Chimie Théorique » QMX

"""Function-like objects creating orthorhombic lattices.

The following lattice creators are defined:

    SimleOrthorhombic

    BaseCenteredOrthorhombic

    BodyCenteredOrthorhombic

    FaceCenteredOrthorhombic

"""

from ase.lattice.bravais import Bravais

import numpy as np

from ase.data import reference_states as _refstate

class SimpleOrthorhombicFactory(Bravais):

    "A factory for creating simple orthorhombic lattices."

    # The name of the crystal structure in ChemicalElements

    xtal_name = "orthorhombic"

    # The natural basis vectors of the crystal structure

    int_basis = np.array([[1, 0, 0],

                          [0, 1, 0],

                          [0, 0, 1]])

    basis_factor = 1.0

    # Converts the natural basis back to the crystallographic basis

    inverse_basis = np.array([[1, 0, 0],

                              [0, 1, 0],

                              [0, 0, 1]])

    inverse_basis_factor = 1.0

    def get_lattice_constant(self):

        "Get the lattice constant of an element with orhtorhombic crystal structure."

        if _refstate[self.atomicnumber]['symmetry'].lower() != self.xtal_name:

            raise ValueError, (("Cannot guess the %s lattice constant of"

                                + " an element with crystal structure %s.")

                               % (self.xtal_name,

                                  _refstate[self.atomicnumber]['symmetry']))

        return _refstate[self.atomicnumber].copy()

    def make_crystal_basis(self):

        "Make the basis matrix for the crystal unit cell and the system unit cell."

        lattice = self.latticeconstant

        if type(lattice) == type({}):

            a = lattice['a']

            try:

                b = lattice['b']

            except KeyError:

                b = a * lattice['b/a']

            try:

                c = lattice['c']

            except KeyError:

                c = a * lattice['c/a']

        else:

            if len(lattice) == 3:

                (a,b,c) = lattice

            else:

                raise ValueError, "Improper lattice constants for orthorhombic crystal."

        lattice = np.array([[a,0,0],[0,b,0],[0,0,c]])

        self.latticeconstant = lattice

        self.miller_basis = lattice

        self.crystal_basis = (self.basis_factor *

                              np.dot(self.int_basis, lattice))

        self.basis = np.dot(self.directions, self.crystal_basis)

        self.check_basis_volume()

    def check_basis_volume(self):

        "Check the volume of the unit cell."

        vol1 = abs(np.linalg.det(self.basis))

        vol2 = self.calc_num_atoms() * np.linalg.det(self.latticeconstant)

        if self.bravais_basis is not None:

            vol2 /= len(self.bravais_basis)

        if abs(vol1-vol2) > 1e-5:

            print "WARNING: Got volume %f, expected %f" % (vol1, vol2)

SimpleOrthorhombic = SimpleOrthorhombicFactory()

class BaseCenteredOrthorhombicFactory(SimpleOrthorhombicFactory):

    "A factory for creating base-centered orthorhombic lattices."

    # The natural basis vectors of the crystal structure

    int_basis = np.array([[1, -1, 0],

                          [1, 1, 0],

                          [0, 0, 2]])

    basis_factor = 0.5

    # Converts the natural basis back to the crystallographic basis

    inverse_basis = np.array([[1, 1, 0],

                              [-1, 1, 0],

                              [0, 0, 1]])

    inverse_basis_factor = 1.0

    def check_basis_volume(self):

        "Check the volume of the unit cell."

        vol1 = abs(np.linalg.det(self.basis))

        vol2 = self.calc_num_atoms() * np.linalg.det(self.latticeconstant) / 2.0

        if abs(vol1-vol2) > 1e-5:

            print "WARNING: Got volume %f, expected %f" % (vol1, vol2)

BaseCenteredOrthorhombic = BaseCenteredOrthorhombicFactory()

class BodyCenteredOrthorhombicFactory(SimpleOrthorhombicFactory):

    "A factory for creating body-centered orthorhombic lattices."

    int_basis = np.array([[-1, 1, 1],

                          [1, -1, 1],

                          [1, 1, -1]])

    basis_factor = 0.5

    inverse_basis = np.array([[0, 1, 1],

                              [1, 0, 1],

                              [1, 1, 0]])

    inverse_basis_factor = 1.0

    def check_basis_volume(self):

        "Check the volume of the unit cell."

        vol1 = abs(np.linalg.det(self.basis))

        vol2 = self.calc_num_atoms() * np.linalg.det(self.latticeconstant) / 2.0

        if abs(vol1-vol2) > 1e-5:

            print "WARNING: Got volume %f, expected %f" % (vol1, vol2)

BodyCenteredOrthorhombic = BodyCenteredOrthorhombicFactory()

class FaceCenteredOrthorhombicFactory(SimpleOrthorhombicFactory):

    "A factory for creating face-centered orthorhombic lattices."

    int_basis = np.array([[0, 1, 1],

                          [1, 0, 1],

                          [1, 1, 0]])

    basis_factor = 0.5

    inverse_basis = np.array([[-1, 1, 1],

                              [1, -1, 1],

                              [1, 1, -1]])

    inverse_basis_factor = 1.0

    def check_basis_volume(self):

        "Check the volume of the unit cell."

        vol1 = abs(np.linalg.det(self.basis))

        vol2 = self.calc_num_atoms() * np.linalg.det(self.latticeconstant) / 4.0

        if abs(vol1-vol2) > 1e-5:

            print "WARNING: Got volume %f, expected %f" % (vol1, vol2)

FaceCenteredOrthorhombic = FaceCenteredOrthorhombicFactory()