pymatgen.analysis.interfaces package

Module that implements various algorithms related to interface construction and analysis.

Submodules

pymatgen.analysis.interfaces.coherent_interfaces module

This module provides classes to store, generate, and manipulate material interfaces.

class CoherentInterfaceBuilder(substrate_structure: Structure, film_structure: Structure, film_miller: tuple[int, int, int], substrate_miller: tuple[int, int, int], zslgen: ZSLGenerator | None = None)[source]

Bases: object

This class constructs the coherent interfaces between two crystalline slabs Coherency is defined by matching lattices not sub-planes.

Parameters:

  • substrate_structure – structure of substrate

  • film_structure – structure of film

  • film_miller – miller index of the film layer

  • substrate_miller – miller index for the substrate layer

  • zslgen – BiDirectionalZSL if you want custom lattice matching tolerances for coherency.

get_interfaces(termination: tuple[str, str], gap: float = 2.0, vacuum_over_film: float = 20.0, film_thickness: float = 1, substrate_thickness: float = 1, in_layers: bool = True) → Iterator[Interface][source]

Generates interface structures given the film and substrate structure as well as the desired terminations.

Parameters:

  • termination (tuple[str, str]) – termination from self.termination list

  • gap (float, optional) – gap between film and substrate. Defaults to 2.0.

  • vacuum_over_film (float, optional) – vacuum over the top of the film. Defaults to 20.0.

  • film_thickness (float, optional) – the film thickness. Defaults to 1.

  • substrate_thickness (float, optional) – substrate thickness. Defaults to 1.

  • in_layers (bool, optional) – set the thickness in layer units. Defaults to True.

Yields:

Iterator[Interface] – interfaces from slabs

from_2d_to_3d(mat: ndarray) → ndarray[source]

Converts a 2D matrix to a 3D matrix.

get_2d_transform(start: Sequence, end: Sequence) → np.ndarray[source]

Gets a 2d transformation matrix that converts start to end.

get_rot_3d_for_2d(film_matrix, sub_matrix) → ndarray[source]

Find transformation matrix that will rotate and strain the film to the substrate while preserving the c-axis.

pymatgen.analysis.interfaces.substrate_analyzer module

This module provides classes to identify optimal substrates for film growth.

class SubstrateAnalyzer(film_max_miller=1, substrate_max_miller=1, **kwargs)[source]

Bases: ZSLGenerator

This class applies a set of search criteria to identify suitable substrates for film growth. It first uses a topological search by Zur and McGill to identify matching super-lattices on various faces of the two materials. Additional criteria can then be used to identify the most suitable substrate. Currently, the only additional criteria is the elastic strain energy of the super-lattices.

Initializes the substrate analyzer

Parameters:

  • zslgen (ZSLGenerator) – Defaults to a ZSLGenerator with standard tolerances, but can be fed one with custom tolerances

  • film_max_miller (int) – maximum miller index to generate for film surfaces

  • substrate_max_miller (int) – maximum miller index to generate for substrate surfaces.

calculate(film, substrate, elasticity_tensor=None, film_millers=None, substrate_millers=None, ground_state_energy=0, lowest=False)[source]

Finds all topological matches for the substrate and calculates elastic strain energy and total energy for the film if elasticity tensor and ground state energy are provided:

Parameters:

  • film (Structure) – conventional standard structure for the film

  • substrate (Structure) – conventional standard structure for the substrate

  • elasticity_tensor (ElasticTensor) – elasticity tensor for the film in the IEEE orientation

  • film_millers (array) – film facets to consider in search as defined by miller indices

  • substrate_millers (array) – substrate facets to consider in search as defined by miller indices

  • ground_state_energy (float) – ground state energy for the film

  • lowest (bool) – only consider lowest matching area for each surface

generate_surface_vectors(film_millers, substrate_millers)[source]

Generates the film/substrate slab combinations for a set of given miller indices.

Parameters:

  • film_millers (array) – all miller indices to generate slabs for film

  • substrate_millers (array) – all miller indices to generate slabs for substrate

class SubstrateMatch(film_sl_vectors: list, substrate_sl_vectors: list, film_vectors: list, substrate_vectors: list, film_transformation: list, substrate_transformation: list, film_miller: tuple[int, int, int], substrate_miller: tuple[int, int, int], strain: Strain, von_mises_strain: float, ground_state_energy: float, elastic_energy: float)[source]

Bases: ZSLMatch

A substrate match building on the Zur and McGill algorithm. This match class includes the miller planes of the film and substrate the full strain tensor, the Von Mises strain, the ground state energy if provided, and the elastic energy.

elastic_energy: float[source]
film_miller: tuple[int, int, int][source]
classmethod from_zsl(match: ZSLMatch, film: Structure, film_miller, substrate_miller, elasticity_tensor=None, ground_state_energy=0)[source]

Generate a substrate match from a ZSL match plus metadata.

ground_state_energy: float[source]
strain: Strain[source]
substrate_miller: tuple[int, int, int][source]
property total_energy[source]

Total energy of this match.

von_mises_strain: float[source]

pymatgen.analysis.interfaces.zsl module

This module implements the Zur and McGill lattice matching algorithm.

class ZSLGenerator(max_area_ratio_tol=0.09, max_area=400, max_length_tol=0.03, max_angle_tol=0.01, bidirectional=False)[source]

Bases: MSONable

This class generate matching interface super lattices based on the methodology of lattice vector matching for heterostructural interfaces proposed by Zur and McGill: Journal of Applied Physics 55 (1984), 378 ; doi: 10.1063/1.333084 The process of generating all possible matching super lattices is: 1.) Reduce the surface lattice vectors and calculate area for the surfaces 2.) Generate all super lattice transformations within a maximum allowed area

limit that give nearly equal area super-lattices for the two surfaces - generate_sl_transformation_sets

3.) For each superlattice set:

1.) Reduce super lattice vectors 2.) Check length and angle between film and substrate super lattice

vectors to determine if the super lattices are the nearly same and therefore coincident - get_equiv_transformations.

Initialize a Zur Super Lattice Generator for a specific film and

substrate

Parameters:

  • max_area_ratio_tol (float) – Max tolerance on ratio of super-lattices to consider equal

  • max_area (float) – max super lattice area to generate in search

  • max_length_tol – maximum length tolerance in checking if two vectors are of nearly the same length

  • max_angle_tol – maximum angle tolerance in checking of two sets of vectors have nearly the same angle between them.

generate_sl_transformation_sets(film_area, substrate_area)[source]

Generates transformation sets for film/substrate pair given the area of the unit cell area for the film and substrate. The transformation sets map the film and substrate unit cells to super lattices with a maximum area

Parameters:

  • film_area (int) – the unit cell area for the film

  • substrate_area (int) – the unit cell area for the substrate

Returns:

a set of transformation_sets defined as:

1.) the transformation matrices for the film to create a super lattice of area i*film area 2.) the transformation matrices for the substrate to create a super lattice of area j*film area.

Return type:

transformation_sets

get_equiv_transformations(transformation_sets, film_vectors, substrate_vectors)[source]

Applies the transformation_sets to the film and substrate vectors to generate super-lattices and checks if they matches. Returns all matching vectors sets.

Parameters:

  • transformation_sets (array) – an array of transformation sets: each transformation set is an array with the (i,j) indicating the area multiples of the film and substrate it corresponds to, an array with all possible transformations for the film area multiple i and another array for the substrate area multiple j.

  • film_vectors (array) – film vectors to generate super lattices

  • substrate_vectors (array) – substrate vectors to generate super lattices

class ZSLMatch(film_sl_vectors: list, substrate_sl_vectors: list, film_vectors: list, substrate_vectors: list, film_transformation: list, substrate_transformation: list)[source]

Bases: MSONable

A match from the Zur and McGill Algorithm. The super_lattice vectors are listed as _sl_vectors. These are reduced according to the algorithm in the paper which effectively a rotation in 3D space. Use the match_transformation property to get the appropriate transformation matrix.

film_sl_vectors: list[source]
film_transformation: list[source]
film_vectors: list[source]
property match_area[source]

The area of the match between the substrate and film super lattice vectors.

property match_transformation[source]

The transformation matrix to convert the film super lattice vectors to the substrate.

substrate_sl_vectors: list[source]
substrate_transformation: list[source]
substrate_vectors: list[source]
fast_norm(a)[source]

Much faster variant of numpy linalg norm.

Note that if numba is installed, this cannot be provided a list of ints; please ensure input a is an np.array of floats.

gen_sl_transform_matrices(area_multiple)[source]

Generates the transformation matrices that convert a set of 2D vectors into a super lattice of integer area multiple as proven in Cassels:

Cassels, John William Scott. An introduction to the geometry of numbers. Springer Science & Business Media, 2012.

Parameters:

  • area_multiple (int) – integer multiple of unit cell area for super

  • area (lattice) –

Returns:

transformation matrices to convert unit vectors to super lattice vectors

Return type:

matrix_list

get_factors(n)[source]

Generate all factors of n.

is_same_vectors(vec_set1, vec_set2, bidirectional=False, max_length_tol=0.03, max_angle_tol=0.01) → bool[source]

Determine if two sets of vectors are the same within length and angle tolerances :param vec_set1: an array of two vectors :type vec_set1: array[array] :param vec_set2: second array of two vectors. :type vec_set2: array[array]

reduce_vectors(a, b)[source]

Generate independent and unique basis vectors based on the methodology of Zur and McGill.

rel_angle(vec_set1, vec_set2)[source]

Calculate the relative angle between two vector sets.

Parameters:

  • vec_set1 (array[array]) – an array of two vectors

  • vec_set2 (array[array]) – second array of two vectors

rel_strain(vec1, vec2)[source]

Calculate relative strain between two vectors.

vec_angle(a, b)[source]

Calculate angle between two vectors.

vec_area(a, b)[source]

Area of lattice plane defined by two vectors.