Question

$BaTi{O}_3$ crystallizes in the perovskite structure. This structure may be described as a cubic lattice with barium ions occupying the corner of the unit cell, oxide ions occupying the face-centers and titanium ion occupying the center of the unit cell.

(a) If titanium is described as occupying holes in $BaO$ lattice, what type of holes it occupy?

(b)What fraction of this type of holes does it occupy?

• A. $\left(a\right)$ Tetrahedral $\left(b\right)\frac{1}{2}$
• B. $\left(a\right)$ Tetrahedral $\left(b\right)\frac{1}{4}$
• C. $\left(a\right)$ Octahedral $\left(b\right)\frac{1}{2}$
• D. $\left(a\right)$ Octahedral $\left(b\right)\frac{1}{4}$

Answer 1

The correct option is D $\left(a\right)$ Octahedral $\left(b\right)\frac{1}{4}$

(a) If titanium is described as occupying holes in $BaO$ lattice, the type of holes it occupy is octahedral voids.

(b) The fraction of this type of holes does it occupy is one-fourth $\left(\frac{1}{4}\right)$

There is one $Ti$ atom in each unit cell and there are four octahedral voids in each unit cell with each octahedral void contributing $1$ atom to the unit cell.

One fourth of four octahedral voids contributes $1$ $Ti$ atom to the unit cell.