In spite of intrinsic limitations, neutron powder diffraction is, and will still be in the future, the primary and most straightforward technique for magnetic structure determination. In this paper some recent improvements in the analysis of magnetic neutron powder diffraction data are discussed. After an introduction to the subject, the main formulas governing the analysis of the Bragg magnetic scattering are summarized and shortly discussed. Next, we discuss the method of profile fitting without a structural model to get precise integrated intensities and refine the propagation vector(s) of the magnetic structure. The simulated annealing approach for magnetic structure determination is briefly discussed and, finally, some features of the program FullProf concerning the magnetic structure refinement are presented and discussed. The different themes are illustrated with simple examples.

Recent advances in magnetic structure determination by neutron powder diffraction

Fityk is portable, open-source software for nonlinear curve fitting and data analysis. It specializes in fitting a sum of bell-shaped functions to experimental data. In particular, it enables Pawley refinement of powder diffraction data and size–strain analysis.

Fityk: a general-purpose peak fitting program

A set of general guidelines for structure refinement using the Rietveld (whole-profile) method has been formulated by the International Union of Crystallography Commission on Powder Diffraction. The practical rather than the theoretical aspects of each step in a typical Rietveld refinement are discussed with a view to guiding newcomers in the field. The focus is on X-ray powder diffraction data collected on a laboratory instrument, but features specific to data from neutron (both constant-wavelength and time-of-flight) and synchrotron radiation sources are also addressed. The topics covered include (i) data collection, (ii) background contribution, (iii) peak-shape function, (iv) refinement of profile parameters, (v) Fourier analysis with powder diffraction data, (vi) refinement of structural parameters, (vii) use of geometric restraints, (viii) calculation of e.s.d.'s, (ix) interpretation of R values and (x) some common problems and possible solutions.

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Rietveld refinement guidelines

The efficiency of the successive dichotomy method for powder diffraction pattern indexing [Louer & Louer (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 refinement of the `zero-point' position, (iii) a reviewing of all input lines from the solution found from, generally, the first 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 significant `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 file have been extended to 25 A for the linear parameters and 2500 A3 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 `difficult' cases are also discussed. Additionally, a few recommendations for the correct practice of powder pattern indexing are reported.

Powder pattern indexing with the dichotomy method

Anisotropic line-shape broadening (peak width which is not a smooth function of d-spacing) is frequently observed in powder diffraction patterns, and can be a source of considerable difficulty for whole-pattern fitting or Rietveld analysis. A model of the multi-dimensional distribution of lattice metrics within a powder sample is developed, leading naturally to a few parameters which can be varied to achieve optimal line-shape fits. Conditions on these parameters are derived for all crystal systems, and the method is illustrated with two examples: sodium p-hydroxybenzoate and rubidium fulleride.

J.L. Fourquet

Papers

Ab-initio structure determination of LiSbWO6 by X-ray powder diffraction

Crystal structure of the metastable form of aluminum trifluoride β-AlF3 and the gallium and indium homologs

LiNbWO6: Crystal structure of its two allotropic forms

Crystal structure and thermal behaviour of H2Ti3O7: A new defective ramsdellite form from Li+H+ exchange on Li2Ti3O7

Structure determination of A2NaAl3F12 (A=K, Rb)