Layer Group API¶

Symmetry analysis and classification tables for the 80 layer groups. Shared types such as moyopy.Cell, moyopy.Operations, moyopy.UnimodularTransformation, and moyopy.PointGroup are documented on the API Reference hub.

Symmetry datasets¶

Run a symmetry analysis on a moyopy.Cell treated as a layer (slab) and inspect the result.

moyopy.MoyoLayerDataset ¶

MoyoLayerDataset(cell: Cell, *, symprec: float = 0.0001, angle_tolerance: float | None = None, setting: LayerSetting | None = None, rotate_basis: bool = True)

A dataset containing layer-group symmetry information of the input crystal structure (a 2D-periodic system whose third basis vector is the aperiodic stacking direction).

Parameters:

Name	Type	Description	Default
`cell`	`Cell`	Input crystal structure. The third basis vector `c` must be the aperiodic stacking direction and perpendicular to `a, b`; `a, b` must lie in the xy-plane.	required
`symprec`	`float`	Symmetry search tolerance in the unit of cell.basis.	`0.0001`
`angle_tolerance`	`float \| None`	Symmetry search tolerance in the unit of radians.	`None`
`setting`	`LayerSetting \| None`	Preference for the Hall setting of the layer group.	`None`
`rotate_basis`	`bool`	Whether to rotate the basis vectors of the input cell to those of the standardized cell.	`True`

angle_tolerance `property` ¶

angle_tolerance: float | None

Actually used angle_tolerance in the symmetry search.

hall_number `property` ¶

hall_number: int

Layer Hall symbol number (1 - 116).

mapping_std_prim `property` ¶

mapping_std_prim: list[int]

Mapping sites in the input cell to those in the primitive standardized layer cell.

number `property` ¶

number: int

Layer group number (1 - 80).

operations `property` ¶

operations: Operations

Layer-group operations in the input cell.

orbits `property` ¶

orbits: list[int]

The i-th atom in the input cell is equivalent to the orbits[i]-th atom in the input cell.

pearson_symbol `property` ¶

pearson_symbol: str

Pearson symbol for the standardized layer cell.

prim_std_cell `property` ¶

prim_std_cell: Cell

Primitive standardized layer cell.

prim_std_linear `property` ¶

prim_std_linear: list[list[float]]

Linear part of transformation from the input cell to the primitive standardized layer cell.

prim_std_origin_shift `property` ¶

prim_std_origin_shift: list[float]

Origin shift of transformation from the input cell to the primitive standardized layer cell.

site_symmetry_symbols `property` ¶

site_symmetry_symbols: list[str]

Site symmetry symbols for each site in the input cell.

The orientation of the site symmetry is w.r.t. the standardized cell.

std_cell `property` ¶

std_cell: Cell

Conventional standardized layer cell.

The input cell is related to the standardized cell by (std_linear, std_origin_shift) and std_rotation_matrix::

std_cell.basis.T = std_rotation_matrix @ cell.basis.T @ std_linear
x_std = np.linalg.inv(std_linear) @ (x_input - std_origin_shift)

std_linear `property` ¶

std_linear: list[list[float]]

Linear part of transformation from the input cell to the standardized layer cell.

std_origin_shift `property` ¶

std_origin_shift: list[float]

Origin shift of transformation from the input cell to the standardized layer cell.

std_rotation_matrix `property` ¶

std_rotation_matrix: list[list[float]]

Rigid rotation (orthogonal matrix) applied to the lattice basis.

symprec `property` ¶

symprec: float

Actually used symprec in the symmetry search.

wyckoffs `property` ¶

wyckoffs: list[str]

Wyckoff letters for each site in the input cell.

as_dict ¶

as_dict() -> dict[str, Any]

Convert an object to a dictionary.

deserialize_json `classmethod` ¶

deserialize_json(json_str: str) -> Self

Deserialize an object from a JSON string.

from_dict `classmethod` ¶

from_dict(obj: dict[str, Any]) -> Self

Create an object from a dictionary.

serialize_json ¶

serialize_json() -> str

Serialize an object to a JSON string.

Crystallographic data¶

Layer-group settings, classification tables, and helpers to fetch operations by layer-group number.

moyopy.LayerSetting ¶

Preference for the Hall setting of a layer group.

as_dict ¶

as_dict() -> dict[str, Any]

Convert an object to a dictionary

hall_number `classmethod` ¶

hall_number(hall_number: int) -> LayerSetting

Specific layer Hall number from 1 to 116.

serialize_json ¶

serialize_json() -> str

Serialize an object to a JSON string

spglib `classmethod` ¶

spglib() -> LayerSetting

The setting with the smallest layer Hall number for each layer group.

standard `classmethod` ¶

standard() -> LayerSetting

BCS / ITE standard setting per de la Flor et al., Acta Cryst. A77, 559-571 (2021).

moyopy.LayerCentering ¶

Centering of a layer-group conventional cell. Only P (primitive) and C (rectangular-centered) occur for layer groups.

lattice_points `property` ¶

lattice_points: list[list[float]]

Unique lattice points (in fractional coordinates) of the conventional cell. The third (c) component is always zero because layer-group centerings are purely in-plane.

linear `property` ¶

linear: list[list[int]]

Transformation matrix from the primitive cell to the conventional cell. The aperiodic axis c is left untouched.

order `property` ¶

order: int

Order of the centering.

as_dict ¶

as_dict() -> dict[str, Any]

Convert an object to a dictionary

serialize_json ¶

serialize_json() -> str

Serialize an object to a JSON string

moyopy.LayerHallSymbolEntry ¶

LayerHallSymbolEntry(hall_number: int)

An entry containing layer-group information for a specified layer hall_number.

arithmetic_number `property` ¶

arithmetic_number: int

Number for layer arithmetic crystal classes (1 - 43).

centering `property` ¶

centering: LayerCentering

Layer centering.

hall_number `property` ¶

hall_number: int

Sequential number for layer-group Hall settings (1 - 116).

hall_symbol `property` ¶

hall_symbol: str

Layer Hall symbol with lowercase p/c lattice prefix.

hm_full `property` ¶

hm_full: str

Hermann-Mauguin symbol in full notation.

hm_short `property` ¶

hm_short: str

Hermann-Mauguin symbol in short notation.

number `property` ¶

number: int

Layer-group number (1 - 80).

setting `property` ¶

setting: str

Setting code (paper Table 5 axis/origin labels: "", "a", "b", "b-ac", "c", "c1", "c2", "c3", "1", "2").

as_dict ¶

as_dict() -> dict[str, Any]

Convert an object to a dictionary

serialize_json ¶

serialize_json() -> str

Serialize an object to a JSON string

moyopy.LayerGroupType ¶

LayerGroupType(number: int)

Layer-group type information.

arithmetic_number `property` ¶

arithmetic_number: int

Number for layer arithmetic crystal classes (1 - 43).

arithmetic_symbol `property` ¶

arithmetic_symbol: str

Symbol for the layer arithmetic crystal class.

bravais_class `property` ¶

bravais_class: str

Bravais class for the layer group's 2D lattice (one of "mp", "op", "oc", "tp", "hp").

geometric_crystal_class `property` ¶

geometric_crystal_class: str

Geometric crystal class. Cubic classes never occur for layer groups.

See https://github.com/spglib/moyo/blob/main/moyo/src/data/classification.rs for string values.

hm_full `property` ¶

hm_full: str

Hermann-Mauguin symbol in full notation.

hm_short `property` ¶

hm_short: str

Hermann-Mauguin symbol in short notation.

lattice_system `property` ¶

lattice_system: str

Lattice system (one of "Oblique", "Rectangular", "Square", "Hexagonal").

number `property` ¶

number: int

Layer-group number (1 - 80).

as_dict ¶

as_dict() -> dict[str, Any]

Convert an object to a dictionary

serialize_json ¶

serialize_json() -> str

Serialize an object to a JSON string

moyopy.LayerArithmeticCrystalClass ¶

LayerArithmeticCrystalClass(arithmetic_number: int)

Layer arithmetic crystal class information.

arithmetic_number `property` ¶

arithmetic_number: int

Number for layer arithmetic crystal classes (1 - 43).

bravais_class `property` ¶

bravais_class: str

Bravais class for the layer group's 2D lattice (one of "mp", "op", "oc", "tp", "hp").

geometric_crystal_class `property` ¶

geometric_crystal_class: str

Geometric crystal class. Cubic classes never occur for layer groups.

lattice_system `property` ¶

lattice_system: str

Lattice system (one of "Oblique", "Rectangular", "Square", "Hexagonal").

symbol `property` ¶

symbol: str

Symbol for the layer arithmetic crystal class (e.g. "p1", "c2/m11").

as_dict ¶

as_dict() -> dict[str, Any]

Convert an object to a dictionary

serialize_json ¶

serialize_json() -> str

Serialize an object to a JSON string

moyopy.operations_from_layer_number ¶

operations_from_layer_number(number: int, *, setting: LayerSetting | None = None, primitive: bool = False) -> Operations

Layer Group API¶

Symmetry datasets¶

moyopy.MoyoLayerDataset ¶

angle_tolerance property ¶

hall_number property ¶

mapping_std_prim property ¶

number property ¶

operations property ¶

orbits property ¶

pearson_symbol property ¶

prim_std_cell property ¶

prim_std_linear property ¶

prim_std_origin_shift property ¶

site_symmetry_symbols property ¶

std_cell property ¶

std_linear property ¶

std_origin_shift property ¶

std_rotation_matrix property ¶

symprec property ¶

wyckoffs property ¶

as_dict ¶

deserialize_json classmethod ¶

from_dict classmethod ¶

serialize_json ¶

Crystallographic data¶

moyopy.LayerSetting ¶

as_dict ¶

hall_number classmethod ¶

serialize_json ¶

spglib classmethod ¶

standard classmethod ¶

moyopy.LayerCentering ¶

lattice_points property ¶

linear property ¶

order property ¶

as_dict ¶

serialize_json ¶

moyopy.LayerHallSymbolEntry ¶

arithmetic_number property ¶

centering property ¶

hall_number property ¶

hall_symbol property ¶

hm_full property ¶

hm_short property ¶

number property ¶

setting property ¶

as_dict ¶

serialize_json ¶

moyopy.LayerGroupType ¶

arithmetic_number property ¶

arithmetic_symbol property ¶

bravais_class property ¶

geometric_crystal_class property ¶

hm_full property ¶

hm_short property ¶

lattice_system property ¶

number property ¶

as_dict ¶

serialize_json ¶

moyopy.LayerArithmeticCrystalClass ¶

arithmetic_number property ¶

bravais_class property ¶

geometric_crystal_class property ¶

lattice_system property ¶

symbol property ¶

as_dict ¶

serialize_json ¶

moyopy.operations_from_layer_number ¶

angle_tolerance `property` ¶

hall_number `property` ¶

mapping_std_prim `property` ¶

number `property` ¶

operations `property` ¶

orbits `property` ¶

pearson_symbol `property` ¶

prim_std_cell `property` ¶

prim_std_linear `property` ¶

prim_std_origin_shift `property` ¶

site_symmetry_symbols `property` ¶

std_cell `property` ¶

std_linear `property` ¶

std_origin_shift `property` ¶

std_rotation_matrix `property` ¶

symprec `property` ¶

wyckoffs `property` ¶

deserialize_json `classmethod` ¶

from_dict `classmethod` ¶

hall_number `classmethod` ¶

spglib `classmethod` ¶

standard `classmethod` ¶

lattice_points `property` ¶

linear `property` ¶

order `property` ¶

arithmetic_number `property` ¶

centering `property` ¶

hall_number `property` ¶

hall_symbol `property` ¶

hm_full `property` ¶

hm_short `property` ¶

number `property` ¶

setting `property` ¶

arithmetic_number `property` ¶

arithmetic_symbol `property` ¶

bravais_class `property` ¶

geometric_crystal_class `property` ¶

hm_full `property` ¶

hm_short `property` ¶

lattice_system `property` ¶

number `property` ¶

arithmetic_number `property` ¶

bravais_class `property` ¶

geometric_crystal_class `property` ¶

lattice_system `property` ¶

symbol `property` ¶