Chemistry Assignment Help with Bravais Lattices

10.5 Bravais Lattices

An arrangement of spheres as given above leads to simple or primitive unit cell, when there are points only at the corner of the unit lattice. However certain unit cells have lattice points at other sides in additions to the corners. Such unit cells are called non-primitive unit cells. Bravais showed from geometrical considerations that there can be only 14 different ways in which similar points (spheres) can be arranged. These fourteen types of lattice are known as Bravais lattices. They can be divided into seven crystal systems as shown below:

CRYSTAL SYSTEMS TABLE

S.No.	Crystal System	Axial Characteristics	Examples
1.	Cubic	a = b = c a = b = g = 90º	NaCl, KCl, CsCl, zinc blende, Cu, Ag, diamond
2.	Tetragonal	a = b ¹ c a = b = g = 90º	White tin, SnO2, TiO2
3.	Orthorhombic	a ¹ b ¹ c a = b = g = 90º	Rhombic sulphur, KNO3, PbCO3, PbSO4
4.	Monoclinic	a ¹ b ¹ c; a = g = 90º; b ¹ 90º	Monoclinic sulphur, CaSO4, 2H2O, Na2SO4, 10H2O
5.	Rhombohedral or trigonal	a = b = c; a = g =90º, b ¹ 90º	Calcite, quartz, As, Sb, NaNO3, ICl
6.	Triclinic	a ¹ b ¹ c; a ¹ b ¹ g ¹ 90º	K2Cr2O7, H3BO3, CuSO4, 5H2O
7.	Hexagonal	a = b ¹ c; a = b = 90º; g = 120º	Graphite

The bravais lattice associated with the seven crystal systems are shown in figure.

(1) Cubic

(2) Orthorhombic

(3) Tetragonal		(4) Monoclinic

(5) Triclinic	(6) Hexagonal	(7) Rhombohedral

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