150 lines
6.0 KiB
Python
150 lines
6.0 KiB
Python
import numpy as np
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from .lattice import Lattice
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from .rotation import Rotation
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class Orientation:
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"""
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Crystallographic orientation.
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A crystallographic orientation contains a rotation and a lattice.
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"""
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__slots__ = ['rotation','lattice']
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def __repr__(self):
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"""Report lattice type and orientation."""
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return self.lattice.__repr__()+'\n'+self.rotation.__repr__()
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def __init__(self, rotation, lattice):
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"""
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New orientation from rotation and lattice.
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Parameters
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----------
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rotation : Rotation
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Rotation specifying the lattice orientation.
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lattice : Lattice
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Lattice type of the crystal.
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"""
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if isinstance(lattice, Lattice):
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self.lattice = lattice
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else:
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self.lattice = Lattice(lattice) # assume string
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if isinstance(rotation, Rotation):
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self.rotation = rotation
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else:
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self.rotation = Rotation.fromQuaternion(rotation) # assume quaternion
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def disorientation(self,
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other,
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SST = True,
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symmetries = False):
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"""
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Disorientation between myself and given other orientation.
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Rotation axis falls into SST if SST == True.
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(Currently requires same symmetry for both orientations.
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Look into A. Heinz and P. Neumann 1991 for cases with differing sym.)
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"""
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if self.lattice.symmetry != other.lattice.symmetry:
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raise NotImplementedError('disorientation between different symmetry classes not supported yet.')
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mySymEqs = self.equivalentOrientations() if SST else self.equivalentOrientations([0]) # take all or only first sym operation
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otherSymEqs = other.equivalentOrientations()
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for i,sA in enumerate(mySymEqs):
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aInv = sA.rotation.inversed()
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for j,sB in enumerate(otherSymEqs):
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b = sB.rotation
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r = b*aInv
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for k in range(2):
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r.inverse()
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breaker = self.lattice.symmetry.inFZ(r.asRodrigues(vector=True)) \
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and (not SST or other.lattice.symmetry.inDisorientationSST(r.asRodrigues(vector=True)))
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if breaker: break
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if breaker: break
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if breaker: break
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return (Orientation(r,self.lattice), i,j, k == 1) if symmetries else r # disorientation ...
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# ... own sym, other sym,
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# self-->other: True, self<--other: False
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def inFZ(self):
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return self.lattice.symmetry.inFZ(self.rotation.asRodrigues(vector=True))
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def equivalentOrientations(self,members=[]):
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"""List of orientations which are symmetrically equivalent."""
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try:
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iter(members) # asking for (even empty) list of members?
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except TypeError:
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return self.__class__(self.lattice.symmetry.symmetryOperations(members)*self.rotation,self.lattice) # no, return rotation object
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else:
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return [self.__class__(q*self.rotation,self.lattice) \
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for q in self.lattice.symmetry.symmetryOperations(members)] # yes, return list of rotations
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def relatedOrientations(self,model):
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"""List of orientations related by the given orientation relationship."""
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r = self.lattice.relationOperations(model)
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return [self.__class__(o*self.rotation,r['lattice']) for o in r['rotations']]
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def reduced(self):
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"""Transform orientation to fall into fundamental zone according to symmetry."""
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for me in self.equivalentOrientations():
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if self.lattice.symmetry.inFZ(me.rotation.asRodrigues(vector=True)): break
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return self.__class__(me.rotation,self.lattice)
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def inversePole(self,
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axis,
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proper = False,
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SST = True):
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"""Axis rotated according to orientation (using crystal symmetry to ensure location falls into SST)."""
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if SST: # pole requested to be within SST
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for i,o in enumerate(self.equivalentOrientations()): # test all symmetric equivalent quaternions
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pole = o.rotation*axis # align crystal direction to axis
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if self.lattice.symmetry.inSST(pole,proper): break # found SST version
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else:
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pole = self.rotation*axis # align crystal direction to axis
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return (pole,i if SST else 0)
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def IPFcolor(self,axis):
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"""TSL color of inverse pole figure for given axis."""
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color = np.zeros(3,'d')
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for o in self.equivalentOrientations():
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pole = o.rotation*axis # align crystal direction to axis
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inSST,color = self.lattice.symmetry.inSST(pole,color=True)
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if inSST: break
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return color
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@staticmethod
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def fromAverage(orientations,
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weights = []):
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"""Create orientation from average of list of orientations."""
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if not all(isinstance(item, Orientation) for item in orientations):
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raise TypeError("Only instances of Orientation can be averaged.")
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closest = []
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ref = orientations[0]
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for o in orientations:
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closest.append(o.equivalentOrientations(
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ref.disorientation(o,
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SST = False, # select (o[ther]'s) sym orientation
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symmetries = True)[2]).rotation) # with lowest misorientation
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return Orientation(Rotation.fromAverage(closest,weights),ref.lattice)
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def average(self,other):
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"""Calculate the average rotation."""
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return Orientation.fromAverage([self,other])
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