Question

ReO3 structure is cubic with an Re atom at each corner of the unit cell and one O atom on each unit cell edge midway between Re atoms. Sketch the unit cell and determine (a) the coordination numbers of the ions and (b) number of atoms in the unit cell.

Answer 1

In this structure, Re atoms are present at corner, contribution of Re towards unir cell= 8*1/8=1

O at present at edge centre, contribution of O towards unit cell= 12*1/4=3

S, No. of atoms present in unit cell = 1+3= 4

In the ReO3 structure, each Re6+ ion has six nearest neighbor oxygen atoms, so coordination number is 6

Each O2- has two nearest neighbor atoms, so coordination number is 2.

Answer 2

a) Each Re atom is surrounded by 6 O atoms. Hence, coordination number of Re is 6.

Each O atom is surrounded by only 2 Re atoms. Hence, coordination number of O is 2.

b) There are 8 Re atoms at 8 corners of the cubic cell and each Re atom contributes 1/8 th to the unit cell. Hence, number of Re atoms per unit cell = 8x(1/8) = 1

There are 12 O atoms at the centre of each edge of the cubic cell and each O atom contributes 1/4 th to the unit cell. Hence, number of O atoms per unit cell = 12x(1/4) = 3

Therefore no. of atoms per unit cell = 1 + 3 = 4.