Question

What are primitive unit cells and what are non-primitive unit cells?

Answer 1

Hint: Unit cell is known to be the building block of crystal. It is the smallest portion of the crystal lattice. Knowing about unit cells very well will help us to understand what a primitive and non-primitive unit cell is.

Complete step by step answer:
First of all, we must know what is a crystal lattice and unit cell? Crystal lattice is the arrangement of atoms, ions or molecules in a symmetrical three-dimensional arrangement. We can also say it is a geometrical representation of atoms, ions or molecules. Smallest unit of the crystal lattice represents the unit cell.
 Unit cell is defined as the smallest repeating portion of the crystal. It is the basic structural unit or building block of the crystal. Unit cells can be classified as primitive and non-primitive unit cells. Unit cells have two parameters namely: cell dimensions such as $$abc$$ and interfacial angles such as $$\alpha \beta \gamma$$.
- Primitive Unit cell:
A unit cell which has only one lattice point in the crystal are called primitive unit cells.
This lattice point is present on the edges or corner of the unit cell.
- Non-primitive unit cell:
When a unit cell has not only one lattice point at the corner but also additional lattice points are present it is called a non primitive unit cell. It is also known as a centred unit cell. There are three types of centred unit cells. They are
- Body centered
- Face centred
- End centered
Body centred:
When the atoms are present at the centre of the body of the crystal, it is called Body-centred.
Face-centred:
When atoms are present at the centre of the face of the crystal, it is called face-centred.
End-centered:
When the atoms are present at the centre of the opposite faces of the crystal, it is known as End-centred.

Additional information:
There are seven crystal systems and 14 Bravais lattices in this crystal system.

Crystal system	Bravais lattices	Cell dimensions	Interfacial angles
Cubic	Primitive, Face-centered, Body-centered=3	$$a=b=c$$	$$\alpha =\beta =\gamma =90{}^{\circ }$$
Tetragonal	Primitive, Body-centered=2	$$a=b\ne c$$	$$\alpha =\beta =\gamma =90{}^{\circ }$$
Orthorhombic	Primitive, Face-centered, Body-centered, End-centered=4	$$a\ne b\ne c$$	$$\alpha =\beta =\gamma =90{}^{\circ }$$
Monoclinic	Primitive, End-centered=2	$$a\ne b\ne c$$	$$\alpha =\gamma =90{}^{\circ },\beta \ne 90{}^{\circ }$$
Triclinic	Primitive=1	$$a\ne b\ne c$$	$$\alpha \ne \beta \ne \gamma \ne 90{}^{\circ }$$
Hexagonal	Primitive=1	$$a=b\ne c$$	$$\alpha =\beta =90{}^{\circ },\gamma =120{}^{\circ }$$
Trigonal or Rhombohedral	Primitive=1	$$a=b=c$$	$$\alpha =\beta =\gamma \ne 90{}^{\circ }$$

Note: - The arrangement of atoms in the crystal can sometimes cause some defects, these defects are of two types: stoichiometric and non-stoichiometric defects.
- Examples of stoichiometric defects are Frenkel and Schottky defects.
- Examples of non-stoichiometric defects are metal excess and metal deficiency defects.