# This file is part of BurnMan - a thermoelastic and thermodynamic toolkit for
# the Earth and Planetary Sciences
# Copyright (C) 2012 - 2021 by the BurnMan team, released under the GNU
# GPL v2 or later.
import numpy as np
from .. import constants
[docs]
def molar_volume_from_unit_cell_volume(unit_cell_v, z):
"""
Converts a unit cell volume from Angstroms^3 per unitcell,
to m^3/mol.
:param unit_cell_v: Unit cell volumes [A^3/unit cell].
:type unit_cell_v: float
:param z: Number of formula units per unit cell.
:type z: float
:returns: Volume [m^3/mol]
:rtype: float
"""
V = unit_cell_v * constants.Avogadro / 1.0e30 / z
return V
[docs]
def cell_parameters_to_vectors(cell_parameters, frame_convention):
"""
Converts cell parameters to unit cell vectors.
:param cell_parameters: An array containing the three lengths of the
unit cell vectors [m], and the three angles [degrees].
The first angle (:math:`\\alpha`) corresponds to the angle between the
second and the third cell vectors, the second (:math:`\\beta`) to the
angle between the first and third cell vectors, and the third
(:math:`\\gamma`) to the angle between the first and second vectors.
:type cell_parameters: numpy.array (1D)
:param frame_convention: A list (c) defining the reference frame
convention. This function dictates that the c[0]th cell vector
is colinear with the c[0]th axis, the c[1]th cell vector is
perpendicular to the c[2]th axis,
and the c[2]th cell vector is defined to give a right-handed
coordinate system.
In common crystallographic shorthand, x[c[0]] // a[c[0]],
x[c[2]] // a[c[2]]^* (i.e. perpendicular to a[c[0]] and a[c[1]]).
:type frame_convention: list of three integers
:returns: The three vectors defining the parallelopiped cell [m].
:rtype: numpy.array (2D)
"""
lengths = cell_parameters[:3]
angles_deg = cell_parameters[3:]
angles = np.radians(angles_deg)
c = frame_convention
n2 = (np.cos(angles[c[0]]) - np.cos(angles[c[2]]) * np.cos(angles[c[1]])) / np.sin(
angles[c[2]]
)
MT = np.zeros((3, 3))
MT[c[0], c[0]] = lengths[c[0]]
MT[c[1], c[0]] = lengths[c[1]] * np.cos(angles[c[2]])
MT[c[1], c[1]] = lengths[c[1]] * np.sin(angles[c[2]])
MT[c[2], c[0]] = lengths[c[2]] * np.cos(angles[c[1]])
MT[c[2], c[1]] = lengths[c[2]] * n2
MT[c[2], c[2]] = lengths[c[2]] * np.sqrt(np.sin(angles[c[1]]) ** 2 - n2**2)
return MT
[docs]
def cell_vectors_to_parameters(vectors, frame_convention):
"""
Converts unit cell vectors to cell parameters.
:param vectors: The three vectors defining the parallelopiped cell [m].
:type vectors: numpy.array (2D)
:param frame_convention: A list (c) defining the reference frame
convention. This function dictates that the c[0]th cell vector
is colinear with the c[0]th axis, the c[1]th cell vector is
perpendicular to the c[2]th axis,
and the c[2]th cell vector is defined to give a right-handed
coordinate system.
In common crystallographic shorthand, x[c[0]] // a[c[0]],
x[c[2]] // a[c[2]]^* (i.e. perpendicular to a[c[0]] and a[c[1]]).
:type frame_convention: list of three integers
:returns: An array containing the three lengths of the unit cell vectors [m],
and the three angles [degrees].
The first angle (:math:`\\alpha`) corresponds to the angle between the
second and the third cell vectors, the second (:math:`\\beta`) to the
angle between the first and third cell vectors, and the third
(:math:`\\gamma`) to the angle between the first and second vectors.
:rtype: numpy.array (1D)
"""
c = frame_convention
assert np.abs(vectors[c[0], c[1]]) < np.finfo(float).eps
assert np.abs(vectors[c[0], c[2]]) < np.finfo(float).eps
assert np.abs(vectors[c[1], c[2]]) < np.finfo(float).eps
lengths = np.empty(3)
angles = np.empty(3)
lengths[c[0]] = vectors[c[0], c[0]]
lengths[c[1]] = np.sqrt(
np.power(vectors[c[1], c[0]], 2.0) + np.power(vectors[c[1], c[1]], 2.0)
)
lengths[c[2]] = np.sqrt(
np.power(vectors[c[2], c[0]], 2.0)
+ np.power(vectors[c[2], c[1]], 2.0)
+ np.power(vectors[c[2], c[2]], 2.0)
)
angles[c[2]] = np.arccos(vectors[c[1], c[0]] / lengths[c[1]])
angles[c[1]] = np.arccos(vectors[c[2], c[0]] / lengths[c[2]])
angles[c[0]] = np.arccos(
vectors[c[2], c[1]] / lengths[c[2]] * np.sin(angles[c[2]])
+ np.cos(angles[c[2]]) * np.cos(angles[c[1]])
)
angles_deg = np.degrees(angles)
return np.array([*lengths, *angles_deg])