GROUP THEORY SYMBOL

GTReciprocalBasis

GTReciprocalBasis[lattice vectors]
calculates the reciprocal lattice vectors from a given set of lattice vectors.

DetailsDetails

  • 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

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

First load the package:

In[1]:=
Click for copyable input

The basis of a simple cubic lattice is given:

In[2]:=
Click for copyable input

The reciprocal basis follows as :

In[3]:=
Click for copyable input
Out[3]=

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

In[4]:=
Click for copyable input
Out[4]//MatrixForm=

For an fcc lattice we get:

In[5]:=
Click for copyable input
Out[5]=
In[6]:=
Click for copyable input
Out[6]//MatrixForm=
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
Top