Matter exists in three states
viz. solids, liquids and gases. All these states are composed of atoms and molecules.
In case of solids, they are classified
into many types based on several properties like electrical, mechanical, magnetic, optical,
thermal etc. The main reason for these different properties
of solids is their crystal structure.

Crystal Structure

*Periodic arrangement of atoms/ions over large atomic distances.*Leads to structure displaying LONG-RANGE ORDER that is Measurable and Quantifiable.

CRYSTAL

It is a substance in which the constituent particles are arranged
in a systematic geometrical pattern.

SPACE LATTICE OR CRYSTAL LATTICE

A lattice is a regular and periodic arrangement of points in
three dimension. It is defined as an infinite
array of points in three dimension in which every point has surroundings
identical to that of every other point in the array. The Space lattice is otherwise called the Crystal
lattice.

Consider the points P, Q and R.

Let us join the
points P and Q by a straight line, and the point P and R by another straight
line.

The line PQ is taken
as X-axis and the line PR is taken as Y-axis.

The distance between
any two successive lattice points in the X-direction is taken as `a’.

Similarly, the distance between any two successive lattice
points along the Y-direction is taken as `b’.

Here a and b are said
to be lattice translational vectors. Consider a square lattice in which a = b.

Consider two sets of points A, B, C, D, E, F and A', B', C',
D', E', F'. In these two sets,
the surrounding environment looks symmetrical; i.e. the distances AB and A'B', AC and A'C', AD and A'D',
AE and A'E' and AF and A'F' are equal.