Chimie Théorique » QMX

"""Function-like object creating triclinic lattices.

The following lattice creator is defined:

    Triclinic

"""

from ase.lattice.bravais import Bravais

import numpy as np

from ase.data import reference_states as _refstate

class TriclinicFactory(Bravais):

    "A factory for creating triclinic lattices."

    # The name of the crystal structure in ChemicalElements

    xtal_name = "triclinic"

    # 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 triclinic 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']

            alpha = lattice['alpha']

            beta = lattice['beta']

            gamma = lattice['gamma']

        else:

            if len(lattice) == 6:

                (a,b,c,alpha,beta,gamma) = lattice

            else:

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

        degree = np.pi / 180.0

        cosa = np.cos(alpha*degree)

        cosb = np.cos(beta*degree)

        sinb = np.sin(beta*degree)

        cosg = np.cos(gamma*degree)

        sing = np.sin(gamma*degree)

        lattice = np.array([[a,0,0],

                            [b*cosg, b*sing,0],

                            [c*cosb, c*(cosa-cosb*cosg)/sing,

                             c*np.sqrt(sinb**2 - ((cosa-cosb*cosg)/sing)**2)]])

        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)

        assert abs(np.dot(lattice[0],lattice[1]) - a*b*cosg) < 1e-5

        assert abs(np.dot(lattice[0],lattice[2]) - a*c*cosb) < 1e-5

        assert abs(np.dot(lattice[1],lattice[2]) - b*c*cosa) < 1e-5

        assert abs(np.dot(lattice[0],lattice[0]) - a*a) < 1e-5

        assert abs(np.dot(lattice[1],lattice[1]) - b*b) < 1e-5

        assert abs(np.dot(lattice[2],lattice[2]) - c*c) < 1e-5

Triclinic = TriclinicFactory()