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 Ba1.14Sr0.10Al2.38Ti5.59O16, Ba1.17Rb0.19Al2.46Ti5.53O16, and Ba1.18Cs0.21Al2.44Ti5.53O16 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 ΘD 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 (ΔfGox°) are (−194.9 ± 11.4), (−195.0 ± 12.8), and (−201.1 ± 12.8) kJ · mol−1, and those from elements (ΔfGel°) 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 ΔfGox° 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.