schrodinger.application.matsci.nano.plane module¶

Classes and functions for crystal planes.

schrodinger.application.matsci.nano.plane.ext_gcd(a, b)¶

Solve ax + by = gcd(a, b) using the Extended Euclidean Algorithm. Return (1) the greatest common divisor (gcd) of integers a and b and (2) the integer Bezout coefficients x and y.

Parameters:	a (int) – the a coefficient b (int) – the b coefficient
Return type:	int, int, int
Returns:	gcd(a, b), Bezout coefficient x, and Bezout coefficient y

class schrodinger.application.matsci.nano.plane.CrystalPlane(h_index, k_index, l_index, a_vec, b_vec, c_vec, origin=None, logger=None)¶

Bases: object

Manage a crystal plane object.

SQUARE = {1: array([-1., 1., 0.]), 2: array([-1., -1., 0.]), 3: array([ 1., -1., 0.]), 4: array([1., 1., 0.])}¶

DISTANCE_THRESH = -0.001¶

SAME_VECTOR_THRESH = 0.0001¶

SLAB_THRESHOLD = 1e-07¶

__init__(h_index, k_index, l_index, a_vec, b_vec, c_vec, origin=None, logger=None)¶

Create an instance.

Parameters:

h_index (int) – the h Miller index
k_index (int) – the k Miller index
l_index (int) – the l Miller index
a_vec (numpy.array) – the a lattice vector
b_vec (numpy.array) – the b lattice vector
c_vec (numpy.array) – the c lattice vector
origin (numpy.array) – the origin of the lattice vectors
logger (logging.getLogger) – output logger

checkMillerIndices()¶: Check the user provided Miller indices.

getReciprocals()¶

Return the reciprocal lattice vectors.

Return type:	three numpy.array
Returns:	the three reciprocal lattice vectors.

getNormal()¶

Return the normal vector.

Return type:	numpy.array
Returns:	the normal vector for this plane

getLinDepPlaneVectors()¶

Return three typically used plane vectors that are linearly dependent.

Return type:	numpy.array, numpy.array, numpy.array
Returns:	typically used plane vectors that are linearly dependent

transformVectors(a_vec, b_vec, c_vec)¶

Transform the given vectors using the basis transform.

Parameters:	a_vec (numpy.array) – the first vector b_vec (numpy.array) – the second vector c_vec (numpy.array) – the third vector
Return type:	numpy.array, numpy.array, numpy.array
Returns:	the three transformed vectors

getSimpleSlabVectors()¶: This sets the simple, i.e. two of the Miller indices are zero, transformation matrix into self.basis and sets the simple slab vectors.

getSlabVectors()¶: This sets the transformation matrix into self.basis. Basis vectors are chosen such that a and b axes are in the plane of the Miller plane, and c-axis is out of this plane (NOT necessarily normal to it). Also sets the slab vectors.

getSpanningVectors(ncella=1, ncellb=1, ncellc=1)¶

Return the spanning vectors of this bounding box.

Parameters:	ncella (int) – the number of cells along a ncellb (int) – the number of cells along b ncellc (int) – the number of cells along c
Return type:	list of numpy.array
Returns:	contains vectors spanning the parallelepiped and its sides

getNumPlanes(ncella=1, ncellb=1, ncellc=1)¶

Return the number of planes that will fit inside the bounding box.

Parameters:	ncella (int) – the number of cells along a ncellb (int) – the number of cells along b ncellc (int) – the number of cells along c
Return type:	int
Returns:	the number of planes that will fit inside the bounding box

getInterPlanarSeparation()¶

Return the inter-planar separation in Angstrom.

Return type:	float
Returns:	the inter-planar separation in Angstrom

getRotationToZ()¶

Return the rotation matrix needed to rotate this plane to the XY-plane as well as its inverse.

Return type:	two numpy.array
Returns:	the rotation matrix that rotates this plane to the XY-plane and its inverse.

getSquareVertices()¶

Return the vertices of a square that lies in this plane. The square has and edge-length of 2 Angstrom. It is rotated from the XY-plane, centered on origin, into this plane.

Return type:	list of numpy.array
Returns:	the vertices of the squre that lies in this plane

getParallelepipedLineSegments(ncella=1, ncellb=1, ncellc=1)¶

Return the line segments that make this bounding box.

Parameters:	ncella (int) – the number of cells along a ncellb (int) – the number of cells along b ncellc (int) – the number of cells along c
Return type:	list of tuples of heads and tails of 12 line segments.
Returns:	the line segments that make this bounding box

getPlaneBoxIntersections(vertices, ncella=1, ncellb=1, ncellc=1)¶

Return the points where the plane containing the specified vertices intersects the parallelepiped.

Parameters:	vertices (list of numpy.array) – the vertices of the square that lies in this plane ncella (int) – the number of cells along a ncellb (int) – the number of cells along b ncellc (int) – the number of cells along c
Return type:	list of numpy.array
Returns:	the points of intersection

getOrderedIntersections(intersections)¶

Return the provided list of planar points in counter-clockwise order.

Parameters:	intersections (list of numpy.array) – some intersection points in a plane
Return type:	list of numpy.array
Returns:	those planar intersections in counter-clockwise order

getVerticesOfAllPlanes(ncella=1, ncellb=1, ncellc=1, nplanes=None)¶

Return a list of lists of points where the set of planes intersect the parallelepiped.

Parameters:	ncella (int) – the number of cells along a ncellb (int) – the number of cells along b ncellc (int) – the number of cells along c nplanes (int) – the number of planes to generate in the backwards and forwards direction
Return type:	list of list of numpy.array
Returns:	where the planes intersect the parallelepiped

__class__¶: alias of builtins.type

__delattr__¶: Implement delattr(self, name).

__dict__ = mappingproxy({'__module__': 'schrodinger.application.matsci.nano.plane', '__doc__': '\n Manage a crystal plane object.\n ', 'SQUARE': OrderedDict([(1, array([-1., 1., 0.])), (2, array([-1., -1., 0.])), (3, array([ 1., -1., 0.])), (4, array([1., 1., 0.]))]), 'DISTANCE_THRESH': -0.001, 'SAME_VECTOR_THRESH': 0.0001, 'SLAB_THRESHOLD': 1e-07, '__init__': <function CrystalPlane.__init__>, 'checkMillerIndices': <function CrystalPlane.checkMillerIndices>, 'getReciprocals': <function CrystalPlane.getReciprocals>, 'getNormal': <function CrystalPlane.getNormal>, 'getLinDepPlaneVectors': <function CrystalPlane.getLinDepPlaneVectors>, 'transformVectors': <function CrystalPlane.transformVectors>, 'getSimpleSlabVectors': <function CrystalPlane.getSimpleSlabVectors>, 'getSlabVectors': <function CrystalPlane.getSlabVectors>, 'getSpanningVectors': <function CrystalPlane.getSpanningVectors>, 'getNumPlanes': <function CrystalPlane.getNumPlanes>, 'getInterPlanarSeparation': <function CrystalPlane.getInterPlanarSeparation>, 'getRotationToZ': <function CrystalPlane.getRotationToZ>, 'getSquareVertices': <function CrystalPlane.getSquareVertices>, 'getParallelepipedLineSegments': <function CrystalPlane.getParallelepipedLineSegments>, 'getPlaneBoxIntersections': <function CrystalPlane.getPlaneBoxIntersections>, 'getOrderedIntersections': <function CrystalPlane.getOrderedIntersections>, 'getVerticesOfAllPlanes': <function CrystalPlane.getVerticesOfAllPlanes>, '__dict__': <attribute '__dict__' of 'CrystalPlane' objects>, '__weakref__': <attribute '__weakref__' of 'CrystalPlane' objects>})¶

__dir__() → list¶: default dir() implementation

__eq__¶: Return self==value.

__format__()¶: default object formatter

__ge__¶: Return self>=value.

__getattribute__¶: Return getattr(self, name).

__gt__¶: Return self>value.

__hash__¶: Return hash(self).

__init_subclass__()¶

This method is called when a class is subclassed.

The default implementation does nothing. It may be overridden to extend subclasses.

__le__¶: Return self<=value.

__lt__¶: Return self<value.

__module__ = 'schrodinger.application.matsci.nano.plane'¶

__ne__¶: Return self!=value.

__new__()¶: Create and return a new object. See help(type) for accurate signature.

__reduce__()¶: helper for pickle

__reduce_ex__()¶: helper for pickle

__repr__¶: Return repr(self).

__setattr__¶: Implement setattr(self, name, value).

__sizeof__() → int¶: size of object in memory, in bytes

__str__¶: Return str(self).

__subclasshook__()¶

Abstract classes can override this to customize issubclass().

This is invoked early on by abc.ABCMeta.__subclasscheck__(). It should return True, False or NotImplemented. If it returns NotImplemented, the normal algorithm is used. Otherwise, it overrides the normal algorithm (and the outcome is cached).

__weakref__¶: list of weak references to the object (if defined)

schrodinger.application.matsci.nano.plane module¶

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