pymatgen.analysis.adsorption — pymatgen 2020.7.3 documentation

# Source code for pymatgen.analysis.adsorption

    # coding: utf-8
    # Copyright (c) Pymatgen Development Team.
    # Distributed under the terms of the MIT License.

    """
    This module provides classes used to enumerate surface sites
    and to find adsorption sites on slabs
    """

    import numpy as np
    from pymatgen import Structure, vis
    import itertools
    import os
    from monty.serialization import loadfn
    from scipy.spatial import Delaunay

    from pymatgen.core.operations import SymmOp
    from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
    from pymatgen.util.coord import in_coord_list_pbc
    from pymatgen.analysis.local_env import VoronoiNN
    from pymatgen.core.surface import generate_all_slabs
    from pymatgen.analysis.structure_matcher import StructureMatcher

    from matplotlib import patches
    from matplotlib.path import Path

    __author__ = "Joseph Montoya"
    __copyright__ = "Copyright 2016, The Materials Project"
    __version__ = "0.1"
    __maintainer__ = "Joseph Montoya"
    __credits__ = "Richard Tran"
    __email__ = "montoyjh@lbl.gov"
    __status__ = "Development"
    __date__ = "December 2, 2015"

    class AdsorbateSiteFinder:
        """
        This class finds adsorbate sites on slabs and generates
        adsorbate structures according to user-defined criteria.
        The algorithm for finding sites is essentially as follows:
            1. Determine "surface sites" by finding those within
                a height threshold along the miller index of the
                highest site
            2. Create a network of surface sites using the Delaunay
                triangulation of the surface sites
            3. Assign on-top, bridge, and hollow adsorption sites
                at the nodes, edges, and face centers of the Del.
                Triangulation
            4. Generate structures from a molecule positioned at
                these sites
        """

        def __init__(self, slab, selective_dynamics=False,
                     height=0.9, mi_vec=None):
            """
            Create an AdsorbateSiteFinder object.

            Args:
                slab (Slab): slab object for which to find adsorbate sites
                selective_dynamics (bool): flag for whether to assign
                    non-surface sites as fixed for selective dynamics
                height (float): height criteria for selection of surface sites
                mi_vec (3-D array-like): vector corresponding to the vector
                    concurrent with the miller index, this enables use with
                    slabs that have been reoriented, but the miller vector
                    must be supplied manually

            """
            # get surface normal from miller index
            if mi_vec:
                self.mvec = mi_vec
            else:
                self.mvec = get_mi_vec(slab)
            slab = self.assign_site_properties(slab, height)
            if selective_dynamics:
                slab = self.assign_selective_dynamics(slab)
            self.slab = slab

        @classmethod
        def from_bulk_and_miller(cls, structure, miller_index, min_slab_size=8.0,
                                 min_vacuum_size=10.0, max_normal_search=None,
                                 center_slab=True, selective_dynamics=False,
                                 undercoord_threshold=0.09):
            """
            This method constructs the adsorbate site finder from a bulk
            structure and a miller index, which allows the surface sites
            to be determined from the difference in bulk and slab coordination,
            as opposed to the height threshold.

            Args:
                structure (Structure): structure from which slab
                    input to the ASF is constructed
                miller_index (3-tuple or list): miller index to be used
                min_slab_size (float): min slab size for slab generation
                min_vacuum_size (float): min vacuum size for slab generation
                max_normal_search (int): max normal search for slab generation
                center_slab (bool): whether to center slab in slab generation
                selective dynamics (bool): whether to assign surface sites
                    to selective dynamics
                undercoord_threshold (float): threshold of "undercoordation"
                    to use for the assignment of surface sites.  Default is
                    0.1, for which surface sites will be designated if they
                    are 10% less coordinated than their bulk counterpart
            """
            # TODO: for some reason this works poorly with primitive cells
            #       may want to switch the coordination algorithm eventually
            vnn_bulk = VoronoiNN(tol=0.05)
            bulk_coords = [len(vnn_bulk.get_nn(structure, n))
                           for n in range(len(structure))]
            struct = structure.copy(site_properties={'bulk_coordinations': bulk_coords})
            slabs = generate_all_slabs(struct, max_index=max(miller_index),
                                       min_slab_size=min_slab_size,
                                       min_vacuum_size=min_vacuum_size,
                                       max_normal_search=max_normal_search,
                                       center_slab=center_slab)

            slab_dict = {slab.miller_index: slab for slab in slabs}

            if miller_index not in slab_dict:
                raise ValueError("Miller index not in slab dict")

            this_slab = slab_dict[miller_index]

            vnn_surface = VoronoiNN(tol=0.05, allow_pathological=True)

            surf_props, undercoords = [], []
            this_mi_vec = get_mi_vec(this_slab)
            mi_mags = [np.dot(this_mi_vec, site.coords) for site in this_slab]
            average_mi_mag = np.average(mi_mags)
            for n, site in enumerate(this_slab):
                bulk_coord = this_slab.site_properties['bulk_coordinations'][n]
                slab_coord = len(vnn_surface.get_nn(this_slab, n))
                mi_mag = np.dot(this_mi_vec, site.coords)
                undercoord = (bulk_coord - slab_coord) / bulk_coord
                undercoords += [undercoord]
                if undercoord > undercoord_threshold and mi_mag > average_mi_mag:
                    surf_props += ['surface']
                else:
                    surf_props += ['subsurface']
            new_site_properties = {'surface_properties': surf_props,
                                   'undercoords': undercoords}
            new_slab = this_slab.copy(site_properties=new_site_properties)
            return cls(new_slab, selective_dynamics)

        def find_surface_sites_by_height(self, slab, height=0.9, xy_tol=0.05):
            """
            This method finds surface sites by determining which sites are within
            a threshold value in height from the topmost site in a list of sites

            Args:
                site_list (list): list of sites from which to select surface sites
                height (float): threshold in angstroms of distance from topmost
                    site in slab along the slab c-vector to include in surface
                    site determination
                xy_tol (float): if supplied, will remove any sites which are
                    within a certain distance in the miller plane.

            Returns:
                list of sites selected to be within a threshold of the highest
            """

            # Get projection of coordinates along the miller index
            m_projs = np.array([np.dot(site.coords, self.mvec)
                                for site in slab.sites])

            # Mask based on window threshold along the miller index.
            mask = (m_projs - np.amax(m_projs)) >= -height
            surf_sites = [slab.sites[n] for n in np.where(mask)[0]]
            if xy_tol:
                # sort surface sites by height
                surf_sites = [s for (h, s) in zip(m_projs[mask], surf_sites)]
                surf_sites.reverse()
                unique_sites, unique_perp_fracs = [], []
                for site in surf_sites:
                    this_perp = site.coords - np.dot(site.coords, self.mvec)
                    this_perp_frac = slab.lattice.get_fractional_coords(this_perp)
                    if not in_coord_list_pbc(unique_perp_fracs, this_perp_frac):
                        unique_sites.append(site)
                        unique_perp_fracs.append(this_perp_frac)
                surf_sites = unique_sites

            return surf_sites

        def assign_site_properties(self, slab, height=0.9):
            """
            Assigns site properties.
            """
            if 'surface_properties' in slab.site_properties.keys():
                return slab
            else:
                surf_sites = self.find_surface_sites_by_height(slab, height)
            surf_props = ['surface' if site in surf_sites
                          else 'subsurface' for site in slab.sites]
            return slab.copy(
                site_properties={'surface_properties': surf_props})

        def get_extended_surface_mesh(self, repeat=(5, 5, 1)):
            """
            Gets an extended surface mesh for to use for adsorption
            site finding by constructing supercell of surface sites

            Args:
                repeat (3-tuple): repeat for getting extended surface mesh
            """
            surf_str = Structure.from_sites(self.surface_sites)
            surf_str.make_supercell(repeat)
            return surf_str

        @property
        def surface_sites(self):
            """
            convenience method to return a list of surface sites
            """
            return [site for site in self.slab.sites
                    if site.properties['surface_properties'] == 'surface']

        def subsurface_sites(self):
            """
            convenience method to return list of subsurface sites
            """
            return [site for site in self.slab.sites
                    if site.properties['surface_properties'] == 'subsurface']

        def find_adsorption_sites(self, distance=2.0, put_inside=True,
                                  symm_reduce=1e-2, near_reduce=1e-2,
                                  positions=['ontop', 'bridge', 'hollow'],
                                  no_obtuse_hollow=True):
            """
            Finds surface sites according to the above algorithm.  Returns
            a list of corresponding cartesian coordinates.

            Args:
                distance (float): distance from the coordinating ensemble
                    of atoms along the miller index for the site (i. e.
                    the distance from the slab itself)
                put_inside (bool): whether to put the site inside the cell
                symm_reduce (float): symm reduction threshold
                near_reduce (float): near reduction threshold
                positions (list): which positions to include in the site finding
                    "ontop": sites on top of surface sites
                    "bridge": sites at edges between surface sites in Delaunay
                        triangulation of surface sites in the miller plane
                    "hollow": sites at centers of Delaunay triangulation faces
                    "subsurface": subsurface positions projected into miller plane
                no_obtuse_hollow (bool): flag to indicate whether to include
                    obtuse triangular ensembles in hollow sites
            """
            ads_sites = {k: [] for k in positions}
            if 'ontop' in positions:
                ads_sites['ontop'] = [s.coords for s in self.surface_sites]
            if 'subsurface' in positions:
                # Get highest site
                ref = self.slab.sites[np.argmax(self.slab.cart_coords[:, 2])]
                # Project diff between highest site and subs site into miller
                ss_sites = [self.mvec * np.dot(ref.coords - s.coords, self.mvec)
                            + s.coords for s in self.subsurface_sites()]
                ads_sites['subsurface'] = ss_sites
            if 'bridge' in positions or 'hollow' in positions:
                mesh = self.get_extended_surface_mesh()
                sop = get_rot(self.slab)
                dt = Delaunay([sop.operate(m.coords)[:2] for m in mesh])
                # TODO: refactor below to properly account for >3-fold
                for v in dt.simplices:
                    if -1 not in v:
                        dots = []
                        for i_corner, i_opp in zip(range(3), ((1, 2), (0, 2), (0, 1))):
                            corner, opp = v[i_corner], [v[o] for o in i_opp]
                            vecs = [mesh[d].coords - mesh[corner].coords for d in opp]
                            vecs = [vec / np.linalg.norm(vec) for vec in vecs]
                            dots.append(np.dot(*vecs))
                            # Add bridge sites at midpoints of edges of D. Tri
                            if 'bridge' in positions:
                                ads_sites["bridge"].append(
                                    self.ensemble_center(mesh, opp))
                        # Prevent addition of hollow sites in obtuse triangles
                        obtuse = no_obtuse_hollow and (np.array(dots) < 1e-5).any()
                        # Add hollow sites at centers of D. Tri faces
                        if 'hollow' in positions and not obtuse:
                            ads_sites['hollow'].append(
                                self.ensemble_center(mesh, v))
            for key, sites in ads_sites.items():
                # Pare off outer sites for bridge/hollow
                if key in ['bridge', 'hollow']:
                    frac_coords = [self.slab.lattice.get_fractional_coords(ads_site)
                                   for ads_site in sites]
                    frac_coords = [frac_coord for frac_coord in frac_coords
                                   if (frac_coord[0] > 1 and frac_coord[0] < 4
                                       and frac_coord[1] > 1 and frac_coord[1] < 4)]
                    sites = [self.slab.lattice.get_cartesian_coords(frac_coord)
                             for frac_coord in frac_coords]
                if near_reduce:
                    sites = self.near_reduce(sites, threshold=near_reduce)
                if put_inside:
                    sites = [put_coord_inside(self.slab.lattice, coord)
                             for coord in sites]
                if symm_reduce:
                    sites = self.symm_reduce(sites, threshold=symm_reduce)
                sites = [site + distance * self.mvec for site in sites]

                ads_sites[key] = sites
            ads_sites['all'] = sum(ads_sites.values(), [])
            return ads_sites

        def symm_reduce(self, coords_set, threshold=1e-6):
            """
            Reduces the set of adsorbate sites by finding removing
            symmetrically equivalent duplicates

            Args:
                coords_set: coordinate set in cartesian coordinates
                threshold: tolerance for distance equivalence, used
                    as input to in_coord_list_pbc for dupl. checking
            """
            surf_sg = SpacegroupAnalyzer(self.slab, 0.1)
            symm_ops = surf_sg.get_symmetry_operations()
            unique_coords = []
            # Convert to fractional
            coords_set = [self.slab.lattice.get_fractional_coords(coords)
                          for coords in coords_set]
            for coords in coords_set:
                incoord = False
                for op in symm_ops:
                    if in_coord_list_pbc(unique_coords, op.operate(coords),
                                         atol=threshold):
                        incoord = True
                        break
                if not incoord:
                    unique_coords += [coords]
            # convert back to cartesian
            return [self.slab.lattice.get_cartesian_coords(coords)
                    for coords in unique_coords]

        def near_reduce(self, coords_set, threshold=1e-4):
            """
            Prunes coordinate set for coordinates that are within
            threshold

            Args:
                coords_set (Nx3 array-like): list or array of coordinates
                threshold (float): threshold value for distance
            """
            unique_coords = []
            coords_set = [self.slab.lattice.get_fractional_coords(coords)
                          for coords in coords_set]
            for coord in coords_set:
                if not in_coord_list_pbc(unique_coords, coord, threshold):
                    unique_coords += [coord]
            return [self.slab.lattice.get_cartesian_coords(coords)
                    for coords in unique_coords]

        def ensemble_center(self, site_list, indices, cartesian=True):
            """
            Finds the center of an ensemble of sites selected from
            a list of sites.  Helper method for the find_adsorption_sites
            algorithm.

            Args:
                site_list (list of sites): list of sites
                indices (list of ints): list of ints from which to select
                    sites from site list
                cartesian (bool): whether to get average fractional or
                    cartesian coordinate
            """
            if cartesian:
                return np.average([site_list[i].coords for i in indices],
                                  axis=0)
            else:
                return np.average([site_list[i].frac_coords for i in indices],
                                  axis=0)

        def add_adsorbate(self, molecule, ads_coord, repeat=None, translate=True,
                          reorient=True):
            """
            Adds an adsorbate at a particular coordinate.  Adsorbate
            represented by a Molecule object and is translated to (0, 0, 0) if
            translate is True, or positioned relative to the input adsorbate
            coordinate if translate is False.

            Args:
                molecule (Molecule): molecule object representing the adsorbate
                ads_coord (array): coordinate of adsorbate position
                repeat (3-tuple or list): input for making a supercell of slab
                    prior to placing the adsorbate
                translate (bool): flag on whether to translate the molecule so
                    that its CoM is at the origin prior to adding it to the surface
                reorient (bool): flag on whether to reorient the molecule to
                    have its z-axis concurrent with miller index
            """
            molecule = molecule.copy()
            if translate:
                # Translate the molecule so that the center of mass of the atoms
                # that have the most negative z coordinate is at (0, 0, 0)
                front_atoms = molecule.copy()
                front_atoms._sites = [s for s in molecule.sites
                                      if s.coords[2] == min([s.coords[2]
                                                             for s in molecule.sites])]
                x, y, z = front_atoms.center_of_mass
                molecule.translate_sites(vector=[-x, -y, -z])
            if reorient:
                # Reorient the molecule along slab m_index
                sop = get_rot(self.slab)
                molecule.apply_operation(sop.inverse)
            struct = self.slab.copy()
            if repeat:
                struct.make_supercell(repeat)
            if 'surface_properties' in struct.site_properties.keys():
                molecule.add_site_property("surface_properties",
                                           ["adsorbate"] * molecule.num_sites)
            if 'selective_dynamics' in struct.site_properties.keys():
                molecule.add_site_property("selective_dynamics",
                                           [[True, True, True]] * molecule.num_sites)
            for site in molecule:
                struct.append(site.specie, ads_coord + site.coords, coords_are_cartesian=True,
                              properties=site.properties)
            return struct

        def assign_selective_dynamics(self, slab):
            """
            Helper function to assign selective dynamics site_properties
            based on surface, subsurface site properties

            Args:
                slab (Slab): slab for which to assign selective dynamics
            """
            sd_list = []
            sd_list = [[False, False, False] if site.properties['surface_properties'] == 'subsurface'
                       else [True, True, True] for site in slab.sites]
            new_sp = slab.site_properties
            new_sp['selective_dynamics'] = sd_list
            return slab.copy(site_properties=new_sp)

        def generate_adsorption_structures(self, molecule, repeat=None, min_lw=5.0,
                                           translate=True, reorient=True, find_args=None):
            """
            Function that generates all adsorption structures for a given
            molecular adsorbate.  Can take repeat argument or minimum
            length/width of precursor slab as an input

            Args:
                molecule (Molecule): molecule corresponding to adsorbate
                repeat (3-tuple or list): repeat argument for supercell generation
                min_lw (float): minimum length and width of the slab, only used
                    if repeat is None
                translate (bool): flag on whether to translate the molecule so
                    that its CoM is at the origin prior to adding it to the surface
                reorient (bool): flag on whether or not to reorient adsorbate
                    along the miller index
                find_args (dict): dictionary of arguments to be passed to the
                    call to self.find_adsorption_sites, e.g. {"distance":2.0}
            """
            if repeat is None:
                xrep = np.ceil(min_lw / np.linalg.norm(self.slab.lattice.matrix[0]))
                yrep = np.ceil(min_lw / np.linalg.norm(self.slab.lattice.matrix[1]))
                repeat = [xrep, yrep, 1]
            structs = []

            find_args = find_args or {}
            for coords in self.find_adsorption_sites(**find_args)['all']:
                structs.append(self.add_adsorbate(molecule, coords,
                                                  repeat=repeat, translate=translate, reorient=reorient))
            return structs

        def adsorb_both_surfaces(self, molecule, repeat=None, min_lw=5.0,
                                 translate=True, reorient=True, find_args=None):
            """
            Function that generates all adsorption structures for a given
            molecular adsorbate on both surfaces of a slab. This is useful
            for calculating surface energy where both surfaces need to be
            equivalent or if we want to calculate nonpolar systems.

            Args:
                molecule (Molecule): molecule corresponding to adsorbate
                repeat (3-tuple or list): repeat argument for supercell generation
                min_lw (float): minimum length and width of the slab, only used
                    if repeat is None
                reorient (bool): flag on whether or not to reorient adsorbate
                    along the miller index
                find_args (dict): dictionary of arguments to be passed to the
                    call to self.find_adsorption_sites, e.g. {"distance":2.0}
            """

            # Get the adsorbed surfaces first
            find_args = find_args or {}
            adslabs = self.generate_adsorption_structures(molecule, repeat=repeat,
                                                          min_lw=min_lw,
                                                          translate=translate,
                                                          reorient=reorient,
                                                          find_args=find_args)

            new_adslabs = []
            for adslab in adslabs:

                # Find the adsorbate sites and indices in each slab
                _, adsorbates, indices = False, [], []
                for i, site in enumerate(adslab.sites):
                    if site.surface_properties == "adsorbate":
                        adsorbates.append(site)
                        indices.append(i)

                # Start with the clean slab
                adslab.remove_sites(indices)
                slab = adslab.copy()

                # For each site, we add it back to the slab along with a
                # symmetrically equivalent position on the other side of
                # the slab using symmetry operations
                for adsorbate in adsorbates:
                    p2 = adslab.get_symmetric_site(adsorbate.frac_coords)
                    slab.append(adsorbate.specie, p2,
                                properties={"surface_properties": "adsorbate"})
                    slab.append(adsorbate.specie, adsorbate.frac_coords,
                                properties={"surface_properties": "adsorbate"})
                new_adslabs.append(slab)

            return new_adslabs

        def generate_substitution_structures(self, atom, target_species=None,
                                             sub_both_sides=False, range_tol=1e-2,
                                             dist_from_surf=0):
            """
            Function that performs substitution-type doping on the surface and
                returns all possible configurations where one dopant is substituted
                per surface. Can substitute one surface or both.

            Args:
                atom (str): atom corresponding to substitutional dopant
                sub_both_sides (bool): If true, substitute an equivalent
                    site on the other surface
                target_species (list): List of specific species to substitute
                range_tol (float): Find viable substitution sites at a specific
                    distance from the surface +- this tolerance
                dist_from_surf (float): Distance from the surface to find viable
                    substitution sites, defaults to 0 to substitute at the surface
            """

            target_species = target_species or []

            # Get symmetrized structure in case we want to substitue both sides
            sym_slab = SpacegroupAnalyzer(self.slab).get_symmetrized_structure()

            # Define a function for substituting a site
            def substitute(site, i):
                slab = self.slab.copy()
                props = self.slab.site_properties
                if sub_both_sides:
                    # Find an equivalent site on the other surface
                    eq_indices = [indices for indices in
                                  sym_slab.equivalent_indices if i in indices][0]
                    for ii in eq_indices:
                        if "%.6f" % (sym_slab[ii].frac_coords[2]) != \
                                "%.6f" % (site.frac_coords[2]):
                            props["surface_properties"][ii] = "substitute"
                            slab.replace(ii, atom)
                            break

                props["surface_properties"][i] = "substitute"
                slab.replace(i, atom)
                slab.add_site_property("surface_properties",
                                       props["surface_properties"])
                return slab

            # Get all possible substitution sites
            substituted_slabs = []
            # Sort sites so that we can define a range relative to the position of the
            # surface atoms, i.e. search for sites above (below) the bottom (top) surface
            sorted_sites = sorted(sym_slab, key=lambda site: site.frac_coords[2])
            if sorted_sites[0].surface_properties == "surface":
                d = sorted_sites[0].frac_coords[2] + dist_from_surf
            else:
                d = sorted_sites[-1].frac_coords[2] - dist_from_surf

            for i, site in enumerate(sym_slab):
                if d - range_tol < site.frac_coords[2] < d + range_tol:
                    if target_species and site.species_string in target_species:
                        substituted_slabs.append(substitute(site, i))
                    elif not target_species:
                        substituted_slabs.append(substitute(site, i))

            matcher = StructureMatcher()
            return [s[0] for s in matcher.group_structures(substituted_slabs)]

    def get_mi_vec(slab):
        """
        Convenience function which returns the unit vector aligned
        with the miller index.
        """
        mvec = np.cross(slab.lattice.matrix[0], slab.lattice.matrix[1])
        return mvec / np.linalg.norm(mvec)

    def get_rot(slab):
        """
        Gets the transformation to rotate the z axis into the miller index
        """
        new_z = get_mi_vec(slab)
        a, b, c = slab.lattice.matrix
        new_x = a / np.linalg.norm(a)
        new_y = np.cross(new_z, new_x)
        x, y, z = np.eye(3)
        rot_matrix = np.array([np.dot(*el) for el in
                               itertools.product([x, y, z],
                                                 [new_x, new_y, new_z])]).reshape(3, 3)
        rot_matrix = np.transpose(rot_matrix)
        sop = SymmOp.from_rotation_and_translation(rot_matrix)
        return sop

    def put_coord_inside(lattice, cart_coordinate):
        """
        converts a cartesian coordinate such that it is inside the unit cell.
        """
        fc = lattice.get_fractional_coords(cart_coordinate)
        return lattice.get_cartesian_coords([c - np.floor(c) for c in fc])

    def reorient_z(structure):
        """
        reorients a structure such that the z axis is concurrent with the
        normal to the A-B plane
        """
        struct = structure.copy()
        sop = get_rot(struct)
        struct.apply_operation(sop)
        return struct

    # Get color dictionary
    colors = loadfn(os.path.join(os.path.dirname(vis.__file__),
                                 "ElementColorSchemes.yaml"))
    color_dict = {el: [j / 256.001 for j in colors["Jmol"][el]]
                  for el in colors["Jmol"].keys()}

    def plot_slab(slab, ax, scale=0.8, repeat=5, window=1.5,
                  draw_unit_cell=True, decay=0.2, adsorption_sites=True):
        """
        Function that helps visualize the slab in a 2-D plot, for
        convenient viewing of output of AdsorbateSiteFinder.

        Args:
            slab (slab): Slab object to be visualized
            ax (axes): matplotlib axes with which to visualize
            scale (float): radius scaling for sites
            repeat (int): number of repeating unit cells to visualize
            window (float): window for setting the axes limits, is essentially
                a fraction of the unit cell limits
            draw_unit_cell (bool): flag indicating whether or not to draw cell
            decay (float): how the alpha-value decays along the z-axis
        """
        orig_slab = slab.copy()
        slab = reorient_z(slab)
        orig_cell = slab.lattice.matrix.copy()
        if repeat:
            slab.make_supercell([repeat, repeat, 1])
        coords = np.array(sorted(slab.cart_coords, key=lambda x: x[2]))
        sites = sorted(slab.sites, key=lambda x: x.coords[2])
        alphas = 1 - decay * (np.max(coords[:, 2]) - coords[:, 2])
        alphas = alphas.clip(min=0)
        corner = [0, 0, slab.lattice.get_fractional_coords(coords[-1])[-1]]
        corner = slab.lattice.get_cartesian_coords(corner)[:2]
        verts = orig_cell[:2, :2]
        lattsum = verts[0] + verts[1]
        # Draw circles at sites and stack them accordingly
        for n, coord in enumerate(coords):
            r = sites[n].specie.atomic_radius * scale
            ax.add_patch(patches.Circle(coord[:2] - lattsum * (repeat // 2),
                                        r, color='w', zorder=2 * n))
            color = color_dict[sites[n].species_string]
            ax.add_patch(patches.Circle(coord[:2] - lattsum * (repeat // 2), r,
                                        facecolor=color, alpha=alphas[n],
                                        edgecolor='k', lw=0.3, zorder=2 * n + 1))
        # Adsorption sites
        if adsorption_sites:
            asf = AdsorbateSiteFinder(orig_slab)
            ads_sites = asf.find_adsorption_sites()['all']
            sop = get_rot(orig_slab)
            ads_sites = [sop.operate(ads_site)[:2].tolist()
                         for ads_site in ads_sites]
            ax.plot(*zip(*ads_sites), color='k', marker='x',
                    markersize=10, mew=1, linestyle='', zorder=10000)
        # Draw unit cell
        if draw_unit_cell:
            verts = np.insert(verts, 1, lattsum, axis=0).tolist()
            verts += [[0., 0.]]
            verts = [[0., 0.]] + verts
            codes = [Path.MOVETO, Path.LINETO, Path.LINETO,
                     Path.LINETO, Path.CLOSEPOLY]
            verts = [(np.array(vert) + corner).tolist() for vert in verts]
            path = Path(verts, codes)
            patch = patches.PathPatch(path, facecolor='none', lw=2,
                                      alpha=0.5, zorder=2 * n + 2)
            ax.add_patch(patch)
        ax.set_aspect("equal")
        center = corner + lattsum / 2.
        extent = np.max(lattsum)
        lim_array = [center - extent * window, center + extent * window]
        x_lim = [ele[0] for ele in lim_array]
        y_lim = [ele[1] for ele in lim_array]
        ax.set_xlim(x_lim)
        ax.set_ylim(y_lim)
        return ax