# 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):
"""
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)
:returns: The three vectors defining the parallelopiped cell [m].
This function assumes that the first cell vector is colinear with the
x-axis, and the second is perpendicular to the z-axis, and the third is
defined in a right-handed sense.
:rtype: numpy.array (2D)
"""
a, b, c, alpha_deg, beta_deg, gamma_deg = cell_parameters
alpha = np.radians(alpha_deg)
beta = np.radians(beta_deg)
gamma = np.radians(gamma_deg)
n2 = (np.cos(alpha) - np.cos(gamma) * np.cos(beta)) / np.sin(gamma)
M = np.array(
[
[a, 0, 0],
[b * np.cos(gamma), b * np.sin(gamma), 0],
[c * np.cos(beta), c * n2, c * np.sqrt(np.sin(beta) ** 2 - n2**2)],
]
)
return M
[docs]def cell_vectors_to_parameters(M):
"""
Converts unit cell vectors to cell parameters.
:param M: The three vectors defining the parallelopiped cell [m].
This function assumes that the first cell vector is colinear with the
x-axis, the second is perpendicular to the z-axis, and the third is
defined in a right-handed sense.
:type M: numpy.array (2D)
: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)
"""
assert M[0, 1] == 0
assert M[0, 2] == 0
assert M[1, 2] == 0
a = M[0, 0]
b = np.sqrt(np.power(M[1, 0], 2.0) + np.power(M[1, 1], 2.0))
c = np.sqrt(
np.power(M[2, 0], 2.0) + np.power(M[2, 1], 2.0) + np.power(M[2, 2], 2.0)
)
gamma = np.arccos(M[1, 0] / b)
beta = np.arccos(M[2, 0] / c)
alpha = np.arccos(M[2, 1] / c * np.sin(gamma) + np.cos(gamma) * np.cos(beta))
gamma_deg = np.degrees(gamma)
beta_deg = np.degrees(beta)
alpha_deg = np.degrees(alpha)
return np.array([a, b, c, alpha_deg, beta_deg, gamma_deg])