Molar heat capacities and thermodynamic functions of CaHfTi₂O₇(cr) and CaZr_0.26Hf_0.74Ti₂O₇(cr)

As part of an ongoing study of titanate-based ceramic materials for the disposal of surplus weapons plutonium, we report the molar heat capacities and thermodynamic functions for the zirconolite (CaZrTi₂O₇) analogue Hf-zirconolite (CaHfTi₂O₇) and a solid solution of the two: CaZr_0.26Hf_0.74Ti₂O₇. Measurements have been made on the solid solution to probe the extent (zirconolite + Hf-zirconolite) form ideal solutions. The molar heat capacity for both samples was measured from T = 13 K to T = 400 K in an adiabatic calorimeter and extrapolated to T = 1500 K with an equation fitted to the low-temperature results. The results at T = 298.15 K are Δ₀^{298.15 K}S_m^o = (196.98 ± 0.39) J·K⁻¹·mol⁻¹ for CaHfTi₂O₇ and δ₀^{298.15 K}S_m^o = (199.76 ± 0.39) J·K⁻¹·mol⁻¹ for CaZr_0.26Hf_0.74Ti₂O₇. Recent crystallographic measurements on zirconolite established the existence of disorder at the Ti(2) site which results in a zero-point entropy contribution of (1/2)·R·ln 2 not previously included in the thermodynamic tabulation for zirconolite. The molar entropies of CaHfTi₂O₇ and CaZr_0.26Hf_0.74Ti₂O₇ reported here include this zero-point entropy, and the solid solution includes an additional zero-point entropy contribution of 4.765 J·K⁻¹·mol⁻¹ to account for the random mixing of Zr⁴⁺ and Hf⁴⁺ on the zirconium crystallographic site. The large zero-point entropy associated with the solid solution implies a substantial entropy stabilization contribution for other nuclear waste disposition mixtures.