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The thermodynamic properties of di-caesium telluride, Cs2Te, from 5 to 800 K
M-2017 J. Chem. Thermodynamics 1987, 19,293-291
The thermodynamic di-caesium telluride, 800 K
properties of Cs,Te, from 5 to
E. H. P. CORDFUNKE,” W. OUWELTJES,” J. C. VAN MILTENBURGP and A. SCHUIJFF b a Netherlands Energy Research Foundation ECN, Petten, The Netherlands b Department of General Chemistry, State University Utrecht, Padualaan 8, 3508 TB Utrecht, The Netherlands (Received 2 April 1986; in final form 18 June 1986) The low-temperature (5 to 330 K) heat capacity of Cs,Te has been measured by adiabatic calorimetry, and smoothed values of its thermodynamic functions C&,,(T), A&Y:(T), and AT298,15KHk(T) have been computed. High-temperature enthalpy increments of this compound have been measured by drop calorimetry. From the results smoothed thermodynamic functions of the compound are given up to 1000 K.
1. Introduction In (tellurium + caesium) several compounds have been identified.(l) Of these Cs,Te is of importance because it plays a role in the safety of water-cooled nuclear reactors, tellurium and caesium being produced by fission of the uranium fuel and both belonging to the main volatile products of the “source term”. Although it is known that Cs,Te is volatile,“) quantitative results are lacking on its stability at the temperatures that would result during a loss-of-coolant experiment. Hence, we investigated the thermodynamic properties of this compound. In this paper we present the results of a study of the low-temperature heat capacity and the hightemperature enthalpy increments.
2. Experimental Cs,Te was prepared by direct reaction of caesium vapour with solid tellurium at about 500 K, in a closed evacuated Pyrex capsule. Before reaction, tellurium was purified by melting it in a hydrogen stream at 775 K for 3 h. After the experiment TeO, could be removed from the surface. Powdered tellurium was put into a Pyrex capsule; in the same capsule three smaller Pyrex capsules containing the caesium were placed. The large capsule was then evacuated, sealed, and slowly heated. From 400 K on the reaction started, and caesium vapour escaping from the small capsules reacted with tellurium in the bottom of the large capsule. The temperature was 0021-9614/87/030293 +05 $02.00/O
0 1987 Academic Press Inc. (London) Limited
294
E. H. P. CORDFUNKE
ET AL.
gradually raised to 500 K at which temperature the capsule was kept for 3 d. Then, the temperature was raised again to 550 K at which temperature the large capsule was kept for 5 d. Finally, still further heating to 575 K for 5 d completed the reaction. The resulting product was mostly black due to the presence of Cs,Te,. To convert this to Cs,Te, the sample was thoroughly powdered in a glove box and heated with some extra caesium at 575 K. The excess caesium was removed by distilling off at about 625 K. The resulting product was yellow green, and, according to the X-ray pattern,“) phase pure. The tellurium content was determined gravimetrically as tellurium metal.13’ After a correction for a small contamination by quartz glass, of which the mass percentage after dissolving the Cs,Te in (3.0 mol. dmn3 H,SO, + 0.10 mol. dmm3 K,Cr,O, + 0.010 mol. dm- 3 MnSO,} was determined to be (0.57 *0.26), the mass percentage of tellurium appeared to be (32.3140.03); the calculated value is 32.43. The caesium content was determined with kalignost (after removal of tellurium and SiO,); the mass percentage was (67.59 k 0.08) and the calculated value is 67.57. Cs,Te is extremely sensitive to oxygen and water vapour; for this reason all handlings were carried out in a glove box filled with dry argon. The apparatus and the general measuring procedure for low-temperature heat capacities have been described in detail. (4) About 16 g of the sample was used in the calorimeter which was evacuated and closed after admission of about 1 kPa of helium. The heat-capacity measurements were made in calorimeter V which was tested with a standard sample of sapphirec5’ and with n-heptane.@) For standard sapphire a correspondence with the results of the N.B.S. from 80 to 340 K to within 0.1 per cent was found. Below 80 K the correspondence for n-heptane ranges from 0.1 per cent at 80 K to 2 per cent at 15 K. Temperatures were determined with a 100 Q platinum thermometer calibrated by Oxford Instruments to within 0.01 K. An automatic a.c. bridge was used; relative temperatures were read to 0.0002 K. The collection of results and the timing of the runs were automated. The thermal history of the sample was as follows: after loading the calorimeter it was cooled to about 80 K, left overnight, then the cryostat was cooled using liquid helium, and the sample was cooled to about 5 K in 20 h. The remaining liquid helium was sufficient for a 30 h measuring period between 5 and 80 K without refilling. Below 30 K several runs were made; these runs are incorporated in the experimental values in order of increasing temperature. The experimental results in table 1 have been corrected for a small impurity of SiOz ((0.57kO.26) mass per cent), and the experimental molar heat capacities are listed in order of ascending temperature. The measurements of high-temperature enthalpy increments were performed in a diphenyl-ether drop calorimeter described by Cordfunke et al.(‘) The energy equivalent of the calorimeter was determined by means of calibrations with spherical pieces of a-quartz. A calibration factor of the ratio of energy input to the mass of mercury of (79.977 kO.063) J. g- l was obtained. For the drop-calorimetric studies, a spherical vitreous silica ampoule with 0.6 mm wall thickness and 20 mm diameter was used to contain the sample. The ampoule was about 4.2 cm3 in volume and had a mass of about 1.5 g empty. Energy from the sample and ampoule, when they were dropped into the calorimeter, melted solid diphenyl in equilibrium with its liquid in
THERMODYNAMIC
PROPERTIES
OF Cs,Te
295
TABLE 1. Molar heat capacity of Cs,Te at constant pressure and at the mean temperature (T) measurements
C;,, J.K-‘.mol-’
5.42 5.61 5.98 6.23 6.33 6.44 6.54 6.88 7.15 7.36 7.66 7.78 8.11 8.20
8.51 8.65 8.74 9.12 9.89 10.82 11.62 13.19 15.40 16.18 16.25 16.96 17.03 17.69 17.74 20.28 22.07 23.66 25.10 26.43 27.68
2.49 2.84 3.09 3.48 3.74 3.90 4.07 4.33 4.69 4.88
5.10 5.50 5.64 6.08 6.17 6.55 6.74 7.17 8.17 9.44 10.39 14.28
18.80 20.18 20.26 21.69 21.84 23.07 23.13 28.15 31.21 33.91 36.22 38.09 40.15
CT) K 30.68 33.15 35.40 37.48 39.41 41.23 42.96 44.60 46.18 48.99
51.03 52.98 54.85 56.66 58.41 60.10 61.75 63.35 64.91 66.44 67.94 69.41 10.86 72.28 73.68 75.06 76.42 77.76 79.09 80.39 81.68 82.96 84.22 85.47 86.71
C;a,
CT)
J.K-‘.mol-’ 44.19 47.10 49.59 51.42 52.93 54.35 55.67 56.79 57.79 59.35 60.45 61.33 62.24 62.95 63.76 64.52 65.23 65.95 66.58 66.98 67.18 67.42 67.56 67.75 68.00 68.25 68.50 68.78 69.05 69.24 69.42 69.62 69.81 69.96 70.03
K
C;,, J.K-‘,mol-’
-
87.93 89.15 91.38 92.33 93.27 96.95 101.46 105.86
110.18 114.41
/
118.57 122.66 130.72 134.67 138.58 142.45 146.29
150.10 153.88 157.63 161.35 165.05 168.73 172.39 176.03 179.66 183.26 186.85 190.43 193.99 197.53 201.07 204.59 208.11 211.61
70.34 70.48 70.48 70.40 70.47 71.00 71.47 71.96 72.29 72.60 72.89 13.49 73.58 73.73 73.89 74.08 74.25 74.43 74.58 74.15 74.89 75.01 75.13 75.23 75.33 75.46 75.52 75.64 75.83 75.95 75.91 76.02 76.11 76.18 76.26
(7’) 7
of the
c;. m J.K-‘.mol-’
215.10 218.58 222.06 225.52 228.97 232.42 235.86 239.29 242.72 246.14 249.55 252.95 256.35 259.74 263.12 266.50 269.87 273.24 276.61 283.31 286.62 289.90 293.18 296.46 299.74 303.01 304.15 307.41 310.67 313.94 317.22 330.28 336.17 340.00
76.37 76.43 76.54 76.61 76.69 76.78 76.80 76.87 76.94 77.02 77.08 77.41 77.24 77.32 77.41 77.54 77.58 77.69 77.80 77.65 77.86 78.29 78.12 78.31 78.19 78.37 78.40 78.52 78.59 78.91 78.80 78.86 78.96 78.96
TABLE 2. Calorimetric enthalpy-increment measurements; 6 is the discrepancy from equation (1) T
AT98.15KH~(T)/(J.mol-‘)
K
expt
talc.
467.9 485.7 520.0 548.4 585.5 592.6 619.7 647.7
13685 15128 17966 20361 23360 24046 26370 28875
13622 15090 17942 20324 23466 24071 26391 28807
10% 0.46 0.25 0.13
0.18 -0.45
-0.10 -0.08 0.24
T
AT98.15KH~(T)I(J.mol-1)
z
expt
talc.
672.9 680.9 702.6 703.9 728.7 770.0 798.7
30792 31755 33655 33548 36187 39307 42335
30998 31697 33599 33714 35903 39582 42163
1026
-0.66 0.18 0.17 -0.49 0.79 -0.69 0.41
296
E. H. P. CORDFUNKE
ET AL.
a closed system. The resulting volume increase of the ether was determined by weighing the displaced mercury. Temperature measurements in the furnace were made with calibrated Pt-to-(Pt + 10 mass per cent of Rh) thermocouples to within +O.l K. The enthalpy contributions of the vitreous silica were determined in separate experiments. The ampoule contained 5.7625 g of Cs,Te. The results of the measurements are listed in table 2. A correction was made for the difference in enthalpy between the final calorimeter temperature and the standard reference temperature, 298.15 K, using C&(298.15 K). 3. Results Smoothed standard molar heat capacities Ci, m and values of A$;( 7’) and A,TH;( T) at regular temperature intervals are given in table 3. These values were calculated by first interpolating the experimental heat capacities (using the Newton algorithm) every 2 K; numerical integration of these values yielded the other functions. The low-temperature entropy and the enthalpy (below 15 K) were obtained by fitting the experimental results using a plot of T2 against C&,/T and extrapolating to T = 0 and C&/T = 0. The results of the drop-calorimetric measurements, as given in table 2, can be represented over the range of the experimental measurements as a function of temperature by a polynomial expression of the form: A,T,,.ISKH~(T)/(J.mol-l) = 71.0132(T/K)+12.0523~ 10-3(T/K)2-22244, (1) the coefficients of which were obtained by least squares. The boundary condition applied was C,, ,(298.15 K) = 78.2 J. K- * . mol-‘. The standard deviation is 0.43 per cent. It should be noted that in the usual expression: ATgbs.r5kH&(T) = a(T/K) + b( T/K)2 + c(K/T) + D, c = 0. Smoothed values of the thermodynamic functions of Cs,Te are listed in table 3. TABLE T E 5 10 50 100 150 200 250 300 298.15
co,. Ill J.K-‘.mol-’ 1.94 8.20 59.9 71.3 74.4 16.0 17.2 78.2 78.2
A%%(T) J,K-‘.mol-’ 0.65 3.87 56.1 103.1 132.7 154.4 171.4 185.6 185.1
3. Thermodynamic A;W1(7’) J,mol-’ 2.43 21.40 1621 5003 8662 12421 16255 20142 19997
functions T jf
of Cs,Te
VP. m J.K-‘.mol-’
298.15 300 400 500 600 700 800 900 1000
A,7XdT) J.K-‘.mol-l
78.2 78.3 80.7 83.1 85.5 87.9 90.3 92.7 95.1
185.1 185.6 208.4 226.7 242.0 255.4 267.3 278.1 288.0
Gw,,,,GdTl J.mol-’ 0 145 8090 16276 24703 33371 42280 51430 60822
4. Discussion The high-temperature enthalpy increments fit the low-temperature heat capacities smoothly. Any previous thermochemical measurements on Cs,Te(s) are lacking, as
THERMODYNAMIC
PROPERTIES
OF Cs,Te
297
far as we know. The molar heat capacity of Cs,Te at low temperatures compares well with that of 2CsI. It has been shown from lattice-dynamics calculations that CsI, which has the C&l-structure, below 80 K behaves as a quasi-harmonic oscillator. At higher temperatures anharmonic contributions to the heat capacity can be described satisfactorily with a deformation-dipole model. Below 25 K the heat capacity of Cs,Te increases more rapidly than that of CsI which indicates that O,(O), the Debye temperature of Cs,Te at T -+ 0, and thus vD, the frequency of the Debye distribution, has a lower value. From the expression for the molar heat capacity C, m = (127c4/5)R( T/0,J3 we calculate for T --) 0, On(O) z 70 K, a value which is indeed low compared with 127 K for CSI.(*,~) The authors wish to thank analyses.
Mr P. van Vlaanderen
for carrying out the X-ray
REFERENCES 1. Prim, G.; Cordfunke, E. H. P. J. Less Common Met. 1984, 104, Ll. 2. Cordfunke, E. H. P.; Kleverlaan, F. Thermochim. Acta 1986, 102, 387. 3. Vogel, A. I. A Textbook of Quantitative Inorganic Analysis. 3rd Edition. Longmans Green: London. 1961, p. 509. 4. Schaake, R. C. F.; Offringa, J. C. A.; Berg, G. J. K. van der; Miltenburg, J. C. van. Rec. Trav. Chim. Pays-Bas 1979, 9816, 408. 5. Certificate of the National Bureau of Standards, Standard Reference Material 720, Washington, 1982. 6. McCullough, J. P.; Messerly, J. F. U.S. Bur. Mines Bull. 596 1961. 7. Cordfunke, E. H. P.; Muis, R. P.; Prim, G. J. Chem. Thermodynamics 1979, 11, 819. 8. Sorai, M. J. Phys. Sot. Jpn 1968, 25, 421. 9. Lawless, W. N. Phys. Rev. B 1984, 30, 6057.
The thermodynamic di-caesium telluride, 800 K
properties of Cs,Te, from 5 to
E. H. P. CORDFUNKE,” W. OUWELTJES,” J. C. VAN MILTENBURGP and A. SCHUIJFF b a Netherlands Energy Research Foundation ECN, Petten, The Netherlands b Department of General Chemistry, State University Utrecht, Padualaan 8, 3508 TB Utrecht, The Netherlands (Received 2 April 1986; in final form 18 June 1986) The low-temperature (5 to 330 K) heat capacity of Cs,Te has been measured by adiabatic calorimetry, and smoothed values of its thermodynamic functions C&,,(T), A&Y:(T), and AT298,15KHk(T) have been computed. High-temperature enthalpy increments of this compound have been measured by drop calorimetry. From the results smoothed thermodynamic functions of the compound are given up to 1000 K.
1. Introduction In (tellurium + caesium) several compounds have been identified.(l) Of these Cs,Te is of importance because it plays a role in the safety of water-cooled nuclear reactors, tellurium and caesium being produced by fission of the uranium fuel and both belonging to the main volatile products of the “source term”. Although it is known that Cs,Te is volatile,“) quantitative results are lacking on its stability at the temperatures that would result during a loss-of-coolant experiment. Hence, we investigated the thermodynamic properties of this compound. In this paper we present the results of a study of the low-temperature heat capacity and the hightemperature enthalpy increments.
2. Experimental Cs,Te was prepared by direct reaction of caesium vapour with solid tellurium at about 500 K, in a closed evacuated Pyrex capsule. Before reaction, tellurium was purified by melting it in a hydrogen stream at 775 K for 3 h. After the experiment TeO, could be removed from the surface. Powdered tellurium was put into a Pyrex capsule; in the same capsule three smaller Pyrex capsules containing the caesium were placed. The large capsule was then evacuated, sealed, and slowly heated. From 400 K on the reaction started, and caesium vapour escaping from the small capsules reacted with tellurium in the bottom of the large capsule. The temperature was 0021-9614/87/030293 +05 $02.00/O
0 1987 Academic Press Inc. (London) Limited
294
E. H. P. CORDFUNKE
ET AL.
gradually raised to 500 K at which temperature the capsule was kept for 3 d. Then, the temperature was raised again to 550 K at which temperature the large capsule was kept for 5 d. Finally, still further heating to 575 K for 5 d completed the reaction. The resulting product was mostly black due to the presence of Cs,Te,. To convert this to Cs,Te, the sample was thoroughly powdered in a glove box and heated with some extra caesium at 575 K. The excess caesium was removed by distilling off at about 625 K. The resulting product was yellow green, and, according to the X-ray pattern,“) phase pure. The tellurium content was determined gravimetrically as tellurium metal.13’ After a correction for a small contamination by quartz glass, of which the mass percentage after dissolving the Cs,Te in (3.0 mol. dmn3 H,SO, + 0.10 mol. dmm3 K,Cr,O, + 0.010 mol. dm- 3 MnSO,} was determined to be (0.57 *0.26), the mass percentage of tellurium appeared to be (32.3140.03); the calculated value is 32.43. The caesium content was determined with kalignost (after removal of tellurium and SiO,); the mass percentage was (67.59 k 0.08) and the calculated value is 67.57. Cs,Te is extremely sensitive to oxygen and water vapour; for this reason all handlings were carried out in a glove box filled with dry argon. The apparatus and the general measuring procedure for low-temperature heat capacities have been described in detail. (4) About 16 g of the sample was used in the calorimeter which was evacuated and closed after admission of about 1 kPa of helium. The heat-capacity measurements were made in calorimeter V which was tested with a standard sample of sapphirec5’ and with n-heptane.@) For standard sapphire a correspondence with the results of the N.B.S. from 80 to 340 K to within 0.1 per cent was found. Below 80 K the correspondence for n-heptane ranges from 0.1 per cent at 80 K to 2 per cent at 15 K. Temperatures were determined with a 100 Q platinum thermometer calibrated by Oxford Instruments to within 0.01 K. An automatic a.c. bridge was used; relative temperatures were read to 0.0002 K. The collection of results and the timing of the runs were automated. The thermal history of the sample was as follows: after loading the calorimeter it was cooled to about 80 K, left overnight, then the cryostat was cooled using liquid helium, and the sample was cooled to about 5 K in 20 h. The remaining liquid helium was sufficient for a 30 h measuring period between 5 and 80 K without refilling. Below 30 K several runs were made; these runs are incorporated in the experimental values in order of increasing temperature. The experimental results in table 1 have been corrected for a small impurity of SiOz ((0.57kO.26) mass per cent), and the experimental molar heat capacities are listed in order of ascending temperature. The measurements of high-temperature enthalpy increments were performed in a diphenyl-ether drop calorimeter described by Cordfunke et al.(‘) The energy equivalent of the calorimeter was determined by means of calibrations with spherical pieces of a-quartz. A calibration factor of the ratio of energy input to the mass of mercury of (79.977 kO.063) J. g- l was obtained. For the drop-calorimetric studies, a spherical vitreous silica ampoule with 0.6 mm wall thickness and 20 mm diameter was used to contain the sample. The ampoule was about 4.2 cm3 in volume and had a mass of about 1.5 g empty. Energy from the sample and ampoule, when they were dropped into the calorimeter, melted solid diphenyl in equilibrium with its liquid in
THERMODYNAMIC
PROPERTIES
OF Cs,Te
295
TABLE 1. Molar heat capacity of Cs,Te at constant pressure and at the mean temperature (T) measurements
C;,, J.K-‘.mol-’
5.42 5.61 5.98 6.23 6.33 6.44 6.54 6.88 7.15 7.36 7.66 7.78 8.11 8.20
8.51 8.65 8.74 9.12 9.89 10.82 11.62 13.19 15.40 16.18 16.25 16.96 17.03 17.69 17.74 20.28 22.07 23.66 25.10 26.43 27.68
2.49 2.84 3.09 3.48 3.74 3.90 4.07 4.33 4.69 4.88
5.10 5.50 5.64 6.08 6.17 6.55 6.74 7.17 8.17 9.44 10.39 14.28
18.80 20.18 20.26 21.69 21.84 23.07 23.13 28.15 31.21 33.91 36.22 38.09 40.15
CT) K 30.68 33.15 35.40 37.48 39.41 41.23 42.96 44.60 46.18 48.99
51.03 52.98 54.85 56.66 58.41 60.10 61.75 63.35 64.91 66.44 67.94 69.41 10.86 72.28 73.68 75.06 76.42 77.76 79.09 80.39 81.68 82.96 84.22 85.47 86.71
C;a,
CT)
J.K-‘.mol-’ 44.19 47.10 49.59 51.42 52.93 54.35 55.67 56.79 57.79 59.35 60.45 61.33 62.24 62.95 63.76 64.52 65.23 65.95 66.58 66.98 67.18 67.42 67.56 67.75 68.00 68.25 68.50 68.78 69.05 69.24 69.42 69.62 69.81 69.96 70.03
K
C;,, J.K-‘,mol-’
-
87.93 89.15 91.38 92.33 93.27 96.95 101.46 105.86
110.18 114.41
/
118.57 122.66 130.72 134.67 138.58 142.45 146.29
150.10 153.88 157.63 161.35 165.05 168.73 172.39 176.03 179.66 183.26 186.85 190.43 193.99 197.53 201.07 204.59 208.11 211.61
70.34 70.48 70.48 70.40 70.47 71.00 71.47 71.96 72.29 72.60 72.89 13.49 73.58 73.73 73.89 74.08 74.25 74.43 74.58 74.15 74.89 75.01 75.13 75.23 75.33 75.46 75.52 75.64 75.83 75.95 75.91 76.02 76.11 76.18 76.26
(7’) 7
of the
c;. m J.K-‘.mol-’
215.10 218.58 222.06 225.52 228.97 232.42 235.86 239.29 242.72 246.14 249.55 252.95 256.35 259.74 263.12 266.50 269.87 273.24 276.61 283.31 286.62 289.90 293.18 296.46 299.74 303.01 304.15 307.41 310.67 313.94 317.22 330.28 336.17 340.00
76.37 76.43 76.54 76.61 76.69 76.78 76.80 76.87 76.94 77.02 77.08 77.41 77.24 77.32 77.41 77.54 77.58 77.69 77.80 77.65 77.86 78.29 78.12 78.31 78.19 78.37 78.40 78.52 78.59 78.91 78.80 78.86 78.96 78.96
TABLE 2. Calorimetric enthalpy-increment measurements; 6 is the discrepancy from equation (1) T
AT98.15KH~(T)/(J.mol-‘)
K
expt
talc.
467.9 485.7 520.0 548.4 585.5 592.6 619.7 647.7
13685 15128 17966 20361 23360 24046 26370 28875
13622 15090 17942 20324 23466 24071 26391 28807
10% 0.46 0.25 0.13
0.18 -0.45
-0.10 -0.08 0.24
T
AT98.15KH~(T)I(J.mol-1)
z
expt
talc.
672.9 680.9 702.6 703.9 728.7 770.0 798.7
30792 31755 33655 33548 36187 39307 42335
30998 31697 33599 33714 35903 39582 42163
1026
-0.66 0.18 0.17 -0.49 0.79 -0.69 0.41
296
E. H. P. CORDFUNKE
ET AL.
a closed system. The resulting volume increase of the ether was determined by weighing the displaced mercury. Temperature measurements in the furnace were made with calibrated Pt-to-(Pt + 10 mass per cent of Rh) thermocouples to within +O.l K. The enthalpy contributions of the vitreous silica were determined in separate experiments. The ampoule contained 5.7625 g of Cs,Te. The results of the measurements are listed in table 2. A correction was made for the difference in enthalpy between the final calorimeter temperature and the standard reference temperature, 298.15 K, using C&(298.15 K). 3. Results Smoothed standard molar heat capacities Ci, m and values of A$;( 7’) and A,TH;( T) at regular temperature intervals are given in table 3. These values were calculated by first interpolating the experimental heat capacities (using the Newton algorithm) every 2 K; numerical integration of these values yielded the other functions. The low-temperature entropy and the enthalpy (below 15 K) were obtained by fitting the experimental results using a plot of T2 against C&,/T and extrapolating to T = 0 and C&/T = 0. The results of the drop-calorimetric measurements, as given in table 2, can be represented over the range of the experimental measurements as a function of temperature by a polynomial expression of the form: A,T,,.ISKH~(T)/(J.mol-l) = 71.0132(T/K)+12.0523~ 10-3(T/K)2-22244, (1) the coefficients of which were obtained by least squares. The boundary condition applied was C,, ,(298.15 K) = 78.2 J. K- * . mol-‘. The standard deviation is 0.43 per cent. It should be noted that in the usual expression: ATgbs.r5kH&(T) = a(T/K) + b( T/K)2 + c(K/T) + D, c = 0. Smoothed values of the thermodynamic functions of Cs,Te are listed in table 3. TABLE T E 5 10 50 100 150 200 250 300 298.15
co,. Ill J.K-‘.mol-’ 1.94 8.20 59.9 71.3 74.4 16.0 17.2 78.2 78.2
A%%(T) J,K-‘.mol-’ 0.65 3.87 56.1 103.1 132.7 154.4 171.4 185.6 185.1
3. Thermodynamic A;W1(7’) J,mol-’ 2.43 21.40 1621 5003 8662 12421 16255 20142 19997
functions T jf
of Cs,Te
VP. m J.K-‘.mol-’
298.15 300 400 500 600 700 800 900 1000
A,7XdT) J.K-‘.mol-l
78.2 78.3 80.7 83.1 85.5 87.9 90.3 92.7 95.1
185.1 185.6 208.4 226.7 242.0 255.4 267.3 278.1 288.0
Gw,,,,GdTl J.mol-’ 0 145 8090 16276 24703 33371 42280 51430 60822
4. Discussion The high-temperature enthalpy increments fit the low-temperature heat capacities smoothly. Any previous thermochemical measurements on Cs,Te(s) are lacking, as
THERMODYNAMIC
PROPERTIES
OF Cs,Te
297
far as we know. The molar heat capacity of Cs,Te at low temperatures compares well with that of 2CsI. It has been shown from lattice-dynamics calculations that CsI, which has the C&l-structure, below 80 K behaves as a quasi-harmonic oscillator. At higher temperatures anharmonic contributions to the heat capacity can be described satisfactorily with a deformation-dipole model. Below 25 K the heat capacity of Cs,Te increases more rapidly than that of CsI which indicates that O,(O), the Debye temperature of Cs,Te at T -+ 0, and thus vD, the frequency of the Debye distribution, has a lower value. From the expression for the molar heat capacity C, m = (127c4/5)R( T/0,J3 we calculate for T --) 0, On(O) z 70 K, a value which is indeed low compared with 127 K for CSI.(*,~) The authors wish to thank analyses.
Mr P. van Vlaanderen
for carrying out the X-ray
REFERENCES 1. Prim, G.; Cordfunke, E. H. P. J. Less Common Met. 1984, 104, Ll. 2. Cordfunke, E. H. P.; Kleverlaan, F. Thermochim. Acta 1986, 102, 387. 3. Vogel, A. I. A Textbook of Quantitative Inorganic Analysis. 3rd Edition. Longmans Green: London. 1961, p. 509. 4. Schaake, R. C. F.; Offringa, J. C. A.; Berg, G. J. K. van der; Miltenburg, J. C. van. Rec. Trav. Chim. Pays-Bas 1979, 9816, 408. 5. Certificate of the National Bureau of Standards, Standard Reference Material 720, Washington, 1982. 6. McCullough, J. P.; Messerly, J. F. U.S. Bur. Mines Bull. 596 1961. 7. Cordfunke, E. H. P.; Muis, R. P.; Prim, G. J. Chem. Thermodynamics 1979, 11, 819. 8. Sorai, M. J. Phys. Sot. Jpn 1968, 25, 421. 9. Lawless, W. N. Phys. Rev. B 1984, 30, 6057.