Indexing in single-crystal diffractometry with an obstinate list of reflections

TLDR

The paper presents an indexing method for single‑crystal diffractometry that handles challenging cases such as twin lattices, incommensurate structures, fragmented crystals, long axes, and unreliable data. The method finds the reciprocal lattice by projecting observed reflections onto normals of planes defined by triples of points, identifying elementary periods in one‑dimensional rows; each row’s direction and spacing yields a direct axis vector, from which a primitive cell is chosen and refined against the fitting reflections, producing a main lattice or a main lattice plus alien reflections. Row periodicity and offending reflections are easily recognized, and the method operates semi‑automatically in DIRAX, successfully handling hundreds of CAD4 reflection files, including many auto‑indexing‑resistant lists.

Abstract

An indexing method for single-crystal diffractometry is described which is applicable to especially difficult cases such as twin lattices, incommensurate structures, fragmented crystals, long axes and unreliable data. Finding the reciprocal lattice from a cloud of reciprocal-lattice points (reflections) is reduced to finding elementary periods in one-dimensional rows, obtained by projecting all observed points onto the normal to the plane formed by any three of these points. Row periodicity and offending reflections are easily recognized. Each row, by its direction and (reciprocal) spacing, defines one direct axis vector, based upon all cooperating observations. From the direct vectors so obtained a primitive direct cell is chosen and refined against the fitting reflections. The result is one main lattice, or a main lattice and a set of alien reflections. The method operates semi-automatically in the program DIRAX and has been tested, without failure, on hundreds of CAD4 reflection files, among which there were many auto-indexing-resistant lists.