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