Introduction

Solids are of two types: Amorphous and crystalline. In amorphous solids, there is no order in the arrangement of their constituent atoms (molecules). Hence no definite structure could be assigned to them. A substance is said to be crystalline when the arrangement of the units (atoms, molecules or ions) of matter inside it is regular and periodic.

Space lattice

An array of points which describe the three dimensional arrangement of particles (atoms, molecules or ions) in a crystal structure is called space lattice. Here environment about each point should be identical.

Basis

A crystal structure is formed by associating with every lattice point a unit assembly of units or molecules identical in composition. This unit assembly is called basis.

A crystal structure is formed by the addition of a basis to every lattice point.

I.e., lattice + Basis = crystal structure.

Thus the crystal structure is real and the crystal lattice is imaginary.

Bravais lattice

For a crystal lattice, if each lattice point substitutes for an identical set of one or more atoms, then the lattice points become equivalent and the lattice is called Bravais lattice. On the other hand, if some of the lattice points are non-equivalent, then it is said to be a non-Bravais lattice.

Unit cell

The smallest portion of the crystal which can generate the complete crystal by repeating its own dimensions in various directions is called unit cell.

The position vector R for any lattice point in a space lattice can be written as

R= n₁a+n₂b+n₃c

Where a,b and c are the basis vector set. The angles between the vectors b and c, c and a, a and b are denoted asa,b and g and are called interfacial angles. The three basis vectors and the three interfacial angles, form a set of six parameters that define the unit cell, and are called lattice parameters.

Primitive cell

A primitive cell is a minimum volume unit cell. Consider a bravais lattice (in two dimensions) as shown below:

We can imagine two ways of identifying the unit cell in this structure. One is, with a₁ and b₁ as the basis vectors in which case, the unit cell will be a parallelogram. Here four lattice points are located at the vertices. This is a primitive cell. Other one is with the basis vectors a₂ and b₂ which would make a rectangle for the unit cell. Here in addition to the 4 points at the corners, one lattice point is at the centre. This is a nonprimitive cell.