How dopant size influences the protonic energy landscape in BaSn 1−x M x O 3−x/2 (M = Ga, Sc, In, Y, Gd, La)

The energy landscape of the protonic defect is investigated in acceptor-doped barium stannate using density-functional calculations. Several trivalent dopants are studied (Ga, Sc, In, Y, Gd, La), covering a wide range of ionic radii. All the dopants are found attractive with respect to the proton, with (negative) association energies varying from −0.40 to −0.07 eV. A radius rc1 is defined to separate the “small” dopants that induce tensile stress from the “large” ones that induce compressive stress in the host matrix (rc1 ≈ 0.72 Å). The protonic energy surface exhibits a non-trivial evolution with ionic radius of the dopant: for low dopant radii, the most stable protonic site is the oxygen first-neighbor of the dopant, while for high dopant radii, the most stable position is obtained when the proton is bonded to an oxygen second-neighbor of the dopant. This evolution of the protonic energy surface with dopant ionic radius is smooth and the transition takes place between In and Y, i.e. for a critical radius rc2 between 0.80 and 0.90 Å (rc2 > rc1 significantly). The dopant–proton association energy exhibits a minimal value ≈−0.07 eV (weakest attraction) at this transition, i.e. in the case of yttrium, for which the first-neighbor and second-neighbor positions are almost degenerate. Other dopants, smaller or larger, are more attractive to protons. The present study gives useful information about the modification of the trapping effect according to the dopant ionic size.