Proton–polaron and energy landscape among acceptor doped ACeO₃ (A = Ba²⁺, Sr²⁺, Ca²⁺, Mg²⁺) proton conductors: a first principles approach

The physiochemical impact of the acceptor on the local electronic structure of proton conductors remains obscure due to multifarious issues ranging from proton-polaron interaction to defect scattering events. Meanwhile, structural phase transition and cationic disorder also impart an artificial barrier with local proton traps for long-range diffusion through the lattice. The synergetic response imposes critical challenge to analyse the minimum energy pathway for long-range proton diffusion. As a result, in the present study we investigate the proton landscape and vacancy formation energy (<i>E</i>_vac) corresponding to different sized acceptors (M = Gd³⁺, Y³⁺, In³⁺, Sc³⁺) in ACe_1-<i>x</i>M_<i>x</i>O₃ (A = Ba²⁺, Sr²⁺, Ca²⁺ and Mg²⁺) (<i>x</i> = 0, 0.125, 0.25, 0.375, 0.5) proton conductors to understand the impact of various electrostatic barriers and afore-mentioned inconsistency on proton diffusion through the lattice <i>via</i> a first principles approach using density functional theory (DFT). We also demonstrate the significance of optimal doping concentration across different acceptor substituents and highlight the influence defect and dopant cluster on polaron formation. As a result, the climbing image nudged elastic band calculations provide a comprehensive overview on proton-polaron interaction and the advent of local proton traps on the trapping and de-trapping effect across different proton and lattice configurations.