European Powder Diffraction EPDIC 8

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Authors: Marek Andrzej Kojdecki
Abstract: A polycrystalline material may be considered as a set of crystallites. Since the crystallites have rather regular shapes, the assumption about the same shape is not far from physical reality for most polycrystals, especially powders. Such a system may be characterised in a statistical manner by two functions, the crystallite size distribution and the crystalline lattice strain distribution (for some materials other lattice distortions inside the crystallites, like stacking faults or dislocations, are to be considered additionally). The crystalline microstructure can be determined by investigating an X-ray diffraction pattern, what should be based on comparing an experimental pattern with a simulated one, derived from an appropriate physical model. Pure X-ray diffraction line profiles, containing information about crystalline microstructure, can be extracted from experimental data. An important step in analysing them is the separation of contributions from crystallite shapes and sizes and from strains, enabling the proper determination of both distributions together with the estimation of prevalent crystallite shape. A model of polycrystalline material combined with a description of X-ray diffraction on it, making such an analysis possible, is presented in this article. An approximate formula for separating both effects is based on results of computer simulation of pure X-ray diffraction line profiles from different crystalline powders, done under simplifying assumptions that the crystallites are prismatic or spherical, the size distribution is logarithmic-normal and the second-order strain distribution is normal.
Authors: Radomír Kužel, D. Šimek, J. Kub, Rinat K. Islamgaliev
Abstract: Two methods were used for the analysis of submicro-crystalline copper prepared by high-pressure (6 GPa) severe plastic deformation. Conventional powder XRD study was carried in terms of the modified Williamson-Hall (WH) plots and shown large line-broadening anisotropy. A new high-resolution small-angle transmission diffuse scattering method was applied for determination of crystallite size. Two methods were used for the evaluation of the diffuse scattering - calculation of the autocorrelation function of the crystalline shape by the transformation of the measured signal and by the direct fitting. Bimodal block size distribution has to be assumed for annealed samples. This was also confirmed by classical back-reflection film method as well as by the long tails of conventional diffraction profiles.
Authors: J. Lhotka, Radomír Kužel, G. Cappuccio, V. Valvoda
Abstract: The thickness measurement based on absorption of X-rays in thin films has been tested on a polycrystalline titanium nitride films deposited on a tungsten carbide substrate. Intensities of three reflections from each material were measured for incidence angles of the primary beam ranging from 0.5° to 35°. After experimental correction for texture effects, data from the TiN film and the WC substrate were fitted by known functions using least squares routines. The substrate reflection intensities were found to be more suitable for determining the thickness of the overlaying thin film. The average thickness of TiN film (2.00± 0.17 µm) determined from the substrate reflections was in fair agreement with the average value obtained from optical microscopy (2.2± 0.8 µm). The thickness values determined from the TiN thin film reflections are very unreliable due to a high sensitivity of measurements to disturbing instrumental and sample effects at small angles.
Authors: I. Lucks, P. Lamparter, Jian Xu, Eric J. Mittemeijer
Abstract: Palladium powder was deformed by ball milling under an argon atmosphere in two types of mills for different milling times. Two methods for X-ray diffraction line profile analysis, the Williamson-Hall method and the Warren-Averbach method, yielded similar trends, but different quantitative results for crystallite sizes (column lengths) and microstrains. With both methods, from the anisotropic line broadening for planetary milled Pd smaller crystallite sizes and larger microstrains were obtained along the <100> direction than along <111>. Milling in a shaker mill causes microstrain higher by a factor of about two than milling in a planetary mill. The evolution of the crystallite size upon milling was discussed in terms of bimodal size distributions.
Authors: Juan Rodríquez-Carvajal, T. Roisnel
Abstract: A short account of the methodology used within FullProf to extract average micro-structural properties from the analysis of broadened lines of constant wavelength diffraction patterns is presented. The approach is based on the Voigt approximation and can be combined with the Rietveld method as well as with the profile matching (Le Bail fit) procedure. Both the instrumental and sample profiles are supposed to be well described by Voigt functions. To get reliable sample parameters a good knowledge of the Instrumental Resolution Function (IRF) is needed. Only a phenomenological treatment, in terms of coherent size domains and strains due to structural defects, is performed.
Authors: Arnold C. Vermeulen, Rob Delhez
Abstract: All methods of analyzing the broadening of XRD line profiles have to take into account two basic effects: broadening by the instrument - including the X-ray spectrum - and the characteristics of broadening by size effects and by lattice defects - including their interaction. These effects are handled in practice by a wide range of auxiliary assumptions. In this paper these assumptions and their quality with respect to "appropriateness of purpose" are listed and compared. By systematic ranking of these assumptions in accordance with their quality, a 2-dimensional map can be constructed that visualizes the differences in the quality of the assumptions. This 2-dimensional map brings a new viewpoint to the various methods for line profile analysis, because it enables a qualitative comparison of the assumptions of existing methods and new developments.
Authors: U. Welzel, Eric J. Mittemeijer
Abstract: The so-called crystallite group (CGM) method, employed for diffraction stress analysis, involves that a possibly complex texture is approximated by a set of one or a few so-called ideal orientations. It has been shown that this approximation can lead to pronounced errors in the determined stress values. The range of applicability of the CGM has been investigated from a theoretical point of view. Numerical simulations of diffraction strain measurements have been performed using orientation distribution functions representing textures of different strength and sharpness. Special emphasis has been put on the fibre-textured case.
Authors: Leszek Tarkowski, L. Laskosz, Jan T. Bonarski
Abstract: The traditionally applied registration method of the back-reflection pole figure is based on the equiangular measurement lattice. It determines also the equiangular character of presentation of measurement results in form of stereographic projection, termed as the pole figure. The mentioned registration mode is characterized by an unequal density of the measurement points on the pole figure. It is the evident disadvantage of the traditional registration mode. In order to eliminate the drawback, and to increase the efficiency of the measurement procedure, an optimization of the registration method was made. The optimization consists in dividing a reference sphere of the stereographical projection into uniform regions, so called equal solid angles (ESA). As a result of the applied optimization, over 40% reduction in number of the measurement points and in the registration time at preserved pole figure quality was obtained. For verification of the new solution, a set of experimental pole figures of cold rolled copper by the traditional mode as well as the introduced ESA one was recorded. Comparison of the results of texture analysis based on the orientation distribution function was carried out. The results of measurements performed by the ESA method confirm the efficiency of the introduced optimization.
Authors: I. Tomov
Abstract: A method of pole density measurements is described, which uses the differences in X-ray beam polarisation of two monochromators. The method requires a single reflection at an intermediate diffraction angle. Experimental verification is provided by pole density measurements of Ag films and comparison the results obtained with the proposed method with results from the reflection-pair method [8-10].
Authors: H. Toraya, H. Hibino, Takashi Ida
Abstract: A quantitative basis for rocking curve measurements of preferentially oriented polycrystalline thin films is presented. The Gaussian function is used for modeling the preferred orientation of crystallites around the plane normal of the specimen surface. A theoretical rocking curve is fitted to the observed curve by the least-squares method, and the degree of preferred orientation, given in volume fraction, can be derived from a refined preferred orientation parameter of the distribution function even when the preferred orientation is very small. Uses of diffractometers equipped with parallel-beam optics and the integrated intensity rather than peak intensity are important for reliable rocking curve measurement.

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