Molar heat capacity and thermodynamic functions of zirconolite CaZrTi2O7

J. Chem. Thermodynamics 1999, 31, 245–253 Article No. jcht.1998.0447 Available online at http://www.idealibrary.com on

Molar heat capacity and thermodynamic functions of zirconolite CaZrTi2 O7 Brian F. Woodfield,a Juliana Boerio-Goates, Jennifer L. Shapiro, Brigham Young University, Department of Chemistry and Biochemistry, Provo, UT 84602, U.S.A.

Robert L. Putnam, and Alexandra Navrotsky University of California, Davis, Thermochemistry Facility, Department of Chemical Engineering and Materials Science, Davis, CA 95616, U.S.A. Zirconolite (CaZrTi2 O7 ) has been proposed as a host phase for excess weapons plutonium, K S o and other derived thermodynamic functions are and the standard molar entropy 1298.15 m 0 needed to describe it completely. The heat capacity of CaZrTi2 O7 has been measured from T ≈ 20 K to T ≈ 400 K with an adiabatic calorimeter. A six-term fitting equation based on Debye and Einstein functions has been shown to represent the heat capacity over the entire range of temperature to within the experimental uncertainty. This equation has been used to calculate the thermodynamic functions to T = 400 K and to extrapolate these functions K S o for CaZrTi O is 193.3 J · K−1 · mol−1 . to T = 1500 K. In particular, 1298.15 2 7 m 0

c 1999 Academic Press

KEYWORDS: zirconolite; CaZrTi2 O7 ; entropy; heat capacity; nuclear waste; plutonium disposition

1. Introduction With the end of the Cold War significant quantities of weapons-grade plutonium and uranium have been classified as “surplus” material requiring disposition. In their present form, these materials could easily be utilized in weapons and pose a substantial national security risk. Chemical immobilization in a ceramic mineral form,(1–4) or vitrification(4, 5) of the plutonium and uranium reduces this risk to a level similar to that of spent nuclear fuel and makes plutonium recovery for weapons use difficult. The U.S. Department of Energy has identified ceramic minerals as the preferred form for plutonium disposition by immobilization. Among the proposed ceramic host phases are zircon (A,Zr)SiO4 ,(6) zirconolite, and pyrochlore Ca(A,Zr)Ti2 O7 ,(4) where A is an actinide element, primarily U4+ and Pu4+ . These minerals have been chosen because they occur naturally and contain significant quantities of actinide elements. The natural samples are also extremely refractory and have been a To whom correspondence should be addressed (E-mail: brian [email protected]).

0021–9614/99/020245 + 09 $30.00/0

c 1999 Academic Press

246

B. F. Woodfield et al.

shown to retain their actinide elements over periods of up to 2 · 109 years under a variety of weathering conditions.(4, 7) Both UO2 and PuO2 have been shown to have significant solid solubility in these minerals beyond the small amount found in natural samples; thus, these phases have potential as host ceramics for radioactive waste disposal. Little, however, is known about the thermodynamic stability of these minerals, especially when actinides are substituted on the scale that would be necessary for use as an economical waste form. So far, attempts at optimizing the compositions of pure waste forms have been wholly empirical,(4) yet the thermodynamic stability of a waste form has important implications for both the actual synthesis of the material and its long-term durability. In the United States, the waste forms are to be buried in a geological repository such as Yucca Mountain, Nevada. The susceptibility of the waste ceramic to dissolution or leaching by groundwater must be evaluated to ascertain its suitability as a disposal form.(4) Considerable effort has been expended to determine the dissolution chemistry and kinetics of proposed waste material formulations(4, 7) in aqueous fluids. Because dissolution and transport in groundwater involves both kinetic and thermodynamic parameters, the thermodynamic data provide a starting point for predicting the solubilities of newer, less characterized actinide-bearing mineral formulations. A multi-laboratory collaboration has been established to obtain the formation energetics for a series of proposed ceramic waste forms. High-temperature oxide-melt solution calorimetry, which has been used to characterize a wide variety of materials,(8–10) provides a means to obtain enthalpies of formation for refractory oxides such as the proposed waste storage materials. (See Navrotsky(11) for a review of this technique.) Low-temperature heat capacity measurements allow the third-law entropy and the enthalpy to be calculated as a function of temperature, which, in turn, can be used to calculate the Gibbs free energy as a function of temperature. These data are critical components of the thermodynamic data bases used to design and assess disposition materials. They are necessary to predict relative solubilities of differing waste form compositions and hosts, to model phase equilibria and stability fields for mineral synthesis and waste form optimization, and to validate non-radioactive analogs (e.g. Ce4+ ) for the actinide elements in the solid state. In this paper, we report heat capacity measurements from T ≈ 20 K to T ≈ 400 K for zirconolite, one of the principal end-member materials proposed as a waste form. Third-law entropies and other thermodynamic functions have been obtained from appropriate integrations of the experimental heat capacities. The heat capacity results and thermodynamic functions have been extrapolated to T = 1500 K using an empirical fitting equation.

2. Experimental The zirconolite sample was synthesized at Lawrence Livermore National Laboratory from Ca(OH)2 , Zr(NO3 )4 · 5H2 O, and TiO2 as starting materials. Details of the synthetic method can be found in reference 12. Powder X-ray diffraction showed the sample to be zirconolite, but electron microprobe analysis revealed the presence of tetragonal ZrO2 as small singlephase inclusions within the zirconolite grains. Therefore, the sample was considered to be a mechanical mixture of ZrO2 and zirconolite. The electron microprobe analysis also showed there to be 8.24 · 10−2 mol of ZrO2 per mol of CaZrTi2 O7 .(12) The sample mass used in

C p,m and thermodynamic function of zirconolite CaZrTi2 O7

247

the calorimetric measurements was 15.9640 g; after correcting for the ZrO2 inclusions, the resulting mass of CaZrTi2 O7 was 15.4998 g and the mass of ZrO2 was 0.4642 g. The basic calorimeter, cryostat, and data acquisition system have been described elsewhere.(13, 14) However, some aspects of the apparatus have been modified. The Labview® (National Instruments, Austin, Texas) software that interfaced the data acquisition instrumentation to the computer has been replaced by a BASIC program that allows for a postexperiment examination of the temperature drifts. This provides for more flexibility and consistency in temperature extrapolations. The (Au, Co + Chromel P) thermocouple between the calorimeter and adiabatic shield has been replaced by a Type E (Alumel + Chromel P) thermocouple so that the upper operating temperature of the calorimeter could be extended to T = 400 K. The Leeds and Northrup 25.5  capsule thermometer has been calibrated against a Lakeshore germanium thermometer (serial number 26945) below T = 13.8 K, and against a Rosemount model 162D 25.5  platinum thermometer (serial number 4253) from T = 13.8 K to T = 300 K. The temperature scale of both reference thermometers is traceable to the ITS-90 scale by their manufacturers. The newly calibrated Leeds and Northrup thermometer is believed to reproduce the ITS-90 scale to within ±1·10−2 K from T = 4.2 K to T = 8 K, ±8 · 10−3 K from T = 8 K to T = 20 K, and ±5 · 10−3 from T = 20 K to T = 300 K. Above T = 300 K, we use the original IPTS-68 calibration of the thermometer and apply a correction factor to those temperatures using the equation of Ott and Goates.(15) In the highest temperature range, we estimate that we reproduce the ITS-90 temperature scale to within 1 · 10−2 K.

3. Results The experimental heat capacities, corrected for the empty calorimeter, helium exchange gas, gold gasket, and the ZrO2 impurity, are listed in table 1 in chronological order, and displayed graphically in figure 1. Corrections for curvature were made by using conventional procedures, and the heat capacity contribution of tetragonal ZrO2 was taken from Kelley,(16) and Coughlin and King.(17) At T = 400 K, the zirconolite contribution is 25 per cent of the measured heat capacity and decreases to less than 5 per cent at T < 20 K. Given this small sample contribution and the increased uncertainty in the measurements at T < 20 K, the data in table 1 are tabulated only above T = 20 K. The ZrO2 impurity contributes at most 0.7 per cent to the total heat capacity.

4. Discussion In order to calculate the smoothed heat capacity and thermodynamic functions, it is typical to fit the experimental data with some smoothing function and to use a T 3 limiting law below the lowest temperature to extrapolate to T → 0. In the case of the data reported here, we were hesitant to use a simple limiting law because the zirconolite contributes such a small fraction to the total heat capacity at low temperatures, and because the results have larger uncertainties at T < 20 K. Kelley and King(18) describe a method of extrapolating

248

B. F. Woodfield et al. TABLE 1. Experimental molar heat capacity C p,m of CaZrTi2 O7 corrected for the ZrO2 impurity and curvature (M = 339.10 g · mol−1 ) T K

C p,m −1 J · K−1 · mol

Series 1 58.12 66.28 70.75 75.50 80.29 85.13 90.01 94.92

26.813 35.598 40.410 45.685 51.179 56.729 62.350 67.944

Series 2 94.84 99.77 104.73 109.72 114.73 119.75 124.79 129.85 134.91 139.99 145.07 150.17

67.799 73.332 78.844 84.322 89.725 95.006 100.18 105.38 110.29 115.17 120.03 124.69

T K

C p,m −1 −1 J · K · mol

T K

203.93 209.07 214.22

166.19 169.54 172.61

331.49 336.68 Series 6

184.05 189.37 194.51 199.65 204.79 209.94 215.09 220.24 225.40 230.55 235.71 240.87 246.03 251.19 256.35 261.52 266.68 271.85 277.02 282.18

152.62 156.48 160.12 163.63 166.92 170.22 173.40 176.66 179.61 182.40 185.14 187.97 190.30 192.59 195.01 197.54 199.56 201.36 204.18 206.46

Series 5 117.53 122.30 126.96 131.42 135.80 140.00 144.03 147.98 151.80 155.62 159.31 162.84

222.33 223.89

Series 4

Series 3 142.43 147.55 152.65 157.75 162.86 167.98 173.10 178.23 183.36 188.50 193.64 198.78

C p,m −1 J · K−1 · mol

274.66 279.71 284.89 290.06 295.23 300.41 305.59 310.77 315.96 321.14 326.31

203.16 205.30 207.29 209.42 211.06 212.61 214.01 215.98 217.62 219.21 220.78

332.79 337.57 342.75 347.93 353.11 358.30 363.48 368.66 373.84 379.02 384.20 389.38 394.56

223.21 224.30 225.66 227.10 228.61 229.95 230.85 232.12 233.24 234.45 235.45 236.54 237.53

Series 7 21.15 23.03 27.93 32.42 34.89 37.90 41.19 44.85 48.94 53.31 57.78

1.7966 2.1886 4.0199 5.5850 6.9108 8.7832 11.123 13.997 18.224 21.372 25.648

Series 8 53.52 58.28 62.82 67.45 72.15

22.425 27.151 31.702 36.688 41.893

C p,m and thermodynamic function of zirconolite CaZrTi2 O7

249

250 200 360

400

600

800

1000

1200

1400

340 30

320

200

300 25

o

Cp,m/(J·K–1mol–1)

280 260

150

240

20

220 200

15

180

100

160 10 140 120

50

5

100

0

0

0

50

100

10

150

20

200

30

250

40

300

0 60

50

350

400

T/K FIGURE 1. Experimental heat capacities C op,m of CaZrTi2 O7 corrected for the ZrO2 impurity. The inset on the lower right shows the low-temperature data on an expanded scale, and the inset on the upper left shows the high-temperature heat capacities to T = 400 K and the heat capacity point at T = 1023 K calculated from enthalpy increment measurements. —, fit with equation (3) for which the coefficients are given in table 2. The series are represented by various symbols. (M = 339.10 g · mol−1 .)

TABLE 2. Coefficients obtained from a fit of the experimental heat capacity with equation (3), and used in the calculation of the data in table 3 Parameter

Coefficient

m

5.5902

θD

417.33 K

n

4.8832

θE

725.66 K

A1

22.550

A2

0.028109

250

B. F. Woodfield et al. TABLE 3. Standard molar thermodynamic properties of CaZrTi2 O7 . The values at T > 400 K are extrapolated using equation (3) and the coefficients in table 2. o − 1T H o /T (M = 339.10 g · mol−1 and p o = 101.325 kPa) 8om ≡ 10T Sm 0 m T K

C op,m −1 J · K−1 · mol

o 10T Sm

−1 J · K−1 · mol

o /T 10T Hm

−1 J · K−1 · mol

8om −1 −1 J · K · mol

5

0.1321

0.1193

0.0613

0.0581

10

0.3778

0.2767

0.1511

0.1257

15

0.8491

0.5096

0.2974

0.2122

20

1.658

0.8553

0.5282

0.3270

25

2.917

1.351

0.8717

0.4795

30

4.731

2.034

1.355

0.6788

7.186

35

2.939

2.005

0.9342

40

10.32

4.096

2.841

1.254

45

14.11

5.524

3.877

1.647

50

18.49

7.233

5.115

2.118

60

28.56

11.47

8.163

3.309

70

39.63

16.70

11.86

4.837

80

51.05

22.73

16.04

6.690

90

62.46

29.41

20.57

100

73.66

36.57

25.32

11.25

110

84.58

44.11

30.21

13.89

120

95.16

51.92

35.19

16.73

8.838

130

105.4

59.94

40.20

19.75

140

115.1

68.11

45.20

22.91

150

124.4

76.37

50.18

26.20

160

133.3

84.69

55.10

29.59

170

141.6

93.02

59.94

33.08

180

149.5

101.3

64.70

36.64

190

156.9

109.6

69.36

40.26

200

163.8

117.9

73.91

43.94

210

170.3

126.0

78.35

47.65

220

176.3

134.1

82.67

51.40

230

182.0

142.0

86.87

55.17

240

187.3

149.9

90.94

58.95

250

192.2

157.6

94.89

62.74

260

196.8

165.3

98.73

66.54

270

201.2

172.8

102.4

70.33

273.15

202.5

175.1

103.6

71.53

C p,m and thermodynamic function of zirconolite CaZrTi2 O7

251

TABLE 3—continued T K

C op,m

o 10T Sm

o /T 10T Hm

8om −1 −1 J · K · mol

−1 J · K−1 · mol

−1 J · K−1 · mol

−1 J · K−1 · mol

280

205.2

180.2

106.0

74.13

290

209.0

187.4

109.5

77.91

298.15

211.9

193.3

112.3

80.98

300

212.6

194.6

112.9

81.68

320

219.1

208.5

119.3

89.17

340

224.8

222.0

125.4

360

230.0

235.0

131.0

103.9

380

234.7

247.5

136.4

111.1

400

238.9

259.7

141.4

118.3

420

242.7

271.4

146.1

125.3

440

246.3

282.8

150.6

132.2

460

249.6

293.8

154.8

139.0

480

252.6

304.5

158.9

145.7

500

255.5

314.9

162.7

152.2

550

262.0

339.5

171.4

168.1

600

267.7

362.6

179.2

183.4

650

273.0

384.2

186.2

198.0

700

278.0

404.6

192.6

212.1

750

282.7

424.0

198.4

225.5

800

287.4

442.4

203.9

238.5

850

291.9

459.9

208.9

251.0

900

296.4

476.8

213.6

263.1

950

300.9

492.9

218.1

274.8

1000

305.5

508.5

222.4

286.1

1050

310.1

523.5

226.4

297.0

1100

314.7

538.0

230.3

307.7

1150

319.5

552.1

234.1

318.0

1200

324.3

565.8

237.8

328.0

1250

329.2

579.1

241.3

337.8

1300

334.2

592.1

244.8

347.3

1350

339.3

604.8

248.2

356.6

1400

344.6

617.3

251.6

365.7

1450

349.9

629.5

254.9

374.6

1500

355.4

641.4

258.1

383.3

96.59

252

B. F. Woodfield et al.

heat capacity data to low temperatures by using an equation of the form: o = 3R · {m · D(θD /T ) + n · E(θE /T )}, C V,m

(1)

where D(θD /T ) and E(θE /T ) are Debye and Einstein functions, respectively; m, n, θD , and θE are adjustable parameters; and (m + n) should be close to the number of atoms in the o and C op,m are very nearly the same, and equation (1) molecule. At low temperatures, C V,m should fit the experimental heat capacities well; however, to represent the experimental data o ˙ must be converted to C op,m . Zywoci´ nski(19) has suggested that, at higher temperatures C V,m o o to a first approximation, the correction of C V,m to C p,m can be of the form: o + A1 · (T /K) + A2 · (T /K)2 . C op,m = C V,m

(2)

Combining equations (1) and (2) then gives a fitting equation of the form: C op,m = 3R · {m · D(θD /T ) + n · E(θE /T )} + A1 · (T /K) + A2 · (T /K)2 .

(3)

The linear term in equation (3) can give high values to C op,m at T < 10 K but, because C op,m is small, the error will be insignificant when calculating the thermodynamic functions. We have fit our experimental data with equation (3) and have found deviations from the fit to be less than ±0.2 per cent above T = 50 K, and increasing to ±5 per cent at T = 20 K. Parameters obtained from the fit are given in table 2. Considering the relatively small contribution the zirconolite makes to the total measured heat capacity, we believe that this is an excellent representation of the experimental data. Smoothed heat capacities and thermodynamic functions calculated using this fit with equation (3) are given in table 3. o for CaZrTi O derived from the Sm It is instructive to compare the value of 1298.15 2 7 0 o of the Sm heat capacity measurements with estimates obtained by summing the 1298.15 0 298.15 o 298.15 o (20) Sm for zirconolite calculated from 10 Sm for CaO, constituent oxides. The 10 −1

ZrO2 , 2TiO2 is 189.7 J · K−1 · mol J · K−1

o calculated using perovskite CaTiO , , while 1298.15 Sm 3 0 −1

· mol . Thus, these two entropy estimates bracket the ZrO2 , and TiO2 , is 194.6 −1 −1 value of 193.3 J · K · mol obtained from our heat capacity measurements. As part of the thermodynamic description of the ceramic host materials, it would be useful to extend the calculated thermodynamic functions to temperatures above T = 1000 K. We have used equation (3) to provide an estimate of C op,m to T = 1500 K. Included at the end of table 3 are extrapolated values for C op,m and the thermodynamic functions at smoothed temperatures up to T = 1500 K. To test the validity of the extrapolation, a mean −1 value for C op,m of (308.8 ± 6) J · K−1 · mol was calculated at T = 1023 K from enthalpy increments measured at T = 973 K, T = 1046 K, and T = 1073 K on the same sample of CaZrTi2 O7 .(12) Our extrapolated value for C op,m from the fitting equation at T = 1023 K −1 is 307.6 J · K−1 · mol , which is in excellent agreement with that calculated from the enthalpy measurements. We wish to acknowledge Bart Ebbinghaus and Rich VanKonynenburg at Lawrence Livermore National Laboratory for synthesis of the zirconolite sample

C p,m and thermodynamic function of zirconolite CaZrTi2 O7

253

References 1. }Ewing, R. C.; Weber, W. J.; Lutz, W. Disposal of Weapon Plutonium, Crystalline Ceramics: waste forms for the disposal of weapons plutonium. Merz, E. R.; Walter, C. E.: editors. Kluwer: Netherlands. 1996. 2. }Ebbinghaus, B. B.; VanKonynenburg, R. A.; Vance, E. R.; Jostons, A.; Anthony, R. G.; Philip, C. V.; Wronkiewicz, D. J. Proceedings of the U.S. Department of Energy Plutonium Stabilization and Immobilization Workshop. Department of Energy: Washington DC. 1995, pp. 253–261. 3. }Vance, E. R.; Jostsons, A.; Day, R. A.; Ball, C. J.; Begg, B. D.; Angel, P. J. Mater. Res. Soc. Symp. Proc. 1996, 412, 41–47. 4. }Radioactive Waste forms for the Future. Lutze, W.; Ewing, R. C.: editors. North Holland: New York. 1988. 5. }Makhijani, A.; Makhijani, A. Fissile Materials: in a glass, darkly. IEER Press: Takoma Park, MD. 1995. 6. }Ewing, R. C.; Lutze, W.; Weber, W. J. J. Mater. Res. 1995, 10, 2, 243–246. 7. }Smith, K. L.; Blackford, M. G.; Lumpkin, G. R.; Hart, K. P.; Robinson, B. J. Mater. Res. Soc. Symp. Proc. 1996, 412, 313–319. 8. }Liu, J.; Topor, L.; Zhang, J.; Navrotsky, A.; Lieberman, R. S. Phys. Chem. Miner. 1996, 23, 11–16. 9. }Lamberti, V. E.; Rodriguez, M. A.; Trybulski, J. D.; Navrotsky, A. Materials 1997, 9, 932. 10. }Leinweber, K.; Linton, J.; Navrotsky, A.; Parise, J. B. Phys. Chem. Miner. 1995, 22, 251–258. 11. }Navrotsky, A. Phys. Chem. Mineral. 1997, 24, 222. 12. }Putnam, R. L.; Navrotsky, A.; Woodfield, B. F.; Boerio-Goates, J.; Shapiro, J. L. J. Chem. Thermodynamics 1999, 31, 229–243. 13. }Boerio-Goates, J.; Woodfield, B. F. Can. J. Chem 1988, 66, 645–650. 14. }Battley, E. H.; Putnam, R. L.; Boerio-Goates, J. Thermochim. Acta 1997, 298, 37. 15. }Ott, J. B.; Goates, J. R. J. Chem. Eng. Ref. Data 1996, 41, 669. 16. }Kelley, K. K. Ind. Eng. Chem. 1944, 36, 377. 17. }Coughlin, J. P.; King, E. G. J. Amer. Chem. Soc. 1950, 72, 2262–2265. 18. }Kelley, K. K.; King, E. G. Contribution to the Data on Theoretical Metallurgy. Part XIV. Entropies of the elements and inorganic compounds. Bulletin 592 (U.S. Bureau of Mines). 1961. 19. Zywoci´ }˙ nski, A. Personal communication, Institutue of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland. 20. }Robie, R. A.; Hemingway, B. S. Thermodynamic Properties of Minerals and Related Substances at 298.15 K and 1 bar (105 Pascals) Pressure and at Higher Temperatures. U.S. Government and Printing Office: Washington DC. 1995, p. 2131. (Received 1 April 1998; in final form 16 September 1998)

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