GroupTheory`

GTCompatibility

calculates the compatibility relations of two point groups.

Details and Options

The groups of the wave vector along symmetry lines are subgroups of the corresponding point groups at the symmetry points. For the fcc structure is at Γ but along . Irreducible representations at Γ are reducible along (line ). Degeneracies will be lifted. The compatibility of the irreducible representation of group1 to the irreducible representation of group2 ⊂ group1 are presented in a table.
group1 and group2 can be names of the groups as symbols or strings. The groups will be installed internally for the the calculations. The groups can also be represented by lists.
The following options can be given:

GOFast	GOFastValue	Specifies if the input is validated
GOIrepNotation	"Bethe"	Specifies the notation of the irreducible representation
GOVerbose	False	Controls the output of additional information

See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 9.2.2.

Examples

open allclose all

Basic Examples (1)

First load the package

Compatibility relations will be only calculated, if one of the groups is a subgroup of the other. Internally the character tables are calculated. This may take some time. If it takes too long time restart helps.

The group subgroup relationship will be checked.

The groups can be defined by a list.

Options (3)

GOFast (1)

If GOFast 

True

, it is not checked whether group1 and group2 are really groups.

GOIrepNotation (1)

Different notations can be selected.

GOVerbose (1)

Information about both groups will be also printed.

Possible Issues (1)

Compatibility relations will be only calculated if one of the groups is subgroup of the other.

Please check carefully in wich way a certain point group is implemented. Sometimes you have to use simply a corresponding isomorphic group in your task that might be installed in terms of generators.