def mycut(atoms,
a_atom,
b_atom,
c_atom,
origo_atom,
nlayers=None,
extend=1.0,
tolerance=0.01,
maxatoms=None):
"""
atoms: atoms
a_atoms,b_atoms,c_atoms: the symol_number of the atoms (a_atom-origo_atom)-> a; ...
origo_atom: the atom at the origin.
other parameters are as ase.io.geometry.cut
"""
symdict = symbol_number(atoms)
origo = symdict[origo_atom]
a = symdict[a_atom]
b = symdict[b_atom]
c = symdict[c_atom]
atoms = cut(atoms,
a=a,
b=b,
c=c,
clength=None,
origo=origo,
nlayers=None,
extend=1.0,
tolerance=0.01,
maxatoms=None)
return atoms
def rh2hex(lattice):
""" return Atomic objects with 3 times volume hexgonal cell of the input rhombohedral cell
exist slightly different cut vectors, see ITC vol. A
"""
from ase.utils.geometry import cut
re=cut(lattice, (1.0, -1.0, 0.0), (0.0, 1.0, -1.0), (1.0, 1.0,1.0), origo=(0,0,0))
return re
def primitive_from_conventional_cell(atoms, spacegroup=1, setting=1):
"""Returns primitive cell given an Atoms object for a conventional
cell and it's spacegroup."""
from ase.lattice.spacegroup import Spacegroup
from ase.utils.geometry import cut
sg = Spacegroup(spacegroup, setting)
prim_cell = sg.scaled_primitive_cell # Check if we need to transpose
return cut(atoms, a=prim_cell[0], b=prim_cell[1], c=prim_cell[2])
def primitive_from_conventional_cell(atoms, spacegroup=1, setting=1):
"""Returns primitive cell given an Atoms object for a conventional
cell and it's spacegroup."""
from ase.lattice.spacegroup import Spacegroup
from ase.utils.geometry import cut
sg = Spacegroup(spacegroup, setting)
prim_cell = sg.scaled_primitive_cell # Check if we need to transpose
return cut(atoms, a=prim_cell[0], b=prim_cell[1], c=prim_cell[2])
def cut_z(atoms, symnum1, symnum2, shift):
"""
cut along the z direction.
"""
symdict = symbol_number(atoms)
z1 = atoms.get_positions()[symdict[symnum1]][2] - shift
z2 = atoms.get_positions()[symdict[symnum2]][2] - shift
c = atoms.get_cell()[2][2]
dz = z2 - z1
newatoms = cut(atoms, clength=dz, origo=(0, 0, z1 / c))
newatoms.translate([0, 0, -shift])
return newatoms
"Test the ase.utils.geometry module"
import numpy as np
from ase.lattice.spacegroup import crystal
from ase.utils.geometry import get_layers, cut, stack
np.set_printoptions(suppress=True)
al = crystal('Al', [(0, 0, 0)], spacegroup=225, cellpar=4.05)
# Cut out slab of 5 Al(001) layers
al001 = cut(al, nlayers=5)
correct_pos = np.array([[0., 0., 0.], [0., 0.5, 0.2], [0.5, 0., 0.2],
[0.5, 0.5, 0.], [0., 0., 0.4], [0., 0.5, 0.6],
[0.5, 0., 0.6], [0.5, 0.5, 0.4], [0., 0., 0.8],
[0.5, 0.5, 0.8]])
assert np.allclose(correct_pos, al001.get_scaled_positions())
# Check layers along 001
tags, levels = get_layers(al001, (0, 0, 1))
assert np.allclose(tags, [0, 1, 1, 0, 2, 3, 3, 2, 4, 4])
assert np.allclose(levels, [0., 2.025, 4.05, 6.075, 8.1])
# Check layers along 101
tags, levels = get_layers(al001, (1, 0, 1))
assert np.allclose(tags, [0, 1, 5, 3, 2, 4, 8, 7, 6, 9])
assert np.allclose(
levels,
[0.000, 0.752, 1.504, 1.880, 2.256, 2.632, 3.008, 3.384, 4.136, 4.888],
atol=0.001)
import numpy as np
import ase.utils.geometry as geometry
import ase.io as io
# Create a new atoms instance with Co at origo including all atoms on the
# surface of the unit cell
cosb3 = geometry.cut(skutterudite, origo=(0.25, 0.25, 0.25), extend=1.01)
# Define the atomic bonds to show
bondatoms = []
symbols = cosb3.get_chemical_symbols()
for i in xrange(len(cosb3)):
for j in xrange(i):
if (symbols[i] == symbols[j] == 'Co'
and cosb3.get_distance(i, j) < 4.53):
bondatoms.append((i, j))
elif (symbols[i] == symbols[j] == 'Sb'
and cosb3.get_distance(i, j) < 2.99):
bondatoms.append((i, j))
# Create nice-looking image using povray
io.write(
'spacegroup-cosb3.pov',
cosb3,
transparent=False,
display=False,
run_povray=True,
camera_type='perspective',
canvas_width=320,
radii=0.4,
rotation='90y',
"""Test the ase.utils.geometry module"""
import numpy as np
from ase.lattice.spacegroup import crystal
from ase.utils.geometry import get_layers, cut, stack
from ase.atoms import Atoms
np.set_printoptions(suppress=True)
al = crystal("Al", [(0, 0, 0)], spacegroup=225, cellpar=4.05)
# Cut out slab of 5 Al(001) layers
al001 = cut(al, nlayers=5)
correct_pos = np.array(
[
[0.0, 0.0, 0.0],
[0.0, 0.5, 0.2],
[0.5, 0.0, 0.2],
[0.5, 0.5, 0.0],
[0.0, 0.0, 0.4],
[0.0, 0.5, 0.6],
[0.5, 0.0, 0.6],
[0.5, 0.5, 0.4],
[0.0, 0.0, 0.8],
[0.5, 0.5, 0.8],
]
)
assert np.allclose(correct_pos, al001.get_scaled_positions())
def crystal(symbols=None, basis=None, spacegroup=1, setting=1,
cell=None, cellpar=None,
ab_normal=(0,0,1), a_direction=None, size=(1,1,1),
ondublicates='warn', symprec=0.001,
pbc=True, primitive_cell=False, **kwargs):
"""Create an Atoms instance for a conventional unit cell of a
space group.
Parameters:
symbols : str | sequence of str | sequence of Atom | Atoms
Element symbols of the unique sites. Can either be a string
formula or a sequence of element symbols. E.g. ('Na', 'Cl')
and 'NaCl' are equivalent. Can also be given as a sequence of
Atom objects or an Atoms object.
basis : list of scaled coordinates
Positions of the unique sites corresponding to symbols given
either as scaled positions or through an atoms instance. Not
needed if *symbols* is a sequence of Atom objects or an Atoms
object.
spacegroup : int | string | Spacegroup instance
Space group given either as its number in International Tables
or as its Hermann-Mauguin symbol.
setting : 1 | 2
Space group setting.
cell : 3x3 matrix
Unit cell vectors.
cellpar : [a, b, c, alpha, beta, gamma]
Cell parameters with angles in degree. Is not used when `cell`
is given.
ab_normal : vector
Is used to define the orientation of the unit cell relative
to the Cartesian system when `cell` is not given. It is the
normal vector of the plane spanned by a and b.
a_direction : vector
Defines the orientation of the unit cell a vector. a will be
parallel to the projection of `a_direction` onto the a-b plane.
size : 3 positive integers
How many times the conventional unit cell should be repeated
in each direction.
ondublicates : 'keep' | 'replace' | 'warn' | 'error'
Action if `basis` contain symmetry-equivalent positions:
'keep' - ignore additional symmetry-equivalent positions
'replace' - replace
'warn' - like 'keep', but issue an UserWarning
'error' - raises a SpacegroupValueError
symprec : float
Minimum "distance" betweed two sites in scaled coordinates
before they are counted as the same site.
pbc : one or three bools
Periodic boundary conditions flags. Examples: True,
False, 0, 1, (1, 1, 0), (True, False, False). Default
is True.
primitive_cell : bool
Wheter to return the primitive instead of the conventional
unit cell.
Keyword arguments:
All additional keyword arguments are passed on to the Atoms
constructor. Currently, probably the most useful additional
keyword arguments are `info`, `constraint` and `calculator`.
Examples:
Two diamond unit cells (space group number 227)
>>> diamond = crystal('C', [(0,0,0)], spacegroup=227,
... cellpar=[3.57, 3.57, 3.57, 90, 90, 90], size=(2,1,1))
>>> ase.view(diamond) # doctest: +SKIP
A CoSb3 skutterudite unit cell containing 32 atoms
>>> skutterudite = crystal(('Co', 'Sb'),
... basis=[(0.25,0.25,0.25), (0.0, 0.335, 0.158)],
... spacegroup=204, cellpar=[9.04, 9.04, 9.04, 90, 90, 90])
>>> len(skutterudite)
32
"""
sg = Spacegroup(spacegroup, setting)
if (not isinstance(symbols, str) and
hasattr(symbols, '__getitem__') and
len(symbols) > 0 and
isinstance(symbols[0], ase.Atom)):
symbols = ase.Atoms(symbols)
if isinstance(symbols, ase.Atoms):
basis = symbols
symbols = basis.get_chemical_symbols()
if isinstance(basis, ase.Atoms):
basis_coords = basis.get_scaled_positions()
if cell is None and cellpar is None:
cell = basis.cell
if symbols is None:
symbols = basis.get_chemical_symbols()
else:
basis_coords = np.array(basis, dtype=float, copy=False, ndmin=2)
sites, kinds = sg.equivalent_sites(basis_coords,
ondublicates=ondublicates,
symprec=symprec)
symbols = parse_symbols(symbols)
symbols = [symbols[i] for i in kinds]
if cell is None:
cell = cellpar_to_cell(cellpar, ab_normal, a_direction)
info = dict(spacegroup=sg)
if primitive_cell:
info['unit_cell'] = 'primitive'
else:
info['unit_cell'] = 'conventional'
if 'info' in kwargs:
info.update(kwargs['info'])
kwargs['info'] = info
atoms = ase.Atoms(symbols,
scaled_positions=sites,
cell=cell,
pbc=pbc,
**kwargs)
if isinstance(basis, ase.Atoms):
for name in basis.arrays:
if not atoms.has(name):
array = basis.get_array(name)
atoms.new_array(name, [array[i] for i in kinds],
dtype=array.dtype, shape=array.shape[1:])
if primitive_cell:
from ase.utils.geometry import cut
prim_cell = sg.scaled_primitive_cell
atoms = cut(atoms, a=prim_cell[0], b=prim_cell[1], c=prim_cell[2])
if size != (1, 1, 1):
atoms = atoms.repeat(size)
return atoms
def cut111(crystal,nlayers=6):
"""Cleave the 111 surface"""
crystal111 = cut(crystal,[1,0,1],[1,1,0],nlayers=nlayers)
return crystal111
def cut001(crystal,nlayers=6):
"""Cleave the 001 surface"""
crystal001 = cut(crystal,[0,1,0],[0,0,1],nlayers=nlayers)
return crystal001
def cut010(crystal,nlayers=6):
"""Cleave the 010 surface"""
crystal010 = cut(crystal,[1,0,0],[0,0,1],nlayers=nlayers)
return crystal010
def cut100(crystal,nlayers=6):
"""Cleave the 100 surface"""
crystal100 = cut(crystal,[0,0,1],[0,1,0],nlayers=nlayers)
return crystal100
def crystal(symbols=None,
basis=None,
spacegroup=1,
setting=1,
cell=None,
cellpar=None,
ab_normal=(0, 0, 1),
a_direction=None,
size=(1, 1, 1),
ondublicates='warn',
symprec=0.001,
pbc=True,
primitive_cell=False,
**kwargs):
"""Create an Atoms instance for a conventional unit cell of a
space group.
Parameters:
symbols : str | sequence of str | sequence of Atom | Atoms
Element symbols of the unique sites. Can either be a string
formula or a sequence of element symbols. E.g. ('Na', 'Cl')
and 'NaCl' are equivalent. Can also be given as a sequence of
Atom objects or an Atoms object.
basis : list of scaled coordinates
Positions of the unique sites corresponding to symbols given
either as scaled positions or through an atoms instance. Not
needed if *symbols* is a sequence of Atom objects or an Atoms
object.
spacegroup : int | string | Spacegroup instance
Space group given either as its number in International Tables
or as its Hermann-Mauguin symbol.
setting : 1 | 2
Space group setting.
cell : 3x3 matrix
Unit cell vectors.
cellpar : [a, b, c, alpha, beta, gamma]
Cell parameters with angles in degree. Is not used when `cell`
is given.
ab_normal : vector
Is used to define the orientation of the unit cell relative
to the Cartesian system when `cell` is not given. It is the
normal vector of the plane spanned by a and b.
a_direction : vector
Defines the orientation of the unit cell a vector. a will be
parallel to the projection of `a_direction` onto the a-b plane.
size : 3 positive integers
How many times the conventional unit cell should be repeated
in each direction.
ondublicates : 'keep' | 'replace' | 'warn' | 'error'
Action if `basis` contain symmetry-equivalent positions:
'keep' - ignore additional symmetry-equivalent positions
'replace' - replace
'warn' - like 'keep', but issue an UserWarning
'error' - raises a SpacegroupValueError
symprec : float
Minimum "distance" betweed two sites in scaled coordinates
before they are counted as the same site.
pbc : one or three bools
Periodic boundary conditions flags. Examples: True,
False, 0, 1, (1, 1, 0), (True, False, False). Default
is True.
primitive_cell : bool
Wheter to return the primitive instead of the conventional
unit cell.
Keyword arguments:
All additional keyword arguments are passed on to the Atoms
constructor. Currently, probably the most useful additional
keyword arguments are `info`, `constraint` and `calculator`.
Examples:
Two diamond unit cells (space group number 227)
>>> diamond = crystal('C', [(0,0,0)], spacegroup=227,
... cellpar=[3.57, 3.57, 3.57, 90, 90, 90], size=(2,1,1))
>>> ase.view(diamond) # doctest: +SKIP
A CoSb3 skutterudite unit cell containing 32 atoms
>>> skutterudite = crystal(('Co', 'Sb'),
... basis=[(0.25,0.25,0.25), (0.0, 0.335, 0.158)],
... spacegroup=204, cellpar=[9.04, 9.04, 9.04, 90, 90, 90])
>>> len(skutterudite)
32
"""
sg = Spacegroup(spacegroup, setting)
if (not isinstance(symbols, str) and hasattr(symbols, '__getitem__')
and len(symbols) > 0 and isinstance(symbols[0], ase.Atom)):
symbols = ase.Atoms(symbols)
if isinstance(symbols, ase.Atoms):
basis = symbols
symbols = basis.get_chemical_symbols()
if isinstance(basis, ase.Atoms):
basis_coords = basis.get_scaled_positions()
if cell is None and cellpar is None:
cell = basis.cell
if symbols is None:
symbols = basis.get_chemical_symbols()
else:
basis_coords = np.array(basis, dtype=float, copy=False, ndmin=2)
sites, kinds = sg.equivalent_sites(basis_coords,
ondublicates=ondublicates,
symprec=symprec)
symbols = parse_symbols(symbols)
symbols = [symbols[i] for i in kinds]
if cell is None:
cell = cellpar_to_cell(cellpar, ab_normal, a_direction)
info = dict(spacegroup=sg)
if primitive_cell:
info['unit_cell'] = 'primitive'
else:
info['unit_cell'] = 'conventional'
if 'info' in kwargs:
info.update(kwargs['info'])
kwargs['info'] = info
atoms = ase.Atoms(symbols,
scaled_positions=sites,
cell=cell,
pbc=pbc,
**kwargs)
if isinstance(basis, ase.Atoms):
for name in basis.arrays:
if not atoms.has(name):
array = basis.get_array(name)
atoms.new_array(name, [array[i] for i in kinds],
dtype=array.dtype,
shape=array.shape[1:])
if primitive_cell:
from ase.utils.geometry import cut
prim_cell = sg.scaled_primitive_cell
atoms = cut(atoms, a=prim_cell[0], b=prim_cell[1], c=prim_cell[2])
if size != (1, 1, 1):
atoms = atoms.repeat(size)
return atoms
import numpy as np
import ase.utils.geometry as geometry
import ase.io as io
# Create a new atoms instance with Co at origo including all atoms on the
# surface of the unit cell
cosb3 = geometry.cut(skutterudite, origo=(0.25, 0.25, 0.25), extend=1.01)
# Define the atomic bonds to show
bondatoms = []
symbols = cosb3.get_chemical_symbols()
for i in xrange(len(cosb3)):
for j in xrange(i):
if (symbols[i] == symbols[j] == 'Co' and
cosb3.get_distance(i, j) < 4.53):
bondatoms.append((i, j))
elif (symbols[i] == symbols[j] == 'Sb' and
cosb3.get_distance(i, j) < 2.99):
bondatoms.append((i, j))
# Create nice-looking image using povray
io.write('spacegroup-cosb3.pov', cosb3,
transparent=False,
display=False,
run_povray=True,
camera_type='perspective',
canvas_width=320,
radii=0.4,
rotation='90y',
bondlinewidth=0.07,
bondatoms=bondatoms,