Crystal

class Crystal(cell_vectors, atom_r, atom_type, atom_mass)

Stores lattice and atom information

Variables:

  • cell_vectors – Shape (3, 3) float Quantity in length units. Cartesian unit cell vectors. cell_vectors[0] = a, cell_vectors[:, 0] = x etc.

  • n_atoms – Number of atoms in the unit cell

  • atom_r – Shape (n_atoms, 3) float ndarray. The fractional position of each atom within the unit cell

  • atom_type – Shape (n_atoms,) string ndarray. The chemical symbols of each atom in the unit cell

  • atom_mass – Shape (n_atoms,) float Quantity in mass units. The mass of each atom in the unit cell

Parameters:

  • cell_vectors (Quantity)

  • atom_r (ndarray)

  • atom_type (ndarray)

  • atom_mass (Quantity)

__init__(cell_vectors, atom_r, atom_type, atom_mass)
Parameters:

  • cell_vectors (Quantity) – Shape (3, 3) float Quantity in length units. Cartesian unit cell vectors. cell_vectors[0] = a, cell_vectors[:, 0] = x etc.

  • atom_r (ndarray) – Shape (n_atoms, 3) float ndarray. The fractional position of each atom within the unit cell

  • atom_type (ndarray) – Shape (n_atoms,) string ndarray. The chemical symbols of each atom in the unit cell

  • atom_mass (Quantity) – Shape (n_atoms,) float Quantity in mass units. The mass of each atom in the unit cell

Return type:

None

reciprocal_cell()

Calculates the reciprocal lattice vectors

Returns:

recip – Shape (3, 3) float Quantity in 1/length units, the reciprocal lattice vectors

Return type:

Quantity

cell_volume()

Calculates the cell volume

Returns:

volume – Scalar float Quantity in length**3 units. The cell volume

Return type:

Quantity

get_mp_grid_spec(spacing=<Quantity(0.1, '1 / angstrom')>)

Get suggested divisions for Monkhorst-Pack grid

Determine a mesh for even Monkhorst-Pack sampling of the reciprocal cell

Parameters:

spacing (Quantity) – Scalar float quantity in 1/length units. Maximum reciprocal-space distance between q-point samples

Returns:

grid_spec – The number of divisions for each reciprocal lattice vector

Return type:

tuple[int, int, int]

to_spglib_cell()

Convert to a ‘cell’ as defined by spglib

Returns:

cell – cell = (lattice, positions, numbers), where lattice is the lattice vectors, positions are the fractional atomic positions, and numbers are integers distinguishing the atomic species

Return type:

tuple[list[list[float]], list[list[float]], list[int]]

get_species_idx()

Returns a dictionary of each species and their indices

Returns:

species_idx – An ordered dictionary containing each unique species symbol as the keys, and their indices as the values, in the same order as they appear in atom_type

Return type:

OrderedDict[str, ndarray]

get_symmetry_equivalent_atoms(tol=<Quantity(1e-05, 'angstrom')>)

Returns the rotational and translational symmetry operations as obtained by spglib.get_symmetry, and also the equivalent atoms that each atom gets mapped onto for each symmetry operation

Parameters:

tol (Quantity) – Scalar float Quantity in length units. The distance tolerance, if the distance between atoms is less than this, they are considered to be equivalent. This is also passed to spglib.get_symmetry as symprec

Returns:

  • rotations – Shape (n_symmetry_ops, 3, 3) integer np.ndarray. The rotational symmetry matrices as returned by spglib.get_symmetry

  • translations – Shape (n_symmetry_ops, 3) float np.ndarray. The rotational symmetry matrices as returned by spglib.get_symmetry

  • equivalent_atoms – Shape (n_symmetry_ops, n_atoms) integer np.ndarray. The equivalent atoms for each symmetry operation. e.g. equivalent_atoms[s, i] = j means symmetry operation s maps atom i to atom j

Return type:

tuple[ndarray, ndarray, ndarray]

to_dict()

Convert to a dictionary. See Crystal.from_dict for details on keys/values

Returns:

dict

Return type:

dict[str, Any]

to_json_file(filename)

Write to a JSON file. JSON fields are equivalent to Crystal.from_dict keys

Parameters:

filename (Path | str) – Name of the JSON file to write to

Return type:

None

classmethod from_dict(d)

Convert a dictionary to a Crystal object

Parameters:

d (dict[str, Any]) –

A dictionary with the following keys/values:

  • ’cell_vectors’: (3, 3) float ndarray

  • ’cell_vectors_unit’: str

  • ’atom_r’: (n_atoms, 3) float ndarray

  • ’atom_type’: (n_atoms,) str ndarray

  • ’atom_mass’: (n_atoms,) float np.ndaaray

  • ’atom_mass_unit’: str

Returns:

crystal

Return type:

Self

classmethod from_json_file(filename)

Read from a JSON file. See Crystal.from_dict for required fields

Parameters:

filename (Path | str) – The file to read from

Returns:

crystal

Return type:

Self

classmethod from_cell_vectors(cell_vectors)

Create a Crystal object from just cell vectors, containing no detailed structure information (atomic positions, species, masses)

Parameters:

cell_vectors (Quantity) – Shape (3, 3) float Quantity in length units. Cartesian unit cell vectors. cell_vectors[0] = a, cell_vectors[:, 0] = x etc.

Returns:

crystal

Return type:

Self