Ab Initio Calculation of Proton Transport in DyPO₄

Proton mobilities in xenotime-structured DyPO₄ have been investigated through first-principles calculations based on electronic density functional theory. The calculated mobility is shown to be highly anisotropic, consistent with the tetragonal symmetry of the xenotime crystal structure. Due to the presence of one-dimensional channels along the c-axis, the hopping rate is significantly enhanced along this direction. Specifically, the activation energy for hopping along the a- and b-axes is computed to be 0.45 eV away from aliovalent dopant impurities, while the calculated energy barrier within the channels that run along the c-axis is 0.15 eV. The corresponding hopping rates along the c-axis channels are more than 2 orders of magnitude larger than those calculated previously for the monoclinic monazite-structured LaPO₄ compound. The effects of aliovalent dopants on proton migration have also been investigated, considering the case of Ca²⁺ substitution for Dy³⁺. These calculations reveal a dopant-proton binding energy of approximately 0.4 eV and an increase in the hopping barriers near the dopant by up to 0.2 eV. These dopant effects were found to be relatively localized, with minimal changes to the energetics of the protons obtained more than approximately 5 Å away from the aliovalent impurity.