Lattice parameter

Lattice parameters are the unit lengths along each crystallographic axis and their interaxial angles. A parameter, either a measure of length or angle, that defines the sizeand shape of the unit cell of a crystal lattice. The lattice constants of a crystal structure define the unit cell metric i.e. the translation lattice. The length of the basis vectors a, b, c must be given in Å, the angles α , β , γ in degrees. The agreement of the given lattice parameters with the defined crystal system derived from the space-group number and the used setting will be checked automatically to the greatest possible extent by PowderCell.

The volume of the unit cell can be calculated from the lattice constant lengths and angles. If the unit cell sides are represented as vectors, then the volume is the dot product of one vector with the cross product of the other two vectors. The volume is represented by the letter V.

V = abc√ 1+2cos(α) cos(β) cos(γ) - cos2(α) - cos2(β)-cos2(γ)

For monoclinic lattices with α = 90°, γ = 90°, this simplifies to

V = abc√sin(β)