# Source code for pymatgen.core.surface

```
# coding: utf-8
# Copyright (c) Pymatgen Development Team.
# Distributed under the terms of the MIT License.
"""
This module implements representations of slabs and surfaces, as well as
algorithms for generating them. If you use this module, please consider
citing the following work::
R. Tran, Z. Xu, B. Radhakrishnan, D. Winston, W. Sun, K. A. Persson,
S. P. Ong, "Surface Energies of Elemental Crystals", Scientific Data,
2016, 3:160080, doi: 10.1038/sdata.2016.80.
as well as::
Sun, W.; Ceder, G. Efficient creation and convergence of surface slabs,
Surface Science, 2013, 617, 53–59, doi:10.1016/j.susc.2013.05.016.
"""
from functools import reduce
from math import gcd
import math
import itertools
import logging
import warnings
import copy
import os
import json
import numpy as np
from scipy.spatial.distance import squareform
from scipy.cluster.hierarchy import linkage, fcluster
from monty.fractions import lcm
from pymatgen.core.periodic_table import get_el_sp
from pymatgen.core.structure import Structure
from pymatgen.core.lattice import Lattice
from pymatgen.core.sites import PeriodicSite
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
from pymatgen.util.coord import in_coord_list
from pymatgen.analysis.structure_matcher import StructureMatcher
__author__ = "Richard Tran, Wenhao Sun, Zihan Xu, Shyue Ping Ong"
__copyright__ = "Copyright 2014, The Materials Virtual Lab"
__version__ = "0.1"
__maintainer__ = "Shyue Ping Ong"
__email__ = "ongsp@ucsd.edu"
__date__ = "6/10/14"
logger = logging.getLogger(__name__)
[docs]class Slab(Structure):
"""
Subclass of Structure representing a Slab. Implements additional
attributes pertaining to slabs, but the init method does not
actually implement any algorithm that creates a slab. This is a
DUMMY class who's init method only holds information about the
slab. Also has additional methods that returns other information
about a slab such as the surface area, normal, and atom adsorption.
Note that all Slabs have the surface normal oriented perpendicular to the a
and b lattice vectors. This means the lattice vectors a and b are in the
surface plane and the c vector is out of the surface plane (though not
necessarily perpendicular to the surface).
.. attribute:: miller_index
Miller index of plane parallel to surface.
.. attribute:: scale_factor
Final computed scale factor that brings the parent cell to the
surface cell.
.. attribute:: shift
The shift value in Angstrom that indicates how much this
slab has been shifted.
"""
def __init__(self, lattice, species, coords, miller_index,
oriented_unit_cell, shift, scale_factor, reorient_lattice=True,
validate_proximity=False, to_unit_cell=False,
reconstruction=None, coords_are_cartesian=False,
site_properties=None, energy=None):
"""
Makes a Slab structure, a structure object with additional information
and methods pertaining to slabs.
Args:
lattice (Lattice/3x3 array): The lattice, either as a
:class:`pymatgen.core.lattice.Lattice` or
simply as any 2D array. Each row should correspond to a lattice
vector. E.g., [[10,0,0], [20,10,0], [0,0,30]] specifies a
lattice with lattice vectors [10,0,0], [20,10,0] and [0,0,30].
species ([Specie]): Sequence of species on each site. Can take in
flexible input, including:
i. A sequence of element / specie specified either as string
symbols, e.g. ["Li", "Fe2+", "P", ...] or atomic numbers,
e.g., (3, 56, ...) or actual Element or Specie objects.
ii. List of dict of elements/species and occupancies, e.g.,
[{"Fe" : 0.5, "Mn":0.5}, ...]. This allows the setup of
disordered structures.
coords (Nx3 array): list of fractional/cartesian coordinates of
each species.
miller_index ([h, k, l]): Miller index of plane parallel to
surface. Note that this is referenced to the input structure. If
you need this to be based on the conventional cell,
you should supply the conventional structure.
oriented_unit_cell (Structure): The oriented_unit_cell from which
this Slab is created (by scaling in the c-direction).
shift (float): The shift in the c-direction applied to get the
termination.
scale_factor (array): scale_factor Final computed scale factor
that brings the parent cell to the surface cell.
reorient_lattice (bool): reorients the lattice parameters such that
the c direction is the third vector of the lattice matrix
validate_proximity (bool): Whether to check if there are sites
that are less than 0.01 Ang apart. Defaults to False.
reconstruction (str): Type of reconstruction. Defaultst to None if
the slab is not reconstructed.
coords_are_cartesian (bool): Set to True if you are providing
coordinates in cartesian coordinates. Defaults to False.
site_properties (dict): Properties associated with the sites as a
dict of sequences, e.g., {"magmom":[5,5,5,5]}. The sequences
have to be the same length as the atomic species and
fractional_coords. Defaults to None for no properties.
energy (float): A value for the energy.
"""
self.oriented_unit_cell = oriented_unit_cell
self.miller_index = tuple(miller_index)
self.shift = shift
self.reconstruction = reconstruction
self.scale_factor = scale_factor
self.energy = energy
self.reorient_lattice = reorient_lattice
lattice = Lattice.from_parameters(lattice.a, lattice.b, lattice.c,
lattice.alpha, lattice.beta,
lattice.gamma) \
if self.reorient_lattice else lattice
super().__init__(
lattice, species, coords, validate_proximity=validate_proximity,
to_unit_cell=to_unit_cell,
coords_are_cartesian=coords_are_cartesian,
site_properties=site_properties)
[docs] def get_orthogonal_c_slab(self):
"""
This method returns a Slab where the normal (c lattice vector) is
"forced" to be exactly orthogonal to the surface a and b lattice
vectors. **Note that this breaks inherent symmetries in the slab.**
It should be pointed out that orthogonality is not required to get good
surface energies, but it can be useful in cases where the slabs are
subsequently used for postprocessing of some kind, e.g. generating
GBs or interfaces.
"""
a, b, c = self.lattice.matrix
new_c = np.cross(a, b)
new_c /= np.linalg.norm(new_c)
new_c = np.dot(c, new_c) * new_c
new_latt = Lattice([a, b, new_c])
return Slab(lattice=new_latt, species=self.species_and_occu,
coords=self.cart_coords, miller_index=self.miller_index,
oriented_unit_cell=self.oriented_unit_cell,
shift=self.shift, scale_factor=self.scale_factor,
coords_are_cartesian=True, energy=self.energy,
reorient_lattice=self.reorient_lattice,
site_properties=self.site_properties)
[docs] def get_tasker2_slabs(self, tol=0.01, same_species_only=True):
"""
Get a list of slabs that have been Tasker 2 corrected.
Args:
tol (float): Tolerance to determine if atoms are within same plane.
This is a fractional tolerance, not an absolute one.
same_species_only (bool): If True, only that are of the exact same
species as the atom at the outermost surface are considered for
moving. Otherwise, all atoms regardless of species that is
within tol are considered for moving. Default is True (usually
the desired behavior).
Returns:
([Slab]) List of tasker 2 corrected slabs.
"""
sites = list(self.sites)
slabs = []
sortedcsites = sorted(sites, key=lambda site: site.c)
# Determine what fraction the slab is of the total cell size in the
# c direction. Round to nearest rational number.
nlayers_total = int(round(self.lattice.c /
self.oriented_unit_cell.lattice.c))
nlayers_slab = int(round((sortedcsites[-1].c - sortedcsites[0].c)
* nlayers_total))
slab_ratio = nlayers_slab / nlayers_total
a = SpacegroupAnalyzer(self)
symm_structure = a.get_symmetrized_structure()
def equi_index(site):
for i, equi_sites in enumerate(symm_structure.equivalent_sites):
if site in equi_sites:
return i
raise ValueError("Cannot determine equi index!")
for surface_site, shift in [(sortedcsites[0], slab_ratio),
(sortedcsites[-1], -slab_ratio)]:
tomove = []
fixed = []
for site in sites:
if abs(site.c - surface_site.c) < tol and (
(not same_species_only) or
site.species == surface_site.species):
tomove.append(site)
else:
fixed.append(site)
# Sort and group the sites by the species and symmetry equivalence
tomove = sorted(tomove, key=lambda s: equi_index(s))
grouped = [list(sites) for k, sites in itertools.groupby(
tomove, key=lambda s: equi_index(s))]
if len(tomove) == 0 or any([len(g) % 2 != 0 for g in grouped]):
warnings.warn("Odd number of sites to divide! Try changing "
"the tolerance to ensure even division of "
"sites or create supercells in a or b directions "
"to allow for atoms to be moved!")
continue
combinations = []
for g in grouped:
combinations.append(
[c for c in itertools.combinations(g, int(len(g) / 2))])
for selection in itertools.product(*combinations):
species = [site.species for site in fixed]
fcoords = [site.frac_coords for site in fixed]
for s in tomove:
species.append(s.species)
for group in selection:
if s in group:
fcoords.append(s.frac_coords)
break
else:
# Move unselected atom to the opposite surface.
fcoords.append(s.frac_coords + [0, 0, shift])
# sort by species to put all similar species together.
sp_fcoord = sorted(zip(species, fcoords), key=lambda x: x[0])
species = [x[0] for x in sp_fcoord]
fcoords = [x[1] for x in sp_fcoord]
slab = Slab(self.lattice, species, fcoords, self.miller_index,
self.oriented_unit_cell, self.shift,
self.scale_factor, energy=self.energy,
reorient_lattice=self.reorient_lattice)
slabs.append(slab)
s = StructureMatcher()
unique = [ss[0] for ss in s.group_structures(slabs)]
return unique
[docs] def is_symmetric(self, symprec=0.1):
"""
Checks if slab is symmetric, i.e., contains inversion symmetry.
Args:
symprec (float): Symmetry precision used for SpaceGroup analyzer.
Returns:
(bool) Whether slab contains inversion symmetry.
"""
sg = SpacegroupAnalyzer(self, symprec=symprec)
return sg.is_laue()
[docs] def get_sorted_structure(self, key=None, reverse=False):
"""
Get a sorted copy of the structure. The parameters have the same
meaning as in list.sort. By default, sites are sorted by the
electronegativity of the species. Note that Slab has to override this
because of the different __init__ args.
Args:
key: Specifies a function of one argument that is used to extract
a comparison key from each list element: key=str.lower. The
default value is None (compare the elements directly).
reverse (bool): If set to True, then the list elements are sorted
as if each comparison were reversed.
"""
sites = sorted(self, key=key, reverse=reverse)
s = Structure.from_sites(sites)
return Slab(s.lattice, s.species_and_occu, s.frac_coords,
self.miller_index, self.oriented_unit_cell, self.shift,
self.scale_factor, site_properties=s.site_properties,
reorient_lattice=self.reorient_lattice)
[docs] def copy(self, site_properties=None, sanitize=False):
"""
Convenience method to get a copy of the structure, with options to add
site properties.
Args:
site_properties (dict): Properties to add or override. The
properties are specified in the same way as the constructor,
i.e., as a dict of the form {property: [values]}. The
properties should be in the order of the *original* structure
if you are performing sanitization.
sanitize (bool): If True, this method will return a sanitized
structure. Sanitization performs a few things: (i) The sites are
sorted by electronegativity, (ii) a LLL lattice reduction is
carried out to obtain a relatively orthogonalized cell,
(iii) all fractional coords for sites are mapped into the
unit cell.
Returns:
A copy of the Structure, with optionally new site_properties and
optionally sanitized.
"""
props = self.site_properties
if site_properties:
props.update(site_properties)
return Slab(self.lattice, self.species_and_occu, self.frac_coords,
self.miller_index, self.oriented_unit_cell, self.shift,
self.scale_factor, site_properties=props,
reorient_lattice=self.reorient_lattice)
@property
def dipole(self):
"""
Calculates the dipole of the Slab in the direction of the surface
normal. Note that the Slab must be oxidation state-decorated for this
to work properly. Otherwise, the Slab will always have a dipole of 0.
"""
dipole = np.zeros(3)
mid_pt = np.sum(self.cart_coords, axis=0) / len(self)
normal = self.normal
for site in self:
charge = sum([getattr(sp, "oxi_state", 0) * amt
for sp, amt in site.species.items()])
dipole += charge * np.dot(site.coords - mid_pt, normal) * normal
return dipole
[docs] def is_polar(self, tol_dipole_per_unit_area=1e-3):
"""
Checks whether the surface is polar by computing the dipole per unit
area. Note that the Slab must be oxidation state-decorated for this
to work properly. Otherwise, the Slab will always be non-polar.
Args:
tol_dipole_per_unit_area (float): A tolerance. If the dipole
magnitude per unit area is less than this value, the Slab is
considered non-polar. Defaults to 1e-3, which is usually
pretty good. Normalized dipole per unit area is used as it is
more reliable than using the total, which tends to be larger for
slabs with larger surface areas.
"""
dip_per_unit_area = self.dipole / self.surface_area
return np.linalg.norm(dip_per_unit_area) > tol_dipole_per_unit_area
@property
def normal(self):
"""
Calculates the surface normal vector of the slab
"""
normal = np.cross(self.lattice.matrix[0], self.lattice.matrix[1])
normal /= np.linalg.norm(normal)
return normal
@property
def surface_area(self):
"""
Calculates the surface area of the slab
"""
m = self.lattice.matrix
return np.linalg.norm(np.cross(m[0], m[1]))
@property
def center_of_mass(self):
"""
Calculates the center of mass of the slab
"""
weights = [s.species.weight for s in self]
center_of_mass = np.average(self.frac_coords,
weights=weights, axis=0)
return center_of_mass
[docs] def add_adsorbate_atom(self, indices, specie, distance):
"""
Gets the structure of single atom adsorption.
slab structure from the Slab class(in [0, 0, 1])
Args:
indices ([int]): Indices of sites on which to put the absorbate.
Absorbed atom will be displaced relative to the center of
these sites.
specie (Specie/Element/str): adsorbed atom species
distance (float): between centers of the adsorbed atom and the
given site in Angstroms.
"""
# Let's do the work in cartesian coords
center = np.sum([self[i].coords for i in indices], axis=0) / len(
indices)
coords = center + self.normal * distance / np.linalg.norm(self.normal)
self.append(specie, coords, coords_are_cartesian=True)
def __str__(self):
comp = self.composition
outs = [
"Slab Summary (%s)" % comp.formula,
"Reduced Formula: %s" % comp.reduced_formula,
"Miller index: %s" % (self.miller_index,),
"Shift: %.4f, Scale Factor: %s" % (self.shift,
self.scale_factor.__str__())]
def to_s(x):
return "%0.6f" % x
outs.append("abc : " + " ".join([to_s(i).rjust(10)
for i in self.lattice.abc]))
outs.append("angles: " + " ".join([to_s(i).rjust(10)
for i in self.lattice.angles]))
outs.append("Sites ({i})".format(i=len(self)))
for i, site in enumerate(self):
outs.append(" ".join([str(i + 1), site.species_string,
" ".join([to_s(j).rjust(12)
for j in site.frac_coords])]))
return "\n".join(outs)
[docs] def as_dict(self):
"""
:return: MSONAble dict
"""
d = super().as_dict()
d["@module"] = self.__class__.__module__
d["@class"] = self.__class__.__name__
d["oriented_unit_cell"] = self.oriented_unit_cell.as_dict()
d["miller_index"] = self.miller_index
d["shift"] = self.shift
d["scale_factor"] = self.scale_factor.tolist()
d["reconstruction"] = self.reconstruction
d["energy"] = self.energy
return d
[docs] @classmethod
def from_dict(cls, d):
"""
:param d: dict
:return: Creates slab from dict.
"""
lattice = Lattice.from_dict(d["lattice"])
sites = [PeriodicSite.from_dict(sd, lattice) for sd in d["sites"]]
s = Structure.from_sites(sites)
return Slab(
lattice=lattice,
species=s.species_and_occu, coords=s.frac_coords,
miller_index=d["miller_index"],
oriented_unit_cell=Structure.from_dict(d["oriented_unit_cell"]),
shift=d["shift"], scale_factor=d["scale_factor"],
site_properties=s.site_properties, energy=d["energy"]
)
[docs] def get_surface_sites(self, tag=False):
"""
Returns the surface sites and their indices in a dictionary. The
oriented unit cell of the slab will determine the coordination number
of a typical site. We use VoronoiNN to determine the
coordination number of bulk sites and slab sites. Due to the
pathological error resulting from some surface sites in the
VoronoiNN, we assume any site that has this error is a surface
site as well. This will work for elemental systems only for now. Useful
for analysis involving broken bonds and for finding adsorption sites.
Args:
tag (bool): Option to adds site attribute "is_surfsite" (bool)
to all sites of slab. Defaults to False
Returns:
A dictionary grouping sites on top and bottom of the slab
together.
{"top": [sites with indices], "bottom": [sites with indices}
TODO:
Is there a way to determine site equivalence between sites in a slab
and bulk system? This would allow us get the coordination number of
a specific site for multi-elemental systems or systems with more
than one unequivalent site. This will allow us to use this for
compound systems.
"""
from pymatgen.analysis.local_env import VoronoiNN
# Get a dictionary of coordination numbers
# for each distinct site in the structure
a = SpacegroupAnalyzer(self.oriented_unit_cell)
ucell = a.get_symmetrized_structure()
cn_dict = {}
v = VoronoiNN()
unique_indices = [equ[0] for equ in ucell.equivalent_indices]
for i in unique_indices:
el = ucell[i].species_string
if el not in cn_dict.keys():
cn_dict[el] = []
# Since this will get the cn as a result of the weighted polyhedra, the
# slightest difference in cn will indicate a different environment for a
# species, eg. bond distance of each neighbor or neighbor species. The
# decimal place to get some cn to be equal.
cn = v.get_cn(ucell, i, use_weights=True)
cn = float('%.5f' % (round(cn, 5)))
if cn not in cn_dict[el]:
cn_dict[el].append(cn)
v = VoronoiNN()
surf_sites_dict, properties = {"top": [], "bottom": []}, []
for i, site in enumerate(self):
# Determine if site is closer to the top or bottom of the slab
top = site.frac_coords[2] > self.center_of_mass[2]
try:
# A site is a surface site, if its environment does
# not fit the environment of other sites
cn = float('%.5f' % (round(v.get_cn(self, i, use_weights=True), 5)))
if cn < min(cn_dict[site.species_string]):
properties.append(True)
key = "top" if top else "bottom"
surf_sites_dict[key].append([site, i])
else:
properties.append(False)
except RuntimeError:
# or if pathological error is returned, indicating a surface site
properties.append(True)
key = "top" if top else "bottom"
surf_sites_dict[key].append([site, i])
if tag:
self.add_site_property("is_surf_site", properties)
return surf_sites_dict
[docs] def have_equivalent_surfaces(self):
"""
Check if we have same number of equivalent sites on both surfaces.
This is an alternative to checking Laue symmetry (is_symmetric())
if we want to ensure both surfaces in the slab are the same
"""
# tag the sites as either surface sites or not
self.get_surface_sites(tag=True)
a = SpacegroupAnalyzer(self)
symm_structure = a.get_symmetrized_structure()
# ensure each site on one surface has a
# corresponding equivalent site on the other
equal_surf_sites = []
for equ in symm_structure.equivalent_sites:
# Top and bottom are arbitrary, we will just determine
# if one site is on one side of the slab or the other
top, bottom = 0, 0
for s in equ:
if s.is_surf_site:
if s.frac_coords[2] > self.center_of_mass[2]:
top += 1
else:
bottom += 1
# Check to see if the number of equivalent sites
# on one side of the slab are equal to the other
equal_surf_sites.append(top == bottom)
return all(equal_surf_sites)
[docs] def get_symmetric_site(self, point, cartesian=False):
"""
This method uses symmetry operations to find equivalent sites on
both sides of the slab. Works mainly for slabs with Laue
symmetry. This is useful for retaining the non-polar and
symmetric properties of a slab when creating adsorbed
structures or symmetric reconstructions.
Arg:
point: Fractional coordinate.
Returns:
point: Fractional coordinate. A point equivalent to the
parameter point, but on the other side of the slab
"""
sg = SpacegroupAnalyzer(self)
ops = sg.get_symmetry_operations(cartesian=cartesian)
# Each operation on a point will return an equivalent point.
# We want to find the point on the other side of the slab.
for op in ops:
slab = self.copy()
site2 = op.operate(point)
if "%.6f" % (site2[2]) == "%.6f" % (point[2]):
continue
# Add dummy site to check the overall structure is symmetric
slab.append("O", point, coords_are_cartesian=cartesian)
slab.append("O", site2, coords_are_cartesian=cartesian)
sg = SpacegroupAnalyzer(slab)
if sg.is_laue():
break
else:
# If not symmetric, remove the two added
# sites and try another symmetry operator
slab.remove_sites([len(slab) - 1])
slab.remove_sites([len(slab) - 1])
return site2
[docs] def symmetrically_add_atom(self, specie, point, coords_are_cartesian=False):
"""
Class method for adding a site at a specified point in a slab.
Will add the corresponding site on the other side of the
slab to maintain equivalent surfaces.
Arg:
specie (str): The specie to add
point (coords): The coordinate of the site in the slab to add.
coords_are_cartesian (bool): Is the point in cartesian coordinates
Returns:
(Slab): The modified slab
"""
# For now just use the species of the
# surface atom as the element to add
# Get the index of the corresponding site at the bottom
point2 = self.get_symmetric_site(point, cartesian=coords_are_cartesian)
self.append(specie, point, coords_are_cartesian=coords_are_cartesian)
self.append(specie, point2, coords_are_cartesian=coords_are_cartesian)
[docs] def symmetrically_remove_atoms(self, indices):
"""
Class method for removing sites corresponding to a list of indices.
Will remove the corresponding site on the other side of the
slab to maintain equivalent surfaces.
Arg:
indices ([indices]): The indices of the sites
in the slab to remove.
"""
slabcopy = SpacegroupAnalyzer(self.copy()).get_symmetrized_structure()
points = [slabcopy[i].frac_coords for i in indices]
removal_list = []
for pt in points:
# Get the index of the original site on top
cart_point = slabcopy.lattice.get_cartesian_coords(pt)
dist = [site.distance_from_point(cart_point) for site in slabcopy]
site1 = dist.index(min(dist))
# Get the index of the corresponding site at the bottom
for i, eq_sites in enumerate(slabcopy.equivalent_sites):
if slabcopy[site1] in eq_sites:
eq_indices = slabcopy.equivalent_indices[i]
break
i1 = eq_indices[eq_sites.index(slabcopy[site1])]
for i2 in eq_indices:
if i2 == i1:
continue
if slabcopy[i2].frac_coords[2] == slabcopy[i1].frac_coords[2]:
continue
# Test site remove to see if it results in symmetric slab
s = self.copy()
s.remove_sites([i1, i2])
if s.is_symmetric():
removal_list.extend([i1, i2])
break
# If expected, 2 atoms are removed per index
if len(removal_list) == 2 * len(indices):
self.remove_sites(removal_list)
else:
warnings.warn("Equivalent sites could not be found for removal for all indices. Surface unchanged.")
[docs]class SlabGenerator:
"""
This class generates different slabs using shift values determined by where
a unique termination can be found along with other criterias such as where a
termination doesn't break a polyhedral bond. The shift value then indicates
where the slab layer will begin and terminate in the slab-vacuum system.
.. attribute:: oriented_unit_cell
A unit cell of the parent structure with the miller
index of plane parallel to surface
.. attribute:: parent
Parent structure from which Slab was derived.
.. attribute:: lll_reduce
Whether or not the slabs will be orthogonalized
.. attribute:: center_slab
Whether or not the slabs will be centered between
the vacuum layer
.. attribute:: slab_scale_factor
Final computed scale factor that brings the parent cell to the
surface cell.
.. attribute:: miller_index
Miller index of plane parallel to surface.
.. attribute:: min_slab_size
Minimum size in angstroms of layers containing atoms
.. attribute:: min_vac_size
Minimize size in angstroms of layers containing vacuum
"""
def __init__(self, initial_structure, miller_index, min_slab_size,
min_vacuum_size, lll_reduce=False, center_slab=False,
in_unit_planes=False, primitive=True, max_normal_search=None,
reorient_lattice=True):
"""
Calculates the slab scale factor and uses it to generate a unit cell
of the initial structure that has been oriented by its miller index.
Also stores the initial information needed later on to generate a slab.
Args:
initial_structure (Structure): Initial input structure. Note that to
ensure that the miller indices correspond to usual
crystallographic definitions, you should supply a conventional
unit cell structure.
miller_index ([h, k, l]): Miller index of plane parallel to
surface. Note that this is referenced to the input structure. If
you need this to be based on the conventional cell,
you should supply the conventional structure.
min_slab_size (float): In Angstroms or number of hkl planes
min_vacuum_size (float): In Angstroms or number of hkl planes
lll_reduce (bool): Whether to perform an LLL reduction on the
eventual structure.
center_slab (bool): Whether to center the slab in the cell with
equal vacuum spacing from the top and bottom.
in_unit_planes (bool): Whether to set min_slab_size and min_vac_size
in units of hkl planes (True) or Angstrom (False/default).
Setting in units of planes is useful for ensuring some slabs
have a certain nlayer of atoms. e.g. for Cs (100), a 10 Ang
slab will result in a slab with only 2 layer of atoms, whereas
Fe (100) will have more layer of atoms. By using units of hkl
planes instead, we ensure both slabs
have the same number of atoms. The slab thickness will be in
min_slab_size/math.ceil(self._proj_height/dhkl)
multiples of oriented unit cells.
primitive (bool): Whether to reduce any generated slabs to a
primitive cell (this does **not** mean the slab is generated
from a primitive cell, it simply means that after slab
generation, we attempt to find shorter lattice vectors,
which lead to less surface area and smaller cells).
max_normal_search (int): If set to a positive integer, the code will
conduct a search for a normal lattice vector that is as
perpendicular to the surface as possible by considering
multiples linear combinations of lattice vectors up to
max_normal_search. This has no bearing on surface energies,
but may be useful as a preliminary step to generating slabs
for absorption and other sizes. It is typical that this will
not be the smallest possible cell for simulation. Normality
is not guaranteed, but the oriented cell will have the c
vector as normal as possible (within the search range) to the
surface. A value of up to the max absolute Miller index is
usually sufficient.
reorient_lattice (bool): reorients the lattice parameters such that
the c direction is the third vector of the lattice matrix
"""
# Add Wyckoff symbols of the bulk, will help with
# identfying types of sites in the slab system
sg = SpacegroupAnalyzer(initial_structure)
initial_structure.add_site_property("bulk_wyckoff",
sg.get_symmetry_dataset()['wyckoffs'])
initial_structure.add_site_property("bulk_equivalent",
sg.get_symmetry_dataset()['equivalent_atoms'].tolist())
latt = initial_structure.lattice
miller_index = _reduce_vector(miller_index)
# Calculate the surface normal using the reciprocal lattice vector.
recp = latt.reciprocal_lattice_crystallographic
normal = recp.get_cartesian_coords(miller_index)
normal /= np.linalg.norm(normal)
slab_scale_factor = []
non_orth_ind = []
eye = np.eye(3, dtype=np.int)
for i, j in enumerate(miller_index):
if j == 0:
# Lattice vector is perpendicular to surface normal, i.e.,
# in plane of surface. We will simply choose this lattice
# vector as one of the basis vectors.
slab_scale_factor.append(eye[i])
else:
# Calculate projection of lattice vector onto surface normal.
d = abs(np.dot(normal, latt.matrix[i])) / latt.abc[i]
non_orth_ind.append((i, d))
# We want the vector that has maximum magnitude in the
# direction of the surface normal as the c-direction.
# Results in a more "orthogonal" unit cell.
c_index, dist = max(non_orth_ind, key=lambda t: t[1])
if len(non_orth_ind) > 1:
lcm_miller = lcm(*[miller_index[i] for i, d in non_orth_ind])
for (i, di), (j, dj) in itertools.combinations(non_orth_ind, 2):
l = [0, 0, 0]
l[i] = -int(round(lcm_miller / miller_index[i]))
l[j] = int(round(lcm_miller / miller_index[j]))
slab_scale_factor.append(l)
if len(slab_scale_factor) == 2:
break
if max_normal_search is None:
slab_scale_factor.append(eye[c_index])
else:
index_range = sorted(
reversed(range(-max_normal_search, max_normal_search + 1)),
key=lambda x: abs(x))
candidates = []
for uvw in itertools.product(index_range, index_range, index_range):
if (not any(uvw)) or abs(
np.linalg.det(slab_scale_factor + [uvw])) < 1e-8:
continue
vec = latt.get_cartesian_coords(uvw)
l = np.linalg.norm(vec)
cosine = abs(np.dot(vec, normal) / l)
candidates.append((uvw, cosine, l))
if abs(abs(cosine) - 1) < 1e-8:
# If cosine of 1 is found, no need to search further.
break
# We want the indices with the maximum absolute cosine,
# but smallest possible length.
uvw, cosine, l = max(candidates, key=lambda x: (x[1], -x[2]))
slab_scale_factor.append(uvw)
slab_scale_factor = np.array(slab_scale_factor)
# Let's make sure we have a left-handed crystallographic system
if np.linalg.det(slab_scale_factor) < 0:
slab_scale_factor *= -1
# Make sure the slab_scale_factor is reduced to avoid
# unnecessarily large slabs
reduced_scale_factor = [_reduce_vector(v) for v in slab_scale_factor]
slab_scale_factor = np.array(reduced_scale_factor)
single = initial_structure.copy()
single.make_supercell(slab_scale_factor)
# When getting the OUC, lets return the most reduced
# structure as possible to reduce calculations
self.oriented_unit_cell = Structure.from_sites(single,
to_unit_cell=True)
self.max_normal_search = max_normal_search
self.parent = initial_structure
self.lll_reduce = lll_reduce
self.center_slab = center_slab
self.slab_scale_factor = slab_scale_factor
self.miller_index = miller_index
self.min_vac_size = min_vacuum_size
self.min_slab_size = min_slab_size
self.in_unit_planes = in_unit_planes
self.primitive = primitive
self._normal = normal
a, b, c = self.oriented_unit_cell.lattice.matrix
self._proj_height = abs(np.dot(normal, c))
self.reorient_lattice = reorient_lattice
[docs] def get_slab(self, shift=0, tol=0.1, energy=None):
"""
This method takes in shift value for the c lattice direction and
generates a slab based on the given shift. You should rarely use this
method. Instead, it is used by other generation algorithms to obtain
all slabs.
Arg:
shift (float): A shift value in Angstrom that determines how much a
slab should be shifted.
tol (float): Tolerance to determine primitive cell.
energy (float): An energy to assign to the slab.
Returns:
(Slab) A Slab object with a particular shifted oriented unit cell.
"""
h = self._proj_height
p = round(h / self.parent.lattice.d_hkl(self.miller_index), 8)
if self.in_unit_planes:
nlayers_slab = int(math.ceil(self.min_slab_size / p))
nlayers_vac = int(math.ceil(self.min_vac_size / p))
else:
nlayers_slab = int(math.ceil(self.min_slab_size / h))
nlayers_vac = int(math.ceil(self.min_vac_size / h))
nlayers = nlayers_slab + nlayers_vac
species = self.oriented_unit_cell.species_and_occu
props = self.oriented_unit_cell.site_properties
props = {k: v * nlayers_slab for k, v in props.items()}
frac_coords = self.oriented_unit_cell.frac_coords
frac_coords = np.array(frac_coords) + np.array([0, 0, -shift])[None, :]
frac_coords -= np.floor(frac_coords)
a, b, c = self.oriented_unit_cell.lattice.matrix
new_lattice = [a, b, nlayers * c]
frac_coords[:, 2] = frac_coords[:, 2] / nlayers
all_coords = []
for i in range(nlayers_slab):
fcoords = frac_coords.copy()
fcoords[:, 2] += i / nlayers
all_coords.extend(fcoords)
slab = Structure(new_lattice, species * nlayers_slab, all_coords,
site_properties=props)
scale_factor = self.slab_scale_factor
# Whether or not to orthogonalize the structure
if self.lll_reduce:
lll_slab = slab.copy(sanitize=True)
mapping = lll_slab.lattice.find_mapping(slab.lattice)
scale_factor = np.dot(mapping[2], scale_factor)
slab = lll_slab
# Whether or not to center the slab layer around the vacuum
if self.center_slab:
avg_c = np.average([c[2] for c in slab.frac_coords])
slab.translate_sites(list(range(len(slab))), [0, 0, 0.5 - avg_c])
if self.primitive:
prim = slab.get_primitive_structure(tolerance=tol)
if energy is not None:
energy = prim.volume / slab.volume * energy
slab = prim
# Reorient the lattice to get the correct reduced cell
ouc = self.oriented_unit_cell.copy()
if self.primitive:
# find a reduced ouc
slab_l = slab.lattice
ouc = ouc.get_primitive_structure(constrain_latt={"a": slab_l.a, "b": slab_l.b,
"alpha": slab_l.alpha,
"beta": slab_l.beta,
"gamma": slab_l.gamma})
# Check this is the correct oriented unit cell
ouc = self.oriented_unit_cell if slab_l.a != ouc.lattice.a or slab_l.b != ouc.lattice.b else ouc
return Slab(slab.lattice, slab.species_and_occu,
slab.frac_coords, self.miller_index,
ouc, shift, scale_factor, energy=energy,
site_properties=slab.site_properties,
reorient_lattice=self.reorient_lattice)
def _calculate_possible_shifts(self, tol=0.1):
frac_coords = self.oriented_unit_cell.frac_coords
n = len(frac_coords)
if n == 1:
# Clustering does not work when there is only one data point.
shift = frac_coords[0][2] + 0.5
return [shift - math.floor(shift)]
# We cluster the sites according to the c coordinates. But we need to
# take into account PBC. Let's compute a fractional c-coordinate
# distance matrix that accounts for PBC.
dist_matrix = np.zeros((n, n))
h = self._proj_height
# Projection of c lattice vector in
# direction of surface normal.
for i, j in itertools.combinations(list(range(n)), 2):
if i != j:
cdist = frac_coords[i][2] - frac_coords[j][2]
cdist = abs(cdist - round(cdist)) * h
dist_matrix[i, j] = cdist
dist_matrix[j, i] = cdist
condensed_m = squareform(dist_matrix)
z = linkage(condensed_m)
clusters = fcluster(z, tol, criterion="distance")
# Generate dict of cluster# to c val - doesn't matter what the c is.
c_loc = {c: frac_coords[i][2] for i, c in enumerate(clusters)}
# Put all c into the unit cell.
possible_c = [c - math.floor(c) for c in sorted(c_loc.values())]
# Calculate the shifts
nshifts = len(possible_c)
shifts = []
for i in range(nshifts):
if i == nshifts - 1:
# There is an additional shift between the first and last c
# coordinate. But this needs special handling because of PBC.
shift = (possible_c[0] + 1 + possible_c[i]) * 0.5
if shift > 1:
shift -= 1
else:
shift = (possible_c[i] + possible_c[i + 1]) * 0.5
shifts.append(shift - math.floor(shift))
shifts = sorted(shifts)
return shifts
def _get_c_ranges(self, bonds):
c_ranges = set()
bonds = {(get_el_sp(s1), get_el_sp(s2)): dist for (s1, s2), dist in
bonds.items()}
for (sp1, sp2), bond_dist in bonds.items():
for site in self.oriented_unit_cell:
if sp1 in site.species:
for nn in self.oriented_unit_cell.get_neighbors(site, bond_dist):
if sp2 in nn.species:
c_range = tuple(sorted([site.frac_coords[2],
nn.frac_coords[2]]))
if c_range[1] > 1:
# Takes care of PBC when c coordinate of site
# goes beyond the upper boundary of the cell
c_ranges.add((c_range[0], 1))
c_ranges.add((0, c_range[1] - 1))
elif c_range[0] < 0:
# Takes care of PBC when c coordinate of site
# is below the lower boundary of the unit cell
c_ranges.add((0, c_range[1]))
c_ranges.add((c_range[0] + 1, 1))
elif c_range[0] != c_range[1]:
c_ranges.add(c_range)
return c_ranges
[docs] def get_slabs(self, bonds=None, ftol=0.1, tol=0.1, max_broken_bonds=0,
symmetrize=False, repair=False):
"""
This method returns a list of slabs that are generated using the list of
shift values from the method, _calculate_possible_shifts(). Before the
shifts are used to create the slabs however, if the user decides to take
into account whether or not a termination will break any polyhedral
structure (bonds is not None), this method will filter out any shift
values that do so.
Args:
bonds ({(specie1, specie2): max_bond_dist}: bonds are
specified as a dict of tuples: float of specie1, specie2
and the max bonding distance. For example, PO4 groups may be
defined as {("P", "O"): 3}.
tol (float): General tolerance paramter for getting primitive
cells and matching structures
ftol (float): Threshold parameter in fcluster in order to check
if two atoms are lying on the same plane. Default thresh set
to 0.1 Angstrom in the direction of the surface normal.
max_broken_bonds (int): Maximum number of allowable broken bonds
for the slab. Use this to limit # of slabs (some structures
may have a lot of slabs). Defaults to zero, which means no
defined bonds must be broken.
symmetrize (bool): Whether or not to ensure the surfaces of the
slabs are equivalent.
repair (bool): Whether to repair terminations with broken bonds
or just omit them. Set to False as repairing terminations can
lead to many possible slabs as oppose to just omitting them.
Returns:
([Slab]) List of all possible terminations of a particular surface.
Slabs are sorted by the # of bonds broken.
"""
c_ranges = set() if bonds is None else self._get_c_ranges(bonds)
slabs = []
for shift in self._calculate_possible_shifts(tol=ftol):
bonds_broken = 0
for r in c_ranges:
if r[0] <= shift <= r[1]:
bonds_broken += 1
slab = self.get_slab(shift, tol=tol, energy=bonds_broken)
if bonds_broken <= max_broken_bonds:
slabs.append(slab)
elif repair:
# If the number of broken bonds is exceeded,
# we repair the broken bonds on the slab
slabs.append(self.repair_broken_bonds(slab, bonds))
# Further filters out any surfaces made that might be the same
m = StructureMatcher(ltol=tol, stol=tol, primitive_cell=False,
scale=False)
new_slabs = []
for g in m.group_structures(slabs):
# For each unique termination, symmetrize the
# surfaces by removing sites from the bottom.
if symmetrize:
slabs = self.nonstoichiometric_symmetrized_slab(g[0])
new_slabs.extend(slabs)
else:
new_slabs.append(g[0])
match = StructureMatcher(ltol=tol, stol=tol, primitive_cell=False,
scale=False)
new_slabs = [g[0] for g in match.group_structures(new_slabs)]
return sorted(new_slabs, key=lambda s: s.energy)
[docs] def repair_broken_bonds(self, slab, bonds):
"""
This method will find undercoordinated atoms due to slab
cleaving specified by the bonds parameter and move them
to the other surface to make sure the bond is kept intact.
In a future release of surface.py, the ghost_sites will be
used to tell us how the repair bonds should look like.
Arg:
slab (structure): A structure object representing a slab.
bonds ({(specie1, specie2): max_bond_dist}: bonds are
specified as a dict of tuples: float of specie1, specie2
and the max bonding distance. For example, PO4 groups may be
defined as {("P", "O"): 3}.
Returns:
(Slab) A Slab object with a particular shifted oriented unit cell.
"""
for pair in bonds.keys():
blength = bonds[pair]
# First lets determine which element should be the
# reference (center element) to determine broken bonds.
# e.g. P for a PO4 bond. Find integer coordination
# numbers of the pair of elements wrt to each other
cn_dict = {}
for i, el in enumerate(pair):
cnlist = []
for site in self.oriented_unit_cell:
poly_coord = 0
if site.species_string == el:
for nn in self.oriented_unit_cell.get_neighbors(
site, blength):
if nn[0].species_string == pair[i - 1]:
poly_coord += 1
cnlist.append(poly_coord)
cn_dict[el] = cnlist
# We make the element with the higher coordination our reference
if max(cn_dict[pair[0]]) > max(cn_dict[pair[1]]):
element1, element2 = pair
else:
element2, element1 = pair
for i, site in enumerate(slab):
# Determine the coordination of our reference
if site.species_string == element1:
poly_coord = 0
for neighbor in slab.get_neighbors(site, blength):
poly_coord += 1 if neighbor.species_string == element2 else 0
# suppose we find an undercoordinated reference atom
if poly_coord not in cn_dict[element1]:
# We get the reference atom of the broken bonds
# (undercoordinated), move it to the other surface
slab = self.move_to_other_side(slab, [i])
# find its NNs with the corresponding
# species it should be coordinated with
neighbors = slab.get_neighbors(slab[i], blength,
include_index=True)
tomove = [nn[2] for nn in neighbors if
nn[0].species_string == element2]
tomove.append(i)
# and then move those NNs along with the central
# atom back to the other side of the slab again
slab = self.move_to_other_side(slab, tomove)
return slab
[docs] def move_to_other_side(self, init_slab, index_of_sites):
"""
This method will Move a set of sites to the
other side of the slab (opposite surface).
Arg:
init_slab (structure): A structure object representing a slab.
index_of_sites (list of ints): The list of indices representing
the sites we want to move to the other side.
Returns:
(Slab) A Slab object with a particular shifted oriented unit cell.
"""
slab = init_slab.copy()
# Determine what fraction the slab is of the total cell size
# in the c direction. Round to nearest rational number.
h = self._proj_height
p = h / self.parent.lattice.d_hkl(self.miller_index)
if self.in_unit_planes:
nlayers_slab = int(math.ceil(self.min_slab_size / p))
nlayers_vac = int(math.ceil(self.min_vac_size / p))
else:
nlayers_slab = int(math.ceil(self.min_slab_size / h))
nlayers_vac = int(math.ceil(self.min_vac_size / h))
nlayers = nlayers_slab + nlayers_vac
slab_ratio = nlayers_slab / nlayers
# Sort the index of sites based on which side they are on
top_site_index = [i for i in index_of_sites if
slab[i].frac_coords[2] > slab.center_of_mass[2]]
bottom_site_index = [i for i in index_of_sites if
slab[i].frac_coords[2] < slab.center_of_mass[2]]
# Translate sites to the opposite surfaces
slab.translate_sites(top_site_index, [0, 0, slab_ratio])
slab.translate_sites(bottom_site_index, [0, 0, -slab_ratio])
return Slab(init_slab.lattice, slab.species, slab.frac_coords,
init_slab.miller_index, init_slab.oriented_unit_cell,
init_slab.shift, init_slab.scale_factor,
energy=init_slab.energy)
[docs] def nonstoichiometric_symmetrized_slab(self, init_slab, tol=1e-3):
"""
This method checks whether or not the two surfaces of the slab are
equivalent. If the point group of the slab has an inversion symmetry (
ie. belong to one of the Laue groups), then it is assumed that the
surfaces should be equivalent. Otherwise, sites at the bottom of the
slab will be removed until the slab is symmetric. Note the removal of sites
can destroy the stoichiometry of the slab. For non-elemental
structures, the chemical potential will be needed to calculate surface energy.
Arg:
init_slab (Structure): A single slab structure
tol (float): Tolerance for SpaceGroupanalyzer.
Returns:
Slab (structure): A symmetrized Slab object.
"""
sg = SpacegroupAnalyzer(init_slab, symprec=tol)
if sg.is_laue():
return [init_slab]
nonstoich_slabs = []
# Build an equivalent surface slab for each of the different surfaces
for top in [True, False]:
asym = True
slab = init_slab.copy()
slab.energy = init_slab.energy
while asym:
# Keep removing sites from the bottom one by one until both
# surfaces are symmetric or the number of sites removed has
# exceeded 10 percent of the original slab
c_dir = [site[2] for i, site in enumerate(slab.frac_coords)]
if top:
slab.remove_sites([c_dir.index(max(c_dir))])
else:
slab.remove_sites([c_dir.index(min(c_dir))])
if len(slab) <= len(self.parent):
break
# Check if the altered surface is symmetric
sg = SpacegroupAnalyzer(slab, symprec=tol)
if sg.is_laue():
asym = False
nonstoich_slabs.append(slab)
if len(slab) <= len(self.parent):
warnings.warn("Too many sites removed, please use a larger slab "
"size.")
return nonstoich_slabs
module_dir = os.path.dirname(os.path.abspath(__file__))
with open(os.path.join(module_dir,
"reconstructions_archive.json")) as data_file:
reconstructions_archive = json.load(data_file)
[docs]class ReconstructionGenerator:
"""
This class takes in a pre-defined dictionary specifying the parameters
need to build a reconstructed slab such as the SlabGenerator parameters,
transformation matrix, sites to remove/add and slab/vacuum size. It will
then use the formatted instructions provided by the dictionary to build
the desired reconstructed slab from the initial structure.
.. attribute:: slabgen_params
Parameters for the SlabGenerator
.. trans_matrix::
A 3x3 transformation matrix to generate the reconstructed
slab. Only the a and b lattice vectors are actually
changed while the c vector remains the same. This
matrix is what the Wood's notation is based on.
.. reconstruction_json::
The full json or dictionary containing the instructions
for building the reconstructed slab
.. termination::
The index of the termination of the slab
TODO:
- Right now there is no way to specify what atom is being
added. In the future, use basis sets?
"""
def __init__(self, initial_structure, min_slab_size,
min_vacuum_size, reconstruction_name):
"""
Generates reconstructed slabs from a set of instructions
specified by a dictionary or json file.
Args:
initial_structure (Structure): Initial input structure. Note
that to ensure that the miller indices correspond to usual
crystallographic definitions, you should supply a conventional
unit cell structure.
min_slab_size (float): In Angstroms
min_vacuum_size (float): In Angstroms
reconstruction (str): Name of the dict containing the instructions
for building a reconstructed slab. The dictionary can contain
any item the creator deems relevant, however any instructions
archived in pymatgen for public use needs to contain the
following keys and items to ensure compatibility with the
ReconstructionGenerator:
"name" (str): A descriptive name for the type of
reconstruction. Typically the name will have the type
of structure the reconstruction is for, the Miller
index, and Wood's notation along with anything to
describe the reconstruction: e.g.:
"fcc_110_missing_row_1x2"
"description" (str): A longer description of your
reconstruction. This is to help future contributors who
want to add other types of reconstructions to the
archive on pymatgen to check if the reconstruction
already exists. Please read the descriptions carefully
before adding a new type of reconstruction to ensure it
is not in the archive yet.
"reference" (str): Optional reference to where the
reconstruction was taken from or first observed.
"spacegroup" (dict): e.g. {"symbol": "Fm-3m", "number": 225}
Indicates what kind of structure is this reconstruction.
"miller_index" ([h,k,l]): Miller index of your reconstruction
"Woods_notation" (str): For a reconstruction, the a and b
lattice may change to accomodate the symmetry of the
reconstruction. This notation indicates the change in
the vectors relative to the primitive (p) or
conventional (c) slab cell. E.g. p(2x1):
Wood, E. A. (1964). Vocabulary of surface
crystallography. Journal of Applied Physics, 35(4),
1306–1312.
"transformation_matrix" (numpy array): A 3x3 matrix to
transform the slab. Only the a and b lattice vectors
should change while the c vector remains the same.
"SlabGenerator_parameters" (dict): A dictionary containing
the parameters for the SlabGenerator class excluding the
miller_index, min_slab_size and min_vac_size as the
Miller index is already specified and the min_slab_size
and min_vac_size can be changed regardless of what type
of reconstruction is used. Having a consistent set of
SlabGenerator parameters allows for the instructions to
be reused to consistently build a reconstructed slab.
"points_to_remove" (list of coords): A list of sites to
remove where the first two indices are fraction (in a
and b) and the third index is in units of 1/d (in c).
"points_to_add" (list of frac_coords): A list of sites to add
where the first two indices are fraction (in a an b) and
the third index is in units of 1/d (in c).
"base_reconstruction" (dict): Option to base a reconstruction on
an existing reconstruction model also exists to easily build
the instructions without repeating previous work. E.g. the
alpha reconstruction of halites is based on the octopolar
reconstruction but with the topmost atom removed. The dictionary
for the alpha reconstruction would therefore contain the item
"reconstruction_base": "halite_111_octopolar_2x2", and
additional sites for "points_to_remove" and "points_to_add"
can be added to modify this reconstruction.
For "points_to_remove" and "points_to_add", the third index for
the c vector is in units of 1/d where d is the spacing
between atoms along hkl (the c vector) and is relative to
the topmost site in the unreconstructed slab. e.g. a point
of [0.5, 0.25, 1] corresponds to the 0.5 frac_coord of a,
0.25 frac_coord of b and a distance of 1 atomic layer above
the topmost site. [0.5, 0.25, -0.5] where the third index
corresponds to a point half a atomic layer below the topmost
site. [0.5, 0.25, 0] corresponds to a point in the same
position along c as the topmost site. This is done because
while the primitive units of a and b will remain constant,
the user can vary the length of the c direction by changing
the slab layer or the vacuum layer.
NOTE: THE DICTIONARY SHOULD ONLY CONTAIN "points_to_remove" AND
"points_to_add" FOR THE TOP SURFACE. THE ReconstructionGenerator
WILL MODIFY THE BOTTOM SURFACE ACCORDINGLY TO RETURN A SLAB WITH
EQUIVALENT SURFACES.
"""
if reconstruction_name not in reconstructions_archive.keys():
raise KeyError("The reconstruction_name entered (%s) does not exist in the "
"archive. Please select from one of the following reconstructions: %s "
"or add the appropriate dictionary to the archive file "
"reconstructions_archive.json." % (reconstruction_name,
list(reconstructions_archive.keys())))
# Get the instructions to build the reconstruction
# from the reconstruction_archive
recon_json = copy.deepcopy(reconstructions_archive[reconstruction_name])
new_points_to_add, new_points_to_remove = [], []
if "base_reconstruction" in recon_json.keys():
if "points_to_add" in recon_json.keys():
new_points_to_add = recon_json["points_to_add"]
if "points_to_remove" in recon_json.keys():
new_points_to_remove = recon_json["points_to_remove"]
# Build new instructions from a base reconstruction
recon_json = copy.deepcopy(reconstructions_archive[recon_json["base_reconstruction"]])
if "points_to_add" in recon_json.keys():
del recon_json["points_to_add"]
if "points_to_remove" in recon_json.keys():
del recon_json["points_to_remove"]
if new_points_to_add:
recon_json["points_to_add"] = new_points_to_add
if new_points_to_remove:
recon_json["points_to_remove"] = new_points_to_remove
slabgen_params = copy.deepcopy(recon_json["SlabGenerator_parameters"])
slabgen_params["initial_structure"] = initial_structure.copy()
slabgen_params["miller_index"] = recon_json["miller_index"]
slabgen_params["min_slab_size"] = min_slab_size
slabgen_params["min_vacuum_size"] = min_vacuum_size
self.slabgen_params = slabgen_params
self.trans_matrix = recon_json["transformation_matrix"]
self.reconstruction_json = recon_json
self.name = reconstruction_name
[docs] def build_slabs(self):
"""
Builds the reconstructed slab by:
(1) Obtaining the unreconstructed slab using the specified
parameters for the SlabGenerator.
(2) Applying the appropriate lattice transformation in the
a and b lattice vectors.
(3) Remove any specified sites from both surfaces.
(4) Add any specified sites to both surfaces.
Returns:
(Slab): The reconstructed slab.
"""
slabs = self.get_unreconstructed_slabs()
recon_slabs = []
for slab in slabs:
d = get_d(slab)
top_site = sorted(slab, key=lambda site: site.frac_coords[2])[-1].coords
# Remove any specified sites
if "points_to_remove" in self.reconstruction_json.keys():
pts_to_rm = copy.deepcopy(self.reconstruction_json["points_to_remove"])
for p in pts_to_rm:
p[2] = slab.lattice.get_fractional_coords([top_site[0], top_site[1],
top_site[2] + p[2] * d])[2]
cart_point = slab.lattice.get_cartesian_coords(p)
dist = [site.distance_from_point(cart_point) for site in slab]
site1 = dist.index(min(dist))
slab.symmetrically_remove_atoms([site1])
# Add any specified sites
if "points_to_add" in self.reconstruction_json.keys():
pts_to_add = copy.deepcopy(self.reconstruction_json["points_to_add"])
for p in pts_to_add:
p[2] = slab.lattice.get_fractional_coords([top_site[0], top_site[1],
top_site[2] + p[2] * d])[2]
slab.symmetrically_add_atom(slab[0].specie, p)
slab.reconstruction = self.name
setattr(slab, "recon_trans_matrix", self.trans_matrix)
# Get the oriented_unit_cell with the same axb area.
ouc = slab.oriented_unit_cell.copy()
ouc.make_supercell(self.trans_matrix)
slab.oriented_unit_cell = ouc
recon_slabs.append(slab)
return recon_slabs
[docs] def get_unreconstructed_slabs(self):
"""
Generates the unreconstructed or pristine super slab.
"""
slabs = []
for slab in SlabGenerator(**self.slabgen_params).get_slabs():
slab.make_supercell(self.trans_matrix)
slabs.append(slab)
return slabs
[docs]def get_d(slab):
"""
Determine the distance of space between
each layer of atoms along c
"""
sorted_sites = sorted(slab, key=lambda site: site.frac_coords[2])
for i, site in enumerate(sorted_sites):
if "%.6f" % (site.frac_coords[2]) == "%.6f" % (sorted_sites[i + 1].frac_coords[2]):
continue
else:
d = abs(site.frac_coords[2] - sorted_sites[i + 1].frac_coords[2])
break
return slab.lattice.get_cartesian_coords([0, 0, d])[2]
[docs]def is_already_analyzed(
miller_index: tuple, miller_list: list, symm_ops: list) -> bool:
"""
Helper function to check if a given Miller index is
part of the family of indices of any index in a list
Args:
miller_index (tuple): The Miller index to analyze
miller_list (list): List of Miller indices. If the given
Miller index belongs in the same family as any of the
indices in this list, return True, else return False
symm_ops (list): Symmetry operations of a
lattice, used to define family of indices
"""
for op in symm_ops:
if in_coord_list(miller_list, op.operate(miller_index)):
return True
return False
[docs]def get_symmetrically_equivalent_miller_indices(structure, miller_index, return_hkil=True):
"""
Returns all symmetrically equivalent indices for a given structure. Analysis
is based on the symmetry of the reciprocal lattice of the structure.
Args:
miller_index (tuple): Designates the family of Miller indices
to find. Can be hkl or hkil for hexagonal systems
return_hkil (bool): If true, return hkil form of Miller
index for hexagonal systems, otherwise return hkl
"""
# Change to hkl if hkil because in_coord_list only handles tuples of 3
miller_index = (miller_index[0], miller_index[1], miller_index[3]) \
if len(miller_index) == 4 else miller_index
mmi = max(np.abs(miller_index))
r = list(range(-mmi, mmi + 1))
r.reverse()
sg = SpacegroupAnalyzer(structure)
# Get distinct hkl planes from the rhombohedral setting if trigonal
if sg.get_crystal_system() == "trigonal":
prim_structure = SpacegroupAnalyzer(structure).get_primitive_standard_structure()
symm_ops = prim_structure.lattice.get_recp_symmetry_operation()
else:
symm_ops = structure.lattice.get_recp_symmetry_operation()
equivalent_millers = [miller_index]
for miller in itertools.product(r, r, r):
if miller == miller_index:
continue
if any([i != 0 for i in miller]):
if is_already_analyzed(miller, equivalent_millers, symm_ops):
equivalent_millers.append(miller)
# include larger Miller indices in the family of planes
if all([mmi > i for i in np.abs(miller)]) and \
not in_coord_list(equivalent_millers, miller):
if is_already_analyzed(mmi * np.array(miller),
equivalent_millers, symm_ops):
equivalent_millers.append(miller)
if return_hkil and sg.get_crystal_system() in ["trigonal", "hexagonal"]:
return [(hkl[0], hkl[1], -1 * hkl[0] - hkl[1],
hkl[2]) for hkl in equivalent_millers]
return equivalent_millers
[docs]def get_symmetrically_distinct_miller_indices(structure, max_index, return_hkil=False):
"""
Returns all symmetrically distinct indices below a certain max-index for
a given structure. Analysis is based on the symmetry of the reciprocal
lattice of the structure.
Args:
structure (Structure): input structure.
max_index (int): The maximum index. For example, a max_index of 1
means that (100), (110), and (111) are returned for the cubic
structure. All other indices are equivalent to one of these.
return_hkil (bool): If true, return hkil form of Miller
index for hexagonal systems, otherwise return hkl
"""
r = list(range(-max_index, max_index + 1))
r.reverse()
# First we get a list of all hkls for conventional (including equivalent)
conv_hkl_list = [miller for miller in itertools.product(r, r, r) if any([i != 0 for i in miller])]
sg = SpacegroupAnalyzer(structure)
# Get distinct hkl planes from the rhombohedral setting if trigonal
if sg.get_crystal_system() == "trigonal":
transf = sg.get_conventional_to_primitive_transformation_matrix()
miller_list = [hkl_transformation(transf, hkl) for hkl in conv_hkl_list]
prim_structure = SpacegroupAnalyzer(structure).get_primitive_standard_structure()
symm_ops = prim_structure.lattice.get_recp_symmetry_operation()
else:
miller_list = conv_hkl_list
symm_ops = structure.lattice.get_recp_symmetry_operation()
unique_millers, unique_millers_conv = [], []
for i, miller in enumerate(miller_list):
d = abs(reduce(gcd, miller))
miller = tuple([int(i / d) for i in miller])
if not is_already_analyzed(miller, unique_millers, symm_ops):
if sg.get_crystal_system() == "trigonal":
# Now we find the distinct primitive hkls using
# the primitive symmetry operations and their
# corresponding hkls in the conventional setting
unique_millers.append(miller)
d = abs(reduce(gcd, conv_hkl_list[i]))
cmiller = tuple([int(i / d) for i in conv_hkl_list[i]])
unique_millers_conv.append(cmiller)
else:
unique_millers.append(miller)
unique_millers_conv.append(miller)
if return_hkil and sg.get_crystal_system() in ["trigonal", "hexagonal"]:
return [(hkl[0], hkl[1], -1 * hkl[0] - hkl[1],
hkl[2]) for hkl in unique_millers_conv]
return unique_millers_conv
[docs]def hkl_transformation(transf, miller_index):
"""
Returns the Miller index from setting
A to B using a transformation matrix
Args:
transf (3x3 array): The transformation matrix
that transforms a lattice of A to B
miller_index ([h, k, l]): Miller index to transform to setting B
"""
# Get a matrix of whole numbers (ints)
def lcm(a, b):
return a * b // math.gcd(a, b)
reduced_transf = reduce(lcm, [int(1 / i) for i in itertools.chain(*transf) if i != 0]) * transf
reduced_transf = reduced_transf.astype(int)
# perform the transformation
t_hkl = np.dot(reduced_transf, miller_index)
d = abs(reduce(gcd, t_hkl))
t_hkl = np.array([int(i / d) for i in t_hkl])
# get mostly positive oriented Miller index
if len([i for i in t_hkl if i < 0]) > 1:
t_hkl *= -1
return tuple(t_hkl)
[docs]def generate_all_slabs(structure, max_index, min_slab_size, min_vacuum_size,
bonds=None, tol=0.1, ftol=0.1, max_broken_bonds=0,
lll_reduce=False, center_slab=False, primitive=True,
max_normal_search=None, symmetrize=False, repair=False,
include_reconstructions=False, in_unit_planes=False):
"""
A function that finds all different slabs up to a certain miller index.
Slabs oriented under certain Miller indices that are equivalent to other
slabs in other Miller indices are filtered out using symmetry operations
to get rid of any repetitive slabs. For example, under symmetry operations,
CsCl has equivalent slabs in the (0,0,1), (0,1,0), and (1,0,0) direction.
Args:
structure (Structure): Initial input structure. Note that to
ensure that the miller indices correspond to usual
crystallographic definitions, you should supply a conventional
unit cell structure.
max_index (int): The maximum Miller index to go up to.
min_slab_size (float): In Angstroms
min_vacuum_size (float): In Angstroms
bonds ({(specie1, specie2): max_bond_dist}: bonds are
specified as a dict of tuples: float of specie1, specie2
and the max bonding distance. For example, PO4 groups may be
defined as {("P", "O"): 3}.
tol (float): Threshold parameter in fcluster in order to check
if two atoms are lying on the same plane. Default thresh set
to 0.1 Angstrom in the direction of the surface normal.
max_broken_bonds (int): Maximum number of allowable broken bonds
for the slab. Use this to limit # of slabs (some structures
may have a lot of slabs). Defaults to zero, which means no
defined bonds must be broken.
lll_reduce (bool): Whether to perform an LLL reduction on the
eventual structure.
center_slab (bool): Whether to center the slab in the cell with
equal vacuum spacing from the top and bottom.
primitive (bool): Whether to reduce any generated slabs to a
primitive cell (this does **not** mean the slab is generated
from a primitive cell, it simply means that after slab
generation, we attempt to find shorter lattice vectors,
which lead to less surface area and smaller cells).
max_normal_search (int): If set to a positive integer, the code will
conduct a search for a normal lattice vector that is as
perpendicular to the surface as possible by considering
multiples linear combinations of lattice vectors up to
max_normal_search. This has no bearing on surface energies,
but may be useful as a preliminary step to generating slabs
for absorption and other sizes. It is typical that this will
not be the smallest possible cell for simulation. Normality
is not guaranteed, but the oriented cell will have the c
vector as normal as possible (within the search range) to the
surface. A value of up to the max absolute Miller index is
usually sufficient.
symmetrize (bool): Whether or not to ensure the surfaces of the
slabs are equivalent.
repair (bool): Whether to repair terminations with broken bonds
or just omit them
include_reconstructions (bool): Whether to include reconstructed
slabs available in the reconstructions_archive.json file.
"""
all_slabs = []
for miller in get_symmetrically_distinct_miller_indices(structure,
max_index):
gen = SlabGenerator(structure, miller, min_slab_size,
min_vacuum_size, lll_reduce=lll_reduce,
center_slab=center_slab, primitive=primitive,
max_normal_search=max_normal_search,
in_unit_planes=in_unit_planes)
slabs = gen.get_slabs(bonds=bonds, tol=tol, ftol=ftol, symmetrize=symmetrize,
max_broken_bonds=max_broken_bonds, repair=repair)
if len(slabs) > 0:
logger.debug("%s has %d slabs... " % (miller, len(slabs)))
all_slabs.extend(slabs)
if include_reconstructions:
sg = SpacegroupAnalyzer(structure)
symbol = sg.get_space_group_symbol()
# enumerate through all posisble reconstructions in the
# archive available for this particular structure (spacegroup)
for name, instructions in reconstructions_archive.items():
if "base_reconstruction" in instructions.keys():
instructions = reconstructions_archive[instructions["base_reconstruction"]]
if instructions["spacegroup"]["symbol"] == symbol:
# check if this reconstruction has a max index
# equal or less than the given max index
if max(instructions["miller_index"]) > max_index:
continue
recon = ReconstructionGenerator(structure, min_slab_size,
min_vacuum_size, name)
all_slabs.extend(recon.build_slabs())
return all_slabs
[docs]def get_slab_regions(slab, blength=3.5):
"""
Function to get the ranges of the slab regions. Useful for discerning where
the slab ends and vacuum begins if the slab is not fully within the cell
Args:
slab (Structure): Structure object modelling the surface
blength (float, Ang): The bondlength between atoms. You generally
want this value to be larger than the actual bondlengths in
order to find atoms that are part of the slab
"""
fcoords, indices, all_indices = [], [], []
for site in slab:
# find sites with c < 0 (noncontiguous)
neighbors = slab.get_neighbors(site, blength, include_index=True,
include_image=True)
for nn in neighbors:
if nn[0].frac_coords[2] < 0:
# sites are noncontiguous within cell
fcoords.append(nn[0].frac_coords[2])
indices.append(nn[-2])
if nn[-2] not in all_indices:
all_indices.append(nn[-2])
if fcoords:
# If slab is noncontiguous, locate the lowest
# site within the upper region of the slab
while fcoords:
last_fcoords = copy.copy(fcoords)
last_indices = copy.copy(indices)
site = slab[indices[fcoords.index(min(fcoords))]]
neighbors = slab.get_neighbors(site, blength, include_index=True,
include_image=True)
fcoords, indices = [], []
for nn in neighbors:
if 1 > nn[0].frac_coords[2] > 0 and \
nn[0].frac_coords[2] < site.frac_coords[2]:
# sites are noncontiguous within cell
fcoords.append(nn[0].frac_coords[2])
indices.append(nn[-2])
if nn[-2] not in all_indices:
all_indices.append(nn[-2])
# Now locate the highest site within the lower region of the slab
upper_fcoords = []
for site in slab:
if all([nn.index not in all_indices for nn in
slab.get_neighbors(site, blength)]):
upper_fcoords.append(site.frac_coords[2])
coords = copy.copy(last_fcoords) if not fcoords else copy.copy(fcoords)
min_top = slab[last_indices[coords.index(min(coords))]].frac_coords[2]
ranges = [[0, max(upper_fcoords)], [min_top, 1]]
else:
# If the entire slab region is within the slab cell, just
# set the range as the highest and lowest site in the slab
sorted_sites = sorted(slab, key=lambda site: site.frac_coords[2])
ranges = [[sorted_sites[0].frac_coords[2],
sorted_sites[-1].frac_coords[2]]]
return ranges
[docs]def miller_index_from_sites(lattice, coords, coords_are_cartesian=True,
round_dp=4, verbose=True):
"""
Get the Miller index of a plane from a list of site coordinates.
A minimum of 3 sets of coordinates are required. If more than 3 sets of
coordinates are given, the best plane that minimises the distance to all
points will be calculated.
Args:
lattice (list or Lattice): A 3x3 lattice matrix or `Lattice` object (for
example obtained from Structure.lattice).
coords (iterable): A list or numpy array of coordinates. Can be
cartesian or fractional coordinates. If more than three sets of
coordinates are provided, the best plane that minimises the
distance to all sites will be calculated.
coords_are_cartesian (bool, optional): Whether the coordinates are
in cartesian space. If using fractional coordinates set to False.
round_dp (int, optional): The number of decimal places to round the
miller index to.
verbose (bool, optional): Whether to print warnings.
Returns:
(tuple): The Miller index.
"""
if not isinstance(lattice, Lattice):
lattice = Lattice(lattice)
return lattice.get_miller_index_from_coords(
coords, coords_are_cartesian=coords_are_cartesian, round_dp=round_dp,
verbose=verbose)
[docs]def center_slab(slab):
"""
The goal here is to ensure the center of the slab region
is centered close to c=0.5. This makes it easier to
find the surface sites and apply operations like doping.
There are three cases where the slab in not centered:
1. The slab region is completely between two vacuums in the
box but not necessarily centered. We simply shift the
slab by the difference in its center of mass and 0.5
along the c direction.
2. The slab completely spills outside the box from the bottom
and into the top. This makes it incredibly difficult to
locate surface sites. We iterate through all sites that
spill over (z>c) and shift all sites such that this specific
site is now on the other side. Repeat for all sites with z>c.
3. This is a simpler case of scenario 2. Either the top or bottom
slab sites are at c=0 or c=1. Treat as scenario 2.
Args:
slab (Slab): Slab structure to center
Returns:
Returns a centered slab structure
"""
# get a reasonable r cutoff to sample neighbors
bdists = sorted([nn[1] for nn in
slab.get_neighbors(slab[0], 10) if nn[1] > 0])
r = bdists[0] * 3
all_indices = [i for i, site in enumerate(slab)]
# check if structure is case 2 or 3, shift all the
# sites up to the other side until it is case 1
for site in slab:
if any([nn[1] > slab.lattice.c for nn
in slab.get_neighbors(site, r)]):
shift = 1 - site.frac_coords[2] + 0.05
slab.translate_sites(all_indices, [0, 0, shift])
# now the slab is case 1, shift the center of mass of the slab to 0.5
weights = [s.species.weight for s in slab]
center_of_mass = np.average(slab.frac_coords,
weights=weights, axis=0)
shift = 0.5 - center_of_mass[2]
slab.translate_sites(all_indices, [0, 0, shift])
return slab
def _reduce_vector(vector):
# small function to reduce vectors
d = abs(reduce(gcd, vector))
vector = tuple([int(i / d) for i in vector])
return vector
```