pymatgen.analysis.defects.point_defects module

class Defect

Bases: object

Abstract class for point defects

defectsite_count()

Returns the number of symmetrically distinct defect sites

enumerate_defectsites()

Enumerates all the symmetrically distinct defects.

get_coordinated_elements(n)

Elements of sites in structure surrounding the defect site.

Parameters:n – Index of defect list

get_coordinated_sites(n)

The sites in structure surrounding the defect site.

Parameters:n – Index of defects list

get_defectsite(n)

Returns the defect site at the index.

get_defectsite_coordination_number(n)

Coordination number of interstitial site.

Parameters:n – Index of interstitial list

get_defectsite_multiplicity(n)

Returns the symmtric multiplicity of the defect site at the index.

make_supercells_with_defects(scaling_matrix)

Generate the supercell with input multipliers and create the defect. First supercell has no defects. To create unit cell with defect pass unit matrix.

struct_radii

Radii of elements in the structure

struct_valences

Valence of elements in the structure

structure

Returns the structure without any defects Useful for Mott-Littleton calculations.

class Interstitial(structure, valences, radii, site_type='voronoi_vertex', accuracy='Normal', symmetry_flag=True, oxi_state=False)

Bases: pymatgen.analysis.defects.point_defects.Defect

Subclass of Defect to generate interstitial sites

Given a structure, generate symmetrically distinct interstitial sites. For a non-ionic structure, use oxi_state=True and give atomic radii.

Parameters:

• structure – pymatgen.core.structure.Structure
• valences – Dictionary of oxidation states of elements in {el:valence} form
• radii – Radii of elemnts in the structure
• site_type – “voronoi_vertex” uses voronoi nodes “voronoi_edgecenter” uses voronoi polyhedra edge centers “voronoi_facecenter” uses voronoi polyhedra face centers “all” combines vertices, edgecenters and facecenters. Default is “voronoi_vertex”
• accuracy – Flag denoting whether to use high accuracy version of Zeo++. Options are “Normal” and “High”. Default is normal.
• symmetry_flag – If True, only returns symmetrically distinct sites
• oxi_state – If False, input structure is considered devoid of oxidation-state decoration. And oxi-state for each site is determined. Use True, if input structure is oxi-state decorated. This option is useful when the structure is not electro-neutral after deleting/adding sites. In that case oxi-decorate the structure before deleting/adding the sites.

append_defectsite(site)

Append a site to list of possible interstitials

Parameters:site – pymatgen.core.sites.Site

delete_defectsite(n)

Remove a symmetrically distinct interstitial site

Parameters:n – Index of interstitial site

enumerate_defectsites()

Enumerate all the symmetrically distinct interstitial sites. The defect site has “X” as occupied specie.

get_coordsites_charge_sum(n)

Total charge of the interstitial coordinated sites.

Parameters:n – Index of interstitial list

get_coordsites_min_max_charge(n)

Minimum and maximum charge of sites surrounding the interstitial site.

Parameters:n – Index of symmetrical distinct interstitial site

get_radii()

get_radius(n)

Volume of the nth interstitial

Parameters:n – Index of symmetrically distinct vacancies list Returns:floating number representing radius of interstitial sphere

make_supercells_with_defects(scaling_matrix, element)

Returns sequence of supercells in pymatgen.core.structure.Structure format, with each supercell containing an interstitial. First supercell has no defects.

prune_close_defectsites(dist=0.2)

Prune the sites that are very close.

prune_defectsites(el='C', oxi_state=4, dlta=0.1)

Prune all the defect sites which can’t acoomodate the input elment with the input oxidation state.

radius_prune_defectsites(radius)

Remove all the defect sites with voronoi radius less than input radius

reduce_defectsites()

If multiple defect sites have same voronoi radius, only one is kept. Useful if the symmetry based reduction of initial sites returned from Zeo++ is not working properly due to deviation in ideal lattice coordinates.

class InterstitialAnalyzer(inter, el, oxi_state, scd=2)

Bases: object

Use GULP to compute the interstitial formation energy, relaxed structures. Works only for metal oxides due to the use of Buckingham Potentials.

Parameters:

• inter – pymatgen.defects.point_defects.Interstitial
• el – Element name in short hand notation (“El”)
• oxi_state – Oxidtation state
• scd – Super cell dimension as number. The scaling is equal along xyz.

get_energy(n, relax=True)

Formation Energy for nth symmetrically distinct interstitial.

get_percentage_bond_distance_change(n)

Bond distance change after the introduction of interstitial

Parameters:n – Symmetrically distinct interstitial index

get_percentage_lattice_parameter_change(n)

Lattice parameter change after the introduction of interstitial

Parameters:n – Symmetrically distinct interstitial index

get_percentage_volume_change(n)

Volume change after the introduction of interstitial

Parameters:n – Symmetrically distinct interstitial index

get_relaxed_structure(n)

Optimized interstitial structure

Parameters:n – Symmetrically distinct interstitial index

Note

To get relaxed bulk structure pass -1. -ve index will not work as expected.

relaxed_structure_match(i, j)

Check if the relaxed structures of two interstitials match

Parameters:

• i – Symmetrically distinct interstitial index
• j – Symmetrically distinct interstitial index

Note

To use relaxed bulk structure pass -1. -ve index will not work as expected

class InterstitialStructureRelaxer(interstitial, el, oxi_state, supercell_dim=2)

Bases: object

Performs structural relaxation for each interstitial supercell.

Parameters:

• interstitial – Unrelaxed interstitial
• el – Species string in short notation
• oxi_state – Oxidation state of the element
• supercell_dim – Dimensions of super cell

get_relaxed_energy(n)

Get the relaxed structure of nth symmetrically distinct interstitial.

Parameters:n – Symmetrically distinct interstitial index

Note

0 corresponds to relaxed bulk structure

get_relaxed_interstitial()

Get the relaxed structure of nth symmetrically distinct interstitial.

Parameters:n – Symmetrically distinct interstitial index

get_relaxed_structure(n)

Get the relaxed structure of nth symmetrically distinct interstitial.

Parameters:n – Symmetrically distinct interstitial index

Note

0 corresponds to relaxed bulk structure

relax()

Optimize interstitial structures

relaxed_energy_match(i, j)

Check if the relaxed energies of two interstitials match

Parameters:

• i – Symmetrically distinct interstitial index
• j – Symmetrically distinct interstitial index

Note

Index 0 corresponds to bulk.

relaxed_structure_match(i, j)

Check if the relaxed structures of two interstitials match

Parameters:

• i – Symmetrically distinct interstitial index
• j – Symmetrically distinct interstitial index

Note

Index 0 corresponds to bulk.

class RelaxedInterstitial(struct_list, energy_list, valence_dict)

Bases: object

Stores the relaxed supercell structures for each interstitial Used to compute formation energies, displacement of atoms near the the interstitial.

Parameters:

• struct_list – List of structures(supercells). The first structure should represent relaxed bulk structure and the subsequent ones interstitial structures (with the extra interstitial site appended at the end).
• energy_list – List of energies for relaxed interstitial structures. The first energy should correspond to bulk structure
• valence_dict – Valences of elements in dictionary form

defect_count()

Returns the number of distinct interstitials

formation_energy(n, chem_pot=0)

Compute the interstitial formation energy

Parameters:

• n – Index of interstitials
• chem_pot – Chemical potential of interstitial site element. If not given, assumed as zero. The user is strongly urged to supply the chemical potential value

get_bulk_structure()

Return relaxed bulk structure

get_charge_coordination_number(n)

Charge coordination number for nth interstitial.

Parameters:n – Index of interstitials

get_coordinated_bulk_sites(n)

Bulk sites corresponding to the coordinated sites for nth interstitial.

Parameters:n – Index of interstitials

get_coordinated_site_displacement(n)

Compute the total displacement of coordinated sites from the interstitial sites during the relaxation

Parameters:n – Index of defect site

get_coordinated_sites(n)

Coordinated sites for nth interstitial.

Parameters:n – Index of interstitials

get_coordination_number(n)

Coordination number for nth interstitial.

Parameters:n – Index of interstitials

get_defectsite(n)

Returns the defect site of nth interstitial.

Parameters:n – Index of interstitial

get_interstitial_structure(n)

Return relaxed bulk structure

get_percentage_bond_distance_change(n)

Bond distance change after the introduction of interstitial.

Parameters:n – index of interstitials

get_percentage_lattice_parameter_change(n)

Lattice parameter change after the introduction of interstitial

Parameters:n – index of interstitials

get_percentage_volume_change(n)

Volume change after the introduction of interstitial

Parameters:n – index of interstitials

class StructureMotifInterstitial(struct, inter_elem, motif_types=('tet', 'oct'), op_threshs=(0.3, 0.5), dl=0.2, doverlap=1.0, facmaxdl=1.01, verbose=False)

Bases: pymatgen.analysis.defects.point_defects.Defect

Subclass of Defect to generate interstitial sites at positions where the interstitialcy is coordinated by nearest neighbors in a way that resembles basic structure motifs (e.g., tetrahedra, octahedra). The algorithm will be formally introducted in an upcoming publication by Nils E. R. Zimmermann, Anubhav Jain, and Maciej Haranczyk, and it is already used by the Python Charged Defect Toolkit (PyCDT, https://arxiv.org/abs/1611.07481).

Generates symmetrically distinct interstitial sites at positions where the interstitial is coordinated by nearest neighbors in a pattern that resembles a supported structure motif (e.g., tetrahedra, octahedra).

Parameters:

• struct (Structure) – input structure for which symmetrically distinct interstitial sites are to be found.
• inter_elem (string) – element symbol of desired interstitial.
• motif_types ([string]) – list of structure motif types that are to be considered. Permissible types are: tet (tetrahedron), oct (octahedron).
• op_threshs ([float]) – threshold values for the underlying order parameters to still recognize a given structural motif (i.e., for an OP value >= threshold the coordination pattern match is positive, for OP < threshold the match is negative.
• dl (float) – grid fineness in Angstrom. The input structure is divided into a grid of dimension a/dl x b/dl x c/dl along the three crystallographic directions, with a, b, and c being the lengths of the three lattice vectors of the input unit cell.
• doverlap (float) – distance that is considered to flag an overlap between any trial interstitial site and a host atom.
• facmaxdl (float) – factor to be multiplied with the maximum grid width that is then used as a cutoff distance for the clustering prune step.
• verbose (bool) – flag indicating whether (True) or not (False; default) to print additional information to screen.

enumerate_defectsites()

Get all defect sites.

Returns:

list of periodic sites

representing the interstitials.

Return type:defect_sites ([PeriodicSite])

get_coordinating_elements_cns(i)

Get element-specific coordination numbers of defect with index i.

Returns:

dictionary storing the coordination numbers (int)

with string representation of elements as keys. (i.e., {elem1 (string): cn1 (int), …}).

Return type:elem_cn (dict)

get_motif_type(i)

Get the motif type of defect with index i (e.g., “tet”).

Returns:motif type. Return type:motif (string)

get_op_value(i)

Get order-parameter value of defect with index i.

Returns:OP value. Return type:opval (float)

make_supercells_with_defects(scaling_matrix)

Generate a sequence of supercells in which each supercell contains a single interstitial, except for the first supercell in the sequence which is a copy of the defect-free input structure.

Parameters:scaling_matrix (3x3 integer array) – scaling matrix to transform the lattice vectors. Returns:sequence of supercells. Return type:scs ([Structure])

class StructureRelaxer(structure)

Bases: object

get_relaxed_structure()

relax()

class Vacancy(structure, valences, radii)

Bases: pymatgen.analysis.defects.point_defects.Defect

Subclass of Defect to generate vacancies and their analysis.

Parameters:

• structure – pymatgen.core.structure.Structure
• valences – valences of elements as a dictionary
• radii – Radii of elements as a dictionary

enumerate_defectsites()

Returns symmetrically distinct vacancy sites

get_coordsites_min_max_charge(n)

Minimum and maximum charge of sites surrounding the vacancy site.

Parameters:n – Index of vacancy list

get_defectsite_effective_charge(n)

Effective charge (In Kroger-Vink notation, cation vacancy has effectively -ve charge and anion vacancy has +ve charge.)

Parameters:n – Index of vacancy list Returns:Effective charnge of defect site

get_defectsite_structure_index(n)

index of the vacacy site in the structure.sites list

Parameters:n – Index of vacancy list

get_defectsite_structure_indices()

Returns indices of symmetrically distinct vacancy sites

get_surface_area(n)

Surface area of the nth vacancy

Parameters:n – Index of symmetrically distinct vacancies list Returns:floating number representing volume of vacancy

get_volume(n)

Volume of the nth vacancy

Parameters:n – Index of symmetrically distinct vacancies list Returns:floating number representing volume of vacancy

make_supercells_with_defects(scaling_matrix, species=None, limit_return_structures=False)

Generate sequence of supercells in pymatgen.core.structure.Structure format, with each supercell containing one vacancy.

Parameters:

• scaling_matrix – super cell scale parameters in matrix forms
• species – Species in list format only for which vacancy supercells are required. If not specified all the species are considered.
• limit_return_structures – Boolean or positive number If number, only that many structures are returned.

Returns:

Supercells with vacancies. First supercell has no defects.

class VacancyFormationEnergy(vacancy)

Bases: object

Using GULP compute the vacancy formation energy. Works only for binary metal oxides due to the use of Buckingham Potentials

get_energy(n, tol=0.5)

Formation Energy for nth symmetrically distinct vacancy.

class ValenceIonicRadiusEvaluator(structure)

Bases: object

Computes site valences and ionic radii for a structure using bond valence analyzer

Parameters:structure – pymatgen.core.structure.Structure

radii

List of ionic radii of elements in the order of sites.

structure

Returns oxidation state decorated structure.

valences

List of oxidation states of elements in the order of sites.

symmetry_reduced_voronoi_nodes(structure, rad_dict, high_accuracy_flag=False, symm_flag=True)

Obtain symmetry reduced voronoi nodes using Zeo++ and pymatgen.symmetry.finder.SpacegroupAnalyzer

Parameters:

• strucutre – pymatgen Structure object
• rad_dict – Dictionary containing radii of spcies in the structure
• high_accuracy_flag – Flag denotting whether to use high accuracy version of Zeo++
• symm_flag – Flag denoting whether to return symmetrically distinct sites only

Returns:

Symmetrically distinct voronoi nodes as pymatgen Strucutre