The class crystalShape

construct a convex crystal morphology from symmetry-related lattice planes.

Syntax

cS = crystalShape(N)

cS = crystalShape(N, habitus=1, extension=(1, 1, 2))

cS = crystalShape.hex(cs)

cS = crystalShape.quartz(simple=True)

Description

Each supplied Miller normal represents a crystal form: all its symmetry equivalents are generated using the point group of its crystal frame. The shape is the bounded intersection of the half spaces dot(vertex, normal) <= 1. Before the common display scaling, a face is therefore 1/norm(normal) from the origin. Lengthening a normal moves its planes inward; shortening it can move them so far outward that other planes exclude those faces entirely. Supply enough forms to enclose a finite volume.

The optional habitus and extension parameters adjust relative plane distances using the Miller indices. For habitus p > 0, a normal with indices (h, k, l) is divided by ((abs(h)*extension[0])**p + (abs(k)*extension[1])**p + (abs(l)*extension[2])**p)**(1/p) before symmetry expansion. With habitus=0 this step is skipped and extension has no effect. This changes the morphology rather than assigning an absolute size.

The vertices are initially scaled so that their largest distance from the origin is 0.5. For a centrally symmetric crystal this gives diameter one. Read or assign diameter to set a particular size, or multiply the shape by a scale factor. Areas and volumes then have the corresponding squared and cubed length units.

An orientation places the shape in specimen coordinates: ori*cS. A list of orientations gives a list of identically connected shapes; cS+position translates their vertices. Face selection uses cS[normals], while cS[k] selects one shape from a list. Face normals used for selection are in the original crystal coordinates.

Input

Keywords

Output

Properties

Example

Construct a hexagonal prism without a data file, then build a cubic morphology from two families of lattice planes. Both examples use relative lengths; diameter sets the displayed size.

import matplotlib.pyplot as plt
from mtex import crystalFrame, crystalShape, Miller, cat, plot

hexagonal = crystalFrame('6/mmm', [3, 3, 4.7])
prism = crystalShape.hex(hexagonal)
prism.diameter = 2
print('Prism faces:', prism.numFaces)
plot(prism, faceAlpha=0.4, colored=True)

cubic = crystalFrame('m-3m')
normals = cat(Miller(1, 0, 0, cubic), 0.5*Miller(1, 1, 1, cubic))
truncatedCube = crystalShape(normals)
print('Truncated-cube faces:', truncatedCube.numFaces)
plot(truncatedCube, faceAlpha=0.5, colored=True)
plt.show()

The {100} planes bound the cube and the scaled {111} normals cut its corners. Changing a normal length changes its plane distance and therefore the relative prominence of that crystal form.

Prism faces: 8
Truncated-cube faces: 14

References

• J. Enderlein, A package for displaying crystal morphology, Mathematica Journal 7(1), 1997

See also

Miller, crystalShape.cube, crystalShape.hex, crystalShape.innerFace, CrystalShapes

Members

Used on

CrystalShapeSmorf, CrystalShapes

MATLAB’s crystalShape_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}
}