pymatgen.analysis.substrate_analyzer module¶
This module provides classes to identify optimal substrates for film growth

class
SubstrateAnalyzer
(zslgen=<pymatgen.analysis.substrate_analyzer.ZSLGenerator object>, film_max_miller=1, substrate_max_miller=1)[source]¶ Bases:
object
This class applies a set of search criteria to identify suitable substrates for film growth. It first uses a topoplogical search by Zur and McGill to identify matching superlattices 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 superlattices
Initializes the substrate analyzer :param zslgen: Defaults to a ZSLGenerator with standard
tolerances, but can be fed one with custom tolerances
 Parameters
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 indicies
substrate_millers (array) – substrate facets to consider in search as defined by miller indicies
ground_state_energy (float) – ground state energy for the film
lowest (bool) – only consider lowest matching area for each surface

calculate_3D_elastic_energy
(film, match, elasticity_tensor=None, include_strain=False)[source]¶ Calculates the multiplane elastic energy. Returns 999 if no elastic tensor was given on init
 Parameters
film (Structure) – conventional standard structure for the film
match (dictionary) – match dictionary from substrate analyzer
elasticity_tensor (ElasticTensor) – elasticity tensor for the film
include_strain (bool) – include strain in the output or not; changes return from just the energy to a tuple with the energy and strain in voigt notation

generate_surface_vectors
(film_millers, substrate_millers)[source]¶ Generates the film/substrate slab combinations for a set of given miller indicies
 Parameters
film_millers (array) – all miller indices to generate slabs for film
substrate_millers (array) – all miller indicies to generate slabs for substrate

class
ZSLGenerator
(max_area_ratio_tol=0.09, max_area=400, max_length_tol=0.03, max_angle_tol=0.01)[source]¶ Bases:
object
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 superlattices 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
 Intialize a Zur Super Lattice Generator for a specific film and
substrate
 Parameters
max_area_ratio_tol (float) – Max tolerance on ratio of superlattices 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
 Returns
 a set of transformation_sets defined as:
1.) the transformation matricies for the film to create a super lattice of area i*film area 2.) the tranformation matricies 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 superlattices and checks if they matches. Returns all matching vectors sets. :param transformation_sets: an array of transformation sets:
each transformation set is an array with the (i,j) indicating the area multipes of the film and subtrate it corresponds to, an array with all possible transformations for the film area multiple i and another array for the substrate area multiple j.
 Parameters
film_vectors (array) – film vectors to generate super lattices
substrate_vectors (array) – substrate vectors to generate super lattices

gen_sl_transform_matricies
(area_multiple)[source]¶ Generates the transformation matricies 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 matricies to covert unit vectors to super lattice vectors
 Return type
matrix_list

reduce_vectors
(a, b)[source]¶ Generate independent and unique basis vectors based on the methodology of Zur and McGill