Question

$BaTi{O}_3$ crystallizes in the perovskite structure. This structure may be described as a cubic lattice, with barium ions occupying the corners of the unit cell, oxide ions occupying the face centers and titanium ions occupying the centers of the unit cells.
(a) If titanium is described as occupying holes in the $BaO$ lattice, what type of hole does it occupy?
(b) What fraction of the holes of this type does it occupy?
(c) Can you suggest a reason why it has certain holes of this type but not the other of the same type?

Answer 1

(a) Since $T{i}^{+4},$ is very small in size it will occupy octahedral hole present in the body center of FCC lattice.

(b) It occupies $1$ out of $4$ octahedral hole i.e.$\frac{1}{4}$.

(c) Since a lattice has definite symmetry and composition. These both have been changed if $T{i}^{+4}$ have occupied octahedral hole present at edge centers. Also since $T{i}^{+4}$ is very small, it fits perfectly into body centered octahedral hole.