4 space indentation
This commit is contained in:
Martin Diehl
parent
fd11f073f0
commit
9d4cbe5168
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@ -312,330 +312,330 @@ class Symmetry:
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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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References
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----------
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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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"""
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New lattice of given type.
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Lattice system.
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Parameters
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----------
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lattice : str
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Bravais lattice.
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"""
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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 577:s587-s592, 2013
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# also see K. Kitahara et al., Acta Materialia 54:1279-1288, 2006
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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 39:72-81, 2006
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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 39:72-81, 2006
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GTprime = {'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]],
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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]]],dtype='float')}
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# Nishiyama--Wassermann orientation relationship for fcc <-> bcc transformation
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# from H. Kitahara et al., Materials Characterization 54:378-386, 2005
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NW = {'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]]],dtype='float'),
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'directions': np.array([
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[[ 2, -1, -1],[ 0, -1, 1]],
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[[ -1, 2, -1],[ 0, -1, 1]],
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[[ -1, -1, 2],[ 0, -1, 1]],
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[[ -2, -1, -1],[ 0, -1, 1]],
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[[ 1, 2, -1],[ 0, -1, 1]],
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[[ 1, -1, 2],[ 0, -1, 1]],
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[[ 2, 1, -1],[ 0, -1, 1]],
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[[ -1, -2, -1],[ 0, -1, 1]],
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[[ -1, 1, 2],[ 0, -1, 1]],
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[[ 2, -1, 1],[ 0, -1, 1]], #It is wrong in the paper, but matrix is correct
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[[ -1, 2, 1],[ 0, -1, 1]],
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[[ -1, -1, -2],[ 0, -1, 1]]],dtype='float')}
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# Pitsch orientation relationship for fcc <-> bcc transformation
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# from Y. He et al., Acta Materialia 53:1179-1190, 2005
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Pitsch = {'mapping':{'fcc':0,'bcc':1},
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'planes': np.array([
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[[ 0, 1, 0],[ -1, 0, 1]],
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[[ 0, 0, 1],[ 1, -1, 0]],
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[[ 1, 0, 0],[ 0, 1, -1]],
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[[ 1, 0, 0],[ 0, -1, -1]],
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[[ 0, 1, 0],[ -1, 0, -1]],
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[[ 0, 0, 1],[ -1, -1, 0]],
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[[ 0, 1, 0],[ -1, 0, -1]],
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[[ 0, 0, 1],[ -1, -1, 0]],
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[[ 1, 0, 0],[ 0, -1, -1]],
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[[ 1, 0, 0],[ 0, -1, 1]],
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[[ 0, 1, 0],[ 1, 0, -1]],
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[[ 0, 0, 1],[ -1, 1, 0]]],dtype='float'),
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'directions': np.array([
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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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[[ 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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[[ 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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[[ 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]]],dtype='float')}
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# Bain orientation relationship for fcc <-> bcc transformation
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# from Y. He et al., Journal of Applied Crystallography 39:72-81, 2006
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Bain = {'mapping':{'fcc':0,'bcc':1},
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'planes': np.array([
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[[ 1, 0, 0],[ 1, 0, 0]],
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[[ 0, 1, 0],[ 0, 1, 0]],
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[[ 0, 0, 1],[ 0, 0, 1]]],dtype='float'),
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'directions': np.array([
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[[ 0, 1, 0],[ 0, 1, 1]],
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[[ 0, 0, 1],[ 1, 0, 1]],
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[[ 1, 0, 0],[ 1, 1, 0]]],dtype='float')}
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def relationOperations(self,model):
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"""
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Crystallographic orientation relationships for phase transformations.
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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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References
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----------
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S. Morito et al., Journal of Alloys and Compounds 577:s587-s592, 2013
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https://doi.org/10.1016/j.jallcom.2012.02.004
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K. Kitahara et al., Acta Materialia 54(5):1279-1288, 2006
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https://doi.org/10.1016/j.actamat.2005.11.001
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Y. He et al., Journal of Applied Crystallography 39:72-81, 2006
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https://doi.org/10.1107/S0021889805038276
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H. Kitahara et al., Materials Characterization 54(4-5):378-386, 2005
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https://doi.org/10.1016/j.matchar.2004.12.015
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Y. He et al., Acta Materialia 53(4):1179-1190, 2005
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https://doi.org/10.1016/j.actamat.2004.11.021
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https://en.wikipedia.org/wiki/Bravais_lattice
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"""
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models={'KS':self.KS, 'GT':self.GT, 'GT_prime':self.GTprime,
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'NW':self.NW, 'Pitsch': self.Pitsch, 'Bain':self.Bain}
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try:
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relationship = models[model]
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except KeyError :
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raise KeyError('Orientation relationship "{}" is unknown'.format(model))
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if self.lattice not in relationship['mapping']:
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raise ValueError('Relationship "{}" not supported for lattice "{}"'.format(model,self.lattice))
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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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r = {'lattice':Lattice((set(relationship['mapping'])-{self.lattice}).pop()), # target lattice
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'rotations':[] }
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myPlane_id = relationship['mapping'][self.lattice]
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otherPlane_id = (myPlane_id+1)%2
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myDir_id = myPlane_id +2
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otherDir_id = otherPlane_id +2
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def __init__(self, lattice):
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"""
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New lattice of given type.
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for miller in np.hstack((relationship['planes'],relationship['directions'])):
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myPlane = miller[myPlane_id]/ np.linalg.norm(miller[myPlane_id])
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myDir = miller[myDir_id]/ np.linalg.norm(miller[myDir_id])
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myMatrix = np.array([myDir,np.cross(myPlane,myDir),myPlane])
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Parameters
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----------
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lattice : str
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Bravais lattice.
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otherPlane = miller[otherPlane_id]/ np.linalg.norm(miller[otherPlane_id])
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otherDir = miller[otherDir_id]/ np.linalg.norm(miller[otherDir_id])
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otherMatrix = np.array([otherDir,np.cross(otherPlane,otherDir),otherPlane])
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"""
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self.lattice = lattice
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self.symmetry = Symmetry(self.lattices[lattice]['symmetry'])
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r['rotations'].append(Rotation.fromMatrix(np.dot(otherMatrix.T,myMatrix)))
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return r
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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 577:s587-s592, 2013
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# also see K. Kitahara et al., Acta Materialia 54:1279-1288, 2006
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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]],
|
||||
[[ -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
|
||||
|
|
|
|||
|
|
@ -13,137 +13,137 @@ class Orientation:
|
|||
__slots__ = ['rotation','lattice']
|
||||
|
||||
def __repr__(self):
|
||||
"""Report lattice type and orientation."""
|
||||
return self.lattice.__repr__()+'\n'+self.rotation.__repr__()
|
||||
"""Report lattice type and orientation."""
|
||||
return self.lattice.__repr__()+'\n'+self.rotation.__repr__()
|
||||
|
||||
def __init__(self, rotation, lattice):
|
||||
"""
|
||||
New orientation from rotation and lattice.
|
||||
"""
|
||||
New orientation from rotation and lattice.
|
||||
|
||||
Parameters
|
||||
----------
|
||||
rotation : Rotation
|
||||
Rotation specifying the lattice orientation.
|
||||
lattice : Lattice
|
||||
Lattice type of the crystal.
|
||||
Parameters
|
||||
----------
|
||||
rotation : Rotation
|
||||
Rotation specifying the lattice orientation.
|
||||
lattice : Lattice
|
||||
Lattice type of the crystal.
|
||||
|
||||
"""
|
||||
if isinstance(lattice, Lattice):
|
||||
self.lattice = lattice
|
||||
else:
|
||||
self.lattice = Lattice(lattice) # assume string
|
||||
"""
|
||||
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.fromQuaternion(rotation) # assume quaternion
|
||||
if isinstance(rotation, Rotation):
|
||||
self.rotation = rotation
|
||||
else:
|
||||
self.rotation = Rotation.fromQuaternion(rotation) # assume quaternion
|
||||
|
||||
def disorientation(self,
|
||||
other,
|
||||
SST = True,
|
||||
symmetries = False):
|
||||
"""
|
||||
Disorientation between myself and given other orientation.
|
||||
"""
|
||||
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.')
|
||||
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.')
|
||||
|
||||
mySymEqs = self.equivalentOrientations() if SST else self.equivalentOrientations([0]) # take all or only first sym operation
|
||||
otherSymEqs = other.equivalentOrientations()
|
||||
mySymEqs = self.equivalentOrientations() if SST else self.equivalentOrientations([0]) # take all or only first sym operation
|
||||
otherSymEqs = other.equivalentOrientations()
|
||||
|
||||
for i,sA in enumerate(mySymEqs):
|
||||
aInv = sA.rotation.inversed()
|
||||
for j,sB in enumerate(otherSymEqs):
|
||||
b = sB.rotation
|
||||
r = b*aInv
|
||||
for k in range(2):
|
||||
r.inverse()
|
||||
breaker = self.lattice.symmetry.inFZ(r.asRodrigues(vector=True)) \
|
||||
and (not SST or other.lattice.symmetry.inDisorientationSST(r.asRodrigues(vector=True)))
|
||||
for i,sA in enumerate(mySymEqs):
|
||||
aInv = sA.rotation.inversed()
|
||||
for j,sB in enumerate(otherSymEqs):
|
||||
b = sB.rotation
|
||||
r = b*aInv
|
||||
for k in range(2):
|
||||
r.inverse()
|
||||
breaker = self.lattice.symmetry.inFZ(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
|
||||
|
||||
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,
|
||||
# self-->other: True, self<--other: False
|
||||
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=[]):
|
||||
"""List of orientations which are symmetrically equivalent."""
|
||||
try:
|
||||
iter(members) # asking for (even empty) list of members?
|
||||
except TypeError:
|
||||
return self.__class__(self.lattice.symmetry.symmetryOperations(members)*self.rotation,self.lattice) # no, return rotation object
|
||||
else:
|
||||
return [self.__class__(q*self.rotation,self.lattice) \
|
||||
for q in self.lattice.symmetry.symmetryOperations(members)] # yes, return list of rotations
|
||||
"""List of orientations which are symmetrically equivalent."""
|
||||
try:
|
||||
iter(members) # asking for (even empty) list of members?
|
||||
except TypeError:
|
||||
return self.__class__(self.lattice.symmetry.symmetryOperations(members)*self.rotation,self.lattice) # no, return rotation object
|
||||
else:
|
||||
return [self.__class__(q*self.rotation,self.lattice) \
|
||||
for q in self.lattice.symmetry.symmetryOperations(members)] # yes, return list of rotations
|
||||
|
||||
def relatedOrientations(self,model):
|
||||
"""List of orientations related by the given orientation relationship."""
|
||||
r = self.lattice.relationOperations(model)
|
||||
return [self.__class__(o*self.rotation,r['lattice']) for o in r['rotations']]
|
||||
"""List of orientations related by the given orientation relationship."""
|
||||
r = self.lattice.relationOperations(model)
|
||||
return [self.__class__(o*self.rotation,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(vector=True)): break
|
||||
"""Transform orientation to fall into fundamental zone according to symmetry."""
|
||||
for me in self.equivalentOrientations():
|
||||
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,
|
||||
axis,
|
||||
proper = False,
|
||||
SST = True):
|
||||
"""Axis rotated according to orientation (using crystal symmetry to ensure location falls into SST)."""
|
||||
if SST: # pole requested to be within SST
|
||||
for i,o in enumerate(self.equivalentOrientations()): # test all symmetric equivalent quaternions
|
||||
pole = o.rotation*axis # align crystal direction to axis
|
||||
if self.lattice.symmetry.inSST(pole,proper): break # found SST version
|
||||
else:
|
||||
pole = self.rotation*axis # align crystal direction to axis
|
||||
"""Axis rotated according to orientation (using crystal symmetry to ensure location falls into SST)."""
|
||||
if SST: # pole requested to be within SST
|
||||
for i,o in enumerate(self.equivalentOrientations()): # test all symmetric equivalent quaternions
|
||||
pole = o.rotation*axis # align crystal direction to axis
|
||||
if self.lattice.symmetry.inSST(pole,proper): break # found SST version
|
||||
else:
|
||||
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):
|
||||
"""TSL color of inverse pole figure for given axis."""
|
||||
color = np.zeros(3,'d')
|
||||
"""TSL color of inverse pole figure for given axis."""
|
||||
color = np.zeros(3,'d')
|
||||
|
||||
for o in self.equivalentOrientations():
|
||||
pole = o.rotation*axis # align crystal direction to axis
|
||||
inSST,color = self.lattice.symmetry.inSST(pole,color=True)
|
||||
if inSST: break
|
||||
for o in self.equivalentOrientations():
|
||||
pole = o.rotation*axis # align crystal direction to axis
|
||||
inSST,color = self.lattice.symmetry.inSST(pole,color=True)
|
||||
if inSST: break
|
||||
|
||||
return color
|
||||
return color
|
||||
|
||||
|
||||
@staticmethod
|
||||
def fromAverage(orientations,
|
||||
weights = []):
|
||||
"""Create orientation from average of list of orientations."""
|
||||
if not all(isinstance(item, Orientation) for item in orientations):
|
||||
raise TypeError("Only instances of Orientation can be averaged.")
|
||||
"""Create orientation from average of list of orientations."""
|
||||
if not all(isinstance(item, Orientation) for item in orientations):
|
||||
raise TypeError("Only instances of Orientation can be averaged.")
|
||||
|
||||
closest = []
|
||||
ref = orientations[0]
|
||||
for o in orientations:
|
||||
closest.append(o.equivalentOrientations(
|
||||
ref.disorientation(o,
|
||||
SST = False, # select (o[ther]'s) sym orientation
|
||||
symmetries = True)[2]).rotation) # with lowest misorientation
|
||||
closest = []
|
||||
ref = orientations[0]
|
||||
for o in orientations:
|
||||
closest.append(o.equivalentOrientations(
|
||||
ref.disorientation(o,
|
||||
SST = False, # select (o[ther]'s) sym orientation
|
||||
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):
|
||||
"""Calculate the average rotation."""
|
||||
return Orientation.fromAverage([self,other])
|
||||
"""Calculate the average rotation."""
|
||||
return Orientation.fromAverage([self,other])
|
||||
|
|
|
|||
|
|
@ -4,14 +4,10 @@ from . import Lambert
|
|||
|
||||
P = -1
|
||||
|
||||
def isone(a):
|
||||
return np.isclose(a,1.0,atol=1.0e-7,rtol=0.0)
|
||||
|
||||
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:
|
||||
u"""
|
||||
Orientation stored with functionality for conversion to different representations.
|
||||
|
|
|
|||
Loading…
Reference in New Issue