Hydration entropy of BaZrO3 from first principles phonon calculations
The impact of phonons on the hydration and defect thermodynamics of undoped and acceptor (Sc, In, Y and Gd) doped BaZrO3 is addressed by means of first principles supercell calculations. In contrast to previous, similar investigations, we evaluate contributions from all phonon modes, and also pressure/volume effects on the phonon properties. The calculations are performed at the GGA-level with the PBE and RPBE functionals, both of which predict for BaZrO3 a stable cubic perovskite structure. For all dopants, the vibrational formation entropy of the doubly positively charged oxygen vacancy is significantly lower than that of the protonic defect , which therefore also is the dominant contribution to the entropy of hydration, in addition to loss of H2O(g). The large, negative contribution from phonons to the formation entropy of stems both from large local structural relaxations, and contraction of the entire supercell and corresponding blue-shift of the phonon spectrum. Neglect of the phonon contribution to the vacancy free formation energy leads to a considerable error (100 kJ mol−1 at 1000 K). For the acceptor doped systems, the calculated hydration entropy becomes more negative in the order Y < Gd < In < Sc, which stems from that both the formation volume and vibrational formation entropy of and become more negative with increasing dopant ion size. Both functionals also give similar defect entropies for undoped, and Sc- and In-doped BaZrO3. However, for the larger Y- and Gd-ions, PBE underestimates (too negative) the vibrational formation entropies due to a poor representation of low frequency modes at the R point of the Brillouin zone. The calculated hydration entropies are in good agreement with experimental results, lending support to the applicability of the adopted method.