Lattice dynamics and thermal properties of SrHfO₃ by first-principles calculations

First-principles lattice dynamics calculations are systematically made on four polymorphs of SrHfO₃. The hierarchy of the total energy at the ground state is Pm3m > I4/mcm > Cmcm > Pnma, which agrees with the sequence of iterative transitions with temperature as reported by experiments. Three structures, Pm3m, I4/mcm and Cmcm, are found to be dynamically unstable at the ground state. A soft mode of phonons appears in I4/mcm and Cmcm at the Γ-point. The atomic displacements for the soft mode are analogous to those of the R₂₅ mode of Pm3m, which is related to the rotation of the HfO₆ octahedron. Pnma phase shows lowest energy and it is the only dynamically stable structure among the four phases. The volume expansion coefficient, bulk modulus and heat capacity are computed within quasi-harmonic approximations using the vibrational density of states. They are compared to experimental data.