First-principles calculations of proton defect properties in Ca-doped YPO₄

YPO₄ has a xenotime-type structure with one-dimensional percolating channels along the c-axis, and Ca-doped YPO₄ exhibits proton conduction. In the present study, using first-principles calculations, we investigate the behaviors of proton solutions in 3 mol% Ca-doped YPO₄ in the intermediate temperature range on the basis of point-defect formation energies, defect concentrations, and migration barriers. Although the charge-neutrality condition is mainly satisfied by and defects within the defect formation energy diagrams, the defect complex has the lowest formation energy and the highest concentration among examined defects under various temperature and partial-pressure conditions. The migration barriers of isolated protons in the [100] and [001] directions, as obtained from nudged elastic band (NEB) calculations, are 0.49 and 0.17 eV, respectively, confirming that protons in the YPO₄ crystal exhibit anisotropic diffusion and are likely to migrate along the c-axis channels. The activation energy estimated by the sum of the migration energy of the isolated proton and the association energy for the defect complex is comparable to the reported experimental value. Based on concentration calculations and diffusion-property analyses, we identified the Ca doping conditions and temperature ranges that govern proton conduction in YPO₄ and elucidated the diffusion pathways.