Trapping of oxygen vacancies in the twin walls of perovskite

The binding and pairwise interaction of oxygen vacancies in the ferroelastic (100) twin walls of the orthorhombic phase of ${\text{CaTiO}}_3$ perovskite $\left(Pbnm\right)$ have been investigated by numerical simulations using empirical force fields. An oxygen vacancy finds it energetically favorable to reside inside a twin wall, particularly when bridging two titanium ions located in the twin-wall plane. In such case, the binding energy of the vacancy to the wall is $0.7\pm 0.1\text{eV}$, the error bar reflecting variability within two different force fields. A different disposition of the vacancy in the wall sees its binding energy reduced by a factor of 2. This implies that depending on the relative time scales for twin-wall motion and for oxygen-vacancy diffusion, anelastic motion of twin walls can display two different energy dissipation mechanisms associated to these point defects. The strongest interactions among oxygen vacancies in a twin wall are due to short-range repulsion so that no defect clusters were found. The vacancy-wall binding energy is found to increase substantially with pressure.

Figure 1

(Color online) ${\text{CaTiO}}_3$ orthorhombic perovskite showing the tilting of the ${\text{TiO}}_6$ octahedra at room conditions (a) before and (b) after a $90°$ rotation along the $c$ axis. (c) A common unrelaxed twin wall (gray area) between two ferroelastic domains, oriented along the (110) plane of the tetragonal phase (low-symmetry phase), where the unit cell is represented by rectangles with $a$ and $b$ parameters ($c$ is pointing into the paper) with respect to the cubic phase (Ref. 8). (d) A wire frame view along the $y$ axis of the relaxed configuration of the orthorhombic ${\text{CaTiO}}_3$ perovskite structure. Titanium ions reside at the vertices of the sticks and they are bridged by oxygen ions. The (isolated) points are Ca ions. Note the periodicity and the perfect alignment of Ti ions (nontilted octahedra) represented by two straight lines, at the center and at the right corner of the diagram, indicating the actual twin walls locations. The walls are separated by $49.8\text{Å}$.

Figure 2

Octahedral tilting around each of the crystallographic directions: (a) along [010], (b) along [100], and (c) along [001]. Open symbols represent our potential model (M2) and closed symbols correspond to M1 (Ref. 25).

Figure 3

Ti-Ti nearest-neighbors distances perpendicular to the walls. Open symbols show the distances without twin walls and closed symbols, the distances due to the presence of the walls. Circles are for M1 and squares for M2.

Figure 4

Relative energies of oxygen vacancies in ${\text{CaTiO}}_3$ with the distance perpendicular to the walls $\left(P=0\text{GPa}\right)$. Open symbols (and the short dotted line) are for M2 and closed symbols (and the dashed line) are for M1. Circles denote oxygen vacancies bridging titania along [100], squares those bridging along [010] and triangles those bridging along [001].

Figure 5

(Color online) Oxygen vacancy pairs in the plane of the wall.

Figure 6

(Color online) Interaction energy dependence with distance between oxygens for seven different pairs of oxygen vacancies located on the central ferroelastic wall. (a) Results derived from M1 and (b) from M2.

Figure 7

(Color online) Pressure dependence of the stabilization of oxygen vacancies at the domain wall in ${\text{CaTiO}}_3$ perovskite for: (a) M1 (Ref. 25) and (b) M2, measured relative to the stabilization of a vacancy at the [001] Ti-O-Ti bridge at 0 GPa.