The class crystalFrame

the reference frame glued to the lattice basis of a phase, with the point group of the crystal

Syntax

cs = crystalFrame('m-3m', [4.05, 4.05, 4.05], mineral='Aluminium', color='blue')

cs = crystalFrame('2/m', [8.6, 13, 7.2], [90, 116, 90], 'X||a', mineral='Orthoclase')

cs = crystalFrame('cubic')

cs = crystalFrame(LaueId=9)

cs = crystalFrame(spaceId=153)

cs = crystalFrame('I4/mmm', [3.3, 3.3, 5.8])

cs = crystalFrame('432', rotAxes=rot)

cs = crystalFrame([1, 2, 3], [70, 80, 120], 'Z||a*')

cs = crystalFrame(axes, name='Forsterite')

cs = crystalFrame(rot)

cs = crystalFrame(otherFrame)

Description

The basis is the crystal axes a, b, c in Euclidean coordinates, with their lengths; how the Cartesian axes are aligned to them, X||a* and Z||c by default, belongs to the frame, not to the point group. A frame is a handle compared by identity: the constructor answers with the session’s frame of the same lattice, group and name where there is one (intern=False keeps it apart). The name, the mineral, is the frame’s identity in a phase list.

Positional strings are the point group and alignments, ‘X||a’, ‘Z||c*’, ‘EDAX’; everything else is a keyword. The axis angles are in radians, or in degree when one exceeds 2 pi. A space group symbol gives the point group and the centring of the lattice, P, A, B, C, I, F or R, which centering also sets.

Input

Keywords

Output

Example

Define cubic aluminium and hexagonal magnesium frames using lattice lengths in angstroms. The Miller direction belongs to the frame in which it was constructed.

from mtex import crystalFrame, Miller

al = crystalFrame('m-3m', [4.05, 4.05, 4.05], mineral='Aluminium')
mg = crystalFrame('6/mmm', [3.20927, 3.20927, 5.21033], mineral='Magnesium')
cAxis = Miller(0, 0, 0, 1, mg, 'UVTW')
print(al)
print(mg)
print(cAxis)

The point group describes symmetry; the lattice lengths and alignment determine how indices become Cartesian vectors. The magnesium c-axis above uses four direct-lattice indices.

Aluminium
Magnesium
<0001>

See also

specimenFrame, referenceFrame, Miller, orientation, CrystalSymmetries, CrystalReferenceSystem

Members

Used on

CrystalDirections, CrystalOperations, CrystalReferenceSystem, CrystalShapeSmorf, CrystalSymmetries, FundamentalSector, LatticeMetric, SymmetryAlignment, MTEXvsBungeConvention, OrientationEmbeddings, OrientationFibre, OrientationFundamentalRegion

MATLAB’s crystalFrame_index

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}