Finite-temperature investigation of homovalent and heterovalent substituted BaTiO3 from first principles

Barium titanate (BT) solid solutions are used in a wide range of applications such as piezoelectric actuators and high-performance energy storage devices. The key to achieve and tune desired macroscopic properties is the chemical modification, which is done by substituting Ba or Ti with other homovalent or heterovalent cations. This work uses large-scale molecular dynamics simulations based on an effective Hamiltonian approach to calculate the macroscopic properties of BT solid solutions from first principles, thereby offering a framework for the prediction of properties prior to materials synthesis. To this end, we elaborate on the theoretical description of substitution in effective Hamiltonians as well as their parametrization by density functional theory calculations for two model systems: homovalent substituted ${\mathrm{BaZr}}_x{\mathrm{Ti}}_{1\text{\ensuremath{-}}x}{\mathrm{O}}₃$ (BZT) and heterovalent substituted ${\mathrm{BaNb}}_x{\mathrm{Ti}}_{1\text{\ensuremath{-}}x}{\mathrm{O}}₃$ (BNT). The effective Hamiltonian for BZT obtained in this work is first used for benchmarking against other models and experimental data on the phase diagrams and dielectric properties. Subsequently, the effective Hamiltonian is further extended and used to parametrize BNT and compare the model's predictions to the available experimental data. The parameter sets obtained in this work can be used for future studies and provide deep insight into the subject of relaxor ferroelectrics.