Indexing reflections¶
Error types¶
- class crystals.IndexingError¶
Bases:
RuntimeError
Indexing has failed.
New in version 1.3.0.
Single-crystal indexing with the DirAx algorithm¶
- crystals.index_dirax(reflections, initial=None, length_bounds=(2, 20))¶
Find the lattice associated with a list of reflections using the DirAx algorithm.
New in version 1.3.0.
- Parameters:
reflections (iterable of 3-tuple or ndarray, shape (N, 3)) – Iterable of reflections with their three-dimensional reciprocal space coordinates, or ndarray where each row is a reflections. Coordinates are in inverse Angstroms.
initial (
Lattice
orCrystal
, optional) – Initial guess for a lattice. The DirAx algorithm does not need an initial guess, but it can certainly help when many reflections are missing.length_bounds (2-tuple of floats, optional) – Minimum and maximum lattice vector lengths to consider, in Angstrom.
- Returns:
indexed (
Lattice
) – Lattice that best indexes reflections.indices (ndarray, shape (N, 3)) – Miller indices associated with each vector in reflections, in order.
- Raises:
IndexingError – The indexing has failed.
Notes
This indexing routine is based on the reference below. The algorithm is well-suited to situations where reflections might be missing, or situations where the list of reflections contains “alien” reflections not associated with the lattice.
Examples
We generate reflections from a crystal structure and re-index it for demonstration purposes.
>>> from crystals import index_dirax, Crystal >>> import numpy as np >>> graphite = Crystal.from_database('C') >>> # The list of reflections `qs` might be experimental measurements from either >>> # x-ray or electron diffraction. >>> qs = [graphite.scattering_vector(r) for r in graphite.bounded_reflections(bound=3.5)] >>> lattice, hkls = index_dirax(qs) >>> lattice < Lattice object with parameters 2.464Å, 2.464Å, 6.711Å, 90.00°, 90.00°, 120.00° >
References
A. J. M. Duisenberg, Indexing in Single-Crystal Diffractometry with an Obstinate List of Reflections (1992), J. Appl. Cryst vol. 25 pp. 92 - 96