wulfric.Lattice

class wulfric.Lattice(*args, eps_rel=0.0001, angle_tol=0.0001, **kwargs)

General 3D lattice.

When created from the cell orientation of the cell is respected, however the lattice vectors may be renamed with respect to [1].

Since v0.2.2 the standardization of the lattice is not performed by default at the time of the lattice creation. The standardization is performed when is is required, for example, when the kpoints are computed.

Lattice can be created in a three alternative ways:

>>> import wulfric as wulf
>>> l = wulf.Lattice(cell = [[1, 0, 0], [0, 1, 0], [0, 0, 1]])
>>> l = wulf.Lattice(a1 = [1,0,0], a2 = [0,1,0], a3 = [0,0,1])
>>> l = wulf.Lattice(a=1, b=1, c=1, alpha=90, beta=90, gamma=90)

Parameters:

cell(3, 3) array-like

Unit cell, rows are vectors, columns are coordinates.

a1(3,) array-like

First vector of unit cell (cell[0]).

a2(3,) array-like

SEcond vector of unit cell (cell[1]).

a3(3,) array-like

Third vector of unit cell (cell[2]).

afloat, default=1

Length of the \(a_1\) vector.

bfloat, default=1

Length of the \(a_2\) vector.

cfloat, default=1

Length of the \(a_3\) vector.

alphafloat, default=90

Angle between vectors \(a_2\) and \(a_3\). In degrees.

betafloat, default=90

Angle between vectors \(a_1\) and \(a_3\). In degrees.

gammafloat, default=90

Angle between vectors \(a_1\) and \(a_2\). In degrees.

eps_relfloat, default 1e-4

Relative tolerance for distance.

angle_tolfloat, default 1e-4

Absolute tolerance for angles, in degrees.

Attributes:

eps_relfloat, default 1e-4

Relative tolerance for the distance.

References

[1]

Setyawan, W. and Curtarolo, S., 2010. High-throughput electronic band structure calculations: Challenges and tools. Computational materials science, 49(2), pp.299-312.

Methods:

copy()	Create a copy of the lattice.
standardize()	Standardize cell with respect to the Bravais lattice type as defined in [Raad91bf4d954-1].
type([eps_rel, angle_tol])	Identify the lattice type.
voronoi_cell([reciprocal, normalize])	Computes Voronoi edges around (0,0,0) point.

Properties:

C_matrix	Transformation matrix that transforms primitive cell (Lattice.cell()) to the conventional standardized cell.
S_matrix	Transformation matrix that transforms the primitive cell to the standardized primitive cell.
a	Length of the first lattice vector \(\vert\boldsymbol{a_1}\vert\).
a1	First lattice vector \(\boldsymbol{a_1}\).
a2	Second lattice vector \(\boldsymbol{a_2}\).
a3	Third lattice vector \(\boldsymbol{a_3}\).
alpha	Angle between second and third lattice vector.
angle_tol	Absolute tolerance for the angle.
b	Length of the second lattice vector \(\vert\boldsymbol{a_2}\vert\).
b1	First reciprocal lattice vector.
b2	Second reciprocal lattice vector.
b3	Third reciprocal lattice vector.
beta	Angle between first and third lattice vector.
c	Length of the third lattice vector \(\vert\boldsymbol{a_3}\vert\).
cell	Unit cell of the lattice.
centring_type	Centring type.
conv_a	Length of the first vector of the conventional cell.
conv_a1	First vector of the conventional cell.
conv_a2	Second vector of the conventional cell.
conv_a3	Third vector of the conventional cell.
conv_alpha	Angle between second and third conventional lattice vector.
conv_b	Length of the second vector of the conventional cell.
conv_beta	Angle between first and third conventional lattice vector.
conv_c	Length of the third vector of the conventional cell.
conv_cell	Conventional cell.
conv_gamma	Angle between first and second conventional lattice vector.
conv_parameters	Return conventional cell parameters.
conv_unit_cell_volume	Volume of the conventional unit cell.
convention	Convention used for the standardization of the unit cell.
crystal_family	Crystal family.
eps	Absolute tolerance for the distance.
eps_rel	Relative tolerance for the distance.
gamma	Angle between first and second lattice vector.
k_a	Length of the first reciprocal lattice vector \(\vert\boldsymbol{b_1}\vert\).
k_alpha	Angle between second and third reciprocal lattice vector.
k_b	Length of the second reciprocal lattice vector \(\vert\boldsymbol{b_2}\vert\).
k_beta	Angle between first and third reciprocal lattice vector.
k_c	Length of the third reciprocal lattice vector \(\vert\boldsymbol{b_3}\vert\).
k_gamma	Angle between first and second reciprocal lattice vector.
kpoints	Instance of Kpoints with the high symmetry points and path.
name	Human-readable name of the Bravais lattice type.
parameters	Return cell parameters.
pearson_symbol	Pearson symbol.
rcell	Reciprocal cell.
reciprocal_cell	Reciprocal cell.
reciprocal_cell_volume	Volume of the reciprocal cell.
reciprocal_parameters	Return reciprocal cell parameters.
unit_cell_volume	Volume of the unit cell.
variation	Variation of the lattice, if any.