Elastic effects of vacancies in strontium titanate: Short- and long-range strain fields, elastic dipole tensors, and chemical strain

We present a study of the local strain effects associated with vacancy defects in strontium titanate and report the first calculations of elastic dipole tensors and chemical strains for point defects in perovskites. The combination of local and long-range results will enable determination of x-ray scattering signatures that can be compared with experiments. We find that the oxygen vacancy possesses a special property—a highly anisotropic elastic dipole tensor which almost vanishes upon averaging over all possible defect orientations. Moreover, through direct comparison with experimental measurements of chemical strain, we place constraints on the possible defects present in oxygen-poor strontium titanate and introduce a conjecture regarding the nature of the predominant defect in strontium-poor stoichiometries in samples grown via pulsed laser deposition. Finally, during the review process, we learned of recent experimental data, from strontium titanate films deposited via molecular-beam epitaxy, that show good agreement with our calculated value of the chemical strain associated with strontium vacancies.

Figure 1

(Color online) Atomic structure of nonreconstructed cubic strontium titanate: oxygen octahedra surrounding titanium atoms (blue or dark gray diamonds), with strontium atoms (green or gray square) outside the octahedra and equidistant from the titanium sites.

Figure 2

(Color online) Diagonal components of elastic dipole tensor for oxygen vacancy in strontium titanate. Data show linear convergence with inverse linear dimension of supercell size.

Figure 3

(Color online) Local strain pattern for oxygen vacancy in the ${\widehat{e}}_1{\widehat{e}}_2$ plane of strontium titanate: titanium atoms (blue or dark gray diamonds), oxygen atoms (red or gray circles), oxygen vacancy (light red or light gray circle). Atomic displacements exaggerated by a factor of three for clarity (arrows), displayed for significant in-plane displacements $\left(>0.1\text{Å}\right)$ only.

Figure 4

(Color online) Diagonal components of elastic dipole tensor for strontium vacancy in strontium titanate. Data show linear convergence with inverse linear dimension of supercell size.

Figure 5

(Color online) Local strain pattern for strontium vacancy in the ${\widehat{e}}_1{\widehat{e}}_2$ plane of strontium titanate: strontium atoms (green or gray squares), oxygen atoms (red or gray circles), strontium vacancy (light green or light gray square). Atomic displacements exaggerated by a factor of three for clarity (arrows), displayed for significant in-plane displacements $\left(>0.1\text{Å}\right)$ only.

Figure 6

(Color online) Diagonal components of elastic dipole tensor for titanium vacancy in strontium titanate. Data show linear convergence with inverse linear dimension of supercell size.

Figure 7

(Color online) Local strain pattern for titanium vacancy in the ${\widehat{e}}_1{\widehat{e}}_2$ plane of strontium titanate: titanium atoms (blue or dark gray diamonds), oxygen atoms (red or gray circles), titanium vacancy (light blue or light gray diamond). Atomic displacements exaggerated by a factor of three for clarity (arrows), displayed for significant in-plane displacements $\left(>0.1\text{Å}\right)$ only.

Figure 8

(Color online) Diagonal components of elastic dipole tensor for strontium-oxygen divacancy in strontium titanate. Data show linear convergence with inverse linear dimension of supercell size.

Figure 9

(Color online) Local strain pattern for strontium-oxygen divacancy in the ${\widehat{e}}_1{\widehat{e}}_2$ plane of strontium titanate: strontium atoms (green or gray squares), oxygen atoms (red or gray circles), strontium vacancy (light green or light gray square), oxygen vacancy (light red or light gray circle). Atomic displacements exaggerated by a factor of three for clarity (arrows), displayed for significant in-plane displacements $\left(>0.1\text{Å}\right)$ only.

Figure 10

(Color online) Diagonal components of elastic dipole tensor for titanium-oxygen divacancy in strontium titanate. Data show linear convergence with inverse linear dimension of supercell size.

Figure 11

(Color online) Local strain pattern for titanium-oxygen divacancy in the ${\widehat{e}}_1{\widehat{e}}_2$ plane of strontium titanate: titanium atoms (blue or dark gray diamonds), oxygen atoms (red or gray circles), titanium vacancy (light blue or light gray diamond), oxygen vacancy (light red or light gray circle). Atomic displacements exaggerated by a factor of three for clarity (arrows), displayed for significant in-plane displacements $\left(>0.1\text{Å}\right)$ only.