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4 space indentation

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Martin Diehl 2020-02-22 00:19:27 +01:00
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python/damask/lattice.py
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@ -312,330 +312,330 @@ class Symmetry:
# ****************************************************************************************** # ******************************************************************************************
class Lattice: class Lattice:
"""
Lattice system.
Currently, this contains only a mapping from Bravais lattice to symmetry
and orientation relationships. It could include twin and slip systems.
References
----------
https://en.wikipedia.org/wiki/Bravais_lattice
"""
lattices = {
'triclinic':{'symmetry':None},
'bct':{'symmetry':'tetragonal'},
'hex':{'symmetry':'hexagonal'},
'fcc':{'symmetry':'cubic','c/a':1.0},
'bcc':{'symmetry':'cubic','c/a':1.0},
}
def __init__(self, lattice):
""" """
New lattice of given type. Lattice system.
Parameters Currently, this contains only a mapping from Bravais lattice to symmetry
---------- and orientation relationships. It could include twin and slip systems.
lattice : str
Bravais lattice.
"""
self.lattice = lattice
self.symmetry = Symmetry(self.lattices[lattice]['symmetry'])
def __repr__(self):
"""Report basic lattice information."""
return 'Bravais lattice {} ({} symmetry)'.format(self.lattice,self.symmetry)
# Kurdjomov--Sachs orientation relationship for fcc <-> bcc transformation
# from S. Morito et al., Journal of Alloys and Compounds 577:s587-s592, 2013
# also see K. Kitahara et al., Acta Materialia 54:1279-1288, 2006
KS = {'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]],
[[ -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([
[[ -1, 0, 1],[ -1, -1, 1]],
[[ -1, 0, 1],[ -1, 1, -1]],
[[ 0, 1, -1],[ -1, -1, 1]],
[[ 0, 1, -1],[ -1, 1, -1]],
[[ 1, -1, 0],[ -1, -1, 1]],
[[ 1, -1, 0],[ -1, 1, -1]],
[[ 1, 0, -1],[ -1, -1, 1]],
[[ 1, 0, -1],[ -1, 1, -1]],
[[ -1, -1, 0],[ -1, -1, 1]],
[[ -1, -1, 0],[ -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]],
[[ -1, 0, -1],[ -1, -1, 1]],
[[ -1, 0, -1],[ -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]],
[[ 0, -1, -1],[ -1, -1, 1]],
[[ 0, -1, -1],[ -1, 1, -1]],
[[ 1, 0, 1],[ -1, -1, 1]],
[[ 1, 0, 1],[ -1, 1, -1]]],dtype='float')}
# Greninger--Troiano orientation relationship for fcc <-> bcc transformation
# from Y. He et al., Journal of Applied Crystallography 39:72-81, 2006
GT = {'mapping':{'fcc':0,'bcc':1},
'planes': np.array([
[[ 1, 1, 1],[ 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],[ 0, -1, 1]],
[[ -1, 1, 1],[ -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],[ 0, -1, 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],[ 0, -1, 1]],
[[ -1, -1, 1],[ -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],[ 0, -1, 1]],
[[ 1, -1, 1],[ 1, 0, 1]]],dtype='float'),
'directions': np.array([
[[ -5,-12, 17],[-17, -7, 17]],
[[ 17, -5,-12],[ 17,-17, -7]],
[[-12, 17, -5],[ -7, 17,-17]],
[[ 5, 12, 17],[ 17, 7, 17]],
[[-17, 5,-12],[-17, 17, -7]],
[[ 12,-17, -5],[ 7,-17,-17]],
[[ -5, 12,-17],[-17, 7,-17]],
[[ 17, 5, 12],[ 17, 17, 7]],
[[-12,-17, 5],[ -7,-17, 17]],
[[ 5,-12,-17],[ 17, -7,-17]],
[[-17, -5, 12],[-17,-17, 7]],
[[ 12, 17, 5],[ 7, 17, 17]],
[[ -5, 17,-12],[-17, 17, -7]],
[[-12, -5, 17],[ -7,-17, 17]],
[[ 17,-12, -5],[ 17, -7,-17]],
[[ 5,-17,-12],[ 17,-17, -7]],
[[ 12, 5, 17],[ 7, 17, 17]],
[[-17, 12, -5],[-17, 7,-17]],
[[ -5,-17, 12],[-17,-17, 7]],
[[-12, 5,-17],[ -7, 17,-17]],
[[ 17, 12, 5],[ 17, 7, 17]],
[[ 5, 17, 12],[ 17, 17, 7]],
[[ 12, -5,-17],[ 7,-17,-17]],
[[-17,-12, 5],[-17,-7, 17]]],dtype='float')}
# Greninger--Troiano' orientation relationship for fcc <-> bcc transformation
# from Y. He et al., Journal of Applied Crystallography 39:72-81, 2006
GTprime = {'mapping':{'fcc':0,'bcc':1},
'planes': np.array([
[[ 7, 17, 17],[ 12, 5, 17]],
[[ 17, 7, 17],[ 17, 12, 5]],
[[ 17, 17, 7],[ 5, 17, 12]],
[[ -7,-17, 17],[-12, -5, 17]],
[[-17, -7, 17],[-17,-12, 5]],
[[-17,-17, 7],[ -5,-17, 12]],
[[ 7,-17,-17],[ 12, -5,-17]],
[[ 17, -7,-17],[ 17,-12, -5]],
[[ 17,-17, -7],[ 5,-17,-12]],
[[ -7, 17,-17],[-12, 5,-17]],
[[-17, 7,-17],[-17, 12, -5]],
[[-17, 17, -7],[ -5, 17,-12]],
[[ 7, 17, 17],[ 12, 17, 5]],
[[ 17, 7, 17],[ 5, 12, 17]],
[[ 17, 17, 7],[ 17, 5, 12]],
[[ -7,-17, 17],[-12,-17, 5]],
[[-17, -7, 17],[ -5,-12, 17]],
[[-17,-17, 7],[-17, -5, 12]],
[[ 7,-17,-17],[ 12,-17, -5]],
[[ 17, -7,-17],[ 5, -12,-17]],
[[ 17,-17, -7],[ 17, -5,-12]],
[[ -7, 17,-17],[-12, 17, -5]],
[[-17, 7,-17],[ -5, 12,-17]],
[[-17, 17, -7],[-17, 5,-12]]],dtype='float'),
'directions': np.array([
[[ 0, 1, -1],[ 1, 1, -1]],
[[ -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]],
[[ 0, 1, -1],[ -1, 1, -1]],
[[ 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]],
[[ 0, -1, 1],[ 1, -1, 1]],
[[ 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]],
[[ 0, -1, 1],[ -1, -1, 1]],
[[ -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 54:378-386, 2005
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]],
[[ 2, -1, 1],[ 0, -1, 1]], #It is wrong in the paper, but matrix is correct
[[ -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 53:1179-1190, 2005
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 39:72-81, 2006
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):
"""
Crystallographic orientation relationships for phase transformations.
References References
---------- ----------
S. Morito et al., Journal of Alloys and Compounds 577:s587-s592, 2013 https://en.wikipedia.org/wiki/Bravais_lattice
https://doi.org/10.1016/j.jallcom.2012.02.004
K. Kitahara et al., Acta Materialia 54(5):1279-1288, 2006
https://doi.org/10.1016/j.actamat.2005.11.001
Y. He et al., Journal of Applied Crystallography 39:72-81, 2006
https://doi.org/10.1107/S0021889805038276
H. Kitahara et al., Materials Characterization 54(4-5):378-386, 2005
https://doi.org/10.1016/j.matchar.2004.12.015
Y. He et al., Acta Materialia 53(4):1179-1190, 2005
https://doi.org/10.1016/j.actamat.2004.11.021
""" """
models={'KS':self.KS, 'GT':self.GT, 'GT_prime':self.GTprime,
'NW':self.NW, 'Pitsch': self.Pitsch, 'Bain':self.Bain}
try:
relationship = models[model]
except KeyError :
raise KeyError('Orientation relationship "{}" is unknown'.format(model))
if self.lattice not in relationship['mapping']: lattices = {
raise ValueError('Relationship "{}" not supported for lattice "{}"'.format(model,self.lattice)) 'triclinic':{'symmetry':None},
'bct':{'symmetry':'tetragonal'},
'hex':{'symmetry':'hexagonal'},
'fcc':{'symmetry':'cubic','c/a':1.0},
'bcc':{'symmetry':'cubic','c/a':1.0},
}
r = {'lattice':Lattice((set(relationship['mapping'])-{self.lattice}).pop()), # target lattice
'rotations':[] }
myPlane_id = relationship['mapping'][self.lattice] def __init__(self, lattice):
otherPlane_id = (myPlane_id+1)%2 """
myDir_id = myPlane_id +2 New lattice of given type.
otherDir_id = otherPlane_id +2
for miller in np.hstack((relationship['planes'],relationship['directions'])): Parameters
myPlane = miller[myPlane_id]/ np.linalg.norm(miller[myPlane_id]) ----------
myDir = miller[myDir_id]/ np.linalg.norm(miller[myDir_id]) lattice : str
myMatrix = np.array([myDir,np.cross(myPlane,myDir),myPlane]) Bravais lattice.
otherPlane = miller[otherPlane_id]/ np.linalg.norm(miller[otherPlane_id]) """
otherDir = miller[otherDir_id]/ np.linalg.norm(miller[otherDir_id]) self.lattice = lattice
otherMatrix = np.array([otherDir,np.cross(otherPlane,otherDir),otherPlane]) self.symmetry = Symmetry(self.lattices[lattice]['symmetry'])
r['rotations'].append(Rotation.fromMatrix(np.dot(otherMatrix.T,myMatrix)))
return r def __repr__(self):
"""Report basic lattice information."""
return 'Bravais lattice {} ({} symmetry)'.format(self.lattice,self.symmetry)
# Kurdjomov--Sachs orientation relationship for fcc <-> bcc transformation
# from S. Morito et al., Journal of Alloys and Compounds 577:s587-s592, 2013
# also see K. Kitahara et al., Acta Materialia 54:1279-1288, 2006
KS = {'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]],
[[ -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([
[[ -1, 0, 1],[ -1, -1, 1]],
[[ -1, 0, 1],[ -1, 1, -1]],
[[ 0, 1, -1],[ -1, -1, 1]],
[[ 0, 1, -1],[ -1, 1, -1]],
[[ 1, -1, 0],[ -1, -1, 1]],
[[ 1, -1, 0],[ -1, 1, -1]],
[[ 1, 0, -1],[ -1, -1, 1]],
[[ 1, 0, -1],[ -1, 1, -1]],
[[ -1, -1, 0],[ -1, -1, 1]],
[[ -1, -1, 0],[ -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]],
[[ -1, 0, -1],[ -1, -1, 1]],
[[ -1, 0, -1],[ -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]],
[[ 0, -1, -1],[ -1, -1, 1]],
[[ 0, -1, -1],[ -1, 1, -1]],
[[ 1, 0, 1],[ -1, -1, 1]],
[[ 1, 0, 1],[ -1, 1, -1]]],dtype='float')}
# Greninger--Troiano orientation relationship for fcc <-> bcc transformation
# from Y. He et al., Journal of Applied Crystallography 39:72-81, 2006
GT = {'mapping':{'fcc':0,'bcc':1},
'planes': np.array([
[[ 1, 1, 1],[ 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],[ 0, -1, 1]],
[[ -1, 1, 1],[ -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],[ 0, -1, 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],[ 0, -1, 1]],
[[ -1, -1, 1],[ -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],[ 0, -1, 1]],
[[ 1, -1, 1],[ 1, 0, 1]]],dtype='float'),
'directions': np.array([
[[ -5,-12, 17],[-17, -7, 17]],
[[ 17, -5,-12],[ 17,-17, -7]],
[[-12, 17, -5],[ -7, 17,-17]],
[[ 5, 12, 17],[ 17, 7, 17]],
[[-17, 5,-12],[-17, 17, -7]],
[[ 12,-17, -5],[ 7,-17,-17]],
[[ -5, 12,-17],[-17, 7,-17]],
[[ 17, 5, 12],[ 17, 17, 7]],
[[-12,-17, 5],[ -7,-17, 17]],
[[ 5,-12,-17],[ 17, -7,-17]],
[[-17, -5, 12],[-17,-17, 7]],
[[ 12, 17, 5],[ 7, 17, 17]],
[[ -5, 17,-12],[-17, 17, -7]],
[[-12, -5, 17],[ -7,-17, 17]],
[[ 17,-12, -5],[ 17, -7,-17]],
[[ 5,-17,-12],[ 17,-17, -7]],
[[ 12, 5, 17],[ 7, 17, 17]],
[[-17, 12, -5],[-17, 7,-17]],
[[ -5,-17, 12],[-17,-17, 7]],
[[-12, 5,-17],[ -7, 17,-17]],
[[ 17, 12, 5],[ 17, 7, 17]],
[[ 5, 17, 12],[ 17, 17, 7]],
[[ 12, -5,-17],[ 7,-17,-17]],
[[-17,-12, 5],[-17,-7, 17]]],dtype='float')}
# Greninger--Troiano' orientation relationship for fcc <-> bcc transformation
# from Y. He et al., Journal of Applied Crystallography 39:72-81, 2006
GTprime = {'mapping':{'fcc':0,'bcc':1},
'planes': np.array([
[[ 7, 17, 17],[ 12, 5, 17]],
[[ 17, 7, 17],[ 17, 12, 5]],
[[ 17, 17, 7],[ 5, 17, 12]],
[[ -7,-17, 17],[-12, -5, 17]],
[[-17, -7, 17],[-17,-12, 5]],
[[-17,-17, 7],[ -5,-17, 12]],
[[ 7,-17,-17],[ 12, -5,-17]],
[[ 17, -7,-17],[ 17,-12, -5]],
[[ 17,-17, -7],[ 5,-17,-12]],
[[ -7, 17,-17],[-12, 5,-17]],
[[-17, 7,-17],[-17, 12, -5]],
[[-17, 17, -7],[ -5, 17,-12]],
[[ 7, 17, 17],[ 12, 17, 5]],
[[ 17, 7, 17],[ 5, 12, 17]],
[[ 17, 17, 7],[ 17, 5, 12]],
[[ -7,-17, 17],[-12,-17, 5]],
[[-17, -7, 17],[ -5,-12, 17]],
[[-17,-17, 7],[-17, -5, 12]],
[[ 7,-17,-17],[ 12,-17, -5]],
[[ 17, -7,-17],[ 5, -12,-17]],
[[ 17,-17, -7],[ 17, -5,-12]],
[[ -7, 17,-17],[-12, 17, -5]],
[[-17, 7,-17],[ -5, 12,-17]],
[[-17, 17, -7],[-17, 5,-12]]],dtype='float'),
'directions': np.array([
[[ 0, 1, -1],[ 1, 1, -1]],
[[ -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]],
[[ 0, 1, -1],[ -1, 1, -1]],
[[ 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]],
[[ 0, -1, 1],[ 1, -1, 1]],
[[ 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]],
[[ 0, -1, 1],[ -1, -1, 1]],
[[ -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 54:378-386, 2005
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]],
[[ 2, -1, 1],[ 0, -1, 1]], #It is wrong in the paper, but matrix is correct
[[ -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 53:1179-1190, 2005
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 39:72-81, 2006
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):
"""
Crystallographic orientation relationships for phase transformations.
References
----------
S. Morito et al., Journal of Alloys and Compounds 577:s587-s592, 2013
https://doi.org/10.1016/j.jallcom.2012.02.004
K. Kitahara et al., Acta Materialia 54(5):1279-1288, 2006
https://doi.org/10.1016/j.actamat.2005.11.001
Y. He et al., Journal of Applied Crystallography 39:72-81, 2006
https://doi.org/10.1107/S0021889805038276
H. Kitahara et al., Materials Characterization 54(4-5):378-386, 2005
https://doi.org/10.1016/j.matchar.2004.12.015
Y. He et al., Acta Materialia 53(4):1179-1190, 2005
https://doi.org/10.1016/j.actamat.2004.11.021
"""
models={'KS':self.KS, 'GT':self.GT, 'GT_prime':self.GTprime,
'NW':self.NW, 'Pitsch': self.Pitsch, 'Bain':self.Bain}
try:
relationship = models[model]
except KeyError :
raise KeyError('Orientation relationship "{}" is unknown'.format(model))
if self.lattice not in relationship['mapping']:
raise ValueError('Relationship "{}" not supported for lattice "{}"'.format(model,self.lattice))
r = {'lattice':Lattice((set(relationship['mapping'])-{self.lattice}).pop()), # target lattice
'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])
myMatrix = np.array([myDir,np.cross(myPlane,myDir),myPlane])
otherPlane = miller[otherPlane_id]/ np.linalg.norm(miller[otherPlane_id])
otherDir = miller[otherDir_id]/ np.linalg.norm(miller[otherDir_id])
otherMatrix = np.array([otherDir,np.cross(otherPlane,otherDir),otherPlane])
r['rotations'].append(Rotation.fromMatrix(np.dot(otherMatrix.T,myMatrix)))
return r

168
python/damask/orientation.py
View File

@ -13,137 +13,137 @@ class Orientation:
__slots__ = ['rotation','lattice'] __slots__ = ['rotation','lattice']
def __repr__(self): def __repr__(self):
"""Report lattice type and orientation.""" """Report lattice type and orientation."""
return self.lattice.__repr__()+'\n'+self.rotation.__repr__() return self.lattice.__repr__()+'\n'+self.rotation.__repr__()
def __init__(self, rotation, lattice): def __init__(self, rotation, lattice):
""" """
New orientation from rotation and lattice. New orientation from rotation and lattice.
Parameters Parameters
---------- ----------
rotation : Rotation rotation : Rotation
Rotation specifying the lattice orientation. Rotation specifying the lattice orientation.
lattice : Lattice lattice : Lattice
Lattice type of the crystal. Lattice type of the crystal.
""" """
if isinstance(lattice, Lattice): if isinstance(lattice, Lattice):
self.lattice = lattice self.lattice = lattice
else: else:
self.lattice = Lattice(lattice) # assume string self.lattice = Lattice(lattice) # assume string
if isinstance(rotation, Rotation): if isinstance(rotation, Rotation):
self.rotation = rotation self.rotation = rotation
else: else:
self.rotation = Rotation.fromQuaternion(rotation) # assume quaternion self.rotation = Rotation.fromQuaternion(rotation) # assume quaternion
def disorientation(self, def disorientation(self,
other, other,
SST = True, SST = True,
symmetries = False): symmetries = False):
""" """
Disorientation between myself and given other orientation. Disorientation between myself and given other orientation.
Rotation axis falls into SST if SST == True. Rotation axis falls into SST if SST == True.
(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.lattice.symmetry != other.lattice.symmetry: if self.lattice.symmetry != other.lattice.symmetry:
raise NotImplementedError('disorientation between different symmetry classes not supported yet.') raise NotImplementedError('disorientation between different symmetry classes not supported yet.')
mySymEqs = self.equivalentOrientations() if SST else self.equivalentOrientations([0]) # take all or only first sym operation mySymEqs = self.equivalentOrientations() if SST else self.equivalentOrientations([0]) # take all or only first sym operation
otherSymEqs = other.equivalentOrientations() otherSymEqs = other.equivalentOrientations()
for i,sA in enumerate(mySymEqs): for i,sA in enumerate(mySymEqs):
aInv = sA.rotation.inversed() aInv = sA.rotation.inversed()
for j,sB in enumerate(otherSymEqs): for j,sB in enumerate(otherSymEqs):
b = sB.rotation b = sB.rotation
r = b*aInv r = b*aInv
for k in range(2): for k in range(2):
r.inverse() r.inverse()
breaker = self.lattice.symmetry.inFZ(r.asRodrigues(vector=True)) \ breaker = self.lattice.symmetry.inFZ(r.asRodrigues(vector=True)) \
and (not SST or other.lattice.symmetry.inDisorientationSST(r.asRodrigues(vector=True))) and (not SST or other.lattice.symmetry.inDisorientationSST(r.asRodrigues(vector=True)))
if breaker: break
if breaker: break if breaker: break
if breaker: break if breaker: break
if breaker: break
return (Orientation(r,self.lattice), i,j, k == 1) if symmetries else r # disorientation ... return (Orientation(r,self.lattice), i,j, k == 1) if symmetries else r # disorientation ...
# ... own sym, other sym, # ... own sym, other sym,
# self-->other: True, self<--other: False # self-->other: True, self<--other: False
def inFZ(self): def inFZ(self):
return self.lattice.symmetry.inFZ(self.rotation.asRodrigues(vector=True)) return self.lattice.symmetry.inFZ(self.rotation.asRodrigues(vector=True))
def equivalentOrientations(self,members=[]): def equivalentOrientations(self,members=[]):
"""List of orientations which are symmetrically equivalent.""" """List of orientations which are symmetrically equivalent."""
try: try:
iter(members) # asking for (even empty) list of members? iter(members) # asking for (even empty) list of members?
except TypeError: except TypeError:
return self.__class__(self.lattice.symmetry.symmetryOperations(members)*self.rotation,self.lattice) # no, return rotation object return self.__class__(self.lattice.symmetry.symmetryOperations(members)*self.rotation,self.lattice) # no, return rotation object
else: else:
return [self.__class__(q*self.rotation,self.lattice) \ return [self.__class__(q*self.rotation,self.lattice) \
for q in self.lattice.symmetry.symmetryOperations(members)] # yes, return list of rotations for q in self.lattice.symmetry.symmetryOperations(members)] # yes, return list of rotations
def relatedOrientations(self,model): def relatedOrientations(self,model):
"""List of orientations related by the given orientation relationship.""" """List of orientations related by the given orientation relationship."""
r = self.lattice.relationOperations(model) r = self.lattice.relationOperations(model)
return [self.__class__(o*self.rotation,r['lattice']) for o in r['rotations']] return [self.__class__(o*self.rotation,r['lattice']) for o in r['rotations']]
def reduced(self): def reduced(self):
"""Transform orientation to fall into fundamental zone according to symmetry.""" """Transform orientation to fall into fundamental zone according to symmetry."""
for me in self.equivalentOrientations(): for me in self.equivalentOrientations():
if self.lattice.symmetry.inFZ(me.rotation.asRodrigues(vector=True)): break if self.lattice.symmetry.inFZ(me.rotation.asRodrigues(vector=True)): break
return self.__class__(me.rotation,self.lattice) return self.__class__(me.rotation,self.lattice)
def inversePole(self, def inversePole(self,
axis, axis,
proper = False, proper = False,
SST = True): SST = True):
"""Axis rotated according to orientation (using crystal symmetry to ensure location falls into SST).""" """Axis rotated according to orientation (using crystal symmetry to ensure location falls into SST)."""
if SST: # pole requested to be within SST if SST: # pole requested to be within SST
for i,o in enumerate(self.equivalentOrientations()): # test all symmetric equivalent quaternions for i,o in enumerate(self.equivalentOrientations()): # test all symmetric equivalent quaternions
pole = o.rotation*axis # align crystal direction to axis pole = o.rotation*axis # align crystal direction to axis
if self.lattice.symmetry.inSST(pole,proper): break # found SST version if self.lattice.symmetry.inSST(pole,proper): break # found SST version
else: else:
pole = self.rotation*axis # align crystal direction to axis pole = self.rotation*axis # align crystal direction to axis
return (pole,i if SST else 0) return (pole,i if SST else 0)
def IPFcolor(self,axis): def IPFcolor(self,axis):
"""TSL color of inverse pole figure for given axis.""" """TSL color of inverse pole figure for given axis."""
color = np.zeros(3,'d') color = np.zeros(3,'d')
for o in self.equivalentOrientations(): for o in self.equivalentOrientations():
pole = o.rotation*axis # align crystal direction to axis pole = o.rotation*axis # align crystal direction to axis
inSST,color = self.lattice.symmetry.inSST(pole,color=True) inSST,color = self.lattice.symmetry.inSST(pole,color=True)
if inSST: break if inSST: break
return color return color
@staticmethod @staticmethod
def fromAverage(orientations, def fromAverage(orientations,
weights = []): weights = []):
"""Create orientation from average of list of orientations.""" """Create orientation from average of list of orientations."""
if not all(isinstance(item, Orientation) for item in orientations): if not all(isinstance(item, Orientation) for item in orientations):
raise TypeError("Only instances of Orientation can be averaged.") raise TypeError("Only instances of Orientation can be averaged.")
closest = [] closest = []
ref = orientations[0] ref = orientations[0]
for o in orientations: for o in orientations:
closest.append(o.equivalentOrientations( closest.append(o.equivalentOrientations(
ref.disorientation(o, ref.disorientation(o,
SST = False, # select (o[ther]'s) sym orientation SST = False, # select (o[ther]'s) sym orientation
symmetries = True)[2]).rotation) # with lowest misorientation symmetries = True)[2]).rotation) # with lowest misorientation
return Orientation(Rotation.fromAverage(closest,weights),ref.lattice) return Orientation(Rotation.fromAverage(closest,weights),ref.lattice)
def average(self,other): def average(self,other):
"""Calculate the average rotation.""" """Calculate the average rotation."""
return Orientation.fromAverage([self,other]) return Orientation.fromAverage([self,other])

6
python/damask/rotation.py
View File

@ -4,14 +4,10 @@ from . import Lambert
P = -1 P = -1
def isone(a):
return np.isclose(a,1.0,atol=1.0e-7,rtol=0.0)
def iszero(a): def iszero(a):
return np.isclose(a,0.0,atol=1.0e-12,rtol=0.0) return np.isclose(a,0.0,atol=1.0e-12,rtol=0.0)
####################################################################################################
class Rotation: class Rotation:
u""" u"""
Orientation stored with functionality for conversion to different representations. Orientation stored with functionality for conversion to different representations.