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Constructor for an S3 object of class "cryst_symm".

cryst_symm.Rd

This represents a crystallographic space group.

Usage

cryst_symm(SG = NULL, set = NULL)

Arguments

SG

A character string or an integer identifying the space group. There are 230 used space group in crystallography and each one corresponds to a unique and so-called extended Hermann-Mauguin symbol. An example is space group number 19, identified by the extended Hermann-Mauguin symbol "P 21 21 21". Several formats are possible and some of them are now rarely used. Attempts are made to transform the input into a correct Hermann-Mauguin symbol, but if all fails, a warning is raised and the space group P 1 is assigned.

set

An integer defining which setting of many possible for the given space group. Some crystallographic space groups can be implemented with small variants known as "settings". If the input SG is an extended Hermann-Mauguin symbol, set is ignored, as it is already specified by the xHM symbol.

Value

An object of class "cryst_symm". It is a named list of length 4. The names are, "SG", "PG", "T" and "C".

  • 1) SG. This is a string containing the correct extended Hermann-Mauguin symbol.

  • 2) PG. This is a list whose elements are all the \(3\times 3\) matrices forming the point-group part of the symmetry transformation.

  • 3) T. This is a list whose elements are all the \(3\times 1\) vectors forming the translational part of the symmetry transformation.

  • 4) C. This is a list whose elements are all the \(3\times 1\) vectors forming the centering of the unit cell.

Details

The constructor can be used with less than the full set of two input parameters, to create an object of class cryst_symm corresponding to space group P 1. If the input string is not recognised, a warning is raised and space group P 1 is assigned.

Examples

# The symplest symmetry: P 1
crsym <- cryst_symm("P 1")
print(crsym)
#> This is an object of class 'cryst_symm'
#> The space group represented is P 1.
#> The number associated to this group in the International Tables is: 1.
#> Its crystal system is TRICLINIC.
#> 
#> List of symmetry operations:
#>   X,  Y,  Z

# The second space group: P -1
crsym <- cryst_symm(2)
print(crsym)
#> This is an object of class 'cryst_symm'
#> The space group represented is P -1.
#> The number associated to this group in the International Tables is: 2.
#> Its crystal system is TRICLINIC.
#> 
#> List of symmetry operations:
#>   X,  Y,  Z
#>   -X,  -Y,  -Z

# Something more complicated
crsym <- cryst_symm("P 21 21 21")
print(crsym)
#> This is an object of class 'cryst_symm'
#> The space group represented is P 21 21 21.
#> The number associated to this group in the International Tables is: 19.
#> Its crystal system is ORTHOROMBIC.
#> 
#> List of symmetry operations:
#>   X,  Y,  Z
#>   -X+1/2,  -Y,  Z+1/2
#>   X+1/2,  -Y+1/2,  -Z
#>   -X,  Y+1/2,  -Z+1/2