196 lines
10 KiB
Python
196 lines
10 KiB
Python
import numpy as np
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from . import Rotation
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class LatticeFamily():
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def __init__(self,family):
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"""
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Symmetry-related operations for crystal families.
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Parameters
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----------
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family : {'triclinic', 'monoclinic', 'orthorhombic', 'tetragonal', 'hexagonal', 'cubic'}
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Name of the crystal family.
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"""
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if family not in self._immutable.keys():
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raise KeyError(f'invalid lattice family "{family}"')
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self.family = family
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@property
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def symmetry_operations(self):
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"""Symmetry operations as Rotations."""
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return Rotation.from_quaternion(self._symmetry_operations[self.family],accept_homomorph=True)
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@property
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def immutable(self):
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"""Return immutable parameters lattice parameters."""
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return self._immutable[self.family]
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@property
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def basis(self):
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"""
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Corners of the standard triangle.
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Not yet defined for monoclinic.
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References
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----------
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Bases are computed from
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>>> basis = {
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... 'cubic' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
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... [1.,0.,1.]/np.sqrt(2.), # green
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... [1.,1.,1.]/np.sqrt(3.)]).T), # blue
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... 'hexagonal' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
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... [1.,0.,0.], # green
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... [np.sqrt(3.),1.,0.]/np.sqrt(4.)]).T), # blue
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... 'tetragonal' : np.linalg.inv(np.array([[0.,0.,1.], # direction of red
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... [1.,0.,0.], # green
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... [1.,1.,0.]/np.sqrt(2.)]).T), # blue
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... 'orthorhombic': np.linalg.inv(np.array([[0.,0.,1.], # direction of red
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... [1.,0.,0.], # green
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... [0.,1.,0.]]).T), # blue
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... }
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"""
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return self._basis.get(self.family,None)
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_symmetry_operations = {
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'cubic': [
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[ 1.0, 0.0, 0.0, 0.0 ],
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[ 0.0, 1.0, 0.0, 0.0 ],
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[ 0.0, 0.0, 1.0, 0.0 ],
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[ 0.0, 0.0, 0.0, 1.0 ],
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[ 0.0, 0.0, 0.5*np.sqrt(2), 0.5*np.sqrt(2) ],
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[ 0.0, 0.0, 0.5*np.sqrt(2),-0.5*np.sqrt(2) ],
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[ 0.0, 0.5*np.sqrt(2), 0.0, 0.5*np.sqrt(2) ],
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[ 0.0, 0.5*np.sqrt(2), 0.0, -0.5*np.sqrt(2) ],
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[ 0.0, 0.5*np.sqrt(2),-0.5*np.sqrt(2), 0.0 ],
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[ 0.0, -0.5*np.sqrt(2),-0.5*np.sqrt(2), 0.0 ],
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[ 0.5, 0.5, 0.5, 0.5 ],
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[-0.5, 0.5, 0.5, 0.5 ],
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[-0.5, 0.5, 0.5, -0.5 ],
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[-0.5, 0.5, -0.5, 0.5 ],
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[-0.5, -0.5, 0.5, 0.5 ],
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[-0.5, -0.5, 0.5, -0.5 ],
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[-0.5, -0.5, -0.5, 0.5 ],
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[-0.5, 0.5, -0.5, -0.5 ],
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[-0.5*np.sqrt(2), 0.0, 0.0, 0.5*np.sqrt(2) ],
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[ 0.5*np.sqrt(2), 0.0, 0.0, 0.5*np.sqrt(2) ],
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[-0.5*np.sqrt(2), 0.0, 0.5*np.sqrt(2), 0.0 ],
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[-0.5*np.sqrt(2), 0.0, -0.5*np.sqrt(2), 0.0 ],
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[-0.5*np.sqrt(2), 0.5*np.sqrt(2), 0.0, 0.0 ],
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[-0.5*np.sqrt(2),-0.5*np.sqrt(2), 0.0, 0.0 ],
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],
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'hexagonal': [
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[ 1.0, 0.0, 0.0, 0.0 ],
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[-0.5*np.sqrt(3), 0.0, 0.0, -0.5 ],
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[ 0.5, 0.0, 0.0, 0.5*np.sqrt(3) ],
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[ 0.0, 0.0, 0.0, 1.0 ],
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[-0.5, 0.0, 0.0, 0.5*np.sqrt(3) ],
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[-0.5*np.sqrt(3), 0.0, 0.0, 0.5 ],
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[ 0.0, 1.0, 0.0, 0.0 ],
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[ 0.0, -0.5*np.sqrt(3), 0.5, 0.0 ],
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[ 0.0, 0.5, -0.5*np.sqrt(3), 0.0 ],
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[ 0.0, 0.0, 1.0, 0.0 ],
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[ 0.0, -0.5, -0.5*np.sqrt(3), 0.0 ],
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[ 0.0, 0.5*np.sqrt(3), 0.5, 0.0 ],
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],
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'tetragonal': [
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[ 1.0, 0.0, 0.0, 0.0 ],
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[ 0.0, 1.0, 0.0, 0.0 ],
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[ 0.0, 0.0, 1.0, 0.0 ],
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[ 0.0, 0.0, 0.0, 1.0 ],
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[ 0.0, 0.5*np.sqrt(2), 0.5*np.sqrt(2), 0.0 ],
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[ 0.0, -0.5*np.sqrt(2), 0.5*np.sqrt(2), 0.0 ],
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[ 0.5*np.sqrt(2), 0.0, 0.0, 0.5*np.sqrt(2) ],
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[-0.5*np.sqrt(2), 0.0, 0.0, 0.5*np.sqrt(2) ],
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],
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'orthorhombic': [
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[ 1.0,0.0,0.0,0.0 ],
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[ 0.0,1.0,0.0,0.0 ],
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[ 0.0,0.0,1.0,0.0 ],
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[ 0.0,0.0,0.0,1.0 ],
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],
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'monoclinic': [
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[ 1.0,0.0,0.0,0.0 ],
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[ 0.0,0.0,1.0,0.0 ],
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],
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'triclinic': [
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[ 1.0,0.0,0.0,0.0 ],
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]}
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_immutable = {
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'cubic': {
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'b': 1.0,
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'c': 1.0,
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'alpha': np.pi/2.,
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'beta': np.pi/2.,
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'gamma': np.pi/2.,
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},
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'hexagonal': {
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'b': 1.0,
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'alpha': np.pi/2.,
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'beta': np.pi/2.,
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'gamma': 2.*np.pi/3.,
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},
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'tetragonal': {
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'b': 1.0,
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'alpha': np.pi/2.,
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'beta': np.pi/2.,
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'gamma': np.pi/2.,
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},
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'orthorhombic': {
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'alpha': np.pi/2.,
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'beta': np.pi/2.,
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'gamma': np.pi/2.,
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},
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'monoclinic': {
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'alpha': np.pi/2.,
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'gamma': np.pi/2.,
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},
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'triclinic': {}
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}
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_basis = {
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'cubic': {'improper':np.array([ [-1. , 0. , 1. ],
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[ np.sqrt(2.) , -np.sqrt(2.) , 0. ],
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[ 0. , np.sqrt(3.) , 0. ] ]),
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'proper':np.array([ [ 0. , -1. , 1. ],
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[-np.sqrt(2.) , np.sqrt(2.) , 0. ],
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[ np.sqrt(3.) , 0. , 0. ] ]),
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},
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'hexagonal':
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{'improper':np.array([ [ 0. , 0. , 1. ],
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[ 1. , -np.sqrt(3.) , 0. ],
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[ 0. , 2. , 0. ] ]),
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'proper':np.array([ [ 0. , 0. , 1. ],
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[-1. , np.sqrt(3.) , 0. ],
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[ np.sqrt(3.) , -1. , 0. ] ]),
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},
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'tetragonal':
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{'improper':np.array([ [ 0. , 0. , 1. ],
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[ 1. , -1. , 0. ],
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[ 0. , np.sqrt(2.) , 0. ] ]),
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'proper':np.array([ [ 0. , 0. , 1. ],
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[-1. , 1. , 0. ],
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[ np.sqrt(2.) , 0. , 0. ] ]),
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},
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'orthorhombic':
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{'improper':np.array([ [ 0., 0., 1.],
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[ 1., 0., 0.],
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[ 0., 1., 0.] ]),
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'proper':np.array([ [ 0., 0., 1.],
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[-1., 0., 0.],
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[ 0., 1., 0.] ]),
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}}
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