# Crystal Structure

**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 atoms 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 and lattice parameters:**

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**= n_{1}**a** n_{2}**b** n_{3}**c**

Where **a, b **and**c**are the basis vector set and **n _{1}, n_{2}, n_{3} **are a triplet of integers 0,±1,±2, etc., whose value depends on the particular lattice point . The angles between the vectors

**b**and

**c**,

**c**and

**a**,

**a**and

**b**are denoted as α, β andγ 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.