The dichotomy method for indexing powder diffraction patterns for low-symmetry lattices is studied in terms of an optimization of bound relations used in the comparison of observed data with the calculated patterns generated at each level of the analysis. A rigorous mathematical treatment is presented for monoclinic and triclinic cases. A new program, DICVOL91, has been written, working from the cubic end of the symmetry sequence to triclinic lattices. The search of unit cells is exhaustive within input parameter limits, although a few restrictions for the hkl indices of the first two diffraction lines have been introduced in the study of triclinic symmetry. The efficiency of the method has been checked by means of a large number of accurate powder data, with a very high success rate. Calculation times appeared to be quite reasonable for the majority of examples, down to monoclinic symmetry, but were less predictable for triclinic cases. Applications to all symmetries, including cases with a dominant zone, are discussed.

The ef®ciency of the successive dichotomy method for powder diffraction pattern indexing [Loue È r & Loue È r (1972). J. Appl. Cryst. 5, 271±275] has been proved over more than 30 years of usage. Features implemented in the new version of the computer program DICVOL04 include (i) a tolerance to the presence of impurity (or inaccurately measured) diffraction lines, (ii) a re®nement of the`zero-point' position, (iii) a reviewing of all input lines from the solution found from, generally, the ®rst 20 lines, (iv) a cell analysis, based on the concept of the reduced cell, to identify equivalent monoclinic and triclinic solutions, and (v) an optional analysis of input powder data to detect the presence of a signi®cant`zero-point' offset. New search strategies have also been introduced, e.g. each crystal system is scanned separately, within the input volume limits, to limit the risk of missing a solution characterized by a metric lattice singularity. The default values in the input ®le have been extended to 25 A Ê for the linear parameters and 2500 A Ê 3 for the cell volume. The search is carried out exhaustively within the input parameter limits and the absolute error on peak position measurements. Many tests with data from the literature and from powder data of pharmaceutical materials, collected with the capillary technique and laboratory monochromatic X-rays, have been performed with a high success rate, covering all crystal symmetries from cubic to triclinic. Some examples reported as`dif®cult' cases are also discussed. Additionally, a few recommendations for the correct practice of powder pattern indexing are reported.