transition to new class
This commit is contained in:
Martin Diehl
parent
217024667b
commit
907f7ca560
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@ -242,8 +242,11 @@ class Rotation:
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If a quaternion is given, it needs to comply with the convection. Use .fromQuaternion
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If a quaternion is given, it needs to comply with the convection. Use .fromQuaternion
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to check the input.
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to check the input.
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"""
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"""
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self.quaternion = Quaternion2(q=quaternion[0],p=quaternion[1:4])
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if isinstance(quaternion,Quaternion2):
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self.quaternion.homomorph() # ToDo: Needed?
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self.quaternion = quaternion.copy()
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else:
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self.quaternion = Quaternion2(q=quaternion[0],p=quaternion[1:4])
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self.quaternion.homomorph() # ToDo: Needed?
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def __repr__(self):
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def __repr__(self):
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"""Value in selected representation"""
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"""Value in selected representation"""
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@ -253,6 +256,7 @@ class Rotation:
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'Bunge Eulers / deg: {}'.format('\t'.join(list(map(str,self.asEulers(degrees=True)))) ),
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'Bunge Eulers / deg: {}'.format('\t'.join(list(map(str,self.asEulers(degrees=True)))) ),
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])
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])
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################################################################################################
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################################################################################################
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# convert to different orientation representations (numpy arrays)
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# convert to different orientation representations (numpy arrays)
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@ -261,7 +265,11 @@ class Rotation:
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def asEulers(self,
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def asEulers(self,
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degrees = False):
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degrees = False):
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return np.degrees(qu2eu(self.quaternion.asArray())) if degrees else qu2eu(self.quaternion.asArray())
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eu = qu2eu(self.quaternion.asArray())
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if degrees: eu = np.degrees(eu)
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return eu
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def asAngleAxis(self,
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def asAngleAxis(self,
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degrees = False):
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degrees = False):
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@ -370,7 +378,7 @@ class Rotation:
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"""
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"""
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Multiplication
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Multiplication
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Rotation: Details needed (active/passive), more rotation of (3,3,3,3) should be considered
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Rotation: Details needed (active/passive), rotation of (3,3,3,3)-matrix should be considered
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"""
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"""
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if isinstance(other, Rotation): # rotate a rotation
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if isinstance(other, Rotation): # rotate a rotation
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return self.__class__((self.quaternion * other.quaternion).asArray())
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return self.__class__((self.quaternion * other.quaternion).asArray())
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@ -416,7 +424,12 @@ class Rotation:
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def inversed(self):
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def inversed(self):
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"""In-place inverse rotation/backward rotation"""
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"""In-place inverse rotation/backward rotation"""
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return self.__class__(self.quaternion.conjugated().asArray())
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return self.__class__(self.quaternion.conjugated())
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def misorientation(self,other):
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"""Misorientation"""
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return self.__class__(other.quaternion*self.quaternion.conjugated())
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# ******************************************************************************************
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# ******************************************************************************************
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@ -810,11 +823,15 @@ class Quaternion:
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# ******************************************************************************************
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# ******************************************************************************************
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class Symmetry:
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class Symmetry:
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"""
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Symmetry operations for lattice systems
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https://en.wikipedia.org/wiki/Crystal_system
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"""
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lattices = [None,'orthorhombic','tetragonal','hexagonal','cubic',]
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lattices = [None,'orthorhombic','tetragonal','hexagonal','cubic',]
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def __init__(self, symmetry = None):
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def __init__(self, symmetry = None):
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"""Lattice with given symmetry, defaults to None"""
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if isinstance(symmetry, str) and symmetry.lower() in Symmetry.lattices:
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if isinstance(symmetry, str) and symmetry.lower() in Symmetry.lattices:
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self.lattice = symmetry.lower()
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self.lattice = symmetry.lower()
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else:
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else:
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@ -927,25 +944,29 @@ class Symmetry:
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def inFZ(self,R):
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def inFZ(self,R):
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"""Check whether given Rodrigues vector falls into fundamental zone of own symmetry."""
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"""Check whether given Rodrigues vector falls into fundamental zone of own symmetry."""
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if isinstance(R, Quaternion): R = R.asRodrigues() # translate accidentally passed quaternion
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# fundamental zone in Rodrigues space is point symmetric around origin
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# fundamental zone in Rodrigues space is point symmetric around origin
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R = abs(R)
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if R.shape[0]==4: # transition old (length not stored separately) to new
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Rabs = abs(R[0:3]*R[3])
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else:
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Rabs = abs(R)
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if self.lattice == 'cubic':
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if self.lattice == 'cubic':
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return math.sqrt(2.0)-1.0 >= R[0] \
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return math.sqrt(2.0)-1.0 >= Rabs[0] \
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and math.sqrt(2.0)-1.0 >= R[1] \
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and math.sqrt(2.0)-1.0 >= Rabs[1] \
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and math.sqrt(2.0)-1.0 >= R[2] \
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and math.sqrt(2.0)-1.0 >= Rabs[2] \
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and 1.0 >= R[0] + R[1] + R[2]
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and 1.0 >= Rabs[0] + Rabs[1] + Rabs[2]
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elif self.lattice == 'hexagonal':
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elif self.lattice == 'hexagonal':
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return 1.0 >= R[0] and 1.0 >= R[1] and 1.0 >= R[2] \
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return 1.0 >= Rabs[0] and 1.0 >= Rabs[1] and 1.0 >= Rabs[2] \
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and 2.0 >= math.sqrt(3)*R[0] + R[1] \
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and 2.0 >= math.sqrt(3)*Rabs[0] + Rabs[1] \
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and 2.0 >= math.sqrt(3)*R[1] + R[0] \
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and 2.0 >= math.sqrt(3)*Rabs[1] + Rabs[0] \
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and 2.0 >= math.sqrt(3) + R[2]
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and 2.0 >= math.sqrt(3) + Rabs[2]
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elif self.lattice == 'tetragonal':
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elif self.lattice == 'tetragonal':
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return 1.0 >= R[0] and 1.0 >= R[1] \
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return 1.0 >= Rabs[0] and 1.0 >= Rabs[1] \
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and math.sqrt(2.0) >= R[0] + R[1] \
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and math.sqrt(2.0) >= Rabs[0] + Rabs[1] \
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and math.sqrt(2.0) >= R[2] + 1.0
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and math.sqrt(2.0) >= Rabs[2] + 1.0
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elif self.lattice == 'orthorhombic':
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elif self.lattice == 'orthorhombic':
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return 1.0 >= R[0] and 1.0 >= R[1] and 1.0 >= R[2]
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return 1.0 >= Rabs[0] and 1.0 >= Rabs[1] and 1.0 >= Rabs[2]
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else:
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else:
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return True
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return True
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@ -1067,6 +1088,373 @@ class Symmetry:
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# suggested reading: http://web.mit.edu/2.998/www/QuaternionReport1.pdf
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# suggested reading: http://web.mit.edu/2.998/www/QuaternionReport1.pdf
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# ******************************************************************************************
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class Lattice:
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"""
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Lattice system
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Currently, this contains only a mapping from Bravais lattice to symmetry
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and orientation relationships. It could include twin and slip systems.
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https://en.wikipedia.org/wiki/Bravais_lattice
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"""
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lattices = {
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'triclinic':{'symmetry':None},
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'bct':{'symmetry':'tetragonal'},
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'hex':{'symmetry':'hexagonal'},
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'fcc':{'symmetry':'cubic','c/a':1.0},
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'bcc':{'symmetry':'cubic','c/a':1.0},
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}
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def __init__(self, lattice):
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self.lattice = lattice
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self.symmetry = Symmetry(self.lattices[lattice]['symmetry'])
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def __repr__(self):
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"""Report basic lattice information"""
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return 'Bravais lattice {} ({} symmetry)'.format(self.lattice,self.symmetry)
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# Kurdjomov--Sachs orientation relationship for fcc <-> bcc transformation
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# from S. Morito et al./Journal of Alloys and Compounds 5775 (2013) S587-S592
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# also see K. Kitahara et al./Acta Materialia 54 (2006) 1279-1288
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KS = {'mapping':{'fcc':0,'bcc':1},
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'planes': np.array([
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 0, 1, 1]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, -1],[ 0, 1, 1]],
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[[ 1, 1, -1],[ 0, 1, 1]],
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[[ 1, 1, -1],[ 0, 1, 1]],
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[[ 1, 1, -1],[ 0, 1, 1]],
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[[ 1, 1, -1],[ 0, 1, 1]],
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[[ 1, 1, -1],[ 0, 1, 1]]],dtype='float'),
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'directions': np.array([
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[[ -1, 0, 1],[ -1, -1, 1]],
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[[ -1, 0, 1],[ -1, 1, -1]],
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[[ 0, 1, -1],[ -1, -1, 1]],
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[[ 0, 1, -1],[ -1, 1, -1]],
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[[ 1, -1, 0],[ -1, -1, 1]],
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[[ 1, -1, 0],[ -1, 1, -1]],
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[[ 1, 0, -1],[ -1, -1, 1]],
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[[ 1, 0, -1],[ -1, 1, -1]],
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[[ -1, -1, 0],[ -1, -1, 1]],
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[[ -1, -1, 0],[ -1, 1, -1]],
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[[ 0, 1, 1],[ -1, -1, 1]],
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[[ 0, 1, 1],[ -1, 1, -1]],
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[[ 0, -1, 1],[ -1, -1, 1]],
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[[ 0, -1, 1],[ -1, 1, -1]],
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[[ -1, 0, -1],[ -1, -1, 1]],
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[[ -1, 0, -1],[ -1, 1, -1]],
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[[ 1, 1, 0],[ -1, -1, 1]],
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[[ 1, 1, 0],[ -1, 1, -1]],
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[[ -1, 1, 0],[ -1, -1, 1]],
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[[ -1, 1, 0],[ -1, 1, -1]],
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[[ 0, -1, -1],[ -1, -1, 1]],
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[[ 0, -1, -1],[ -1, 1, -1]],
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[[ 1, 0, 1],[ -1, -1, 1]],
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[[ 1, 0, 1],[ -1, 1, -1]]],dtype='float')}
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# Greninger--Troiano orientation relationship for fcc <-> bcc transformation
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# from Y. He et al./Journal of Applied Crystallography (2006). 39, 72-81
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GT = {'mapping':{'fcc':0,'bcc':1},
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'planes': np.array([
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[[ 1, 1, 1],[ 1, 0, 1]],
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[[ 1, 1, 1],[ 1, 1, 0]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ -1, -1, 1],[ -1, 0, 1]],
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[[ -1, -1, 1],[ -1, -1, 0]],
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[[ -1, -1, 1],[ 0, -1, 1]],
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[[ -1, 1, 1],[ -1, 0, 1]],
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[[ -1, 1, 1],[ -1, 1, 0]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ 1, -1, 1],[ 1, 0, 1]],
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[[ 1, -1, 1],[ 1, -1, 0]],
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[[ 1, -1, 1],[ 0, -1, 1]],
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[[ 1, 1, 1],[ 1, 1, 0]],
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[[ 1, 1, 1],[ 0, 1, 1]],
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[[ 1, 1, 1],[ 1, 0, 1]],
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[[ -1, -1, 1],[ -1, -1, 0]],
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[[ -1, -1, 1],[ 0, -1, 1]],
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[[ -1, -1, 1],[ -1, 0, 1]],
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[[ -1, 1, 1],[ -1, 1, 0]],
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[[ -1, 1, 1],[ 0, 1, 1]],
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[[ -1, 1, 1],[ -1, 0, 1]],
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[[ 1, -1, 1],[ 1, -1, 0]],
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[[ 1, -1, 1],[ 0, -1, 1]],
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[[ 1, -1, 1],[ 1, 0, 1]]],dtype='float'),
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'directions': np.array([
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[[ -5,-12, 17],[-17, -7, 17]],
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[[ 17, -5,-12],[ 17,-17, -7]],
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[[-12, 17, -5],[ -7, 17,-17]],
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[[ 5, 12, 17],[ 17, 7, 17]],
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[[-17, 5,-12],[-17, 17, -7]],
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[[ 12,-17, -5],[ 7,-17,-17]],
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[[ -5, 12,-17],[-17, 7,-17]],
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[[ 17, 5, 12],[ 17, 17, 7]],
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[[-12,-17, 5],[ -7,-17, 17]],
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[[ 5,-12,-17],[ 17, -7,-17]],
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[[-17, -5, 12],[-17,-17, 7]],
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[[ 12, 17, 5],[ 7, 17, 17]],
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[[ -5, 17,-12],[-17, 17, -7]],
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[[-12, -5, 17],[ -7,-17, 17]],
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[[ 17,-12, -5],[ 17, -7,-17]],
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[[ 5,-17,-12],[ 17,-17, -7]],
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[[ 12, 5, 17],[ 7, 17, 17]],
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[[-17, 12, -5],[-17, 7,-17]],
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[[ -5,-17, 12],[-17,-17, 7]],
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[[-12, 5,-17],[ -7, 17,-17]],
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[[ 17, 12, 5],[ 17, 7, 17]],
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[[ 5, 17, 12],[ 17, 17, 7]],
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[[ 12, -5,-17],[ 7,-17,-17]],
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[[-17,-12, 5],[-17, 7, 17]]],dtype='float')}
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# Greninger--Troiano' orientation relationship for fcc <-> bcc transformation
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# from Y. He et al./Journal of Applied Crystallography (2006). 39, 72-81
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GTdash = {'mapping':{'fcc':0,'bcc':1},
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'planes': np.array([
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[[ 7, 17, 17],[ 12, 5, 17]],
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[[ 17, 7, 17],[ 17, 12, 5]],
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[[ 17, 17, 7],[ 5, 17, 12]],
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[[ -7,-17, 17],[-12, -5, 17]],
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[[-17, -7, 17],[-17,-12, 5]],
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[[-17,-17, 7],[ -5,-17, 12]],
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[[ 7,-17,-17],[ 12, -5,-17]],
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[[ 17, -7,-17],[ 17,-12, -5]],
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[[ 17,-17, -7],[ 5,-17,-12]],
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[[ -7, 17,-17],[-12, 5,-17]],
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[[-17, 7,-17],[-17, 12, -5]],
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[[-17, 17, -7],[ -5, 17,-12]],
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[[ 7, 17, 17],[ 12, 17, 5]],
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[[ 17, 7, 17],[ 5, 12, 17]],
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[[ 17, 17, 7],[ 17, 5, 12]],
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[[ -7,-17, 17],[-12,-17, 5]],
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[[-17, -7, 17],[ -5,-12, 17]],
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[[-17,-17, 7],[-17, -5, 12]],
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[[ 7,-17,-17],[ 12,-17, -5]],
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[[ 17, -7,-17],[ 5, -12,-17]],
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[[ 17,-17, 7],[ 17, -5,-12]],
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[[ -7, 17,-17],[-12, 17, -5]],
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[[-17, 7,-17],[ -5, 12,-17]],
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[[-17, 17, -7],[-17, 5,-12]]],dtype='float'),
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'directions': np.array([
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[[ 0, 1, -1],[ 1, 1, -1]],
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[[ -1, 0, 1],[ -1, 1, 1]],
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[[ 1, -1, 0],[ 1, -1, 1]],
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[[ 0, -1, -1],[ -1, -1, -1]],
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[[ 1, 0, 1],[ 1, -1, 1]],
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[[ 1, -1, 0],[ 1, -1, -1]],
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[[ 0, 1, -1],[ -1, 1, -1]],
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[[ 1, 0, 1],[ 1, 1, 1]],
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[[ -1, -1, 0],[ -1, -1, 1]],
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[[ 0, -1, -1],[ 1, -1, -1]],
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[[ -1, 0, 1],[ -1, -1, 1]],
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[[ -1, -1, 0],[ -1, -1, -1]],
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[[ 0, -1, 1],[ 1, -1, 1]],
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[[ 1, 0, -1],[ 1, 1, -1]],
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[[ -1, 1, 0],[ -1, 1, 1]],
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[[ 0, 1, 1],[ -1, 1, 1]],
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[[ -1, 0, -1],[ -1, -1, -1]],
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[[ -1, 1, 0],[ -1, 1, -1]],
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[[ 0, -1, 1],[ -1, -1, 1]],
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||||||
|
[[ -1, 0, -1],[ -1, 1, -1]],
|
||||||
|
[[ 1, 1, 0],[ 1, 1, 1]],
|
||||||
|
[[ 0, 1, 1],[ 1, 1, 1]],
|
||||||
|
[[ 1, 0, -1],[ 1, -1, -1]],
|
||||||
|
[[ 1, 1, 0],[ 1, 1, -1]]],dtype='float')}
|
||||||
|
|
||||||
|
# Nishiyama--Wassermann orientation relationship for fcc <-> bcc transformation
|
||||||
|
# from H. Kitahara et al./Materials Characterization 54 (2005) 378-386
|
||||||
|
NW = {'mapping':{'fcc':0,'bcc':1},
|
||||||
|
'planes': np.array([
|
||||||
|
[[ 1, 1, 1],[ 0, 1, 1]],
|
||||||
|
[[ 1, 1, 1],[ 0, 1, 1]],
|
||||||
|
[[ 1, 1, 1],[ 0, 1, 1]],
|
||||||
|
[[ -1, 1, 1],[ 0, 1, 1]],
|
||||||
|
[[ -1, 1, 1],[ 0, 1, 1]],
|
||||||
|
[[ -1, 1, 1],[ 0, 1, 1]],
|
||||||
|
[[ 1, -1, 1],[ 0, 1, 1]],
|
||||||
|
[[ 1, -1, 1],[ 0, 1, 1]],
|
||||||
|
[[ 1, -1, 1],[ 0, 1, 1]],
|
||||||
|
[[ -1, -1, 1],[ 0, 1, 1]],
|
||||||
|
[[ -1, -1, 1],[ 0, 1, 1]],
|
||||||
|
[[ -1, -1, 1],[ 0, 1, 1]]],dtype='float'),
|
||||||
|
'directions': np.array([
|
||||||
|
[[ 2, -1, -1],[ 0, -1, 1]],
|
||||||
|
[[ -1, 2, -1],[ 0, -1, 1]],
|
||||||
|
[[ -1, -1, 2],[ 0, -1, 1]],
|
||||||
|
[[ -2, -1, -1],[ 0, -1, 1]],
|
||||||
|
[[ 1, 2, -1],[ 0, -1, 1]],
|
||||||
|
[[ 1, -1, 2],[ 0, -1, 1]],
|
||||||
|
[[ 2, 1, -1],[ 0, -1, 1]],
|
||||||
|
[[ -1, -2, -1],[ 0, -1, 1]],
|
||||||
|
[[ -1, 1, 2],[ 0, -1, 1]],
|
||||||
|
[[ -1, 2, 1],[ 0, -1, 1]],
|
||||||
|
[[ -1, 2, 1],[ 0, -1, 1]],
|
||||||
|
[[ -1, -1, -2],[ 0, -1, 1]]],dtype='float')}
|
||||||
|
|
||||||
|
# Pitsch orientation relationship for fcc <-> bcc transformation
|
||||||
|
# from Y. He et al./Acta Materialia 53 (2005) 1179-1190
|
||||||
|
Pitsch = {'mapping':{'fcc':0,'bcc':1},
|
||||||
|
'planes': np.array([
|
||||||
|
[[ 0, 1, 0],[ -1, 0, 1]],
|
||||||
|
[[ 0, 0, 1],[ 1, -1, 0]],
|
||||||
|
[[ 1, 0, 0],[ 0, 1, -1]],
|
||||||
|
[[ 1, 0, 0],[ 0, -1, -1]],
|
||||||
|
[[ 0, 1, 0],[ -1, 0, -1]],
|
||||||
|
[[ 0, 0, 1],[ -1, -1, 0]],
|
||||||
|
[[ 0, 1, 0],[ -1, 0, -1]],
|
||||||
|
[[ 0, 0, 1],[ -1, -1, 0]],
|
||||||
|
[[ 1, 0, 0],[ 0, -1, -1]],
|
||||||
|
[[ 1, 0, 0],[ 0, -1, 1]],
|
||||||
|
[[ 0, 1, 0],[ 1, 0, -1]],
|
||||||
|
[[ 0, 0, 1],[ -1, 1, 0]]],dtype='float'),
|
||||||
|
'directions': np.array([
|
||||||
|
[[ 1, 0, 1],[ 1, -1, 1]],
|
||||||
|
[[ 1, 1, 0],[ 1, 1, -1]],
|
||||||
|
[[ 0, 1, 1],[ -1, 1, 1]],
|
||||||
|
[[ 0, 1, -1],[ -1, 1, -1]],
|
||||||
|
[[ -1, 0, 1],[ -1, -1, 1]],
|
||||||
|
[[ 1, -1, 0],[ 1, -1, -1]],
|
||||||
|
[[ 1, 0, -1],[ 1, -1, -1]],
|
||||||
|
[[ -1, 1, 0],[ -1, 1, -1]],
|
||||||
|
[[ 0, -1, 1],[ -1, -1, 1]],
|
||||||
|
[[ 0, 1, 1],[ -1, 1, 1]],
|
||||||
|
[[ 1, 0, 1],[ 1, -1, 1]],
|
||||||
|
[[ 1, 1, 0],[ 1, 1, -1]]],dtype='float')}
|
||||||
|
|
||||||
|
# Bain orientation relationship for fcc <-> bcc transformation
|
||||||
|
# from Y. He et al./Journal of Applied Crystallography (2006). 39, 72-81
|
||||||
|
Bain = {'mapping':{'fcc':0,'bcc':1},
|
||||||
|
'planes': np.array([
|
||||||
|
[[ 1, 0, 0],[ 1, 0, 0]],
|
||||||
|
[[ 0, 1, 0],[ 0, 1, 0]],
|
||||||
|
[[ 0, 0, 1],[ 0, 0, 1]]],dtype='float'),
|
||||||
|
'directions': np.array([
|
||||||
|
[[ 0, 1, 0],[ 0, 1, 1]],
|
||||||
|
[[ 0, 0, 1],[ 1, 0, 1]],
|
||||||
|
[[ 1, 0, 0],[ 1, 1, 0]]],dtype='float')}
|
||||||
|
|
||||||
|
def relationOperations(self,model):
|
||||||
|
|
||||||
|
models={'KS':self.KS, 'GT':self.GT, "GT'":self.GTdash,
|
||||||
|
'NW':self.NW, 'Pitsch': self.Pitsch, 'Bain':self.Bain}
|
||||||
|
|
||||||
|
relationship = models[model]
|
||||||
|
|
||||||
|
r = {'lattice':Lattice((set(relationship['mapping'])-{self.lattice}).pop()),
|
||||||
|
'rotations':[] }
|
||||||
|
|
||||||
|
myPlane_id = relationship['mapping'][self.lattice]
|
||||||
|
otherPlane_id = (myPlane_id+1)%2
|
||||||
|
myDir_id = myPlane_id +2
|
||||||
|
otherDir_id = otherPlane_id +2
|
||||||
|
for miller in np.hstack((relationship['planes'],relationship['directions'])):
|
||||||
|
myPlane = miller[myPlane_id]/ np.linalg.norm(miller[myPlane_id])
|
||||||
|
myDir = miller[myDir_id]/ np.linalg.norm(miller[myDir_id])
|
||||||
|
otherPlane = miller[otherPlane_id]/ np.linalg.norm(miller[otherPlane_id])
|
||||||
|
otherDir = miller[otherDir_id]/ np.linalg.norm(miller[otherDir_id])
|
||||||
|
|
||||||
|
myMatrix = np.array([myDir,np.cross(myPlane,myDir),myPlane]).T
|
||||||
|
otherMatrix = np.array([otherDir,np.cross(otherPlane,otherDir),otherPlane]).T
|
||||||
|
r['rotations'].append(Rotation.fromMatrix(np.dot(otherMatrix,myMatrix.T)))
|
||||||
|
return r
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
class Orientation2:
|
||||||
|
"""
|
||||||
|
Crystallographic orientation
|
||||||
|
|
||||||
|
A crystallographic orientation contains a rotation and a lattice
|
||||||
|
"""
|
||||||
|
|
||||||
|
__slots__ = ['rotation','lattice']
|
||||||
|
|
||||||
|
def __repr__(self):
|
||||||
|
"""Report lattice type and orientation"""
|
||||||
|
return self.lattice.__repr__()+'\n'+self.rotation.__repr__()
|
||||||
|
|
||||||
|
def __init__(self, rotation, lattice):
|
||||||
|
|
||||||
|
if isinstance(lattice, Lattice):
|
||||||
|
self.lattice = lattice
|
||||||
|
else:
|
||||||
|
self.lattice = Lattice(lattice) # assume string
|
||||||
|
|
||||||
|
if isinstance(rotation, Rotation):
|
||||||
|
self.rotation = rotation
|
||||||
|
else:
|
||||||
|
self.rotation = Rotation(rotation) # assume quaternion
|
||||||
|
|
||||||
|
def disorientation(self,
|
||||||
|
other,
|
||||||
|
SST = True):
|
||||||
|
"""
|
||||||
|
Disorientation between myself and given other orientation.
|
||||||
|
|
||||||
|
Rotation axis falls into SST if SST == True.
|
||||||
|
(Currently requires same symmetry for both orientations.
|
||||||
|
Look into A. Heinz and P. Neumann 1991 for cases with differing sym.)
|
||||||
|
"""
|
||||||
|
#if self.lattice.symmetry != other.lattice.symmetry:
|
||||||
|
# raise NotImplementedError('disorientation between different symmetry classes not supported yet.')
|
||||||
|
|
||||||
|
mis = other.rotation*self.rotation.inversed()
|
||||||
|
mySymEqs = self.equivalentOrientations() if SST else self.equivalentOrientations()[:1] # take all or only first sym operation
|
||||||
|
otherSymEqs = other.equivalentOrientations()
|
||||||
|
|
||||||
|
for i,sA in enumerate(mySymEqs):
|
||||||
|
for j,sB in enumerate(otherSymEqs):
|
||||||
|
theQ = sB.rotation*mis*sA.rotation.inversed()
|
||||||
|
for k in range(2):
|
||||||
|
theQ.inversed()
|
||||||
|
breaker = self.lattice.symmetry.inFZ(theQ.asRodriques()) #and (not SST or other.symmetry.inDisorientationSST(theQ))
|
||||||
|
if breaker: break
|
||||||
|
if breaker: break
|
||||||
|
if breaker: break
|
||||||
|
|
||||||
|
# disorientation, own sym, other sym, self-->other: True, self<--other: False
|
||||||
|
return theQ
|
||||||
|
|
||||||
|
def inFZ(self):
|
||||||
|
return self.lattice.symmetry.inFZ(self.rotation.asRodrigues())
|
||||||
|
|
||||||
|
def equivalentOrientations(self):
|
||||||
|
"""List of orientations which are symmetrically equivalent"""
|
||||||
|
q = self.lattice.symmetry.symmetryQuats()
|
||||||
|
q2 = [Quaternion2(q=a.asList()[0],p=a.asList()[1:4]) for a in q] # convert Quaternion to Quaternion2
|
||||||
|
x = [self.__class__(q3*self.rotation.quaternion,self.lattice) for q3 in q2]
|
||||||
|
return x
|
||||||
|
|
||||||
|
def relatedOrientations(self,model):
|
||||||
|
"""List of orientations related by the given orientation relationship"""
|
||||||
|
r = self.lattice.relationOperations(model)
|
||||||
|
return [self.__class__(self.rotation*o,r['lattice']) for o in r['rotations']]
|
||||||
|
|
||||||
|
def reduced(self):
|
||||||
|
"""Transform orientation to fall into fundamental zone according to symmetry"""
|
||||||
|
for me in self.equivalentOrientations():
|
||||||
|
if self.lattice.symmetry.inFZ(me.rotation.asRodrigues()): break
|
||||||
|
|
||||||
|
return self.__class__(me.rotation,self.lattice)
|
||||||
|
|
||||||
# ******************************************************************************************
|
# ******************************************************************************************
|
||||||
class Orientation:
|
class Orientation:
|
||||||
|
|
@ -1173,7 +1561,8 @@ class Orientation:
|
||||||
(Currently requires same symmetry for both orientations.
|
(Currently requires same symmetry for both orientations.
|
||||||
Look into A. Heinz and P. Neumann 1991 for cases with differing sym.)
|
Look into A. Heinz and P. Neumann 1991 for cases with differing sym.)
|
||||||
"""
|
"""
|
||||||
if self.symmetry != other.symmetry: raise TypeError('disorientation between different symmetry classes not supported yet.')
|
if self.symmetry != other.symmetry:
|
||||||
|
raise NotImplementedError('disorientation between different symmetry classes not supported yet.')
|
||||||
|
|
||||||
misQ = other.quaternion*self.quaternion.conjugated()
|
misQ = other.quaternion*self.quaternion.conjugated()
|
||||||
mySymQs = self.symmetry.symmetryQuats() if SST else self.symmetry.symmetryQuats()[:1] # take all or only first sym operation
|
mySymQs = self.symmetry.symmetryQuats() if SST else self.symmetry.symmetryQuats()[:1] # take all or only first sym operation
|
||||||
|
|
@ -1266,14 +1655,6 @@ class Orientation:
|
||||||
if relationModel not in ['KS','GT','GTdash','NW','Pitsch','Bain']: return None
|
if relationModel not in ['KS','GT','GTdash','NW','Pitsch','Bain']: return None
|
||||||
if int(direction) == 0: return None
|
if int(direction) == 0: return None
|
||||||
|
|
||||||
# KS from S. Morito et al./Journal of Alloys and Compounds 5775 (2013) S587-S592
|
|
||||||
# for KS rotation matrices also check K. Kitahara et al./Acta Materialia 54 (2006) 1279-1288
|
|
||||||
# GT from Y. He et al./Journal of Applied Crystallography (2006). 39, 72-81
|
|
||||||
# GT' from Y. He et al./Journal of Applied Crystallography (2006). 39, 72-81
|
|
||||||
# NW from H. Kitahara et al./Materials Characterization 54 (2005) 378-386
|
|
||||||
# Pitsch from Y. He et al./Acta Materialia 53 (2005) 1179-1190
|
|
||||||
# Bain from Y. He et al./Journal of Applied Crystallography (2006). 39, 72-81
|
|
||||||
|
|
||||||
variant = int(abs(direction))-1
|
variant = int(abs(direction))-1
|
||||||
(me,other) = (0,1) if direction > 0 else (1,0)
|
(me,other) = (0,1) if direction > 0 else (1,0)
|
||||||
|
|
||||||
|
|
@ -1789,7 +2170,7 @@ def om2qu(om):
|
||||||
if om[2,1] < om[1,2]: qu[1] *= -1.0
|
if om[2,1] < om[1,2]: qu[1] *= -1.0
|
||||||
if om[0,2] < om[2,0]: qu[2] *= -1.0
|
if om[0,2] < om[2,0]: qu[2] *= -1.0
|
||||||
if om[1,0] < om[0,1]: qu[3] *= -1.0
|
if om[1,0] < om[0,1]: qu[3] *= -1.0
|
||||||
if any(om2ax(om)[0:3]*qu[1:4] < 0.0): print(om2ax(om),qu) # something is wrong here
|
if any(om2ax(om)[0:3]*qu[1:4] < 0.0): print('sign problem',om2ax(om),qu) # something is wrong here
|
||||||
return qu
|
return qu
|
||||||
|
|
||||||
|
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue