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| Symmetry
is a property of systems such that the application of a symmetry operation
(translation, reflection, or rotation) will take the system into a configuration
identical to its initial state.
In
a point lattice (Bravais lattice) a required symetry is that of translation.
A lattice translation vector, T, connects two points in the lattice that
have identical surroundings and is made up of interger steps of the three
unit vectors (a,b,c) of the lattice, such that:
In the diagram, (a) and (b) show planes of symmetry in the cubic lattice. In (c) the three fourfold rotational axes of the cube are shown, (d) shows the four threefold axes , and (e) the six twofold rotational axes. Other lattice structures will have different symmetry operations. From: Kittel, "Introduction to Solid State Physics," Wiley (1971) |
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