### Pioneer Physics Different Online Tutorials

### solid state physics

##### solid state physics

**INTRODUCTION**

Matter, consisting of atoms and molecules, exists in the form of solid or fluid state, the latter being subdivided into the liquid and the gaseous state. Since the atoms or molecule are attached each other with a strong force, it have definite volume and shape.

The solid may be broadly classified as crystalline, semi crystalline (or poly crystalline) and non-crystalline depending on the arrangements of atoms or molecules.

Crystalline solids

The crystalline solids are characterized by a perfect or nearly perfect periodicity of atomic structure. So the crystalline solids are those which contain the regular repeated pattern of atoms or molecules.

Crystalline state of solids are most stable form of solid and held in a low energy state.

Crystalline solids may be subdivided into single crystals and poly crystals. In single crystals the periodicity of atoms extends throughout the material. e.g. diamond, quartz, mica etc. a poly crystalline materials is an aggregate of a number of small crystalline with random orientation separated by well – defined boundaries. The small crystallites are known as grains and boundary as grain boundaries. This is also known as semi crystalline solids.

Non – crystalline or amorphous solids

The solid without having periodicity is called non crystalline solids e.g. glass, plastic, etc.

They don’t have a definite melting points. As the temperature increases, they gradually become soft and their viscosity drops, and begin to behave like an ordinary viscous liquids.

**PERIODICITY IN CRYSTALS**

Space – lattice: it is an imaginary frame work on which he actual crystal structure is based. The arrangement of infinite number of imaginary points in 3 – dimensional space from a space lattice.

To understand periodicity, let us consider the translation of an object (J) to a finite distance (say a) and then repeated systematically along three crystallographic directions x, y, and z to obtain 3 – dimensional space lattice.

Consider a, b, c as translational vectors and three translation direction x, y, z as crystallographic axes with respect to any lattice point as the origin, then the location of any other lattice point can be defined as

Where are any integers.

Basis and crystal structure

The space lattice has been defined as an array of imaginary points which are so arranged in space that each points which are so arranged in space that each point has identical surrounding.

The crystal structure is always described in terms of atoms rather than points. Thus in order to obtain a crystal structure, an atom or a group of atoms must be placed on each lattice point in a regular fashion. Such an atom or group of atom is called the basis and act as a building unit or structural unit for the complete crystal structure.

Space lattice + basis → crystal structure

**UNIT CELL**

In three dimension, any simple parallelepiped formed by the unit translation is considered as unit cell. The entire lattice then can be considered as an infinite collection of such unit cells repeated by its translation in all direction.

The unit cell thus can be defined as the smallest volume which when repeated in all direction builds the crystal.

This parallelepiped defined by translation a, b, c as the shortest possible sides along x, y, z is called a primitive cell.

The volume of the primitive cell defined as

Wigner – Seitz unit cell