High-temperature thermodynamic properties of uranium monosulphide

J. inorg, nucl. Chem., 1971, Vol. 33, pp. 2419 to 2425. Pergamon Press. Printed in Great Britain

HIGH-TEMPERATURE THERMODYNAMIC PROPERTIES OF URANIUM MONOSULPHIDE A. C. MacLEOD Department of Metallurgy, The University of Strathclyde, Glasgow C. l, Scotland

(Received lOJuly 1970) AImtract-The enthalpy of uranium monosulphide has been measured from 400 to 1400 K in an adiabatic drop calorimeter. The data are represented by the equation (Hr-H298.15) = 12"633T+7-7865 x 10-4T~+ 9"0413 X 104T -J - 4 1 3 9 cai mole -J with a mean deviation of 0.55 per cent. Molar thermodynamic properties from 300 to 2000 K have been calculated and a value of - 80 kcal mole -j is derived for the heat of formation from the solid elements at 298.15 K. INTRODUCTION

URANIUM compounds are important in the field of nuclear-reactor technology and the need to determine their enthalpies at high temperatures has been stressed [ 1]. However, very few high-temperature thermodynamic data have been reported for these materials. A typical example is uranium monosulphide for which low t e m p e r a t u r e h e a t c a p a c i t y d a t a h a v e b e e n r e p o r t e d [2] b u t f o r w h i c h c a l o r i m e t r i c data at higher temperatures have not been determined. This paper presents the thermodynamic properties of uranium monosulphide as determined by drop calorimetry from 400 to 1400 K; preliminary results for the investigation have b e e n b r i e f l y r e p o r t e d [3]. EXPERIMENTAL

Method. High-temperature enthalpies were measured by the drop method. The sample, contained in a graphite capsule whose enthalpy was determined in separate experiments, was heated in a furnace to a measured temperature and then dropped rapidly into a copper-block calorimeter of known heat capacity. Cooling corrections could, ideally, be eliminated by an adiabatic method but in practice the determinations for uranium monosulphide were carried out with a small negative drift of the calorimeter temperature and the corrected temperature rise was obtained by a method previously described [4]. This method introduces a small error (ca. 0.2 per cent) into t h e measured enthalpies but it was felt that this procedure was justified on the grounds that the uranium sulphide sample was not sufficiently pure or well-characterised to merit an elaborate adjustment of the controls to ensure a zero drift. The corrected temperature rise of the calorimeter thus obtained was a measure of the change in enthalpy of the sample in cooling from the furnace temperature to the final calorimeter temperature. A small correction was made for the fact that the final calorimeter temperature was above the reference temperature of 298' 15 K and the function (Hr-Hzas.ls) was thus obtained. The apparatus was constructed in such a manner as to allow the capsule to be returned easily to the furnace in preparation for another run while continuously maintaining a vacuum of I × 10-5 torr. The apparatus and graphite 1. 2. 3. 4.

M. H. Rand Thermodynamics of Nuclear Materials p. 71. IAEA, Vienna (1962). E. F. Westrum, R. R. Waiters, H. E. Flotow and D. W. Osborne, J. chem. Phys. 48, 155 (1968). A.C. MacLeod and S. W. J. Hopkins, Proc. Br. Ceram. Soc. 8, 15 (1967). A. C. MacLeod, Trans. Faraday. Soc. 63,307 (1967). 2419

A.C. MacLEOD

2420

capsule have been described in detail elsewhere [4]. It was desirable to use a graphite capsule because very precise enthalpy data for a number of identical capsules were available from previous work [4, 5] and tests showed that US and C were chemically compatible at high temperatures. A specimen of US heated to 1800 K in vacuum in a graphite capsule showed no change in appearance, no change in weight and no carbide phases were present in its X-ray diffraction pattern. The graphite capsule, which had previously been heated to constant weight, also showed no weight change. Materials. The uranium sulphide sample was prepared and analysed in the Chemistry Division, A.E.R.E., Harwell. Metallographic and X-ray diffraction examination of a specimen before and after the enthalpy measurements showed that only the oxysulphide, UOS, was present as a major impurity phase, no UO2 being detectable. The UOS content was estimated[6] by the amount of residue remaining undissolved after treatment with 10% H2SO4 and the following results were found fdr three specimens after completion of the enthalpy measurements.

%U 1 88.26 2 88.29 3 88-25

%0 %S (Calc. from UOS) 11.58 11.68 11.60

0.14 0.16 0.14

The analysis for the original sample (before enthalpy measurements) from which the three specimens were taken gave a uranium oxysulphide content of 2.60 per cent and the average oxygen content of the three specimens is equivalent to 2-62% UOS which would indicate that they suffered little, if any, oxidation during the enthalpy determinations. The sample could therefore be regarded as (US0.as + 2"6% UOS) but in the absence of thermodynamic data for UOS it was assumed that all the uranium and sulphur were combined as US0.as and the molar thermodynamic properties were calculated using a molecular weight of 269.49. RESULTS

The measured enthalpies, and entropy increments calculated by Kelley's method[7], are given in Table 1. The enthalpy data were correlated with the low-temperature heat capacity data of Westrum et al. [2] using the method of Shomate[8]. Assuming a value of 12.08 cal mole-lK -1 for Cv at 298.15 K this procedure gives the equation (Hr-H29s.1s) =

12"633T + 7"7865 X 10-4T 2+ 9"0413 X 104T-1

_

_

4139 cal mole -I

(1) which fits the experimental data from 400 to 1400 K with a mean deviation of 0.55 per cent. Differentiation of Equation ( ! ) gives the heat capacity as Cp = 12.633 + 15.5730 × 10-4T - 9-0413 × 104T-2 cal mole-lK -1.

(2)

The entropy values were fitted with the equation (Sr-'S29s.1s) = 28.8534 log T + 1"5183 × 10-3T + 2"7184 X 1 0 4 T - 2 _ 72" 154 cal mole-lK -1 (3) the average deviation from the tabulated values being 0.04 per cent. 5. 6. 7. 8.

A. C. Macleod, J. inorg,nucl.Chem. 31,715 (1969). M. Albutt,A. R. Junkison and R. F. Carney, Proc. Br. Ceram. Soc. 7, 11 (1967). K. K. Kelley,Bur. Mines Bui1584, 8 (1960). C. H. Shomate,J. phys. Chem. $8, 368 (1954).

Properties of uranium monosulphide

2421

Table 1. Measured enthalpy and entropy of uranium monosulphide (Mass of s a m p l e = 11-5160g; 1 cal = 4.184J)

(Hr-H2os.I~)

(ST-S2a8.15)

T/K

cal mole -1

cal mole -1 K -1

417 "96 474"62 552"35 586"26 650" 11 719"87 794"10 860.82 954"47 997.48 1070"77 1134-91 1228"01 1353-44 1414"93

1500"30 2273 -69 3232-11 3713 "47 4607-37 5469-45 6336"94 7456.44 8724"71 9390.91 10297"84 11303-09 12640.12 14396.82 15331"31

4 '312 5"809 7"963 8-614 10" 101 11.499 12-587 13"855 15"330 15-827 16-912 17"747 18.900 20"284 20-918

Table 2. Molar thermodynamic properties of uranium monosulphide

Cp

ST°

T/K

cal K -1

cal K -1

298"15 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

12-08 12-10 12.68 13"05 13"31 13"54 13'74 13'92 14"10 14-27 14"44 14-60 14"76 14-92 15"08 15"25 15"40 15'57 15'72

18-64 18"71 22"33 25"22 27-62 29"68 31"49 33' 11 34"58 35"92 37"16 38"31 39"39 40.41 41 '36 42-27 43" 14 43 "97 44"76

(H-Ho °) (H-Ho°)/T-(G-Ho°)/T cal cal K -1 cal K -~ 2665 2708 3929 5210 6527 7869 9233 10615 12013 13427 14855 16298 17755 19225 20709 22206 23716 25240 26776

8'94 9'03 9-82 10"42 10"88 11.24 11-54 11-79 12-01 12-21 12"38 12-54 12"68 12"82 12"94 13.06 13' 17 13 '28 13"39

9-70 9-70 12"51 14.80 16"74 19"44 19"95 21 "32 22"57 23"71 24"78 25"77 26"71 27.59 28"42 29-21 29"97 30-69 31-37

The conversion between the reference temperatures OK and 298.15 K is carried out by means of the relation (Hr--Ho°)= (Hr--H2as.~5) + 2665.

Table 2 gives the molar thermodynamic properties of uranium monosulphide at 100 degree intervals. Entropy values were computed from Equation (3)and the quantity xtH 2°9 8 ' 1 5 - H 0 o~ is that obtained by graphical integration of the heat capacity /

2422

A.C. MacLEOD

curve given in Ref. [2]. This curve joins smoothly with the heat capacity values calculated from Equation (2) as shown in Fig. 1. DISCUSSION

The only other data reported for the high-temperature thermodynamic properties of uranium sulphide are heat capacity values determined[9] using a transient technique with a laser as a heat-pulse source. The data are represented by the equation Cp = 12.12 + 7.107 x 1 0 - 4 T - 1"781 x 10aT-~ cal mole -1 K -x (298-1000 K) (4)

T

14

~' u2 /

i E

oo

a

I /

G

Temp., °K Fig. ]. Heat capacity of uranium monosuiphide. O - t h i s work; ©-Westrum and Gr¢nvo]d; x - Moser and Kruger.

and values calculated from this equation are compared with the present data in Fig. 1. The agreement is poor but it should be emphasised that the heat-pulse technique is of low accuracy; according to Becket and Cezairliyan[10] such methods are still in a stage of development and uncertainties of 2-10 per cent or more are to be expected. Values of (Hr-H29a.1s) determined by integration of Equation (4) are c a . 5 per cent lower than the values listed in Table 2. The apparently congruent vaporisation of US between 1840 and 2730 has been studied [ 11, 12] and the results can be used in conjunction with extrapolated data from Equations (1) and (3) to obtain a value for the heat of formation of US. For the reaction USes) --* U(~)+ S(~) (5) 9. J. B. Moser and O. L. Kruger, J. appl. Phys. 38, 3215 (1967). 10. C.W. Beckett and A. Cezairliyan, In Experimental Thermodynamics (Edited by J. P. McCullough" ' and D. W. Scott), Vol. 1. Chap. 14. Butterworths, London (1968). I 1. E. D. Cater, P. W. Gilles and R. J. Thorn,J. chem. Phys. 35,608 (1961). 12. E. D. Cater, E. G. Rauh and R. J. Thorn, J. chem. Phys. 44, 3106 (1966).

Properties of uranium monosulphide

2423

the uranium pressure isgiven in Ref. [12] by the equation -- logpo(atm) = (29,600 _ 170) T -1 - - (7.323 --+0-081 ) which is presumed to be of higher accuracy than the equation given in Ref. [11]. The equilibrium constant for the reaction is 1/2

K =pvl--~u 2[ M,'~)

(6)

~ R T In K = 270,902 -65.028T cal mole-'.

(7)

whence we obtain

It should, however, be remembered that the assumption of congruent vaporisation of US cannot strictly be correct and that there is an unknown error associated with the representation of the equilibrium constant for Reaction (5) by Equation (6). The standard free energy change for reaction (5) is obtained from Equation (7) and H~9s.,5(US) is computed from the relation H~9s.,5 = - - R T In K - A(Gr°-H~os.,5)

(8)

using published free energy functions for U(o)[13] and S(u)[14]. The calculation, for the temperature range 1900-2400 K, yields an average value of-274-12___ 0-18 kcal mole -a for the heat of formation of US from the gaseous elements. (A similar calculation using the vapour pressure equation of Ref. [11] gives an average value o f - 273.53 kcal mole-i). To find the heat of formation at 298.15 K of solid US from rhombic sulphur and solid uranium U(s) -~- S(s, rhombic)~

U S(s); AH~9s (9) = H~o8(U S )

(9)

the heats of formation of the reactions U(,)--) U(o); AH~gs(10) = H~gs[U(a)]

S(s, rhombic)-'~ S(a); AH~os( 11 ) =

H~98[S(~)]

U(u) + S(o) --> US(s); AH~9 s ( 5 ) = - - 274" 12 -----0" 18 c a l m o l e -1

(m) (11) (5)

are added together. For reaction (10) the only reliable data appear to be two sets of mass spectrometric measurements which, rather surprisingly, differ by as much 13. H. Schick, Thermodynamics of Certain Refractory Compounds Vols. 1, 2. Academic Press, New York (1966). 14. D. R. Stuli and G. C. Sinke, Thermodynamic Properties of the Elements. Advances in Chemistry Series No. 18, Am. Chem. Soc. Washington D.C. (1956).

2424

A . C . MacLEOD

as 3 kcal. Pattoret et a/.[15] obtained a best value of AH~0oo(10) = 119.45 kcal mole -1 and, using the relation AH~gs.15 = AH~ooo- f~2s.°°~5 ACv° d T together with enthalpy data for liquid uranium[16] and monatomic gaseous uranium[13] we obtain AH~as(10 ) = 129"12_+2 kcal mole -1. Using a 'similar technique to study the vaporisation behaviour of liquid uranium saturated with Ta, P, S and C in the temperature range 1800-2400 K Ackermann and Rauh [ 17] obtained a value ofAH2as(10) = 126"3 -+ 1"0 kcal mole -1. The heat of formation at 298.15 K for Reaction (11) is best obtained from the scheme, 1 • S ( s , rhombic) --9, 72S2(g),

0

AH29s(12 ) :

(12)

1 H O298 I` / S 2] ~-

½S2S
(13)

S(s, rhombie,

(11)

"">

S(o);AH~aa( 11 ) = AH~os (12) + AH~aa (13)

but there is some uncertainty because of the difficulty of assigning the correct value to Do°(S2) from the three values 3.3 eV (75.7), 3.6 eV (83) and 4-4 eV (102.1 kcal) allowed by spectroscopic measurements. A recent analysis [ 18] of this problem, where data for the established dissociation energies of SnS and PbS[19] were correlated with thermodynamic data in thermochemical cycles, would indicate a value of Do°(Se)= 101"1---1 kcal which gives AH~as(13)= 51.08_+ 1 kcal. The heat of formation of diatomic sulphur gas is given[20] as AH~98(12)--15"42-+0"15 kcal. This was obtained from measurements of the dissociation of H2S at high temperatures on the assumption that only $2 molecules exist in the vapour phase. However, there is a considerable body of evidence [21] Table 3. AH~9afor the reaction Uc,~+ S~+~---> USt,~ - H~gs.15(US )

Ref.

Method

(kcal mole -1)

[23]

Fluorine reaction calorimetry: USv01 + 6"033F2 -* UF6 + 1.011SF6 D T A measurements on the reaction US +~-O2 --* ~U3Os + SO~ at 643 K Tungsten effusion cell (2nd law) (3rd law) Tungsten effusion cell (2nd law) Estimated from thermal data

73"2 + 3.6

[24] [7] [8] [25] 15. 16. 17. 18. 19. 20. 21.

84.1___12 90 89 97 93 _+5

A. Pattoret, J. Drowart and S. Smoes, Trans. Faraday Soc. 65, 98 (1969). L. S. Levinson, J. chem. Phys. 40, 3584 (1964). R.J. Ackermann and E. G. Rauh, J. phys. Chem..73, 769 (1969). J. Drowart and P. Goldfinger, Q. Rev. chem. Soc. XX, No. 4, 545 (1966). R. Colin andJ. Drowart,J. chem. Phys. 37, 1120 (1962). W. H. Evans and D. D. Wagman, J. Res. Natn. Bur. Stand. 49, 141 (1952). J. Berkowitz, ElementalSulphur (Edited by B. Meyer), p. 125. Interscience, New York (1965).

Properties of uranium monosulphide

2425

to suggest that sulphur gas consists of at least four species of molecules $8, $6, Sz and S and according to Goldfmger[22] the ratio S~/S at 2000 K is 1/15. The inclusion of these various complex equilibria into Reaction (10) would make the present thermodynamic analysis intractable and we therefore accept Evans and Wagman's value for AH~98[12] which gives AH~98(ll) = 66.50___ 1 kcal. Finally, for Reaction (9) we obtain H~°gs(US)=--78.50_-+-3 kcalmole -1 using AH~gs(10) from Ref.[15]. or H~gs(US)=-81.32___2 kcalmole -1 using AH~g8(10) from Ref. [ 17]. The available data in the literature on the heat of formation of US are summarised in Table 3. There is reasonable agreement between the values calculated above and that obtained by reaction calorimetry and, with regard to the heat of sublimation of uranium, it might be argued that the thermochemical evidence lends some support to the value of Pattoret et al. [14] rather than that of Ackermann and Rauh[17]. It should, of course, be emphasised that corrections for the non-stoichiometry of uranium sulphide and the polymerisation of sulphur atoms have not been taken into account in the above calculations. Qualitatively, one can say that the effect of including the latter phenomena is to bring the thermochemical and calorimetric values for the heat of formation of uranium sulphide into closer agreement. Acknowledgements-The author is grateful to Dr. S. W. J. Hopkins of Morganite Research and Development Ltd. for his help in carrying out the calorimetric measurements and to staff in the Chemistry Division, U.K.A.E.A., Harwell for the preparation and analyses of the uranium sulphide samples. 22. P. Goldfinger, Proceedings of the XVII Internl. Congress p. 59. Milan (1966). 23. P. A. G. O'Hare, J. L. Settle, H. M. Feder and W. N. Hubbard, Thermodynamics of Nuclear Materials p. 265. I.A.E.A., Vienna (1968). 24. D. Kolar, M. Komac, M. Drofnik, M. Beminc, V. Marinkovic and N. Vene, Thermodynamics of Nuclear Materials, p. 279. I.A.E.A., Vienna (I 968). 25. M. H. Rand and O. Kubaschewski, The Thermochemical Properties of Uranium Compounds. Oliver & Boyd (1963).