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


  • 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 :param film_area: the unit cell area for the film :type film_area: int :param substrate_area: the unit cell area for the substrate :type substrate_area: int


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:


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.

  • 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]

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.


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.

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

  • area (lattice) –


transformation matrices to convert unit vectors to super lattice vectors

Return type:



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

  • 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