Diamond Structures

Diamond lattice structure

The diamond lattice (formed by the carbon atoms in a diamond crystal) consists of two interpenetrating face centered cubic Bravais lattices, displaced along the body diagonal of the cubic cell by one quarter the the length of the diagonal. It can be regarded as a face centered cubic lattice with the two-point basis:

where a is the lattice constant. The conventional cubic cell of the diamond lattice is shown in Fig.1.

Figure 1 (For animation, click on the picture...)

For clarity, the blue and green sites correspond to one of the two interpenetrating fcc lattices, and the light-blue sites correspond to another of the two interpenetrating fcc lattices. Nearest neighbor bonds have been drawn. The four nearest neighbors of each point form the vertices of a regular tetrahedron.
The diamond lattice is not a Bravais lattice, because the environment of each point differs in orientation from the environment of its nearest neighbors.
The 4x4 cell of the diamond lattice is shown in Fig.2.

Figure 2 (To get the big picture, click on it...)

GaAs structure

GaAs has equal numbers of gallium and arsenic ions distributed on a diamond lattice so that each has four of the opposite kind as nearest neighbors, as shown in Fig.3.

Figure 3

In the Fig.3, for example, the blue sites correspond to gallium ions and the green sites correspond to arsenic ions.
This structure is an example of a lattice with basis, which must be so described both because of the geometrical position of the ions and because two types of ions occur.
The 4x4 cell of the GaAs lattice is shown in Fig.4.

Figure 4 (To get the big picture, click on it...)