Simulating valence of dopant in BaTiO₃ at room temperature

We study the valences of dopants in BaTiO3 at room temperature based on a thermodynamic model combined with first-principles simulations. Here we assume that cations and anions are frozen-in at different temperatures during a sintering process. We calculated the defect concentration at two different temperatures (sintering temperature and anion freeze-in temperature) to eventually obtain defect concentrations at the room temperature. Our first-principles results show that variable valence dopants exhibit different valences depending on the simulation temperature.