Bravais Lattice

In 1848, Auguste Bravais demonstrated that there are fourteen possible point lattices and no more. For his efforts, the term bravais lattice is often used in place of point lattice. The fourteen bravais lattices can be grouped into seven systems given in the following table.

Name	Number of Bravais lattices	Conditions
Triclinic	1	a1 ¹ a2 ¹ a3 a ¹ b ¹ g
Monoclinic	2	a1 ¹ a2 ¹ a3 a = b = 90° ¹ g
Orthorhombic	4	a1 ¹ a2 ¹ a3 a = b = g = 90°
Tetragonal	2	a1 = a2 ¹ a3 a = b = g = 90°
Cubic	3	a1 = a2 = a3 a = b = g = 90°
Trigonal	1	a1 = a2 = a3 a = b = g < 120° ¹ 90°
Hexagonal	1	a1 = a2 ¹ a3 a = b = 90° g = 120°

From Pierret Fig. 1.3

Of these 14 bravais lattices, simple cubic, BCC, FCC, will be studied the most in this course. The number of lattice points for the structures are one, two, and four for the simple cubic, BCC and FCC respectively.

Crystal (a) is a simple cubic, crystal (b) is a body centered cubic and crystal (c) is a face centered cubic. Two additional commonly encountered structures are called the zinc-blend and diamond structures. Examples of zinc-blend and diamond structures are GaAs and Si respectively and are shown below.

From Pierret Fig. 1.5