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MaXrd

Guides

  • MaXrd – Mathematica X-ray diffraction package

Tech Notes

  • Applying crystal data
  • Basic computations
  • Computations on reflections
  • Formulas in crystallography
  • Importing crystal data
  • Quick guide to conditions
  • References
  • Symmetry calculations
  • The association structure of crystallographic data
  • Using the rotation options

Symbols

  • AttenuationCoefficient
  • BraggAngle
  • ConstructDomains
  • CrystalDensity
  • CrystalFormulaUnits
  • CrystalPlot
  • DarwinWidth
  • DistortStructure
  • DomainPlot
  • EmbedStructure
  • ExpandCrystal
  • ExportCrystalData
  • ExtinctionLength
  • FindPixelClusters
  • GetAtomCoordinates
  • GetAtomicScatteringFactors
  • GetCrystalMetric
  • GetElements
  • GetLatticeParameters
  • GetLaueClass
  • GetScatteringCrossSections
  • GetSymmetryData
  • GetSymmetryOperations
  • ImportCrystalData
  • InputCheck
  • InterplanarSpacing
  • MergeDomains
  • MergeSymmetryEquivalentReflections
  • MillerNotationToList
  • MillerNotationToString
  • ReciprocalImageCheck
  • ReciprocalSpaceSimulation
  • ReflectionList
  • RelatedFunctionsGraph
  • ResetCrystalData
  • ResizeStructure
  • SimulateDiffractionPattern
  • StructureFactor
  • StructureFactorTable
  • SymmetryEquivalentPositions
  • SymmetryEquivalentReflections
  • SymmetryEquivalentReflectionsQ
  • SynthesiseStructure
  • SystematicAbsentQ
  • ToStandardSetting
  • TransformAtomicDisplacementParameters
  • UnitCellTransformation
  • $CrystalData
  • $GroupSymbolRedirect
  • $LaueClasses
  • $MaXrdPath
  • $MaXrdVersion
  • $PeriodicTable
  • $PointGroups
  • $SpaceGroups
  • $TransformationMatrices
StianRamsnes`MaXrd`
SymmetryEquivalentPositions
​
SymmetryEquivalentPositions
[group,{x,y,z}]
returns a list of coordinates that are equivalent to
{x,y,z}
under the symmetry of
group
.
​
​
SymmetryEquivalentPositions
[group,{{
x
1
,
y
1
,
z
1
}{
x
2
,
y
2
,
z
2
},…}]
returns a list of coordinates, each entry containing the equivalents of
{x,y,z}
i
under the symmetry of
group
.
​
Details and Options

Examples  
(7)
Basic Examples  
(2)
Fractional coordinates:
In[1]:=
SymmetryEquivalentPositions
["Pnma",{0,0,1/2}]
Out[1]=
0,0,
1
2
,
1
2
,0,0,0,
1
2
,
1
2
,
1
2
,
1
2
,0
In[2]:=
SymmetryEquivalentPositions
["F d -3 m:2",{1/8,1/8,1/8},"UseCentring"False]
Out[2]=

1
8
,
1
8
,
1
8
,
7
8
,
3
8
,
3
8

In[3]:=
SymmetryEquivalentPositions
["P -3 1 c",{0,0,1/4}]
Out[3]=
0,0,
1
4
,0,0,
3
4

​
The
Head
of indices may be
String
or
Symbol
as well:
In[1]:=
SymmetryEquivalentPositions
["R -3 c",{0,0,"z"},"UseCentring"False]
Out[1]=
{0,0,z},0,0,
1
2
-z,{0,0,-z},0,0,
1
2
+z
In[2]:=
SymmetryEquivalentPositions
["I4/mcm",{0,"k",0}]
Out[2]=
{0,k,0},{0,-k,0},{-k,0,0},{k,0,0},0,k,
1
2
,0,-k,
1
2
,k,0,
1
2
,-k,0,
1
2
,
1
2
,
1
2
+k,
1
2
,
1
2
,
1
2
-k,
1
2
,
1
2
-k,
1
2
,
1
2
,
1
2
+k,
1
2
,
1
2
,
1
2
,
1
2
+k,0,
1
2
,
1
2
-k,0,
1
2
+k,
1
2
,0,
1
2
-k,
1
2
,0
In[3]:=
SymmetryEquivalentPositions
["F d -3 m",{0,0,0}]
Out[3]=
{0,0,0},0,
1
2
,
1
2
,
1
2
,
1
2
,0,
1
2
,0,
1
2
,
3
4
,
1
4
,
3
4
,
1
4
,
1
4
,
1
4
,
1
4
,
3
4
,
3
4
,
3
4
,
3
4
,
1
4

In[4]:=
SymmetryEquivalentPositions
["P6cc",{♔,,}]
Out[4]=
{♔,,},{-,-+♔,},{-♔,-♔,},{-♔,-,},{,-♔,},{-+♔,♔,},-,-♔,
1
2
+,-♔,,
1
2
+,♔,-+♔,
1
2
+,,♔,
1
2
+,-+♔,-,
1
2
+,-♔,-♔,
1
2
+
Scope  
(3)

Options  
(2)

SeeAlso
AttenuationCoefficient
 
▪
StructureFactor
 
▪
GetSymmetryOperations
 
▪
GetSymmetryData
 
▪
SymmetryEquivalentReflections
 
▪
SymmetryEquivalentReflectionsQ
 
▪
SystematicAbsentQ
 
▪
ToStandardSetting
 
▪
$SpaceGroups
RelatedGuides
▪
MaXrd – Mathematica X-ray diffraction package
""

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