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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

cubic assignment helpcubic assignment helpcubic-assignment-help

(2) Orthorhombic

orthorhombicorthorhombicorthorhombicorthorhombic

(3) Tetragonal

(4) Monoclinic

tetragonal simple body centered tetragonal body-end-centered body-centered
(5) Triclinic (6) Hexagonal (7) Rhombohedral
triclinic hexagon-solutions rhombohedral

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