GEO3020 Internal Order in Crystalline Solids: Translation Symmetry and Lattices
GEO3020 Internal Order in Crystalline Solids: Translation Symmetry and Lattices
- Symmetry of a Crystal.
The purpose of this exercise is to demonstrate the relationship between the symmetry of a lattice and the symmetry of a crystal.
- Space Lattice Types. There are four basic types of space lattice whose unit cells have an unspecified geometrical shape except for the number and locations of lattice points. These are:
(1) Primitive (P): The lattice points are at the corners of the unit cell. There is a total of one lattice point per unit cell because each corner point is shared by 8 unit cells (1/8 x 8 = 1).
(2) Side–centered (B or C): The lattice points are at the corners of the unit cell and centered in pairs of opposite faces of the unit cell. There is a total of two lattice points per unit cell. Each corner point is shared by 8 unit cells (1/8 x 8 = 1). Each side-centered point is shared by two unit cells (1/2 x 2 = 1).
(3) Body centered (I): The lattice points are at the corners of the unit cell and centered in the body of the unit cell. There is a total of two lattice points per unit cell. Each corner point is shared by 8 unit cells (1 lattice point), but the point located in the center of the unit cell is unshared (1 lattice point).
(4) Face centered (F): The lattice points are at the corners of the unit cell and centered in each face of the unit cell. There is a total of four lattice points per unit cell. Each corner point is shared by 8 unit cells (1/8 x 8 = 1). Each face centered point is shared by two unit cells (1/2 x 6 = 3).
DETAILED ASSIGNMENT
