Lattices (erlab.lattice)

Tools related to the real and reciprocal lattice.

Functions

angle_between(v1, v2)	Return the angle between two vectors.
abc2avec(a, b, c, alpha, beta, gamma)	Construct lattice vectors from lattice parameters.
avec2abc(avec)	Determine lattice parameters from lattice vectors.
to_reciprocal(avec)	Construct the reciprocal lattice vectors from real lattice vectors.
to_real(bvec)	Construct the real lattice vectors from reciprocal lattice vectors.

erlab.lattice.abc2avec(a, b, c, alpha, beta, gamma)

Construct lattice vectors from lattice parameters.

Parameters:

• a (floating) – Lattice parameter \(a\).

• b (floating) – Lattice parameter \(b\).

• c (floating) – Lattice parameter \(c\).

• alpha (floating) – Lattice parameter \(\alpha\) in degrees.

• beta (floating) – Lattice parameter \(\beta\) in degrees.

• gamma (floating) – Lattice parameter \(\gamma\) in degrees.

Returns:

avec – Real lattice vectors, given as a 3 by 3 numpy array with each basis vector given in each row.

Return type:

ndarray[tuple[int, …], dtype[floating]]

erlab.lattice.angle_between(v1, v2)

Return the angle between two vectors.

Parameters:

• v1 (array-like) – 1D array of length 3, specifying a vector.

• v2 (array-like) – 1D array of length 3, specifying a vector.

Returns:

float – The angle in degrees.

Return type:

float

erlab.lattice.avec2abc(avec)

Determine lattice parameters from lattice vectors.

Parameters:

avec (ndarray[tuple[int, ...], dtype[floating]]) – Real lattice vectors, given as a 3 by 3 numpy array with each basis vector given in each row.

Returns:

a, b, c, alpha, beta, gamma

Return type:

tuple[float, float, float, float, float, float]

erlab.lattice.to_real(bvec)

Construct the real lattice vectors from reciprocal lattice vectors.

Parameters:

bvec (ndarray[tuple[int, ...], dtype[floating]]) – Reciprocal lattice vectors, given as a 3 by 3 numpy array with each basis vector given in each row.

Returns:

avec – The real lattice vectors.

Return type:

ndarray[tuple[int, …], dtype[floating]]

erlab.lattice.to_reciprocal(avec)

Construct the reciprocal lattice vectors from real lattice vectors.

Parameters:

avec (ndarray[tuple[int, ...], dtype[floating]]) – Real lattice vectors, given as a 3 by 3 numpy array with each basis vector given in each row.

Returns:

bvec – The reciprocal lattice vectors.

Return type:

ndarray[tuple[int, …], dtype[floating]]