A. Le Bail

Bio: A. Le Bail is an academic researcher from Centre national de la recherche scientifique. The author has contributed to research in topics: Crystal structure & Powder diffraction. The author has an hindex of 20, co-authored 91 publications receiving 3934 citations. Previous affiliations of A. Le Bail include University of Maine.

Size–strain line-broadening analysis of the ceria round-robin sample

Abstract: The results of both a line-broadening study on a ceria sample and a size–strain round robin on diffraction line-broadening methods, which was sponsored by the Commission on Powder Diffraction of the International Union of Crystallography, are presented. The sample was prepared by heating hydrated ceria at 923 K for 45 h. Another ceria sample was prepared to correct for the effects of instrumental broadening by annealing commercially obtained ceria at 1573 K for 3 h and slowly cooling it in the furnace. The diffraction measurements were carried out with two laboratory and two synchrotron X-ray sources, two constant-wavelength neutron and a time-of-flight (TOF) neutron source. Diffraction measurements were analyzed by three methods: the model assuming a lognormal size distribution of spherical crystallites, Warren–Averbach analysis and Rietveld refinement. The last two methods detected a relatively small strain in the sample, as opposed to the first method. Assuming a strain-free sample, the results from all three methods agree well. The average real crystallite size, on the assumption of a spherical crystallite shape, is 191 (5) A. The scatter of results given by different instruments is relatively small, although significantly larger than the estimated standard uncertainties. The Rietveld refinement results for this ceria sample indicate that the diffraction peaks can be successfully approximated with a pseudo-Voigt function. In a common approximation used in Rietveld refinement programs, this implies that the size-broadened profile cannot be approximated by a Lorentzian but by a full Voigt or pseudo-Voigt function. In the second part of this paper, the results of the round robin on the size–strain line-broadening analysis methods are presented, which was conducted through the participation of 18 groups from 12 countries. Participants have reported results obtained by analyzing data that were collected on the two ceria samples at seven instruments. The analysis of results received in terms of coherently diffracting, both volume-weighted and area-weighted apparent domain size are reported. Although there is a reasonable agreement, the reported results on the volume-weighted domain size show significantly higher scatter than those on the area-weighted domain size. This is most likely due to a significant number of results reporting a high value of strain. Most of those results were obtained by Rietveld refinement in which the Gaussian size parameter was not refined, thus erroneously assigning size-related broadening to other effects. A comparison of results with the average of the three-way comparative analysis from the first part shows a good agreement.

Monte Carlo indexing with McMaille

Abstract: A Monte Carlo code for indexing powder diffraction patterns is presented. Cell parameters are generated randomly and tested against an idealized powder profile generated from the extracted d’s and I’s. Limits with this program in solving problems associated with zeropoint errors and impurity lines are examined. Most problems (V 2 GHz processor); more time is needed for triclinic cases. Attempts are shown to be successful for the indexation of two-phase samples in simple cases (combining orthorhombic or higher symmetries). © 2004 International Centre for Diffraction Data.Key words: powder diffraction, indexing, Monte Carlo

Modelling the silica glass structure by the Rietveld method

Abstract: To refine amorphous structures like crystalline ones is impossible. This statement needs now some reconsideration in the case of silica glass. Starting with a microstrained crystalline model deriving from the α-carnegieite structure, atomic coordinates refinements by the Rietveld method prove to be possible. The credibility of the study is supported by the simultaneous fit of neutron and X-ray diffraction data. The agreement R χ factors are the best ever obtained with a small-size model built exclusively from [SiO 4 ] tetrahedra linked by corners. However it is concluded that ‘best’ remains insufficient.

A new study of the structure of LaNi5D6.7 using a modified Rietveld method for the refinement of neutron powder diffraction data

Abstract: The Rietveld profile analysis method has been extended using a Fourier analysis of line profiles on the basis of the Warren-Averbach method for separating size and strain effects. Assuming a given size distribution (Cauchy) and an adjustable strain variation in space, this method allows the simultaneous determination of the structural parameters and the size and strain parameters of the sample. It has been used for analysing the neutron diffraction pattern of β-LaNi 5 deuteride which exhibits a strongly anisotropic broadening. The mean coherency domain was chosen as an ellipsoid of revolution along the c axis. The structure is described in the space group P 6 3 mc as well as the P 31 c space group with five types of interstitial sites (three in the hypothetical fully ordered LaNi 5 D 7 phase). The strain parameter, i.e. the distribution of atomic positions around their equilibrium positions, varies by a factor of 2.5 while the mean particle size changes from 80 A to more than 2500 A in [ hk 0] and [00 l ] directions respectively.

Recent advances in magnetic structure determination by neutron powder diffraction

Abstract: 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.

Fityk: a general-purpose peak fitting program

Abstract: 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.

Rietveld refinement guidelines

Abstract: 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.