F. J. KENESHEA, D. CUBICCIOTTI, G. WITHERS,AND H. EDING
1272
Enthalpy and Entropy Increments above 2 9 8 ° K and a Z-Plot Treatment of Vaporization Data for Niobium Pentachloridel by F. J. Keneshea, D. Cubicciotti, G. Withers, and H. Eding Stanford Research Institute, Menlo Park, California 94096
(Received September 98, 1967)
The saturation enthalpy increments above 298°K for the condensed phases of niobium pentachloride were measured in a drop calorimeter up to the critical point. The equation obtained for solid niobium penta(3.535 X 10-2T)] 0.07kcal/mol of NbCla. The chloride is ( H " , - Ho2,)(s)(298-478.9"K) = [-10.53 = [-12.12 (5.726 X 10?Z') equation for the liquid up to 600°K is ( H O T - H0~~~)(1)(478.9-6000K) (7.340 X 10-9T3)] rt 0.22 kcal/mol of NbC15. Above 600°K and to the critical point (804"K),saturation enthalpy increments for the liquid are given in tabular form. Tables of entropy increments above 298°K to the critical point are also given for the condensed phases. These results were applied to literature vapori~ation data in a 2-plot treatment. The values of the heat and entropy of sublimation obtained from this treatment are AH02&mbl) = 22.41 & 0.06 kcal/mol and AS0?98(subl) = 45.40 & 0.11 eu.
+
Introduction Niobium pentachloride gaseous molecules have been shown by electron diffraction to have a trigonal-bipyramidal structure.* Vibrational frequencies have been assigned to the gas molecules based on spectroscopic measurements made on the solid and on organic solutions containing the compo~nd.~34Thermodynamic functions for NbC1, gas have been calculated from these data.3z6 For the condensed phases of niobium pentachloride, the enthalpy of formation has been measuredar7 but other thermodynamic data have only been estiIn order to gain some needed information on the thermodynamics of the condensed phases of niobium pentachloride, we have measured the enthalpy increments above room temperature, using drop calorimetry. These results are reported below, along with derived values of the entropy increments. From the gaseous absolute entropy and the entropy of sublimation, a value for the absolute entropy of the solid a t 298°K can be calculated. We obtained the entropy of sublimation at 298°K by making a 2-plot treatment0 of the many vapor pressure studies which have been reported in the l i t e r a t ~ r e , l 0 - ~using ~ our enthalpy increment data in this treatment. The results of this %plot treatment are also reported below and the resultant value of Sozss(s)is discussed. Experimental Work A. Method. Samples of NbC15 sealed in quartz ampoules were heated to the critical point and dropped into a calorimeter at room temperature to measure the heat evolved. Details of the calorimeter are described in earlier report^.'^^'^ B. Preparation of Samples. Commercially obtained NbC15 was stated to be 99.95% free of metal impurities. The powdered form used, however, contained over 2000 ppm of oxygen, probably present as the oxyohloThe Journal of Physical Chemistry
+
ride and arising from hydrolysis of the pentachloride. The material used was freed of oxygen by sublimation in a stream of He saturated with S0Cl2. The use of SOCL to convert the oxychloride to chloride has been discussed by Schafer and Kahlenberg'* and the technique has been used by Prayloto convert other hydrated chlorides to the anhydrous salt. The reaction that takes place may be written as 1\TbOCl3
+ soclz = NbC15 + so2
(1)
(1) This work was supported by the Space Nuclear Propulsion Office, a joint agency of the U. S. National Aeronautics and Space Administration and U. S. Atomic Energy Commission, under USAEC Contract AT(04-3)-115. (2) H.A. Skinner and L. E . Sutton, Trans. Faraday Soc., 36, 668 (1940). (3) J. Gaunt and J. B. Ainscough, Spectrochim. Acta, 10, 52 (1957). (4) G. L.Carlson, ibid., 19, 1291 (1963). (5) G. Nagarajan, Bull. SOC.Chim. Belges, 71, 324 (1962). (6) H. Schafer and F. Kahlenberg, Z . Anorg. Allgem. Chem., 305, 291 (1960). (7) C. A. Shchukarev, M. Oranskaya, and T. Shemyakina, Russ. J . Inorg. Chem., 5, 1036 (1960). (8) V. M. Amosov, Izv. Vysshikh Uchebn. Zavedenii, Tsvetn. Met., 6 , 104 (1963). (9) D.Cubicciotti, J . Phys. Chem., 70, 2410 (1966). (10) J. W.Johnson, W. Silva, and D. Cubicciotti, to be submitted for publication. (11) W. 't Hart and G. Meyer, Rec. Trav. Chim., 83, 1233 (1964). (12) K. M. Alexander and F. Fairbrother, J . Chem. SOC.,8223 (1949).
(13) J. B.Ainscough, R. J. W. Holt, and F. W. Trowse, ibid., 1034 (1957). (14) M.A. Opykhtina and N. A. Fleisher, Zh. Obshch. Iihim., 7,2016 (1937). (15) D.N. Tarasenkov and A. V. Komandin, ibid., 10, 1319 (1940). (16) H. Eding and D. Cubicciotti, J . Chem. Eng. Data, 9, 524 (1964). (17) D.Cubicciotti and H. Eding, ibid., 10, 343 (1965). (18) H. Sohafer and F. Kahlenberg, 2. Anorg. Allgem. Chem., 305, 327 (1960). (19) A. R.Pray, Inorg. Syn., 5, 163 (1957).
1273
VAPORIZATION DATAFOR NIOBIUM PENTACHLORIDE In our procedure, dry He was bubbled through liquid SOCl2 at room temperature and the saturated gas was passed over impure NbC15, heated to 200". The gas stream from the NbC16 flask then passed through a 10-cm length of glass tubing (10-15 mm 0.d.) heated to about 400". The purified NbC15 was condensed directly into the quartz heat-content ampoules attached to the exit. After the ampoules were filled to the desired level, the system was flushed for at least l hr with He, occasionally heating the SbC16 to its melting point to remove any sulfur-containing gases trapped in the material. Finally the system was evacuated for at least 1 hr and the ampoules sealed off. The mass of the sample was determined by weighing the sealed and empty ampoule. The ampoule internal volume was determined by displacement of water by the sealed capsule and by the quartz alone. Data for the samples used are shown in Table I. After the calorimeter measurements were made, sample 2 was analyzed for Nb by weighing as Nbz05. We found 34.31% Xb, compared to 34.39% calculated for NbC15.
Table I: Data for Heat-Content Samples Weight of NbCls,
Weight of quartz,
Internal volume of capsule,
Sample
g
g
00
1 2 3 4
9.2194 1.4163 1 ,4333 3.5230
5.8155 6.3656 5.6327 3.7830
6.9605 1 ,9278 1.7827 3.2913
The melting temperature of the purified NbC15, determined by visual observation on four different samples sealed in evacuated capsules, was 205.7 A 0.5". (This is actually the triple point, but the difference between it and the melting point is negligible.) By contrast the impure material before treatment with SOC12 had a melting point of 204.7". Values in the literature, reviewed for example by Schafer and Kahlenrange from 202 to 215'. berg6 and by Meyer, et Our value of 205.7 f 0.5" is close to the value of 206.8 f 0.3" obtained by Meyer, et al., by extrapolating the liquidus curve of the NbC15-NbOCb system to 100% NbCls. The critical point of NbC15 was determined on sample 2 by heating it in a furnace provided with a viewing port and measuring the temperature for disappearance of the meniscus between the gas and liquid phases. We found a value of 531 f 3" compared to 534" obtained by Nisel'son, et aLZ1 C. Results of Heat Measurements. A substantial fraction of the heat liberated during each drop was due to the heat content of the quartz; corrections were made using the equation given by Cubicciotti, et a1.22
TEMPERATURE--'K
Figure 1. Enthalpy increments above 298°K for NbC& solid and liquid; samples: 0 , 1; 0, 2; A, 3; A, 4. Critical point shown by I.
A small part of the heat given up by the sample resulted from condensation of the vapor in the ampoule. This heat was calculated for each drop from the liquid and vapor densities,lOJ1the volumes of the ampoules, and the enthalpy of vaporization. The vaporization enthalpy was calculated from the Clausius-Clapeyron equation d_P - _AH - __ dT TAV with dP/dT taken from the vapor pressure equation of Hart and Meyer" and AV (gas volume minus liquid volume) determined from the vapor and liquid densities.10,21 It was assumed that all of the vapor condensed at the drop temperature. The more exact calculation using the integrated heat of condensation and also the correction for the heat capacity of the vapor was considered unnecessary, since the vapor correction used was for the most part less than 0.7% of the total heat. The data obtained from the drop-calorimeter experiments are shown as points in Figure l.23 The enthalpy increments above room temperature were fitted by the method of least squares to polynomial equations in T, T2, and T3. The linear equation obtained for solid NbC15 is
(H,
- H298)(~)(298-478.9"K)= [-10.53
+ (3.535 X 10-'T)]
A
0.07 kcal/mol of NbC15 (3) where the error shown is the standard deviation of the (20) G. Meyer, J. F. Oosterom, and W. J. Van Oeversen, Rec. Trav. Chim., 80, 502 (1961). (21) L. A. Nisel'son, A. I. Pustil'nik, and T. D. Sokolova, Russ. J . Tnorg. Chem., 9, 574 (1964). (22) D. Cubicciotti, H. Eding, F. J. Keneshea, and J. W. Johnson, J. Phya. Chem., 70, 2389 (1966).
Volume 76, Number 4 April 1968
1274
F. J. KENESHEA, D. CUBICCIOTTI, G. WITHERS,AND H. EDINQ
points from the regression line. The liquid data from the melting point of 478.9"K to 750°K were best fitted by an equation in T and T3.
(H,
- Hzsg) (1) (478.9-750°K) [--12.12
f
Temp,
=
+ (5.726 X 10+T)
(7.340 X 10-9T3)J
-
0.22 kcal/mol of NbClj (4)
The solid lines in Figure 1 were derived from eq 3 and 4. The dashed line extending from the solid line to the critical point was drawn so as to pass through as many data points as possible. The enthalpy increment at the critical temperature was estimated by the same method as described for BiC13.22 It has been pointed out b e f ~ r that e ~ the ~ ~drop-calorimeter ~ ~ measurements give the saturation heat capacity, C,, and this is related to the saturation enthalpy and to the heat capacity at constant pressure, CP, by the equations
(dT). bH
=
c, + v(%)
Table I1 : Thermodynamic Functions for NbC16 in Standard-State Condensed Phases up to 600'K'
c
At temperatures where the vapor pressure is less than a few atmospheres, t h e last term is neligible so that drop-calorimeter measurements give constant pressures as well as saturation-enthalpy increments. At higher pressures the differences become significant, although small. Since we have no information on the coefficient of expansion of the liquid, we can only evaluate saturation quantities above the temperature where the vapor pressure is a few atmospheres. We have taken 600"K, where the pressure is 4.5 atm," as the dividing point for treatment of the data in the following sections.
Discussion A . Enthalpy and Entropy Increments to 600OK. The enthalpy increments calculated for the condensed phases from eq 3 and 4 up to 600°K may be taken as standard increments ( i e . , referring to the substance in its standard state-under a constant pressure of 1 atm), since the differences from the saturation values are negligible in these measurements. Values of these standard enthalpy increments are listed for selected temperatures in Table 11. The derivative with respect to temperature of eq 3 and 4 up to 600°K thus gives the constant-pressure heat capacity, Cp, and by integrating Cpd In T , values of the standard-state entropy increments have been calculated and are also listed in Table 11. There are apparently no other experimental data with which to compare our results. The heat capacity of the solid, CP, from eq 3 has the constant value of 35.36 cal/deg mol. Schafer and Kahlenberg6 give an estimated CP (based on CP for ZrC14 and HfC1,) of 38 - (3 X l O T - * ) , which gives values in fair agreement with our results. Amosov's The Journal of Physical Chemistru
a
H O T
- H'm,
SOT
- Pzua,
OK
cal/mol
BU
300 350 400 450 478.9(s) 478.9(1) 500 550 600
75 1,843 3,610 5,378 6,399 14 ,493 15,589 18,149 20,648
0.25 5.67 10.40 14.57 16.77 33.67 35.91 40.77 45.15
Calculated from eq 3 and 4.
+
estimate8 of CP = 26.71 (35.2 X 10-3T), based on Neumann and Kopp's rule, gives a value 20% higher than our CP at the melting point. Extrapolation of the solid and liquid enthalpy curves to the melting point gives a heat of fusion of 8.09 f 0.23 kcal/mol. From the heats of sublimation and vaporization of KbClj, Alexander and FairbrotherlZobtained a heat of fusion of 7.7 kcal/mol, while Meyer, et ~ 1 obtained . ~ 8.30 ~ kcal/mol. ~ The entropy of fusion (16.9 eu/mol of KbC16) is quite large compared to those of the usual molecular solids (e.g.: WC16, 9.4; TiC14, 9.5; ZrCle, 12.7; AIBr3, 7.3). The unusually large value for aluminum trichloride (18.1 eu) is attributed to a change in character on melting from an ionic solid to a molecular liquid. The large value for niobium pentachloride may be due to a dissociation of the dimer molecules NbzC1,,, which are known to exist in the solid,26to monomers in the liquid. The liquid heat capacity from the melting point (478.9"K) to 600°K may be expressed as
Cp = 57.36
-
(22.02 X 10-6T2) cal/deg mol
(7) and gives a value of Cp = 56.8 cal/deg mol at the (23) One reviewer of this paper has commented that in drop calorimetry, in general, there is the inherent possibility for the error that when the sample is quenched, structural defects can be frozen into the sample and the energy associated with them is not released to the calorimeter. Such an error may be involved in the present measurements. However, if the defect energy were appreciable, one would expect to find abnormal scatter of replicate observations made on different samples. No such scatter was observed and the data for 500°K especially bear out the concordance of results. Another pertinent factor is that because these samples were contained in quartz-glass capsules, their rate of cooling was not very rapid. A rough calculation of the half-time for cooling, based on their geometry and the thermal conductivity of quartz, combined with a logarithmic decay of the sample temperature, was about 50 seo. This value is in accord with the observed fact that i t took about 0.6 hr f o r the heat from the samples to be delivered to the calorimeter. Therefore, because of the slow quenching rate and the concordance of replicate determinations, we think that any defect energy stored in the quenched sample was negligible. (24) D. Cubicciotti, H . Eding, and J. W. Johnson, J. Phys. Chem., 70, 2989 (1966). (25) Z. Zalkin and D. E . Sands, Acta Crystallogr., 11, 615 (1958).
1275
VAPORIZATION DATAFOR NIOBIUM PENTACHLORIDE melting point. We estimated a value of 42-48 cal/deg mol, using a Cp value of 7-8 cal/deg g-atom, typical of many inorganic liquids.26 The high experimental value compared to the estimated value may be connected with the dissociation of the dimer, which may persist in the liquid above the melting point. It is interesting t o note that there is a slight curvature in the plot of liquid density vs. temperature just above the melting point,lO,zlwhich may also be due to dimer dissociation. B. Enthalpy and Entropy Increments above 600°K. At some temperature above 600"K, CP and C, differ by the quantity T(bV/bT)p, and since this quantity is not known for the liquid we can only evaluate saturation thermodynamic quantities above 600°K. The saturation enthalpy increments above 298°K were calculated from 600 to 804°K (the critical point) in 20" increments by numerical integration of eq 5. Values of C, up to 750°K were obtained from eq 4, and above 750"K, C, was obtained from the slope of the line through the data (dashed line in Figure 1). The values of V(bP/bT), were calculated from liquid density10Sz1and vapor pressure" data. The resulting values of the enthalpy increments for selected temperatures are shown in Table 111. The entropy increments for the liquid were calculated by integrating the expression Cud In T , and the resulting data are also given in Table 111. The value of (ST- S0298), at the critical point was estimated by extrapolation of the curves for the liquid and vapor entropy increments vs. temperature.
Table I11 : Thermodynamic Functions for Liquid NbC16 under Saturation Conditions to the Critical Point Temp, OK
H T - H'lss. cal/mol
600 620 640 660 680 700 720 740 760 780 804
20,648 21,638 22,621 23,598 24,568 25,531 26,488 27,439 28,385 29,326 32,800
ST
-
\.
-14 So29Et
eu
45.15 46.76 48.31 49.80 51.23 52.61 53.93 55.20 56.43 57.61 60.7
C. %Plot Treatment of Vapor Pressure Data. If a value for the absolute entropy of solid NbC16 at 298°K were available, then the absolute entropies and free energy functions of the condensed phases at higher temperatures could be calculated from the data in Tables I1 and 111. This quantity has not been measured, so it is necessary to estimate it. One way to
1.6
1.7
1.8
1.9 2.0 2.1
2.2 2.3 2.4 2.5 2.6 2.7
IOVT-OK Figure 2. Z plot for NbClj vaporization data: 0 , Ainscough, Holt, and Trowse;la A, Hart and Meyer;" 0, Alexander and Fairbrother;lz 'I,Opykhtina and Fleisher;14 0, Tarasenkov and Kornandin;lt A, Johnson, Silva, and Cubicciotti.10
estimate SZS~(S) is from the entropy of sublimation a t 298°K and the absolute entropy of the gas SZSS(S) = Xzss(g)
- ASzss(sub1)
(8) The entropy of NbCL gas has been calculated from molecular constant data by Gaunt and Ainscougha and Nagarajan.6 The entropy of sublimation at 298°K can be determined from vapor pressure data using the 2-plot method of C~bicciotti.~I n addition to determining AHzgs(sub1) and Af&,(subl), this method (26) 0. %baschewski and E. Evans, "Metallurgical Thermochemistry, Pergamon Press, Inc., New York, N. Y . , 1958, p 186. Volume 78, Number .G
April 1968
F. J. KENESHEA, D. CUBICCIOTTI, G. WITHERS,AND H. EDING
1276
also affords an intercomparison of all vapor pressure data over the solid and the liquid. I n this procedure the quantity 2’ is defined by the equation --Z’
=
R In p(atm)
+ Afef incr
(9)
in which Afef incr = fefr(g) - fef2,8(g) fef,(cond)
+ fefze8(cond) (10)
The compound XbCls has a heat capacity very near the Dulong and Petit value of 3 cal/deg g-atom at 298’11, and thus the method of Latimer28can be used to estimate 8’298(s). For this calculation we used the Nb entropy value of 12.2 eu given by Latimer and estimated the C1 entropy contribution to be 7 . 5 eu/g-atom, based on the entropy estimated2g for WC15. Such a calculation = 50 eu for NbC15. Schagives an estimate of SoZg8(s) fer and Kahlenberg6 give an estimate (based on values for ZrClk, HfC14, UC15, and UCle) of 54 f 2 eu, while Amosovs gives an estimate of 58.6 eu. If the value of 46.5 that we derived from the molecular constants of the gas is correct, the reason that it is lower than these estimates should be explored. On the other hand, the absolute entropy of the gas may be too low because the vibrational frequencies have not been properly assigned. Therefore, a calorimetric value for the absolute entropy of the solid would be very valuable. The estimate for s0298(s) made by Latimer’s rules may be too high, since the estimates for other solids are sometimes too high; e.g., the Latimer estimates for ZrC& and ZrFk are 4 and 7 eu too high, respectively. Also, since niobium pentachloride is a dimeric molecule in the solid, it may have a lower entropy than the average (which Latimer’s values presumably represent). That is, it would probably have a smaller contribution from rotational or “rocking” modes because the molecule is so large. It is also possible that the absolute entropy calculated for the gas from its molecular constants may be too small because the vibrational frequencies may not all have been observed. The vibrational frequencies used in calculating the entropy of the gas were obtained by Raman and infrared spectroscopy on the solid and on liquid solutions of niobium pentachloride dissolved in carbon disulfide or carbon t e t r a ~ h l o r i d e . ~It ’ ~ was assumed by both Gaunt and Ainscough3 and by Carl80114 that the frequencies should be assigned on the basis of Dahsymmetry because the Ir;bC15 gas molecule has been shown by electron diffraction to have a trigonal-bipyramidal structure. However, the solid has been shown by X-ray analysis to consist of nTb2Cllo dimers, in the form of distorted double octahedra sharing a common edge.26 There is evidence that carbon tetrachloride solutions of niobium pentachloride also contain NbzCllodimers.301~1Thus the vibrational frequencies seem to have been determined on systems
and fef is the usual free energy function, (Gor - H0298)/ T. Values for the fef increment for the condensed phases were calculated from the enthalpy and entropy increments in Table I1 by the methods described in ref 9. Values for the fef increment for the gas were calculated from Xagarajan’s data.5 A large-scale plot of the Afef increment was used to find values of the Lfef increment corresponding to each pressure measurement. Only vapor pressure data were used which extended to a temperature of 6OO0K, above which deviations from ideality may become too large. For the 2 plot the vapor pressure data from the following references were included, with temperature range and method of measurement indicated in parentheses : Ainscough, Holt, and Trowse13 (516-53OoK, boiling point) ; Hart and hleyerl’ (544-600°K, static) ; Alexander and FairbrotheP (403-528”K, static) ; Opykhtina and Fleisher14 (373-503”K, transpiration) ; Tarasenkov and Komandin’6 (446-506’11, static, and 504-52OoK, boiling point) ; Johnson, Silva, and Cubicciottilo (504--594”K, boiling point). The 2’ values are shown as a function of 1 / T in Figure 2. With the exception of the points of Alexander and Fairbrother and Opykhtina and Fleisher, all of the data fall quite close to a straight line. The line drawn through the points was evaluated by least squares, using all of the data except those of Alexander and Fairbrother and Opykhtina and Fleisher. The former workers reported a triple point for NbC15 of 209.5 f 0.5’ which is 4’ higher than our value of 205.7” for pure NbC16 and 5” higher than the value for impure WbC15, and their vapor pressure temperatures are also fairly consistently 4-5” higher than the leastsquares line in Figure 2. The values of the heat and entropy of sublimation obtained from the least-squares treatment are AHo298(subl)= 22.41 f 0.06 kcal/mol and AXo2g8(subl)= 45.40 f 0.11 eu. The value of XoZgs(g)was calculated by Nagarajan6 to be 90.9 eu, which was based on the frequency assign(27) G. N. Krynauw, C. W. F. T. Pistorius, and M. C. Pistorius, ments of Gaunt and Ain~cough.~Using the frequency 2. Phys. Chem. (Frankfurt), 43, 213 (1964). values listed by Krynauw, Pistorius, and Pistori~s,~’ (28) W. M. Latimer, “Oxidation Potentials,” 2nd ed, Prentice-Hall Inc., Englewood Cliffs, N. J., 1952, Appendix 111. which were based on Cadson’s data,4 we calculated a (29) “JANAF Thermochemical Tables,” The Dow Chemical Co., Midvalue of 91.9 eu for #‘298(g). Combining this latter land, Mich., Dec 31, 1966. number with the above value for AX’~g~(s), the value of (30) R. F. 7.V. Bader and A. D. Westland, Can. J . Chem., 39, 2306 so298(s)is calculated by eq 8 to be 46.5 eu. (However (1961). see note added in proof.) (31) D. L. Kepert and R. S. Nyholm, J . Chem. Soc., 2871 (1965). The Journal of Physical Chemistry
1277
HEATCONTENT OF KzS FROM 298 TO 1260°K containing the dimer but have been assigned to the monomer. The existence of the dimer was known to Carlson4 but he preferred to interpret the spectroscopic data on the ba,sis of a weak association in the chlorine bridge-type bonding between the Nb atoms, in which the molecule retains an approximate D3h structure. Krynauw, e2 ut.,27have used Carlson's frequencies in a vibrational analysis to derive a set of force constants which they considered satisfactory. However, since the frequencies were not measured for the gas and because of the difficulty of these measurements, some low-lying frequencies may have been missed. Since there is still some uncertainty about the value for Xo298(s),we have not calculated the absolute en-
tropies or free energy functions at temperatures above 298°K from the data in Tables I1 and III.32 (32) NOTE ADDEDI N PROOF.After this report was submitted, Werder, et al. (R. D. Werder, R. A. Frey, and Hs. H. Gunthard, J . Chem. Phgs., 47, 4159 (1967)), published the results of spectroscopic studies of niobium pentachloride in the solid state, in organic solvents, and in low-temperature matrices. Frequency assignments for both the monomer and dimer were made. Their frequency assignments are somewhat different from those of Gaunt, et al.,3 and Krynauw, et aZ.,27 and lead to a value of So2ga(gas)for the monomer of 95.82 eu instead of the value we calculated above (91.9 eu) The assignments made by Werder, et al., are clearly to be preferred since they were able to distinguish between monomer and dimer spectra by means of the matrix isolation technique. Using Sozss(gas) = 95.82 and AS'm(sub1) = 45.40, we calculate S02g8(solid) = 50.42 eu (instead of 46.5), which is in agreement with the Latimer estimate. We think this value is sufficiently well substantiated t h a t reliable values of free energy functions can be calculated from i t and the data in Tables I1 and 111.
Diffuse Transition and Melting in Fluorite and Anti-Fluorite Type of Compounds: Heat Content of Potassium Sulfide from 298 to 1260"Kl by A. S. Dworkin and M. A. Bredig Chemistrv Division, Oak Ridge hrational Laboratory, Oak Ridge, Tennessee
(Received September $6,1967)
The heat content and entropy of KzS from 298 to 1260°K have been measured by meanr of a copper block drop calorimeter. K2S was found to have the low entropy of fusion of 3.16 eu mole-l, similar to those in CaF2 and SrC12 with which it is anti-isotypic. As in these latter crystals, this is connected with the occurrence of a diffuse transition, with a heat capacity maximum of 45 cal deg-l mole+ at about 780" but extending from about 550" to the melting point at 948O, and involving an entropy change of 4 eu mole+. It is suggested that the occurrence of a diffuse transition is a general characteristic of the substances AB2 of fluorite and anti-fluorite types of crystal structure. It is attributable to the gradual distribution of the 13 ions, with rising temperature, over both the octahedrally and tetrahedrally coordinated lattice positions. This leads to the high rate of diffusion and electrical mobility of the R ions. Heat content data found in the literature for such fluorite type crystals as UOZ,ThOz, and Na20 indicate that diffuse transitions also occur in these compounds although more information is needed in these cases.
Introduction Through our observations on the anomalous heat content of solid strontium dichloride2 which is isotypic in structure with calcium difluoride, we have become interested quite generally in the thermal and structural behavior of the substances possessing either the fluorite (MX2) or the anti-fluorite (MzY) type of structure. The former group (MXJ includes certain halides of divalent metals and oxides of tetravalent metals, such as CaF2 and SrC12,and ZrOz, Tho2, and UOz, while the group M,Y consists mainly of the oxides and other chalcogenides of the alkali metalsa3 The present calorimetric study of potassium sulfide was further motivated, as was the earlier one of strontium chloride, by the need for knowledge of the entropy of fusion in
attempts to extract from the fusion equilibria some information about the nature of the solution of the metal in the molten c ~ m p o u n d . ~
Experimental Section The copper block drop calorimeter used for the present heat content measurements and the experimental procedure were the same as described in detail (1) Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corp. (2) (a) A . S. Dworkin and M. A. Bredig, J . Phys. Chem., 67, 697 (1963); (b) A. S. Dworkin and M .A. Bredig, J . Chem. Eng. Data, 8, 416 (1963). (3) Cf., e.g., R. W. G. Wykoff, "Crystal Structures," Vol. 1, Interscience Publishers, Inc., New York, N. Y . , 1963, p 239 ff. (4) A . S. Dworkin and M.A. Bredig, J . Phys. Chem., 71, 764 (1967).
Volume 72,Number 4
April 1968
