Symetry Operations

Various symetries allow the classification and characterization of crystals.

1. Translation T=n₁ a₁+n₂ a₂+n₃ a₃

2. Rotational symetry rotation through integral multiples of 2p/n about

axis where n=1,2,3….

3. Reflection or mirror plane whether the lattice is identical on either side

of an imaginary plane

4. Inversion A point exists in the lattice such that the operation r -> -r

leaves the lattice unchanged.

A few symetries of the cubic lattice is shown below (From Cullity Fig. 2.6)

There are additional symetries depending on the symetry of the basis including rotations, mirror planes and glide operations.