ebsd_Symmetry.Symmetry Class Reference

Detailed Description

Material symmetry class; this class only stores lattice: cubic, hexagonal.

Public Member Functions
def	__cmp__ (self, other)
def	__copy__ (self)
def	__eq__ (self, other)
def	__init__ (self, symmetry=None)
def	__neq__ (self, other)
def	__repr__ (self)
MATERIAL SPECIFIC ROUTINES
def	symmetryQuats (self, who=[])
	List of symmetry operations as quaternions. More...
def	unitCell (self)
	Return unit cell edges. More...
def	equivalentQuaternions (self, quaternion, who=[])
	List of symmetrically equivalent quaternions based on own symmetry. More...
def	inFZ (self, R)
	Check whether given Rodrigues vector falls into fundamental zone of own symmetry. More...
def	inDisorientationSST (self, R)
	Check whether given Rodrigues vector (of misorientation) falls into standard stereographic triangle of own symmetry. More...
def	inSST (self, vector, proper=False, color=False)
	Check whether given vector falls into standard stereographic triangle of own symmetry. More...
Math routines to convert between HKL, XY, RGB
def	xyToHKL (self, inPlane)
	convert xy (coordinates in projection plane (-1<x<1,-1<y<1)) -> hkl More...
def	standardTriangle (self, fileName=None, show=True, stepSize=0.01)
	Plot standard triangle with background, discrete points in color, save to file, add text. More...

Constructor & Destructor Documentation

__init__()

def ebsd_Symmetry.Symmetry.__init__	(		self,
			symmetry = None
	)

Member Function Documentation

__cmp__()

def ebsd_Symmetry.Symmetry.__cmp__	(		self,
			other
	)

__copy__()

def ebsd_Symmetry.Symmetry.__copy__

(

self

)

__eq__()

def ebsd_Symmetry.Symmetry.__eq__	(		self,
			other
	)

__neq__()

def ebsd_Symmetry.Symmetry.__neq__	(		self,
			other
	)

__repr__()

def ebsd_Symmetry.Symmetry.__repr__

(

self

)

equivalentQuaternions()

def ebsd_Symmetry.Symmetry.equivalentQuaternions	(		self,
			quaternion,
			who = []
	)

List of symmetrically equivalent quaternions based on own symmetry.

inDisorientationSST()

def ebsd_Symmetry.Symmetry.inDisorientationSST	(		self,
			R
	)

Check whether given Rodrigues vector (of misorientation) falls into standard stereographic triangle of own symmetry.

Determination of disorientations follow the work of A. Heinz and P. Neumann: Representation of Orientation and Disorientation Data for Cubic, Hexagonal, Tetragonal and Orthorhombic Crystals Acta Cryst. (1991). A47, 780-789

inFZ()

def ebsd_Symmetry.Symmetry.inFZ	(		self,
			R
	)

Check whether given Rodrigues vector falls into fundamental zone of own symmetry.

inSST()

def ebsd_Symmetry.Symmetry.inSST	(		self,
			vector,
			proper = False,
			color = False
	)

Check whether given vector falls into standard stereographic triangle of own symmetry.

Parameters

vector	hkl vector tested/converted to rbg; considers only this vector, no crystal orientation
proper	considers only vectors with z >= 0, hence uses two neighboring SSTs to determine if in SST. i.e. allows more positive results, rgb-value does not depend on this
color	if true, return also color

Returns

whether in SST

(if requested) inverse pole figure color if in SST in RGB values

standardTriangle()

def ebsd_Symmetry.Symmetry.standardTriangle	(		self,
			fileName = None,
			show = True,
			stepSize = 0.01
	)

Plot standard triangle with background, discrete points in color, save to file, add text.

Corner points of triangle

• x=0.41421 =sqrt(2)-1 -> [110] corner at (0.41421,0)
• [111] corner at (0.366025403784,0.366025403784)

Parameters

fileName	save to file
show	True [default] shows figure, else not
stepSize	plotting accuracy: lower value=better quality

symmetryQuats()

def ebsd_Symmetry.Symmetry.symmetryQuats	(		self,
			who = []
	)

List of symmetry operations as quaternions.

unitCell()

def ebsd_Symmetry.Symmetry.unitCell

(

self

)

Return unit cell edges.

xyToHKL()

def ebsd_Symmetry.Symmetry.xyToHKL	(		self,
			inPlane
	)

convert xy (coordinates in projection plane (-1<x<1,-1<y<1)) -> hkl

required for plotting the standardTriangle

Theory

• unscaled vector (x; y; 1) has to be scaled by l such that the scaled vector - unit_vector_Z has the unit length
• scaled: ( xl; yl; l)
• |(xl; yl; l-1)| =!=1
• -> l(x^2+y^2+1)=2 #2 is a random number
• hkl = scaled - unit_vector_Z = (xl; yl; l-1)

Parameters

inPlane

vector coordinates in the plane of the stereograhic projection plane

Returns

hkl vector

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The documentation for this class was generated from the following file:

• pythonEBSD/ebsd_Symmetry.py