Question

Unit cells can be divided into two categories, primitive and centred unit cells.
(A) Differentiate between Unit cell and Crystal lattice
(B) Calculate the number of atoms per unit cell in the following:
(a) Body centred cubic unit cell (bcc)
(b) Face centred cubic unit cell (fcc)

Answer 1

Hint Crystal lattice is the space consisting of each point. It is the arrangement of particles like atoms or molecules in a 3D surface. A unit cell is the smallest repeating unit of an atom. They are building blocks of a crystal lattice.

Complete answer:

Crystal Lattice	Unit Cell
Crystal lattice is the orderly array of points in space.	The smallest group of crystal structure consisting of the symmetry of crystal lattice.
It is made up of many points which represent one part of the crystal, called lattice points.	The 3 edges of the unit cell are a, b, and c, represented as vectors.

The number of atoms per unit cell can be calculated in the following way:
(a) Body centred cubic unit cell (bcc)
There are 8 atoms present in 8 corners of unit cell
There is 1 atom present in the body centre
Since, each corner atom contributes \[{{\dfrac{1}{8}}^{th}}\]to the unit cell.
The contribution of centre atom is 1
So, the number of atoms per unit cell = \[8x\dfrac{1}{8}+1=2\]
(b) Face centred cubic cell (fcc)
There are 8 atoms present in 8 corners of unit cell
There are 6 atoms present at the face centres
Since, each corner atom contributes \[{{\dfrac{1}{8}}^{th}}\]to the unit cell.
The contribution of atom at face centre is \[\dfrac{1}{2}\]
So, the number of atoms per unit cell = \[8x\dfrac{1}{8}+6x\dfrac{1}{2}=4\]

Note: The primitive unit cell has atoms. Ions, or molecules at the lattice corners, and in no other position. Which means, primitive unit cells have a singular lattice point. The simple cubic straw tire has only 1 atom in it.