# ================================== LICENSE ===================================
# Wulfric - Cell, Atoms, K-path, visualization.
# Copyright (C) 2023 Andrey Rybakov
#
# e-mail: anry@uv.es, web: adrybakov.com
#
# 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/>.
#
# ================================ END LICENSE =================================
from math import cos
from math import pi as PI
from math import sin, sqrt
import numpy as np
from wulfric.cell._basic_manipulation import from_params, get_reciprocal
from wulfric.constants._numerical import TORADIANS
from wulfric.constants._sc_convention import SC_BRAVAIS_LATTICE_VARIATIONS
__all__ = [
"SC_CUB",
"SC_FCC",
"SC_BCC",
"SC_TET",
"SC_BCT",
"SC_ORC",
"SC_ORCF",
"SC_ORCI",
"SC_ORCC",
"SC_HEX",
"SC_RHL",
"SC_MCL",
"SC_MCLC",
"SC_TRI",
"sc_get_example",
]
# Primitive cell`s construction
[docs]
def SC_CUB(a: float):
r"""
Constructs primitive cubic cell as defined in [1]_.
.. math::
\begin{matrix}
\boldsymbol{a}_1 &=& (a, &0, &0)\\
\boldsymbol{a}_2 &=& (0, &a, &0)\\
\boldsymbol{a}_3 &=& (0, &0, &a)
\end{matrix}
Parameters
----------
a : float or int
Length of the three lattice vectors of the conventional cell.
Returns
-------
cell : (3, 3) :numpy:`ndarray`
Matrix of a primitive cell, 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],
]
References
----------
.. [1] Setyawan, W. and Curtarolo, S., 2010.
High-throughput electronic band structure calculations: Challenges and tools.
Computational materials science, 49(2), pp. 299-312.
Examples
--------
.. doctest::
>>> import wulfric
>>> wulfric.cell.SC_CUB(a=2)
array([[2, 0, 0],
[0, 2, 0],
[0, 0, 2]])
"""
return np.array([[a, 0, 0], [0, a, 0], [0, 0, a]])
[docs]
def SC_FCC(a: float):
r"""
Constructs primitive face-centred cubic cell as defined in [1]_.
.. math::
\begin{matrix}
\boldsymbol{a}_1 &=& (0, &a/2, &a/2)\\
\boldsymbol{a}_2 &=& (a/2, &0, &a/2)\\
\boldsymbol{a}_3 &=& (a/2, &a/2, &0)
\end{matrix}
Parameters
----------
a : float
Length of the three lattice vectors of the conventional cell.
Returns
-------
cell : (3, 3) :numpy:`ndarray`
Matrix of a primitive cell, 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],
]
References
----------
.. [1] Setyawan, W. and Curtarolo, S., 2010.
High-throughput electronic band structure calculations: Challenges and tools.
Computational materials science, 49(2), pp. 299-312.
Examples
--------
.. doctest::
>>> import wulfric
>>> wulfric.cell.SC_FCC(a=2)
array([[0., 1., 1.],
[1., 0., 1.],
[1., 1., 0.]])
"""
return np.array([[0, a / 2, a / 2], [a / 2, 0, a / 2], [a / 2, a / 2, 0]])
[docs]
def SC_BCC(a: float):
r"""
Constructs primitive body-centred cubic cell as defined in [1]_.
.. math::
\begin{matrix}
\boldsymbol{a}_1 &=& (-a/2,& a/2,& a/2)\\
\boldsymbol{a}_2 &=& (a/2, &-a/2,& a/2)\\
\boldsymbol{a}_3 &=& (a/2, &a/2, &-a/2)
\end{matrix}
Parameters
----------
a : float
Length of the three lattice vectors of the conventional cell.
Returns
-------
cell : (3, 3) :numpy:`ndarray`
Matrix of a primitive cell, 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],
]
References
----------
.. [1] Setyawan, W. and Curtarolo, S., 2010.
High-throughput electronic band structure calculations: Challenges and tools.
Computational materials science, 49(2), pp. 299-312.
Examples
--------
.. doctest::
>>> import wulfric
>>> wulfric.cell.SC_BCC(a=2)
array([[-1., 1., 1.],
[ 1., -1., 1.],
[ 1., 1., -1.]])
"""
return np.array(
[[-a / 2, a / 2, a / 2], [a / 2, -a / 2, a / 2], [a / 2, a / 2, -a / 2]]
)
[docs]
def SC_TET(a: float, c: float):
r"""
Constructs primitive tetragonal cell as defined in [1]_.
.. math::
\begin{matrix}
\boldsymbol{a}_1 &=& (a, &0, &0)\\
\boldsymbol{a}_2 &=& (0, &a, &0)\\
\boldsymbol{a}_3 &=& (0, &0, &c)
\end{matrix}
Parameters
----------
a : float
Length of the first two lattice vectors of the conventional cell.
c : float
Length of the third lattice vector of the conventional cell.
Returns
-------
cell : (3, 3) :numpy:`ndarray`
Matrix of a primitive cell, 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],
]
References
----------
.. [1] Setyawan, W. and Curtarolo, S., 2010.
High-throughput electronic band structure calculations: Challenges and tools.
Computational materials science, 49(2), pp. 299-312.
Examples
--------
.. doctest::
>>> import wulfric
>>> wulfric.cell.SC_TET(a=2, c=5)
array([[2, 0, 0],
[0, 2, 0],
[0, 0, 5]])
"""
return np.array([[a, 0, 0], [0, a, 0], [0, 0, c]])
[docs]
def SC_BCT(a: float, c: float):
r"""
Constructs primitive body-centred tetragonal cell as defined in [1]_.
.. math::
\begin{matrix}
\boldsymbol{a}_1 &=& (-a/2, &a/2, &c/2)\\
\boldsymbol{a}_2 &=& (a/2, &-a/2, &c/2)\\
\boldsymbol{a}_3 &=& (a/2, &a/2, &-c/2)
\end{matrix}
Parameters
----------
a : float
Length of the first two lattice vectors of the conventional cell.
c : float
Length of the third lattice vector of the conventional cell.
Returns
-------
cell : (3, 3) :numpy:`ndarray`
Matrix of a primitive cell, 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],
]
References
----------
.. [1] Setyawan, W. and Curtarolo, S., 2010.
High-throughput electronic band structure calculations: Challenges and tools.
Computational materials science, 49(2), pp. 299-312.
Examples
--------
.. doctest::
>>> import wulfric
>>> wulfric.cell.SC_BCT(a=2, c=5)
array([[-1. , 1. , 2.5],
[ 1. , -1. , 2.5],
[ 1. , 1. , -2.5]])
"""
return np.array(
[[-a / 2, a / 2, c / 2], [a / 2, -a / 2, c / 2], [a / 2, a / 2, -c / 2]]
)
[docs]
def SC_ORC(a: float, b: float, c: float):
r"""
Constructs primitive orthorhombic cell as defined in [1]_.
.. math::
\begin{matrix}
\boldsymbol{a}_1 &=& (a, &0, &0)\\
\boldsymbol{a}_2 &=& (0, &b, &0)\\
\boldsymbol{a}_3 &=& (0, &0, &c)
\end{matrix}
Input values are used as they are, therefore, the cell might not be a standard
primitive one.
Parameters
----------
a : float
Length of the first lattice vector of the conventional cell.
b : float
Length of the second lattice vector of the conventional cell.
c : float
Length of the third lattice vector of the conventional cell.
Returns
-------
cell : (3, 3) :numpy:`ndarray`
Matrix of a primitive cell, 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],
]
References
----------
.. [1] Setyawan, W. and Curtarolo, S., 2010.
High-throughput electronic band structure calculations: Challenges and tools.
Computational materials science, 49(2), pp. 299-312.
Examples
--------
.. doctest::
>>> import wulfric
>>> wulfric.cell.SC_ORC(a=3, b=5, c=7)
array([[3, 0, 0],
[0, 5, 0],
[0, 0, 7]])
"""
return np.array([[a, 0, 0], [0, b, 0], [0, 0, c]])
[docs]
def SC_ORCF(a: float, b: float, c: float):
r"""
Constructs primitive face-centred orthorhombic cell as defined in [1]_.
.. math::
\begin{matrix}
\boldsymbol{a}_1 &=& (0, &b/2, &c/2)\\
\boldsymbol{a}_2 &=& (a/2, &0, &c/2)\\
\boldsymbol{a}_3 &=& (a/2, &b/2, &0)
\end{matrix}
Input values are used as they are, therefore, the cell might not be a standard
primitive one.
Parameters
----------
a : float
Length of the first lattice vector of the conventional cell.
b : float
Length of the second lattice vector of the conventional cell.
c : float
Length of the third lattice vector of the conventional cell.
Returns
-------
cell : (3, 3) :numpy:`ndarray`
Matrix of a primitive cell, 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],
]
References
----------
.. [1] Setyawan, W. and Curtarolo, S., 2010.
High-throughput electronic band structure calculations: Challenges and tools.
Computational materials science, 49(2), pp. 299-312.
Examples
--------
.. doctest::
>>> import wulfric
>>> wulfric.cell.SC_ORCF(a=3, b=5, c=7)
array([[0. , 2.5, 3.5],
[1.5, 0. , 3.5],
[1.5, 2.5, 0. ]])
"""
return np.array([[0, b / 2, c / 2], [a / 2, 0, c / 2], [a / 2, b / 2, 0]])
[docs]
def SC_ORCI(a: float, b: float, c: float):
r"""
Constructs primitive body-centred orthorhombic cell as defined in [1]_.
.. math::
\begin{matrix}
\boldsymbol{a}_1 &=& (-a/2, &b/2, &c/2)\\
\boldsymbol{a}_2 &=& (a/2, &-b/2, &c/2)\\
\boldsymbol{a}_3 &=& (a/2, &b/2, &-c/2)
\end{matrix}
Input values are used as they are, therefore, the cell might not be a standard
primitive one.
Parameters
----------
a : float
Length of the first lattice vector of the conventional cell.
b : float
Length of the second lattice vector of the conventional cell.
c : float
Length of the third lattice vector of the conventional cell.
Returns
-------
cell : (3, 3) :numpy:`ndarray`
Matrix of a primitive cell, 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],
]
References
----------
.. [1] Setyawan, W. and Curtarolo, S., 2010.
High-throughput electronic band structure calculations: Challenges and tools.
Computational materials science, 49(2), pp. 299-312.
Examples
--------
.. doctest::
>>> import wulfric
>>> wulfric.cell.SC_ORCI(a=3, b=5, c=7)
array([[-1.5, 2.5, 3.5],
[ 1.5, -2.5, 3.5],
[ 1.5, 2.5, -3.5]])
"""
return np.array(
[[-a / 2, b / 2, c / 2], [a / 2, -b / 2, c / 2], [a / 2, b / 2, -c / 2]]
)
[docs]
def SC_ORCC(a: float, b: float, c: float):
r"""
Constructs primitive base-centred orthorhombic cell as defined in [1]_.
.. math::
\begin{matrix}
\boldsymbol{a}_1 &=& (a/2, &-b/2, &0)\\
\boldsymbol{a}_2 &=& (a/2, &b/2, &0)\\
\boldsymbol{a}_3 &=& (0, &0, &c)
\end{matrix}
Input values are used as they are, therefore, the cell might not be a standard
primitive one.
Parameters
----------
a : float
Length of the first lattice vector of the conventional cell.
b : float
Length of the second lattice vector of the conventional cell.
c : float
Length of the third lattice vector of the conventional cell.
Returns
-------
cell : (3, 3) :numpy:`ndarray`
Matrix of a primitive cell, 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],
]
References
----------
.. [1] Setyawan, W. and Curtarolo, S., 2010.
High-throughput electronic band structure calculations: Challenges and tools.
Computational materials science, 49(2), pp. 299-312.
Examples
--------
.. doctest::
>>> import wulfric
>>> wulfric.cell.SC_ORCC(a=3, b=5, c=7)
array([[ 1.5, -2.5, 0. ],
[ 1.5, 2.5, 0. ],
[ 0. , 0. , 7. ]])
"""
return np.array([[a / 2, -b / 2, 0], [a / 2, b / 2, 0], [0, 0, c]])
[docs]
def SC_HEX(a: float, c: float):
r"""
Constructs primitive hexagonal cell as defined in [1]_.
.. math::
\begin{matrix}
\boldsymbol{a}_1 &=& (\frac{a}{2}, &\frac{-a\sqrt{3}}{2}, &0)\\
\boldsymbol{a}_2 &=& (\frac{a}{2}, &\frac{a\sqrt{3}}{2}, &0)\\
\boldsymbol{a}_3 &=& (0, &0, &c)
\end{matrix}
Parameters
----------
a : float
Length of the first two lattice vectors of the conventional cell.
c : float
Length of the third lattice vector of the conventional cell.
Returns
-------
cell : (3, 3) :numpy:`ndarray`
Matrix of a primitive cell, 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],
]
References
----------
.. [1] Setyawan, W. and Curtarolo, S., 2010.
High-throughput electronic band structure calculations: Challenges and tools.
Computational materials science, 49(2), pp. 299-312.
Examples
--------
.. doctest::
>>> import wulfric
>>> wulfric.cell.SC_HEX(a=3, c=5)
array([[ 1.5 , -2.59807621, 0. ],
[ 1.5 , 2.59807621, 0. ],
[ 0. , 0. , 5. ]])
"""
return np.array(
[[a / 2, -a * sqrt(3) / 2, 0], [a / 2, a * sqrt(3) / 2, 0], [0, 0, c]]
)
[docs]
def SC_RHL(a: float, alpha: float):
r"""
Constructs primitive rhombohedral cell as defined in [1]_.
.. math::
\begin{matrix}
\boldsymbol{a}_1 &=& (a\cos(\alpha / 2), &-a\sin(\alpha/2), &0)\\
\boldsymbol{a}_2 &=& (a\cos(\alpha / 2), &a\sin(\alpha/2), &0)\\
\boldsymbol{a}_3 &=& \left(\dfrac{\cos\alpha}{\cos(\alpha/2)}\right.,
&0, &\left.a\sqrt{1 - \dfrac{\cos^2\alpha}{\cos^2(\alpha/2)}}\right)
\end{matrix}
Input values are used as they are, therefore, the cell might not be a standard
primitive one.
Parameters
----------
a : float
Length of the lattice vectors of the conventional cell.
alpha : float
Angle between vectors :math:`a_2` and :math:`a_3` of the conventional cell in
degrees.
Returns
-------
cell : (3, 3) :numpy:`ndarray`
Matrix of a primitive cell, 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],
]
References
----------
.. [1] Setyawan, W. and Curtarolo, S., 2010.
High-throughput electronic band structure calculations: Challenges and tools.
Computational materials science, 49(2), pp. 299-312.
Examples
--------
.. doctest::
>>> import wulfric
>>> wulfric.cell.SC_RHL(a=3, alpha=40)
array([[ 2.81907786, -1.02606043, 0. ],
[ 2.81907786, 1.02606043, 0. ],
[ 2.44562241, 0. , 1.73750713]])
"""
alpha *= TORADIANS
return np.array(
[
[a * cos(alpha / 2), -a * sin(alpha / 2), 0],
[a * cos(alpha / 2), a * sin(alpha / 2), 0],
[
a * cos(alpha) / cos(alpha / 2),
0,
a * sqrt(1 - cos(alpha) ** 2 / cos(alpha / 2) ** 2),
],
]
)
[docs]
def SC_MCL(a: float, b: float, c: float, alpha: float):
r"""
Constructs primitive monoclinic cell as defined in [1]_.
.. math::
\begin{matrix}
\boldsymbol{a}_1 &=& (a, &0, &0)\\
\boldsymbol{a}_2 &=& (0, &b, &0)\\
\boldsymbol{a}_3 &=& (0, &c\cos\alpha, &c\sin\alpha)
\end{matrix}
Input values are used as they are, therefore, the cell might not be a standard
primitive one.
Parameters
----------
a : float
Length of the first lattice vector of the conventional cell.
b : float
Length of the second of the two remaining lattice vectors of the conventional
cell.
c : float
Length of the third of the two remaining lattice vectors of the conventional cell.
alpha : float
Angle between vectors :math:`a_2` and :math:`a_3` of the conventional cell in
degrees.
Returns
-------
cell : (3, 3) :numpy:`ndarray`
Matrix of a primitive cell, 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],
]
References
----------
.. [1] Setyawan, W. and Curtarolo, S., 2010.
High-throughput electronic band structure calculations: Challenges and tools.
Computational materials science, 49(2), pp. 299-312.
Examples
--------
.. doctest::
>>> import wulfric
>>> wulfric.cell.SC_MCL(a=3, b=5, c=7, alpha=45)
array([[3. , 0. , 0. ],
[0. , 5. , 0. ],
[0. , 4.94974747, 4.94974747]])
"""
alpha *= TORADIANS
return np.array([[a, 0, 0], [0, b, 0], [0, c * cos(alpha), c * sin(alpha)]])
[docs]
def SC_MCLC(a: float, b: float, c: float, alpha: float):
r"""
Constructs primitive base-centred monoclinic cell as defined in [1]_.
.. math::
\begin{matrix}
\boldsymbol{a}_1 &=& (a/2, &b/2, &0)\\
\boldsymbol{a}_2 &=& (-a/2, &b/2, &0)\\
\boldsymbol{a}_3 &=& (0, &c\cos\alpha, &c\sin\alpha)
\end{matrix}
Input values are used as they are, therefore, the cell might not be a standard
primitive one.
Parameters
----------
a : float
Length of the first lattice vector of the conventional cell.
b : float
Length of the second of the two remaining lattice vectors of the conventional
cell.
c : float
Length of the third of the two remaining lattice vectors of the conventional
cell.
alpha : float
Angle between vectors :math:`a_2` and :math:`a_3` of the conventional cell in
degrees.
Returns
-------
cell : (3, 3) :numpy:`ndarray`
Matrix of a primitive cell, 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],
]
References
----------
.. [1] Setyawan, W. and Curtarolo, S., 2010.
High-throughput electronic band structure calculations: Challenges and tools.
Computational materials science, 49(2), pp. 299-312.
Examples
--------
.. doctest::
>>> import wulfric
>>> wulfric.cell.SC_MCLC(a=3, b=5, c=7, alpha=45)
array([[ 1.5 , 2.5 , 0. ],
[-1.5 , 2.5 , 0. ],
[ 0. , 4.94974747, 4.94974747]])
"""
alpha *= TORADIANS
return np.array(
[
[a / 2, b / 2, 0],
[-a / 2, b / 2, 0],
[0, c * cos(alpha), c * sin(alpha)],
]
)
[docs]
def SC_TRI(
a: float,
b: float,
c: float,
alpha: float,
beta: float,
gamma: float,
input_reciprocal=False,
):
r"""
Constructs primitive triclinic cell as defined in [1]_.
.. math::
\begin{matrix}
\boldsymbol{a}_1 &=& (a, &0, &0)\\
\boldsymbol{a}_2 &=& (b\cos\gamma, &b\sin\gamma, &0)\\
\boldsymbol{a}_3 &=& (c\cos\beta, &\dfrac{c(\cos\alpha - \cos\beta\cos\gamma)}{\sin\gamma}, &\dfrac{c}{\sin\gamma}\sqrt{\sin^2\gamma - \cos^2\alpha - \cos^2\beta + 2\cos\alpha\cos\beta\cos\gamma})
\end{matrix}
Parameters
----------
a : float
Length of the first lattice vector of the conventional cell.
b : float
Length of the second lattice vector of the conventional cell.
c : float
Length of the third lattice vector of the conventional cell.
alpha : float
Angle between vectors :math:`a_2` and :math:`a_3` of the conventional cell in
degrees.
beta : float
Angle between vectors :math:`a_1` and :math:`a_3` of the conventional cell in
degrees.
gamma : float
Angle between vectors :math:`a_1` and :math:`a_2` of the conventional cell in
degrees.
input_reciprocal : bool, default False
Whether to interpret input as reciprocal parameters.
Returns
-------
cell : (3, 3) :numpy:`ndarray`
Matrix of a primitive cell, 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],
]
References
----------
.. [1] Setyawan, W. and Curtarolo, S., 2010.
High-throughput electronic band structure calculations: Challenges and tools.
Computational materials science, 49(2), pp. 299-312.
Examples
--------
.. doctest::
>>> import wulfric
>>> wulfric.cell.SC_TRI(a=3, b=5, c=7, alpha=45, beta=33, gamma=21)
array([[ 3. , 0. , 0. ],
[ 4.66790213, 1.79183975, 0. ],
[ 5.87069398, -1.48176621, 3.51273699]])
"""
cell = from_params(a, b, c, alpha, beta, gamma)
if input_reciprocal:
cell = get_reciprocal(cell)
return cell
[docs]
def sc_get_example(lattice_variation: str = None):
r"""
Examples of the Bravais lattices as defined in the paper by Setyawan and Curtarolo [1]_.
.. versionchanged:: 0.6.3 renamed from ``sc_get_example_cell``.
Parameters
----------
lattice_variation : str, optional
Name of the lattice type or variation to be returned. For available names see
documentation of each :ref:`user-guide_conventions_bravais-lattices`.
Case-insensitive.
Returns
-------
cell : (3, 3) :numpy:`ndarray`
Matrix of a direct cell, 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],
]
References
----------
.. [1] Setyawan, W. and Curtarolo, S., 2010.
High-throughput electronic band structure calculations: Challenges and tools.
Computational materials science, 49(2), pp. 299-312.
Examples
--------
.. doctest::
>>> import wulfric
>>> wulfric.cell.sc_get_example("cub")
array([[3.14159265, 0. , 0. ],
[0. , 3.14159265, 0. ],
[0. , 0. , 3.14159265]])
>>> wulfric.cell.sc_get_example("ORCF3")
array([[0. , 1.96349541, 2.61799388],
[1.57079633, 0. , 2.61799388],
[1.57079633, 1.96349541, 0. ]])
"""
correct_inputs = set(map(lambda x: x.lower(), SC_BRAVAIS_LATTICE_VARIATIONS)).union(
set(
map(
lambda x: x.translate(str.maketrans("", "", "12345ab")).lower(),
SC_BRAVAIS_LATTICE_VARIATIONS,
)
)
)
if (
not isinstance(lattice_variation, str)
or lattice_variation.lower() not in correct_inputs
):
message = (
f'There is no example of "{lattice_variation}" Bravais lattice. '
"Available examples are:\n"
)
for name in correct_inputs:
message += f" * {name}\n"
raise ValueError(message)
lattice_variation = lattice_variation.lower()
if lattice_variation == "cub":
cell = SC_CUB(PI)
elif lattice_variation == "fcc":
cell = SC_FCC(PI)
elif lattice_variation == "bcc":
cell = SC_BCC(PI)
elif lattice_variation == "tet":
cell = SC_TET(PI, 1.5 * PI)
elif lattice_variation in ["bct1", "bct"]:
cell = SC_BCT(1.5 * PI, PI)
elif lattice_variation == "bct2":
cell = SC_BCT(PI, 1.5 * PI)
elif lattice_variation == "orc":
cell = SC_ORC(PI, 1.5 * PI, 2 * PI)
elif lattice_variation in ["orcf1", "orcf"]:
cell = SC_ORCF(0.7 * PI, 5 / 4 * PI, 5 / 3 * PI)
elif lattice_variation == "orcf2":
cell = SC_ORCF(1.2 * PI, 5 / 4 * PI, 5 / 3 * PI)
elif lattice_variation == "orcf3":
cell = SC_ORCF(PI, 5 / 4 * PI, 5 / 3 * PI)
elif lattice_variation == "orci":
return SC_ORCI(PI, 1.3 * PI, 1.7 * PI)
elif lattice_variation == "orcc":
cell = SC_ORCC(PI, 1.3 * PI, 1.7 * PI)
elif lattice_variation == "hex":
cell = SC_HEX(PI, 2 * PI)
elif lattice_variation in ["rhl1", "rhl"]:
# If alpha = 60 it is effectively FCC!
cell = SC_RHL(PI, 70)
elif lattice_variation == "rhl2":
cell = SC_RHL(PI, 110)
elif lattice_variation == "mcl":
cell = SC_MCL(PI, 1.3 * PI, 1.6 * PI, alpha=75)
elif lattice_variation in ["mclc1", "mclc"]:
cell = SC_MCLC(PI, 1.4 * PI, 1.7 * PI, 80)
elif lattice_variation == "mclc2":
cell = SC_MCLC(1.4 * PI * sin(75 * TORADIANS), 1.4 * PI, 1.7 * PI, 75)
elif lattice_variation == "mclc3":
b = PI
x = 1.1
alpha = 78
ralpha = alpha * TORADIANS
c = b * (x**2) / (x**2 - 1) * cos(ralpha) * 1.8
a = x * b * sin(ralpha)
cell = SC_MCLC(a, b, c, alpha)
elif lattice_variation == "mclc4":
b = PI
x = 1.2
alpha = 65
ralpha = alpha * TORADIANS
c = b * (x**2) / (x**2 - 1) * cos(ralpha)
a = x * b * sin(ralpha)
cell = SC_MCLC(a, b, c, alpha)
elif lattice_variation == "mclc5":
b = PI
x = 1.4
alpha = 53
ralpha = alpha * TORADIANS
c = b * (x**2) / (x**2 - 1) * cos(ralpha) * 0.9
a = x * b * sin(ralpha)
cell = SC_MCLC(a, b, c, alpha)
elif lattice_variation in ["tri1a", "tri1", "tri", "tria"]:
cell = SC_TRI(0.5, 0.5, 0.5, 50.0, 60.0, 80.0)
elif lattice_variation in ["tri2a", "tri2"]:
cell = SC_TRI(0.5, 1.0, 1.0, 100.0, 100.0, 140.0)
elif lattice_variation in ["tri1b", "trib"]:
cell = SC_TRI(0.5, 1.0, 1.0, 100.0, 110.0, 60.0)
elif lattice_variation == "tri2b":
cell = SC_TRI(0.5, 1.0, 2.0, 80.0, 100.0, 40.0)
return cell
