Question

The ${\text{BaTi}}{{\text{O}}_{\text{3}}}$ crystallizes in the perovskite structure. This structure may be described as a cubic lattice, with barium ions occupying the corners of the unit cells, oxide ions occupying the face centres and titanium ions occupying the centres of the unit cells.
(A) If titanium is described as occupying holes in the ${\text{BaO}}$ 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

In the above question, it is asked what type of hole does titanium occupied in ${\text{BaTi}}{{\text{O}}_{\text{3}}}$ and the fraction of this type of hole and why it has these types of holes. For this, we have to understand what is perovskite structure and how atoms are arranged. The general chemical formula for perovskite compounds is ${\text{AB}}{{\text{X}}_{\text{3}}}$ . The B-site cations fill $\dfrac{1}{4}$ of the octahedral holes and the A atoms are generally larger than the B atoms.

Complete Step by step solution
The perovskite structure has simple cubic symmetry, but it is also related to the fcc lattice where A site cations and the three O atoms comprise a fcc lattice. The B-site cations fill $\dfrac{1}{4}$ of the octahedral holes and are surrounded by six oxide anions.
The general chemical formula for perovskite compounds is ${\text{AB}}{{\text{X}}_{\text{3}}}$ , where A and B are two cations which are of very different sizes. X is an anion that bonds with both cations. The A atoms are generally larger than the B atoms.
In ${\text{BaTi}}{{\text{O}}_{\text{3}}}$ , ${\text{Ti}}$ cation is smaller than ${\text{Ba}}$ cation. Hence, we can say that:
-Titanium occupies the octahedral hole present in the body centre of FCC lattice.
-The fraction of this type of hole is $\dfrac{1}{4}$ .
-Since, ${\text{T}}{{\text{i}}^{{\text{ + 4}}}}$ is smaller, it comes under B-site cation and hence, it occupies octahedral holes.

Note
-Due to the high photoluminescence quantum efficiency, perovskites can be used in LEDs.
-Researches have shown that perovskites can generate laser lights.