Question

draw the unit cell of ReO3,in which is composed of a primitive lattice of rhenium(open cirlces) with oxides in all edge octahedral holes. verify the stoichiometry of the ionic solid.

Answer 1

Verification of Stoichiometry of the ionic solid :-

Now as you can see in the diagram above, there are 12 oxygen atoms present on 12 edges of the cube, and each oxygen atom is shared by four cubes. So the contribution of one oxygen atom to each unit cell is 1/4. The contribution of 12 oxygen atom to each unit cell is

12 *(1/4) = 3

So each unit cell contains 3 atoms of oxygen.

Now for Rhenium atom,  there are 8 Rhenium atoms present on 8 corner of the cube, and each Rhenium atom is shared by eight cubes. So the contribution of one Rhenium atom to each unit cell is 1/8. The contribution of 8 Rhenium atom to each unit cell is

8*(1/8) = 1

So each unit cell contains 1 atom of Rhenium.

Thus the stoichiometry is verified