Heat capacities, standard entropies and Gibbs energies of Sr-, Rb- and Cs-substituted barium aluminotitanate hollandites

Heat capacities of Sr-, Rb-, and Cs-hollandite with the compositions Ba_1.14Sr_0.10Al_2.38Ti_5.59O₁₆, Ba_1.17Rb_0.19Al_2.46Ti_5.53O₁₆, and Ba_1.18Cs_0.21Al_2.44Ti_5.53O₁₆ were measured from T = (2 to 300) K using a Quantum Design Physical Property Measurement System (PPMS). From the heat capacity results, the following thermodynamic parameters have been determined. The characteristic Debye temperatures Θ_D over the temperature range (30 to 300) K of Sr-, Rb-, and Cs-hollandite are T = (178.2, 189.7, and 189.2) K, respectively, and their standard entropies at T = 298.15 K are (413.9 ± 8.3), (415.1 ± 8.3), and (419.6 ± 8.4) J · K^-1 · mol^-1. Combined with previously reported formation enthalpies, their corresponding Gibbs energies of formation from oxides (Δ_fG_ox°) are (-194.9 ± 11.4), (-195.0 ± 12.8), and (-201.1 ± 12.8) kJ · mol^-1, and those from elements (Δ_fG_el°) are (-7694.6 ± 12.5), (-7697.0 ± 13.9), and (-7697.1 ± 13.9) kJ · mol^-1 at T = 298.15 K. The similarities among the obtained Δ_fG_ox° values suggest that the three substituted hollandites have similar thermodynamic stabilities at standard conditions, which is in agreement with the ease of Cs-Rb-Sr substitutions in the hollandite structure.