radtools.Lattice

class radtools.Lattice(*args, standardize=True, **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].

Creation may change the angles and the lengths of the cell vectors. It preserve the volume, right- or left- handedness, lattice type and variation of the cell.

The lattice vector`s lengths are preserved as a set.

The angles between the lattice vectors are preserved as a set with possible changes of the form: \(angle \rightarrow 180 - angle\).

The returned cell may not be the same as the input one, but it is translationally equivalent.

Lattice can be created in a three alternative ways:

>>> import radtools as rad
>>> l = rad.Lattice(cell = [[1, 0, 0], [0, 1, 0], [0, 0, 1]])
>>> l = rad.Lattice(a1 = [1,0,0], a2 = [0,1,0], a3 = [0,0,1])
>>> l = rad.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.

standardizebool, default True

Whether to standardize the cell. The consistence of the predefined k paths is not guaranteed in the cell is not unified.

Attributes:

eps_relfloat, default 1e-4

Relative epsilon

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:

lattice_points([relative, reciprocal, normalize])	Compute lattice points
type([eps_rel])	Identify the lattice type.
voronoi_cell([reciprocal, normalize])	Computes Voronoi edges around (0,0,0) point.

Properties:

a	Length of the first lattice vector \(\vert\vec{a}_1\vert\).
a1	First lattice vector \(\vec{a}_1\).
a2	Second lattice vector \(\vec{a}_2\).
a3	Third lattice vector \(\vec{a}_3\).
alpha	Angle between second and third lattice vector.
b	Length of the second lattice vector \(\vert\vec{a}_2\vert\).
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 \(\vert\vec{a}_3\vert\).
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.
crystal_family	Crystal family.
eps	Epsilon parameter.
eps_rel	Relative epsilon
gamma	Angle between first and second lattice vector.
k_a	Length of the first reciprocal lattice vector \(\vert\vec{b}_1\vert\).
k_alpha	Angle between second and third reciprocal lattice vector.
k_b	Length of the second reciprocal lattice vector \(\vert\vec{b}_2\vert\).
k_beta	Angle between first and third reciprocal lattice vector.
k_c	Length of the third reciprocal lattice vector \(\vert\vec{b}_3\vert\).
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.
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.