API Reference

This is the API for the Fedorov package.

Classes for 3D crystal initialization

This section contains three classes that allow user to initialize a 3D crystal structure with different user input.

class fedorov.SpaceGroup(space_group_number=1)

A class for space group symmetry operation.

This class provides method to initialize a crystal unit cell with space group and Wyckoff possition information.

Parameters:space_group_number (int) – Space group number between 1 and 230.

All the space group information was obtained from Bilbao Crystallographic Server

get_basis_vectors(base_positions, base_type=[], base_quaternions=None, is_complete=False, apply_orientation=False)

Get the basis vectors for the defined crystall structure.

Parameters:

• base_positions (np.ndarray) – N by 3 np array of the Wyckoff postions
• base_type (list) – a list of string for particle type name
• base_quaternions (np.ndarray) – N by 4 np array of quaternions, default None
• is_complete (bool) – bool value to indicate if the positions are complete postions in a unitcell
• apply_orientations (bool) – bool value to indicate if the space group symmetry should be applied to orientatioin

Returns:

basis_vectors

Return type:

np.ndarray

get_lattice_vectors(**user_lattice_params)

Initialize the unitcell and return lattice vectors [a1, a2, a3].

Parameters:user_lattice_params (float) – unit cell parameters, provide a, b, c, alpha, beta, gamma where applicable Returns:lattice_vectors Return type:np.ndarray

class fedorov.Prototype(space_group_number=1, wyckoff_site='', type_by_site='')

Crystal prototype class.

This class uses the minimal necessay information needed to fully define a crystal structures with space group number, wyckoff postions(in letter name convention) and free parameters for each relavent wyckoff postions.

Parameters:

• space_group_number – space group number between 1 and 230
• wyckoff_site (str) – wyckoff site letters included in the prototype
• type_by_site (str) – type name letter for each site set in wyckoff_sites

All the space group and Wyckoff positions information was obtained from Bilbao Crystallographic Server

get_basis_vectors(**user_basis_params)

Initialize fractional coordinates of the particles in the unitcell.

Parameters:user_basis_params (float) – user defined parameters for different Wyckoff site degree of freedom, when applicable Returns:basis_vectors Return type:np.ndarray

get_lattice_vectors(**user_lattice_params)

Initialize the unitcell and return lattice vectors [a1, a2, a3]

Parameters:user_lattice_params (float) – unit cell parameters, provide a, b, c, alpha, beta, gamma where applicable Returns:lattice_vectors Return type:np.ndarray

class fedorov.AflowPrototype(prototype_index=0, set_type=False)

Bases: fedorov.fedorov.Prototype

Aflow prototype class.

This class uses the crystal prototypes in Aflow database to initialize crystal structures.

Parameters:

• prototype_index (int) – prototype index [0, 589] for all 590 prototypes in AFLOW.
• set_type (bool) – allow setting different type name(in A, B, C order) for different atoms in AFLOW prototype

The list of crystal structures available in Aflow are summarized below:

classmethod from_query(pearson_symbol: str | None = None, space_group: int | None = None, prototype: str | None = None, set_type: bool = False)

Create all AflowPrototype matching the given query.

Args:

pearson_symbol (str, optional): The Pearson symbol to search for,

defaults to None which accepts any Pearson symbol.

space_group (int, optional): The space group to search for,

defaults to None which accepts any space group.

prototype (str, optional): The chemical prototype to search for,

defaults to None which accepts any prototype.

set_type (bool, optional): Set different type name (in alphabetic

order starting with “A”) for different atoms in AFLOW prototype.

Returns:

lattices (list[AflowPrototype]): The list of all

AflowPrototype’s with a given Pearson symbol.

Classes for 3D unit cell

class fedorov.Triclinic

A class for constructing a triclinic unitcell.

classmethod get_lattice_vectors(**user_lattice_params)

Initialize a triclinic unitcell and return lattice vectors.

Parameters:user_lattice_params (float) – unit cell parameters, provide a, b, c, alpha, beta, gamma where applicable Returns:lattice_vectors Return type:np.ndarray

class fedorov.Monoclinic

A class for constructing a monoclinic unitcell

This class provides method to initialize a monoclinic unitcell

classmethod get_lattice_vectors(**user_lattice_params)

Initialize a monoclinic unitcell and return lattice vectors.

Parameters:user_lattice_params (float) – unit cell parameters, provide a, b, c, alpha, beta, gamma where applicable Returns:lattice_vectors Return type:np.ndarray

class fedorov.Orthorhombic

A class for constructing a orthorhombic unitcell.

classmethod get_lattice_vectors(**user_lattice_params)

Initialize a orthorhombi unitcell and return lattice vectors.

Parameters:user_lattice_params (float) – unit cell parameters, provide a, b, c, alpha, beta, gamma where applicable Returns:lattice_vectors Return type:np.ndarray

class fedorov.Tetragonal

A class for constructing a tetragonal unitcell.

classmethod get_lattice_vectors(**user_lattice_params)

Initialize a tetragona unitcell and return lattice vectors.

Parameters:user_lattice_params (float) – unit cell parameters, provide a, b, c, alpha, beta, gamma where applicable Returns:lattice_vectors Return type:np.ndarray

class fedorov.Hexagonal

A class for constructing a hexagonal unitcell.

classmethod get_lattice_vectors(**user_lattice_params)

Initialize a hexagonal unitcell and return lattice vectors.

Parameters:user_lattice_params (float) – unit cell parameters, provide a, b, c, alpha, beta, gamma where applicable Returns:lattice_vectors Return type:np.ndarray

class fedorov.Rhombohedral

A class for constructing a rhombohedral unitcell.

classmethod get_lattice_vectors(**user_lattice_params)

Initialize a rhombohedral unitcell and return lattice vectors.

Parameters:user_lattice_params (float) – unit cell parameters, provide a, b, c, alpha, beta, gamma where applicable Returns:lattice_vectors Return type:np.ndarray

class fedorov.Cubic

A class for constructing a cubic unitcell.

classmethod get_lattice_vectors(**user_lattice_params)

Initialize a cubicc unitcell and return lattice vectors.

Parameters:user_lattice_params (float) – unit cell parameters, provide a, b, c, alpha, beta, gamma where applicable Returns:lattice_vectors Return type:np.ndarray

Class for 2D crystal initialization

This section contains one class that allows user to initialize a 2D crystal structure with different user input.

class fedorov.PlaneGroup(plane_group_number=1)

A class for plane group symmetry operation.

This class provides method to initialize a crystal unit cell with plane group and Wyckoff possition information.

Parameters:plane_group_number (int) – Plane group number between 1 and 17.

All the plane group information was obtained from Bilbao Crystallographic Server

get_basis_vectors(base_positions, base_type=[], base_quaternions=None, is_complete=False, apply_orientation=False)

Get the basis vectors for the defined crystall structure.

Parameters:

• base_positions (np.ndarray) – N by 2 np array of the Wyckoff postions
• base_type (list) – a list of string for particle type name
• base_quaternions (np.ndarray) – N by 4 np array of quaternions, default None
• is_complete (bool) – bool value to indicate if the positions are complete postions in a unitcell
• apply_orientations (bool) – bool value to indicate if the space group symmetry should be applied to orientation

Returns:

basis_vectors

Return type:

np.ndarray

get_lattice_vectors(**user_lattice_params)

Initialize the unitcell and return lattice vectors [a1, a2].

Parameters:user_lattice_params (float) – unit cell parameters, provide a, b, theta where applicable Returns:lattice_vectors Return type:np.ndarray

Classes for 2D unit cell

class fedorov.Oblique2D

A class for constructing a 2D oblique unitcell

This class provides method to initialize a 2D oblique unitcell

classmethod get_lattice_vectors(**user_lattice_params)

Initialize a 2D oblique unitcell and return lattice vectors [a1, a2].

Parameters:user_lattice_params (float) – unit cell parameters, provide a, b, theta where applicable Returns:lattice_vectors Return type:np.ndarray

class fedorov.Rectangular2D

A class for constructing a 2D rectangular unitcell

This class provides method to initialize a 2D rectangular unitcell

classmethod get_lattice_vectors(**user_lattice_params)

Initialize a 2D rectangular unitcell and return lattice vectors.

Parameters:user_lattice_params (float) – unit cell parameters, provide a, b, theta where applicable Returns:lattice_vectors Return type:np.ndarray

class fedorov.Hexagonal2D

A class for constructing a 2D hexagonal unitcell

This class provides method to initialize a 2D hexagonal unitcell

classmethod get_lattice_vectors(**user_lattice_params)

Initialize a 2D hexagonal unitcell and return lattice vectors.

Parameters:user_lattice_params (float) – unit cell parameters, provide a, b, theta where applicable Returns:lattice_vectors Return type:np.ndarray

class fedorov.Square2D

A class for constructing a 2D square unitcell

This class provides method to initialize a 2D square unitcell

classmethod get_lattice_vectors(**user_lattice_params)

Initialize a 2D square unitcell and return lattice vectors [a1, a2].

Parameters:user_lattice_params (float) – unit cell parameters, provide a, b, theta where applicable Returns:lattice_vectors Return type:np.ndarray

Class for Point group symmetry operations

This section contains one class that allows user to obtain all point group symmetry operations.

class fedorov.PointGroup(point_group_number=1)

A class to access all point group symmetry operations.

This class provides method to access all point group symmetry operation in both rotational matrix form or quaternion form.

Parameters:point_group_number (int) – Point group number between 1 and 32.

All the point group information was obtained from Bilbao Crystallographic Server

get_quaternion()

Get the quaternions for the point group symmetry.

Returns:list of quaternions Return type:list

get_rotation_matrix()

Get the rotation matrixes for the point group symmetry.

Returns:n by 3 by 3 numpy array containing n rotational matrixes Return type:numpy.ndarray

Some methods for crystal initialization