# Source code for burnman.utils.unitcell

# 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.

Parameters
----------
unit_cell_v : float
Unit cell volumes [A^3/unit cell]

z : float
Number of formula units per unit cell

Returns
-------
V : float
Volume [m^3/mol]
"""
V = unit_cell_v * constants.Avogadro / 1.e30 / z
return V

[docs]def cell_parameters_to_vectors(cell_parameters):
"""
Converts cell parameters to unit cell vectors.

Parameters
----------
cell_parameters : 1D numpy array
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.

Returns
-------
M : 2D numpy array
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.
"""
a, b, c, alpha_deg, beta_deg, gamma_deg = cell_parameters

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.

Parameters
----------
M : 2D numpy array
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.

Returns
-------
cell_parameters : 1D numpy array
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.
"""

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.) + np.power(M[1, 1], 2.))
c = (np.sqrt(np.power(M[2, 0], 2.)
+ np.power(M[2, 1], 2.)
+ np.power(M[2, 2], 2.)))

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])