pymatgen.core.surface module¶

class
ReconstructionGenerator
(initial_structure, min_slab_size, min_vacuum_size, reconstruction_name)[source]¶ Bases:
object
This class takes in a predefined 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.

slabgen_params
¶ Parameters for the SlabGenerator
TODO:  Right now there is no way to specify what atom is being
added. In the future, use basis sets? Generates reconstructed slabs from a set of instructions
 specified by a dictionary or json file.
Parameters:  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”: “Fm3m”, “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
 FOR THE TOP SURFACE. THE ReconstructionGenerator ("points_to_add") –
 MODIFY THE BOTTOM SURFACE ACCORDINGLY TO RETURN A SLAB WITH (WILL) –
 SURFACES. (EQUIVALENT) –

build_slabs
()[source]¶  Builds the reconstructed slab by:
 Obtaining the unreconstructed slab using the specified parameters for the SlabGenerator.
 Applying the appropriate lattice transformation in the a and b lattice vectors.
 Remove any specified sites from both surfaces.
 Add any specified sites to both surfaces.
Returns: The reconstructed slab. Return type: (Slab)


class
Slab
(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)[source]¶ Bases:
pymatgen.core.structure.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).

miller_index
¶ Miller index of plane parallel to surface.

scale_factor
¶ Final computed scale factor that brings the parent cell to the surface cell.

shift
¶ The shift value in Angstrom that indicates how much this slab has been shifted.
Makes a Slab structure, a structure object with additional information and methods pertaining to slabs.
Parameters:  lattice (Lattice/3x3 array) – The lattice, either as a
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:
 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.
 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 cdirection).
 shift (float) – The shift in the cdirection 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.

add_adsorbate_atom
(indices, specie, distance)[source]¶ Gets the structure of single atom adsorption. slab structure from the Slab class(in [0, 0, 1])
Parameters:  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.

center_of_mass
¶ Calculates the center of mass of the slab

copy
(site_properties=None, sanitize=False)[source]¶ Convenience method to get a copy of the structure, with options to add site properties.
Parameters:  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.

dipole
¶ Calculates the dipole of the Slab in the direction of the surface normal. Note that the Slab must be oxidation statedecorated for this to work properly. Otherwise, the Slab will always have a dipole of 0.

get_orthogonal_c_slab
()[source]¶ 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.

get_sorted_structure
(key=None, reverse=False)[source]¶ 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.
Parameters:  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.

get_surface_sites
(tag=False)[source]¶ 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}

get_symmetric_site
(point, cartesian=False)[source]¶  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 nonpolar and symmetric properties of a slab when creating adsorbed structures or symmetric reconstructions.
 Arg:
 point: Fractional coordinate.
Returns:  Fractional coordinate. A point equivalent to the
 parameter point, but on the other side of the slab
Return type: point

get_tasker2_slabs
(tol=0.01, same_species_only=True)[source]¶ Get a list of slabs that have been Tasker 2 corrected.
Parameters:  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.

have_equivalent_surfaces
()[source]¶ 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

is_polar
(tol_dipole_per_unit_area=0.001)[source]¶ Checks whether the surface is polar by computing the dipole per unit area. Note that the Slab must be oxidation statedecorated for this to work properly. Otherwise, the Slab will always be nonpolar.
Parameters: tol_dipole_per_unit_area (float) – A tolerance. If the dipole magnitude per unit area is less than this value, the Slab is considered nonpolar. Defaults to 1e3, 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.

is_symmetric
(symprec=0.1)[source]¶ Checks if slab is symmetric, i.e., contains inversion symmetry.
Parameters: symprec (float) – Symmetry precision used for SpaceGroup analyzer. Returns: (bool) Whether slab contains inversion symmetry.

normal
¶ Calculates the surface normal vector of the slab

surface_area
¶ Calculates the surface area of the slab

symmetrically_add_atom
(specie, point, coords_are_cartesian=False)[source]¶  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: The modified slab Return type: (Slab)


class
SlabGenerator
(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)[source]¶ Bases:
object
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 slabvacuum system.

oriented_unit_cell
¶ A unit cell of the parent structure with the miller index of plane parallel to surface

parent
¶ Parent structure from which Slab was derived.

lll_reduce
¶ Whether or not the slabs will be orthogonalized

center_slab
¶ Whether or not the slabs will be centered between the vacuum layer

slab_scale_factor
¶ Final computed scale factor that brings the parent cell to the surface cell.

miller_index
¶ Miller index of plane parallel to surface.

min_slab_size
¶ Minimum size in angstroms of layers containing atoms

min_vac_size
¶ Minimize size in angstroms of layers containing vacuum
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.
Parameters:  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

get_slab
(shift=0, tol=0.1, energy=None)[source]¶ 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.

get_slabs
(bonds=None, tol=0.1, max_broken_bonds=0, symmetrize=False, repair=False)[source]¶ 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.
Parameters:  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.
 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.

move_to_other_side
(init_slab, index_of_sites)[source]¶ 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.

nonstoichiometric_symmetrized_slab
(init_slab, tol=0.001)[source]¶ 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 nonelemental 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: A symmetrized Slab object. Return type: Slab (structure)

repair_broken_bonds
(slab, bonds)[source]¶ 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.


center_slab
(slab)[source]¶  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. 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.
 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.
Parameters: slab (Slab) – Slab structure to center Returns: Returns a centered slab structure

generate_all_slabs
(structure, max_index, min_slab_size, min_vacuum_size, bonds=None, tol=0.001, 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)[source]¶ 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.
Parameters:  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.

get_recp_symmetry_operation
(structure, symprec=0.01)[source]¶ Find the symmetric operations of the reciprocal lattice, to be used for hkl transformations :param structure: conventional unit cell :type structure: Structure :param symprec: default is 0.001

get_symmetrically_distinct_miller_indices
(structure, max_index)[source]¶ Returns all symmetrically distinct indices below a certain maxindex for a given structure. Analysis is based on the symmetry of the reciprocal lattice of the structure. :param structure: input structure. :type structure: Structure :param max_index: 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.

hkl_transformation
(transf, miller_index)[source]¶ Returns the Miller index from setting A to B using a transformation matrix :param transf: The transformation matrix
that transforms a lattice of A to BParameters: miller_index ([h, k, l]) – Miller index to transform to setting B

miller_index_from_sites
(lattice, coords, coords_are_cartesian=True, round_dp=4, verbose=True)[source]¶ 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.
Parameters:  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: The Miller index.
Return type: (tuple)