Condensed matter physics deals with the first two of these states of matter. We can also, however, further subdivide the solids in a number of different ways. The first type of material is known as a crystal , while the second is termed an amorphous material. That is, in a crystal the sites of atoms are determined simply by repeating some sub-unit of the crystal at regular intervals to fill all space. For example, the sodium chloride crystal structure is based upon the face centred cubic lattice in which the lattice points are arranged as if at the corners of an array of adjoining cubes, but with an additional lattice point at the centre of each face.
Different materials have different underlying lattices and different kinds of basis.
The 14 different lattices are known as Bravais lattices , and the 7 different symmetry groups are known as the crystal systems . Amorphous materials are less well-studied, which is a shame since they are also very important in the real world. A good example of an amorphous material is glass. However, the lack of a repeating structure means that these materials are much more difficult to deal with from the theoretical point of view. Consequently they won't feature at all in the following material.