Ab initio interphase characteristics in HfO₂ and ZrO₂ and nucleation of the polar phase

Recently, the crystallographic phases of HfO₂ and ZrO₂, including the polar phases, have been well characterized, and also the total and free energies have been calculated. However, less is known about the structure and energy of the crystalline coherent interface—also called the interphase. The formation of domain and phase boundaries is determined by interphase energies and properties, and their knowledge is indispensable to better understand the phase formation and phase stability. We have calculated the interphase energy for HfO₂ and ZrO₂ at T = 0 K for the relevant phase pairs with two methods, which are in good agreement. The method is applicable to any crystalline material with metastable phases. The values range in a few 100 mJ/m², which is consistent with previous estimates from room temperature but too large for estimates from high-temperature processes. We propose a temperature dependence of interphase energy such that it becomes small close to the phase transition.