A First Principles Approach to Modelling Ba$_{(1-x)}$Ca$_{(x)}$ZrO$_{3}$

Dielectric properties are often optimized by varying material composition, so there is a need to understand the impact of doping on the local structure and properties of a material. One study showed that the dielectric constant of BaZrO$_{3}$ (BZ) can be increased by up to 50\% by doping with small amount of Ca [1]. This is interesting because CaZrO$_{3}$ (CZ) actually has a lower epsilon than BZ. We use first principles methods to characterize the local structure of Ba$_{(1-x)}$Ca$_{(x)}$ZrO$_{3}$ (BCZ) at various compositions and compute the contribution to the dielectric response of each normalized mode at 0~K. There arise low frequency phonon modes related to Ca-O motions and a transformation of Raman modes to IR modes caused by the introduction of Ca. [1]Levin, I. et al. J Sol. State Chem. 175 (2003) 170-181