Bravais lattice

Bravais lattice is a set of points constructed by translating a single point in discrete steps by a set of basis vectors in a three-dimensional space. It is a fundamental concept in the fields of crystallography and solid state physics. The concept is named after the French physicist Auguste Bravais, who introduced it in the 19th century.

Definition

A Bravais lattice is defined as an infinite array of discrete points with an arrangement and orientation that appears exactly the same, from whichever of the points the array is viewed. This is formally known as a space lattice or a crystal lattice.

Types of Bravais Lattices

There are 14 unique types of Bravais lattices in three-dimensional space. These are categorized into seven lattice systems. The categorization is based on the lattice parameters, which include the lengths of the cell edges and the angles between them. The seven lattice systems are:

1. Triclinic lattice
2. Monoclinic lattice
3. Orthorhombic lattice
4. Tetragonal lattice
5. Rhombohedral lattice
6. Hexagonal lattice
7. Cubic lattice

Each of these systems is associated with one or more of the 14 Bravais lattices.

Applications

The concept of Bravais lattice is fundamental in crystallography and solid state physics. It is used to model the arrangement of atoms in a crystalline solid. The properties of the Bravais lattice, such as its symmetry, directly influence the physical properties of the material.

See Also

• Crystal structure
• Crystal system
• Lattice constant
• Miller index