equation: log,, {Z(Th+)T/K) = -(29770+22O)K/T+(16.190~0.098). (Th+W)(l): (2) The uncertainties here and elsewhere are standard deviations. An examination of the residuals indicated no curvature within the precision of the measurements. The mass effusion results are given in section A of table 3 and are shown in Figure 1. TABLB

3. Mass effusion results of the measurement of the partial pressures of thorium, hafnium, and zirconium over the liquid metals saturated with tungsten (atm = 101.325 kPa) A.

Partial pressure p(Th) of thorium over thorium saturated with tungsten T/K lokh3 MWaW 2494 -5.869 -5.866 2494 -5.846 2494 -5.846 2494 -6.529 2380 2463 -6.126 2464 -6.177

B.

Partial pressure p(Hf) of hafnium over hafnium saturated with tungsten log,, {p(Hf)/atm> T/K -6.043 2491 -6.068 2490 2489 -6.072

C.

Partial pressure p(Zr) of zirconium over zirconium T/K loih MZrYatml 2483 -5.610 -5.675 2480 -5.705 2418

saturated with tungsten

Equation (2) was normalized to each of these pressures and the constant terms were averaged. Since the solubility of tungsten in thorium is less than 3 moles per cent and almost independent of temperature, and hence considered negligible, no solubility corrections were made and the vapor pressure of liquid thorium is given by log,, (p”(Th, l)jatm} = - (29770 Ifr 220)K/T + (6.024+ 0.098), (T > 2020 K). (3) From the slope of equation (3), the enthalpy of fusion as reported by Levinson(“) (3.3 kcal,, mol-‘), and logp”(Th, 1) at the melting temperature, the vapor pressure of solid thorium is given by the equation: log,, (p”(Th, s)/atm) = -(30490+220)K/T+(6.381+0.098), (T < 2020 K). (4) Equations (3) and (4) are plotted in Figure 1, and for comparison Darnell et al.(‘) are included.

the results of

VAPOR PRESSURES OF Th, Hf, AND Zr

525

T/K

-5 -

2500 2400 2300 I I I

2200 I

2000 I

2100 I

1900 I

1800 I 1

-6 -

-10 -

-11

I

3.8

4.0

IIll

II

4.2

4.4

II

4.6

II

4.8

II

5.0

IIll

5.2

II

5.4

5.6

5.8

lo4 K/T

FIGURE 1. A plot of log,, {p”(Th)/atmJ against 104K/T for pure thorium. Equation (3) represents the vapor pressure of liquid thorium. Equation (4) represents the vapor pressure of solid thorium. 0, Mass effusion results; 0, mass-spectrometric results. THE VAPOR PRESSURE OF HAFNIUM

The results of the mass effusion measurements of the partial pressure of hafnium over liquid hafnium saturated with tungsten are given in section B of table 3 and are shown in Figure 2. The initial mass-spectrometric observations were made on the unmelted sample at temperatures below the Hf + W eutectic, 2222 K. During a period of several hours at about 2100 K the HfO+ intensity decreased somewhat but reached a steady state at about 25 per cent of that of Hf+. The Hf+ ion intensity was measured at nine temperatures in the range 1945 to 2200 K, and the results were expressed by the least squares equation : Hf(s) :

log,, {Z(Hf+)T/K}

= -(31800+150)K/Tf(17.276f0.072).

(5) The sample was then melted and held at 2530 K for 5 h during which time the HfO+ intensity decreased to 2 per cent of that of Hf+. The Hf+ ion intensity was measured at nine temperatures in the range 2230 to 2250 K, and the results were expressed by the least squares equation : (Hf+W)(l):

log,, {Z(Hf*)T/K)

= -(29270rt190)K/T+(16.016+0.080).

(6)

The measurements were repeated on the solid in the range 1945 to 2200 K and resulted in a measured enthalpy of evaporation of (145.5 +0.7) kcal,, mol-’ which is in agreement with that calculated from equation (5), (145.2f0.9) kcala mol-I. The latter value corresponds to a sample not completely deoxygenated while the former

526

R. J. ACKERMANN

AND E. G. RAUII T/K

2500

3.8

4.0

2400

2300

4.2

4.4

2200

4.6

2100

4.8

2000

5.0

1900

5.2

10’ K/l‘ FIGURE 2. A plot of log,, {p(Hf)/atm} against lO*K/T for hafnium. Equation (7) represents the partial pressure of hafnium over liquid hafnium saturated with tungsten. Equation (8) represents the vapor pressure of pure liquid hafnium. Equation (9) represents the vapor pressure of solid hafnium. 0, Mass effusion results; 0, 0, mass-spectrometric results; x , partial pressures corrected for solubility of tungsten. Inset: curve 1, this study; curve 2, Blackburn;‘2) curve 3, Panish and Reif;c3) curve 4, Kibler ef aI.;@) curve 5, Koch ef a/.@)

corresponds to one which may contain as much as 7 moles per cent of dissolved tungsten. (l*) The agreement suggests that neither impurity at these mole fractions has a detectable effect on the measured slope. Equation (6) was normalized to the average of the mass effusion results (section B of table 3). The resulting equation : (Hf+W)(l):

log,, {p(Hf, l)jatm}

= -(29270)220)KjT+(5.694f0.080),

(7)

is shown plotted in Figure 2. The normalized mass-spectrometric results are shown in Figure 2. Equation (7) was used to calculate a partial pressure of hafnium over the liquid saturated with tungsten at each of the temperatures at which solubility measurements are given (section A of table 2). The calculated pressures were corrected by the corresponding mole fractions x(Hf), based on the assumption of an ideal solution, and are shown in Figure 2. A least-squares treatment of the corrected pressures resulted in the equation for the vapor pressure of liquid hafnium: Hf(I) :

log,, {p”(Hf, l)/atm} = -(30440k240)K/T+(6.304f0.085), (T > 2464 K).

(8)

VAPOR PRESSURES OF Th, Hf, AND Zr

527

The errors are estimates based on the uncertainties given in equation (7) and the uncertainties resulting from the least-squares analysis of the corrected pressures (these were + 50 and + 0.023 for the slope and intercept, respectively) and reflect the uncertainties in the solubility measurements. Equation (5) was normalized to the pressure (equation 8) at 2464 K, the melting temperature of hafnium. The resulting equation for the vapor pressure of solid hafnium is Hf(s) :

log,, {p”(Hf, s)/atm} = -(31800~150)K/T+(6.855)0.072), (T < 2464 K),

(9)

and is shown in Figure 2. The normalized mass-spectrometric results are shown in Figure 2. The enthalpy of fusion of hafnium calculated from equations (8) and (9) is (6.2f. 1.2) kcal,, mol-‘. The results of Blackburn, (‘I Parrish and Reif,‘3’ Kibler et u/.,(~) and Koch et a/.(‘) are compared with the results of this study in the inset Figure 2. THE VAPOR

PRESSURE

OF ZIRCONIUM

Partial pressures of zirconium over liquid zirconium saturated with tungsten as measured by the mass effusion method are given in section C of table 3 and are shown in Figure 3. Mass-spectrometric measurements of the temperature dependence of the Zr+ ion intensity, taken after 3 h at 2450 K during which time the ZrO+ intensity decreased from 7 per cent to 2 per cent of the Zr+ intensity, were made over the temperature range 1990 to 2540 K. A definite curvature was observed in a plot of log {I(Zr+)T/K} against l/T and the results were fitted to a three parameter least-squares equation and normalized to the mass effusion results. The resulting equation for the partial pressure of zirconium over liquid zirconium saturated with tungsten, (Zr+W)(l):

log,, {p(Zr, l)/atm) = (4.069&0.616)-(2.0192kO.2763) x 104K/T-(9.782f3.090) x 106(K/T)‘, (10)

and the normalized mass-spectrometric results are shown in Figure 3. Partial pressures calculated from equation (10) at each of the temperatures given in section B of table 2, were corrected for the dissolved tungsten by the corresponding mole fractions x(Zr). A least-squares treatment of the corrected pressures resulted in the equation for the vapor pressure of liquid zirconium : Zr(1) :

log,, {p’(Zr, l)/atm} = -(29940+240)K/T+(6.541+0.080), (T > 2134 K).

(11)

The errors given are estimates based on the uncertainties in equation (10) (the errors on the slope and intercept from the least squares treatment of the five corrected pressures were +50 and kO.025, respectively). A plot of equation (11) and the corrected pressures are shown in Figure 3. The vapor pressure of solid zirconium was calculated from the pressure given by 35

528

R. J. ACKERMANN

AND E. G. RAUH

equation (11) at the melting temperature, 2134 K, and the enthalpy of fusion, 4.05 kcal, mol- ‘, reported by Hultgren et ~1.‘~‘) and is given by the equation : Zr(s) :

log,, (p”(Zr, s)/atm} = -(30810rt:24O)K/T+(6.950+0.080), (T < 2134 K).

The errors are estimated from the uncertainties

in the mass-spectrometric

(12) results

T/K 2500 I

-4

2400 I

2300 I

2200 I

2100 I

2000 I

1900 I

-5

-6 \ c Y -7 9 9 z -8

equation (12)

T-G3

-9

I

-10 .8

3.6

I 4.0

3.9

I

4.2 4.5 4.8 5.1 I I I I I 4.2 4.4 4.6

I

I 4.8

I

I 50

I

I 5.2

104K/T FIGURE 3. A plot of log,, {p(Zr)/atm} against lo4 K/Tfor zirconium. Equation (10) represents partial pressure of zirconium over liquid zirconium saturated with tungsten. Equation (11) represents the vapor pressure of liquid zirconium. Equation (2)l represents vapor pressure of solid zirconium. 0, Mass effusion results; 0, mass-spectrometric results; X, partial pressures corrected for solubility of tungsten. Inset: curve 1, this study; curve 2, Skinner et al.;@) curve 3, Koch and Anable; curve 4, Trulson and Goldstein.@)

which led to equation (11). Equations (11) and (12) are shown in Figure 3. The results of Skinner et aI.,@) Koch and Anable,“) and Trulson and Goldstein’g’ are compared with the results of this study in the inset of Figure 3. The measured enthalpies and entropies of evaporation of thorium, zirconium and the standard deviations are summarized in table 4.

hafnium,

and

VAPOR PRESSURES OF Th, Hf, AND Zr

529

TABLE 4. Enthalpies AW(T) and entropies AS’(T) of evaporation of thorium, hafnium, and zirconium calculated from the equation: (~Tln 10) loglo Cp/atm) =AH”(T)-7’AS”(T) (Cal,h= 4.184 3) Element Th(l), (T > 2020K) m(s), (T< 2020 K) 0 Hf(l), (T> 2464K) Hf(s), (T< 2464 K) B(l), (25 2134 K) B(s). (T-C2134K) O

AW(T)/krz&

mol-1

136.2fl.O 139.65cl.O 139.3fl.l 145.5*0.7 137.0*1.1 141.0+1.1

AS”(T)/cala,K-l mol-’ 27.57f0.45 29.25*0.45 28.85&0.37 31.37&0.33 29.93*0.11 31.80&0.37

o Calculatedfrom datafrom liquid phaseand supplementary thermodynamicinformationgiven in reference19.

3. Discussion An analysis of these results and published results is given in table 5. Values of the enthalpy of sublimation at 298.15 K calculated via the second law AH”(298.15 K, II), and via the third law AH”(298.15 K, III), are given for each set of observations. The values in the last column of table 5 are the variations in AW(298.15 K, III) calculated from least-squares pressures at temperatures differing by 400 K since a common temperature range is necessary for a meaningful comparison. Values of {H”(T)-H”(298.15 K)} and {G”(T) - H”(298.15 K))/T tabulated by Hultgren et ~1.“~) were used for hafnium, zirconium, and gaseous thorium. Those of Rand,(20) based on the measurements of Levin.son,(l’) were used for the condensed phases of thorium. The consistency of the present results for thorium with the enthalpies is demonstrated by the agreement between the calculated values of AH”(298.15 K, II) and AH”(298.15 K, III). The absence of a trend in the latter values (column 6 of table 5) indicates no net systematic error in the combined enthalpies and vapor pressures. The higher pressures of Darnell et al. (r) (Figure 1) may be due in part to the evaporation of ThO from an oxygen-contaminated sample; the difficulty of deoxygenating the sample as experienced in this study suggests that a quasi-steady state rather than an oxide-free condition might have existed in their measurements. The enthalpies for hafnium” 9, are estimated above 1400 K but the estimates are consistent with the measured enthalpies and entropies of sublimation and vaporization. The estimated enthalpy of fusion, 5.8 kcal,,, mol-‘,(19) compares favorably with the derived value, (6.2f 1.2) kcal,, mol -l. A slight discrepancy of 0.4 kcal,, mol-’ beyond the standard deviations exists between AH”(298.15 K, II) and AH”(298.15 K, III) calculated from equation (8) and the thermodynamic data.(19) An error of this magnitude, if experimental, could arise from a relative temperature uncertainty of 4 K, a 3 per cent negative deviation from ideality of the solution of tungsten in hafnium at the lower end of the temperature range of measurement, or an inaccuracy of 8 per cent in the vapor pressure, all of which are quite reasonable errors. The pressures reported by Koch et al.(5) and Kibler et a1.(4) are in good agreement with

1990 1950 2230 1968 2148

this study 6 8

Zr liquid solid liquid solid liquid

t 4 5

1945 2230 2200 2066 2035 2500

this study this study

Hf solid liquid solid solid solid liquid

2010 1747

this study 1

Th liquid solid

TI/K

Reference

Element

2540 2054 2800 2112 2274

2550 2360 2274 2325 2810

2200

2460 1956

TdK

143.7% 1.1 140.4h2.2 148.4*4.4 135.1 k3.6 134.6h4.9

147.9hO.7 149.5+1.1 128.9h5.8 164&16 146.3k2.4 142.5k3.3

143.1kl.O 134.7h2.8

AH”(298.15 K, II) b - kcal tll mol-1

143.1 145.3 147.9 141.6 141.6

148.4 148.0 149.3 145.7 148.1 148.3

142.6 138.2

AH”(298.15 K, III) c kc& mol-l

0.1 0.8 0.07 0.8 1.4

0.03 0.5 3.6 2.3 0.4 0.7

0.1 0.7

gAH”(298.15 K, III) d kcaL mold1

5. Comparison of AH”(298.15 K, II) and AH”(298.15 K, III) the second and third law calculated values of the enthalpy of sublimation, on measurements in the temperature range Tl to Ta a

D {H”(T)-H”(298.15 K)} and {G”(T)-H”(298.15 K)}/T for thorium taken from Randcao) and Hultgren ef al.; (W for hafnium and zirconium Hultgren et oI.(lO) D AH”(298.15 K, II) =AH”(T)-A{H”(T)-ZP(298.15 K)}. c AH”(298.15 K, III)= -RTln (~“/atm)-A{G”(T)-H”(298.15 K)}, calculated at the average temperature. 6 Calculated from least-squares pressures at temperatures differing by 400 K.

TABLE

from

based

VAPOR PRESSURES

531

OF Th, Hf, AND Zr

the present results but only the latter are consistent with the thermodynamic functions for hafnium.‘r9’ For zirconium both the present results and those of Koch and Anable’*’ show second and third law agreement but the pressures differ by a factor of about 2.5. The results of Koch et aL(‘) for hafnium and of Koch and Anable for zirconium, both obtained by the same method and techniques, yield nearly identical values of AH”(298.15 K, III), and consequently, nearly identical pressures. Bedford,(21’ however, determined the ratio of the vapor pressures of hafnium and zirconium by measuring mass-spectrometrically the ratio of the partial pressures over several solid solutions of zirconium in hafnium. The average value of 3.4 at 2000 K compared favorably with a ratio of 3.9 calculated from equations (9) and (12) and suggests that the pressures of zirconium reported by Koch and Anable@’ are somewhat low. The assumption of ideality for hafnium and zirconium in the liquid solutions containing dissolved tungsten appears to be adequate. The importance of the corrections for solubility can be demonstrated by calculations of AH”(298.15 K, II) and AH”(298.15 K, III) from the partial pressures of zirconium given by equation (10). The second-law value calculated from the slope of equation (10) at the mid-temperature, 2265 K, and the third-law values calculated from the partial pressures at 2000 and 2400 K are AH”(298.15 K, II) = 139.1 kcal,, mol- ’ andAH”(298.15 K, III) = 143.9 and 145.0 kcal,, mol- ‘. The resultant discrepancy, 5.4 kcal,, mol- ‘, and the difference between third-law values, 1.1 kcal,, mol-‘, are to be compared with 0.6 and 0.1 kcal,, mol-’ (table 5), respectively, after the corrections have been applied. The thermodynamic anomaly that has appeared in the case of zirconium, namely, that two sets of pressure measurements differing substantially can show second and third law agreement, illustrates that this agreement is a necessary but not a sufficient criterion of accuracy. The ultimate test of accuracy, therefore, must lie in the compatibility with related quantities from other systems. The enthalpies used in a thirdlaw treatment comprise but one set of related quantities. The techniques and methods used in this study have been successful in the measurements of the vapor pressures of yttrium, lanthanum, and cerium; the results have been utilized in consistent thermodynamic interpretations and interreJations of the respective oxide systems.t22*23*24) The authors are indebted to Mr. K. J. Jensen of the Analytical zirconium determinations.

Division

for the

REFERENCES 1. Darnell, A. J.; McCollum, W. A.; Milne, T. A. J. Phys. Chem. lP60,64 341. 2. Blackburn, P. E. Thermodynamic and Kinetic Studies for a Refractory Materials Program. L. A. McClaine, editor, Air Force Materials Laboratory, Research and Technology Division, Air Force Systems Command, Wright-Patterson Air Force Base, Ohio, Report ASD-TDRdZ204, Part III. April 1964, p. 111. 3. Panish, M. B.; Reif, L. J. Chem. Phys. 1963, 38, 253. 4. Kibler, G. M.; Lyon, T. F.; Linevsky, M. J.; DeSantis, V. J. Carbonization of Plastics and Refractory Material Research, AF Materials Laboratory, Research and Technology Division, Air Force Systems Co mmand, Wright-Patterson Air Force Base, Ohio, Report WADD-TR60-646, Part 3, Vol. 2. March lP64, p. 32.

532

R. J. ACKERMANN

AND

E. G. RAUH

5. Koch, R. K.; Anable, W. E.; Beall, R. A. Vapor Pressures of Liquid Columbium (2740-3140 “K) and Liquid Hafkium (2500-28IO”K), Bureau of Mines, U.S. Department of the Interior, Report BM-RI-7125. May 1968. 6. Skinner, G. B.; Edwards, 3. W.; Johnston, H. L. J. Amer. Chem. Sot. 1951, 73, 174. 7. Fedorov, G. B.; Smirnov, E. A. Thermodynamics of Nuclear Materials, International Atomic Energy Agency, Vienna, 1962, p. 285. 8. Koch, R. K.; Anable, W. E. Vapor Pressures of Liquid Molybdenum (2229-2795 “K) and Liquid Zirconium (2229-2795’K), Bureau of Mines, U.S. Department of the Interior, Report BM-RI-7063. Jan 1968. 9. Trulson, 0. C.; Goldstein, H. W. J. Phys. Chem. 1965,69,253 1. 10. Ackermann, R. J.; Gilles, P. W.; Thorn, R. J. J. Chem. Phys. 1956,25, 1089. 11. Ackermann, R. J. ; Rauh, E. G. ; Thorn, R. J. ; Cannon, M. C. J. Phys. Chem. 1963,67,762. 12. See for a description of the equipment and procedure, Thorn, R. J. ; Winslow, G. H. Am. Sot. Mech. Engr. Paper No. 63-WA-244. 1963. 13. The International Practical Temperature Scale of 1968. Metrologia 1969,5,35. See also Rossini, F. D. J. Chem. Thermodynamics 1970,2,447. 14. Wengert, G. B. Anal. Chem. 1952,24, 1449. 15. Ackermann, R. J.; Rauh, E. G. J. Chem. Phys. 1962,36,448. 16. Ackermann, R. J.; Rauh, E. G. High Temperature Science, to be published. 17. Levinson, L. S. J. Nucl. Mater. 1966, 19, 50. 18. Elliott, R. P. Constitution ofBinary Alloys, First Supplement, McGraw-Hill, New York. 1965. 19. Hultgren, R.; Orr, R. L.; Anderson, P. D.; Kelley, K. K. Supplement to Selected Values of Thermodynamic Properties of Metals and Alloys, University of California, Lawrence Radiation Laboratory, Inorganic Materials Research Division and Department of Mineral Technology, Berkeley, California. March 1967. 20. Rand, M. H., personal communication. To be published in Atomic Energy Review, International Atomic Energy Agency, Vienna. The following equations for the enthalpy and Gibbs free energy functions for the condensed phases of thorium were derived: {H”(T)-H”(298.15 K)}/ca&,, mol-1 = -3230+8.94 T/K, for temperatures between 1633 and 2020 K; {H”(T)-H”(298.15 K)}/ca&,, mol-1 = -4160+11.04 T/K, for temperatures between 2020 and 2500 K; --[{G”(T)-iY”(298.15 K)}/Z”j/cal,,, K-l mol-1 = 12.57+4.01 T/K, for temperatures between 1800 and 2500 K. 21. Bedford, R. G. Investigations at High Temperatures: Condensed Phase Equilibria and Vaporization Studies with a Mass Spectrometer, University of California, Lawrence Radiation Laboratory, Livermore, Report UCRL-50886. June 1970. 22. Ackermann, R. J. ; Rauh, E. G.; Walters, R. R. J. Chem. Thermodynamics 1970, 2, 139. 23. Ackermann, R. J.; Rauh, E. G. J. Chem. Thermodynamics 1971,3,445. 24. Ackermann, R. J.; Rauh, E. G. J. Chem. Thermodynamics 1971,3,609.