GroupTheory`
GroupTheory`

GTReciprocalBasis

GTReciprocalBasis[lattice vectors]

calculates the reciprocal lattice vectors from a given set of lattice vectors.

Details and Options

  • If are the lattice vectors and are the corresponding reciprocal lattice vectors, the vectors fullfill the relation
  • The module works for two and three dimensional lattices.
  • Three dimensional reciprocal lattice vectors can be calculated by
  • (cyclic permutations of )
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 6.2

Examples

Basic Examples  (2)

First load the package:

The basis of a simple cubic lattice is given:

The reciprocal basis follows as :

the condition a_i . b_(j )= 2pi delta_(i,j) has to be fulfilled.

For an fcc lattice we get: