Question

(i) What is meant by coordination number?
(ii) What is the coordination number of atoms:
(a) In a cubic close pack structure?
(b) In a body centred cubic structure?

Answer 1

Hint: We consider the number of surrounding atoms around the central atom as the coordination number of that atom. In a body centred cubic structure, there are 8 electrons in the corner and one atom at the body centre. In a cubic close packed structure, the atoms are arranged in 3 different layers. First layer has 6 atoms and the other two layers have 3 atoms each.

Complete answer:
In crystallography, we can define coordination number as the number of atoms, molecules or ions bonded to the central metal atom in a molecule or a crystal.
For solids, we can define the coordination number as the number of atoms touching the atom whose coordination number we are trying to find.
Firstly, let us calculate the coordination number of atoms in a cubic close pack structure.
In a cubic close packed structure, there are 3 different layers. The first layer is the same as the fourth layer. It is of the type ‘a, b, c, a, b, c’. The first layer has 6 atoms, the layer on top of it has 3 atoms and the third layer also has 3 atoms.
For a cubic close packed structure, each atom is touching 12 other atoms. Therefore, the coordination number of a CCP structure is 12.
Now, let us calculate the coordination number in a body centred cubic structure.
In BCC lattice, one atom is placed in the centre of the cube and other atoms are placed at the corners. We know that there are 8 corners in a cube. Therefore, there are 8 atoms in a body centred cubic structure in the corners.
Now, if we consider the central atom, all the eight corner atoms are touching the central atom. Therefore, the coordination number is 8.
And now if we consider the one of the corner atoms, we have to keep in mind that this is a three dimensional structure. There are 8 atoms touching each corner atom- 2 from the bottom cube, 2 from the cube on top of it, 2 from the cube beside it and 2 from the cube in front of it, which makes it 8.
No matter if we consider the central atom or the corner atoms, it still touches 8 other atoms. Therefore, the coordination number of an atom in a body centred cubic structure is 8.

Note:
We know that a lattice is a network which gives us the three dimensional arrangement of atoms. There are 14 different Bravais lattices that we study in case of solids. The body centred and the cubic close packed structures are also Bravais lattice. BCC is one of the primitive lattices and CCP is just like the face centred Bravais lattice.