# RAD-tools - Sandbox (mainly condense matter plotting).
# Copyright (C) 2022-2024 Andrey Rybakov
#
# e-mail: anry@uv.es, web: rad-tools.org
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
from math import cos, pi, sin, sqrt
import numpy as np
from radtools.constants import TORADIANS
from radtools.geometry import angle, parallelepiped_check, volume
__all__ = [
"reciprocal",
"from_params",
"params",
"primitive",
]
[docs]
def reciprocal(cell):
r"""
Computes reciprocal cell.
.. versionadded:: 0.7
Parameters
----------
cell : (3, 3) |array_like|_
Cell matrix, rows are interpreted as vectors.
Returns
-------
reciprocal_cell : (3, 3) :numpy:`ndarray`
Reciprocal cell matrix, rows are interpreted as vectors.
:math:`cell = (\vec{v}_1, \vec{v}_2, \vec{v}_3)`, where
.. math::
\begin{matrix}
\vec{b}_1 = \dfrac{2\pi}{V}\vec{a}_2\times\vec{a}_3 \\
\vec{b}_2 = \dfrac{2\pi}{V}\vec{a}_3\times\vec{a}_1 \\
\vec{b}_3 = \dfrac{2\pi}{V}\vec{a}_1\times\vec{a}_2 \\
\end{matrix}
"""
vol = volume(cell)
reciprocal_cell = np.array(
[
2 * pi / vol * np.cross(cell[1], cell[2]),
2 * pi / vol * np.cross(cell[2], cell[0]),
2 * pi / vol * np.cross(cell[0], cell[1]),
]
)
return reciprocal_cell
[docs]
def from_params(a=1.0, b=1.0, c=1.0, alpha=90.0, beta=90.0, gamma=90.0):
r"""
Return cell from lattice parameters.
.. versionadded:: 0.7
Parameters
----------
a : float, default 1
Length of the :math:`a_1` vector.
b : float, default 1
Length of the :math:`a_2` vector.
c : float, default 1
Length of the :math:`a_3` vector.
alpha : float, default 90
Angle between vectors :math:`a_2` and :math:`a_3`. In degrees.
beta : float, default 90
Angle between vectors :math:`a_1` and :math:`a_3`. In degrees.
gamma : float, default 90
Angle between vectors :math:`a_1` and :math:`a_2`. In degrees.
Returns
-------
cell : (3, 3) :numpy:`ndarray`
Cell matrix.
.. code-block:: python
cell = [[a1_x, a1_y, a1_z],
[a2_x, a2_y, a2_z],
[a3_x, a3_y, a3_z]]
Raises
------
ValueError
If parameters could not form a parallelepiped.
See Also
--------
parallelepiped_check : Check if parameters could form a parallelepiped.
"""
parallelepiped_check(a, b, c, alpha, beta, gamma, raise_error=True)
alpha = alpha * TORADIANS
beta = beta * TORADIANS
gamma = gamma * TORADIANS
return np.array(
[
[a, 0, 0],
[b * cos(gamma), b * sin(gamma), 0],
[
c * cos(beta),
c / sin(gamma) * (cos(alpha) - cos(beta) * cos(gamma)),
c
/ sin(gamma)
* sqrt(
1
+ 2 * cos(alpha) * cos(beta) * cos(gamma)
- cos(alpha) ** 2
- cos(beta) ** 2
- cos(gamma) ** 2
),
],
],
dtype=float,
)
[docs]
def params(cell):
r"""
Return lattice parameters from cell.
.. versionadded:: 0.7
Parameters
----------
cell : (3,3) |array_like|_
Cell matrix, rows are interpreted as vectors.
.. code-block:: python
cell = [[a1_x, a1_y, a1_z],
[a2_x, a2_y, a2_z],
[a3_x, a3_y, a3_z]]
Returns
-------
a : float
Length of the :math:`a_1` vector.
b : float
Length of the :math:`a_2` vector.
c : float
Length of the :math:`a_3` vector.
alpha : float
Angle between vectors :math:`a_2` and :math:`a_3`. In degrees.
beta : float
Angle between vectors :math:`a_1` and :math:`a_3`. In degrees.
gamma : float
Angle between vectors :math:`a_1` and :math:`a_2`. In degrees.
"""
return (
np.linalg.norm(cell[0]),
np.linalg.norm(cell[1]),
np.linalg.norm(cell[2]),
angle(cell[1], cell[2]),
angle(cell[0], cell[2]),
angle(cell[0], cell[1]),
)
# TODO
[docs]
def primitive(cell, atoms):
r"""
Compute primitive cell.
.. versionadded:: ???
Parameters
----------
cell : (3, 3) |array_like|_
Cell matrix, rows are interpreted as vectors.
atoms : list of :py:class:`.Atom`
Atoms in the cell.
``position`` attribute of the atom is interpreted as relative
position in the cell.
Returns
-------
primitive_cell : (3, 3) :numpy:`ndarray`
Primitive cell matrix, rows are interpreted as vectors.
primitive_atoms : list of :py:class:`.Atom`
Atoms in the primitive cell.
``position`` attribute of the atom is interpreted as relative
position in the primitive cell.
"""
raise NotImplementedError
