dscribe.core.lattice module¶

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class dscribe.core.lattice.Lattice(matrix)[source]¶

Bases: object

A lattice object. Essentially a matrix with conversion matrices. In general, it is assumed that length units are in Angstroms and angles are in degrees unless otherwise stated.

Create a lattice from any sequence of 9 numbers. Note that the sequence is assumed to be read one row at a time. Each row represents one lattice vector.

Parameters: matrix – Sequence of numbers in any form. Examples of acceptable input. i) An actual numpy array. ii) [[1, 0, 0], [0, 1, 0], [0, 0, 1]] iii) [1, 0, 0 , 0, 1, 0, 0, 0, 1] iv) (1, 0, 0, 0, 1, 0, 0, 0, 1) Each row should correspond to a lattice vector. E.g., [[10, 0, 0], [20, 10, 0], [0, 0, 30]] specifies a lattice with lattice vectors [10, 0, 0], [20, 10, 0] and [0, 0, 30].

property abc¶: Lengths of the lattice vectors, i.e. (a, b, c)

get_cartesian_coords(fractional_coords)[source]¶

Returns the cartesian coordinates given fractional coordinates.

Parameters: fractional_coords (3x1 array) – Fractional coords.
Returns: Cartesian coordinates

get_fractional_coords(cart_coords)[source]¶

Returns the fractional coordinates given cartesian coordinates.

Parameters: cart_coords (3x1 array) – Cartesian coords.
Returns: Fractional coordinates.

get_points_in_sphere(frac_points, center, r, zip_results=True)[source]¶

Find all points within a sphere from the point taking into account periodic boundary conditions. This includes sites in other periodic images.

Algorithm:

place sphere of radius r in crystal and determine minimum supercell (parallelpiped) which would contain a sphere of radius r. for this we need the projection of a_1 on a unit vector perpendicular to a_2 & a_3 (i.e. the unit vector in the direction b_1) to determine how many a_1”s it will take to contain the sphere.

Nxmax = r * length_of_b_1 / (2 Pi)
keep points falling within r.

Parameters

frac_points – All points in the lattice in fractional coordinates.
center – Cartesian coordinates of center of sphere.
r – radius of sphere.
zip_results (bool) – Whether to zip the results together to group by point, or return the raw fcoord, dist, index arrays

Returns

[(fcoord, dist, index) …] since most of the time, subsequent: processing requires the distance.
else:: fcoords, dists, inds

Return type

if zip_results

property inv_matrix¶: Inverse of lattice matrix.

property lengths¶

property matrix¶: Copy of matrix representing the Lattice

property reciprocal_lattice¶: Return the reciprocal lattice. Note that this is the standard reciprocal lattice used for solid state physics with a factor of 2 * pi. If you are looking for the crystallographic reciprocal lattice, use the reciprocal_lattice_crystallographic property. The property is lazily generated for efficiency.

property reciprocal_lattice_crystallographic¶: Returns the crystallographic reciprocal lattice, i.e., no factor of 2 * pi.