Question: The intermetallic compound \[LiAg\] crystallizes in the cubic lattice in which both lithium and silv...

Question

The intermetallic compound $LiAg$ crystallizes in the cubic lattice in which both lithium and silver have a coordination number of eight. The crystal class is
a) Simple cubic
b) Body centered cubic
c) Face centered cubic
d) None of the above

Answer 1

Solution

In the solid state we have learnt about the different crystal lattices. These lattices have different coordination numbers and different positions of atoms to be placed. We just have to know about the contributions of the positions.

Complete step by step solution:
Coordination number is the number that is used to find out the nearest surrounded and touched by atoms.
Simple cubic lattices have the atoms at the eight corners of a cube. It has a coordination number of $6$ . The packing efficiency of simple cubic lattice is found to be $52.4\%$ .
Body centred cubic lattice have atoms at the eight corners and one in the body centre. Thus the coordination number changes to $8$ . The packing efficiency of body centred cubic lattice is $68\%$ .
Face centred cubic lattices have atoms at the eight corners and at the centre of the face. It has a coordination number of $12$ . The packing efficiency of face centred cubic lattice is $74\%$ .
Thus in the given intermetallic compound, $LiAg$ it is given that it has a coordination number of $8$ . So the coordination of this compound matches with the feature of body centred cubic lattice and it can be said that it has a body centred cubic lattice.
Thus the intermetallic compound $LiAg$ crystallizes in a body centered cubic lattice.
Hence the correct option is (b).

Additional Information: Packing efficiency of a crystal lattice tells us about how much volume of the crystal is occupied by a perfect unit cell. By using the packing efficiency the stability of a crystal system is calculated in $2D$ and $3D$ systems.

Note: Along with all these crystal lattices there is a hexagonal cubic lattice, where the coordination number is $12$ . The packing efficiency of this cubic lattice is $74\%$ .It also has different kinds of voids that are occupied by rest $26\%$ .