GroupTheory`
GroupTheory`

GTLatticeVectors

GTLatticeVectors[list]

gives the lattice vectors from a list of lattice constants and angles.

Details and Options

  • This command has changed compared to previous versions of GTPack!
  • In the previous version a list of the form {a,b,c,α,β,γ} was expected as input. If you provide such a list, the old version of the command will be used.
  • Old version:
  • a,b,c are the lengths of the corresponding to lattice vectors a,b,c. α is the angle between c and b, β is the angle between c and a and finally γ is the angle between a and b. The Cartesian components of the lattice vectors are constructed in such a way that a is parallel to the x axis. The vector b lies in the xy plane. If a and b are found c is constructed to enclose the angles α and β with b and a.
  • New version:
  • The definitions correspond now to AFLOW. The input is now a list containing crystal system and Pearson symbol like {"Cubic","cP"}.
  • See: AFLOW - crystal info on: Encyclopedia of Crystallographic Prototypes
  • See also: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 4.

Examples

Basic Examples  (3)

First, load the package:

old version  (1)

Simple orthorhombic lattice

Hexagonal lattice

new version  (1)

You will get information about possible input

For the simple orthorhombic lattice we get:

The result corresponds to the old definition. For the hexagonal lattice we get:

Thus, the vectors are defined in a different way.