# This file is part of xrayutilities.
#
# xrayutilities 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 2 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 <http://www.gnu.org/licenses/>.
#
# Copyright (c) 2018-2020, 2023 Dominik Kriegner <dominik.kriegner@gmail.com>
"""
implement convenience functions to define Heusler materials.
"""
from . import elements
from .material import Crystal
from .spacegrouplattice import SGLattice
__all__ = [
"FullHeuslerCubic225",
"FullHeuslerCubic225_A2",
"FullHeuslerCubic225_B2",
"FullHeuslerCubic225_DO3",
"HeuslerHexagonal194",
"HeuslerTetragonal119",
"HeuslerTetragonal139",
"InverseHeuslerCubic216",
]
def _check_elements(*elem):
ret = []
for el in elem:
if isinstance(el, str):
ret.append(getattr(elements, el))
else:
ret.append(el)
return ret
[docs]
def FullHeuslerCubic225(X, Y, Z, a, biso=(0, 0, 0), occ=(1, 1, 1)):
"""
Full Heusler structure with formula X2YZ.
Strukturberichte symbol L2_1; space group Fm-3m (225)
Parameters
----------
X, Y, Z : str or Element
elements
a : float
cubic lattice parameter in angstrom
biso : list of floats, optional
Debye Waller factors for X, Y, Z elements
occ : list of floats, optional
occupation numbers for the elements X, Y, Z
Returns
-------
Crystal
Crystal describing the Heusler material
"""
x, y, z = _check_elements(X, Y, Z)
return Crystal(
f"{x.basename}2{y.basename}{z.basename}",
SGLattice(
225, a, atoms=[x, y, z], pos=["8c", "4a", "4b"], b=biso, occ=occ
),
)
[docs]
def FullHeuslerCubic225_B2(X, Y, Z, a, b2dis, biso=(0, 0, 0), occ=(1, 1, 1)):
"""
Full Heusler structure with formula X2YZ.
Strukturberichte symbol L2_1; space group Fm-3m (225) with B2-type (CsCl)
disorder
Parameters
----------
X, Y, Z : str or Element
elements
a : float
cubic lattice parameter in angstrom
b2dis : float
amount of B2-type disorder (0: fully ordered, 1: fully disordered)
biso : list of floats, optional
Debye Waller factors for X, Y, Z elements
occ : list of floats, optional
occupation numbers for the elements X, Y, Z
Returns
-------
Crystal
Crystal describing the Heusler material
"""
x, y, z = _check_elements(X, Y, Z)
return Crystal(
f"{x.basename}2{y.basename}{z.basename}",
SGLattice(
225,
a,
atoms=[x, y, z, y, z],
pos=["8c", "4a", "4b", "4b", "4a"],
occ=[
1 * occ[0],
(1 - b2dis / 2.0) * occ[1],
(1 - b2dis / 2.0) * occ[2],
b2dis / 2.0 * occ[1],
b2dis / 2.0 * occ[2],
],
b=biso + [biso[1], biso[2]],
),
)
[docs]
def FullHeuslerCubic225_A2(X, Y, Z, a, a2dis, biso=(0, 0, 0), occ=(1, 1, 1)):
"""
Full Heusler structure with formula X2YZ.
Strukturberichte symbol L2_1; space group Fm-3m (225) with A2-type (W)
disorder
Parameters
----------
X, Y, Z : str or Element
elements
a : float
cubic lattice parameter in angstrom
a2dis : float
amount of A2-type disorder (0: fully ordered, 1: fully disordered)
biso : list of floats, optional
Debye Waller factors for X, Y, Z elements
occ : list of floats, optional
occupation numbers for the elements X, Y, Z
Returns
-------
Crystal
Crystal describing the Heusler material
"""
x, y, z = _check_elements(X, Y, Z)
return Crystal(
f"{x.basename}2{y.basename}{z.basename}",
SGLattice(
225,
a,
atoms=[x, x, x, y, y, y, z, z, z],
pos=["8c", "4a", "4b", "8c", "4a", "4b", "8c", "4a", "4b"],
occ=[
(1 - a2dis / 2.0) * occ[0],
a2dis / 2.0 * occ[0],
a2dis / 2.0 * occ[0],
a2dis / 4.0 * occ[1],
(1 - a2dis * 3.0 / 4.0) * occ[1],
a2dis / 4.0 * occ[1],
a2dis / 4.0 * occ[2],
a2dis / 4.0 * occ[2],
(1 - a2dis * 3.0 / 4.0) * occ[2],
],
b=[
biso[0],
]
* 3
+ [
biso[1],
]
* 3
+ [
biso[2],
]
* 3,
),
)
[docs]
def FullHeuslerCubic225_DO3(
X, Y, Z, a, do3disxy, do3disxz, biso=(0, 0, 0), occ=(1, 1, 1)
):
"""
Full Heusler structure with formula X2YZ.
Strukturberichte symbol L2_1; space group Fm-3m (225) with DO_3-type (BiF3)
disorder, either between atoms X <-> Y or X <-> Z.
Parameters
----------
X, Y, Z : str or Element
elements
a : float
cubic lattice parameter in angstrom
do3disxy : float
amount of DO_3-type disorder between X and Y atoms (0: fully ordered,
1: fully disordered)
do3disxz : float
amount of DO_3-type disorder between X and Z atoms (0: fully ordered,
1: fully disordered)
biso : list of floats, optional
Debye Waller factors for X, Y, Z elements
occ : list of floats, optional
occupation numbers for the elements X, Y, Z
Returns
-------
Crystal
Crystal describing the Heusler material
"""
x, y, z = _check_elements(X, Y, Z)
return Crystal(
f"{x.basename}2{y.basename}{z.basename}",
SGLattice(
225,
a,
atoms=[x, y, z, x, y, x, z],
pos=["8c", "4a", "4b", "4a", "8c", "4b", "8c"],
occ=[
(1 - do3disxy / 3.0 - do3disxz / 3.0) * occ[0],
(1 - do3disxy * 2 / 3.0) * occ[1],
(1 - do3disxz * 2 / 3.0) * occ[2],
do3disxy * 2 / 3.0 * occ[0],
do3disxy * 1 / 3.0 * occ[1],
do3disxz * 2 / 3.0 * occ[0],
do3disxz * 1 / 3.0 * occ[2],
],
b=biso + [biso[0], biso[1]] + [biso[0], biso[2]],
),
)
[docs]
def InverseHeuslerCubic216(X, Y, Z, a, biso=(0, 0, 0), occ=(1, 1, 1)):
"""
Full Heusler structure with formula (XY)X'Z structure;
space group F-43m (216)
Parameters
----------
X, Y, Z : str or Element
elements
a : float
cubic lattice parameter in angstrom
Returns
-------
Crystal
Crystal describing the Heusler material
"""
x, y, z = _check_elements(X, Y, Z)
return Crystal(
f"({x.basename}{y.basename}){x.basename}'{z.basename}",
SGLattice(
216,
a,
atoms=[x, x, y, z],
pos=["4a", "4d", "4b", "4c"],
b=[
biso[0],
]
+ biso,
occ=[
occ[0],
]
+ occ,
),
)
[docs]
def HeuslerTetragonal139(X, Y, Z, a, c, biso=(0, 0, 0), occ=(1, 1, 1)):
"""
Tetragonal Heusler structure with formula X2YZ
space group I4/mmm (139)
Parameters
----------
X, Y, Z : str or Element
elements
a, c : float
tetragonal lattice parameters in angstrom
Returns
-------
Crystal
Crystal describing the Heusler material
"""
x, y, z = _check_elements(X, Y, Z)
return Crystal(
f"{x.basename}2{y.basename}{z.basename}",
SGLattice(
139, a, c, atoms=[x, y, z], pos=["4d", "2b", "2a"], b=biso, occ=occ
),
)
[docs]
def HeuslerTetragonal119(X, Y, Z, a, c, biso=(0, 0, 0), occ=(1, 1, 1)):
"""
Tetragonal Heusler structure with formula X2YZ
space group I-4m2 (119)
Parameters
----------
X, Y, Z : str or Element
elements
a, c : float
tetragonal lattice parameters in angstrom
Returns
-------
Crystal
Crystal describing the Heusler material
"""
x, y, z = _check_elements(X, Y, Z)
return Crystal(
f"{x.basename}2{y.basename}{z.basename}",
SGLattice(
119,
a,
c,
atoms=[x, x, y, z],
pos=["2b", "2c", "2d", "2a"],
b=[
biso[0],
]
+ biso,
occ=[
occ[0],
]
+ occ,
),
)
[docs]
def HeuslerHexagonal194(X, Y, Z, a, c, biso=(0, 0, 0), occ=(1, 1, 1)):
"""
Hexagonal Heusler structure with formula XYZ
space group P63/mmc (194)
Parameters
----------
X, Y, Z : str or Element
elements
a, c : float
hexagonal lattice parameters in angstrom
Returns
-------
Crystal
Crystal describing the Heusler material
"""
x, y, z = _check_elements(X, Y, Z)
return Crystal(
f"{x.basename}{y.basename}{z.basename}",
SGLattice(
194, a, c, atoms=[x, y, z], pos=["2a", "2c", "2d"], b=biso, occ=occ
),
)