Size and shape of oxygen vacancies and protons in acceptor-doped barium zirconate

TL;DR

This study uses density-functional theory to analyze how oxygen vacancies and protons affect the size, shape, and strain in acceptor-doped barium zirconate, revealing anisotropic distortions and net lattice contraction upon defect formation.

Contribution

It introduces the defect-induced strain tensor to quantify anisotropic distortions and provides detailed insights into defect sizes and their impact on lattice expansion or contraction.

Findings

Both vacancies and protons cause anisotropic lattice distortions.

Vacancies induce larger lattice contraction than protons.

Hydration results in net lattice expansion despite individual contractions.

Abstract

The defect induced chemical expansion in acceptor-doped barium zirconate is investigated using density-functional theory (DFT) calculations. The two defect species involved in the hydration reaction, the +2 charged oxygen vacancy and the proton interstitial forming a hydroxide ion, are considered both as free defects and in association with the dopants Y, In, Sc and Ga. The defect induced strain tensor lambda is introduced, which provides a natural generalisation of the ordinary chemical expansion to three dimensions and to anisotropic distortions. Both the addition of a vacancy and a proton cause anisotropic distortions and a net contraction of the lattice, indicating that both the vacancy and the hydroxide ion are smaller than the oxygen ion. The contraction is considerably larger for the vacancy and the net effect in hydration, when a vacancy is filled and two protons are added, is an expansion, consistent with the experimental findings. The effect of the dopants on the chemical expansion in hydration is found to be quite small, even if it is assumed that both the vacancy and the proton are fully associated with a dopant atom in the lattice.