First-Principles Replica Monte Carlo Sampling of Dopant Disorder in Solid Electrolyte

Oxides such as ZrO₂ and BaZrO₃ are promising candidates for the electrolyte material in medium to high-temperature solid oxide fuel cells. In these materials, aliovalent cation doping is used to introduce ionic defects which act as ionic charge carriers. Optimization of doping conditions is imperative for obtaining sufficient and stable ionic conductivity, but it is yet unclear how dopants are distributed in the material under various processing conditions and how the details of the distribution affect the total conductivity. Since the experimentally found optimal doping concentration can run up to 20%, the degrees of freedom in substitutional dopant placement is enormous (for example, choosing 10 substitutional sites out of 50 corresponds to ₅₀C₁₀~10 billion degrees of freedom). In this work, we harness the power of modern-day supercomputers and perform thermodynamic sampling of dopant placement in BaZrO₃ by directly combining first-principles calculations and the replica exchange Monte Carlo method. We show that dopant-carrier association decreases with increasing dopant concentration, in contrast to popular belief that association effects are responsible for conductivity decrease at high dopant concentrations.