Jenő Gubicza

Crystallite size distribution and dislocation structure determined by diffraction profile analysis: principles and practical application to cubic and hexagonal crystals

Two different methods of diffraction profile analysis are presented. In the first, the breadths and the first few Fourier coefficients of diffraction profiles are analysed by modified Williamson–Hall and Warren–Averbach procedures. A simple and pragmatic method is suggested to determine the crystallite size distribution in the presence of strain. In the second, the Fourier coefficients of the measured physical profiles are fitted by Fourier coefficients of well established ab initio functions of size and strain profiles. In both procedures, strain anisotropy is rationalized by the dislocation model of the mean square strain. The procedures are applied and tested on a nanocrystalline powder of silicon nitride and a severely plastically deformed bulk copper specimen. The X-ray crystallite size distributions are compared with size distributions obtained from transmission electron microscopy (TEM) micrographs. There is good agreement between X-ray and TEM data for nanocrystalline loose powders. In bulk materials, a deeper insight into the microstructure is needed to correlate the X-ray and TEM results.

MWP-fit : a program for multiple whole-profile fitting of diffraction peak profiles by ab initio theoretical functions

A computer program has been developed for the determination of microstructural parameters from diffraction profiles of materials with cubic or hexagonal crystal lattices. The measured profiles or their Fourier transforms are fitted by ab initio theoretical functions for size and strain broadening. In the calculation of the theoretical functions, it is assumed that the crystallites have log-normal size distribution and that the strain is caused by dislocations. Strain and size anisotropy are taken into account by the dislocation contrast factors and the ellipticity of the crystallites. The fitting procedure provides the median and the variance of the size distribution and the ellipticity of the crystallites, and the density and arrangement of the dislocations. The efficiency of the program is illustrated by examples of severely deformed copper and ball-milled lead sulfide specimens.

Nanostructures in Ti processed by severe plastic deformation

Metals and alloys processed by severe plastic deformation (SPD) can demonstrate superior mechanical properties, which are rendered by their unique defect structures. In this investigation, transmission electron microscopy and x-ray analysis were used to systematically study the defect structures, including grain and subgrain structures, dislocation cells, dislocation distributions, grain boundaries, and the hierarchy of these structural features, in nanostructured Ti produced by a two-step SPD procedure—warm equal channel angular pressing followed by cold rolling. The effects of these defect structures on the mechanical behaviors of nanostructured Ti are discussed.

Correlation between subgrains and coherently scattering domains

Crystallite size determined by X-ray line profile analysis is often smaller than the grain or subgrain size obtained by transmission electron microscopy, especially when the material has been produced by plastic deformation. It is shown that besides differences in orientation between grains or subgrains, dipolar dislocation walls without differences in orientation also break down coherency of X-rays scattering. This means that the coherently scattering domain size provided by X-ray line profile analysis provides subgrain or cell size bounded by dislocation boundaries or dipolar walls.

Microstructure of carbon blacks determined by X-ray diffraction profile analysis

The microstructure of carbon blacks is investigated by X-ray diffraction peak profile analysis. Strain anisotropy is accounted for by the dislocation model of the mean square strain in terms of average dislocation contrast factors. Crystallite shape anisotropy is modeled by ellipsoids incorporated into the size profile function. Different grades of carbon blacks, N990, N774 and N134, untreated, heat-treated and compressed at 2.5 GPa have been investigated. The microstructure is characterized in terms of crystallite size-distribution, dislocation density and crystallite shape anisotropy. Heat treatment results in increased vertical and lateral sizes of graphitic crystallites. Postproduction pressure treatment has little effect on the average sizes of the crystallites, however, it affects the crystallite size distribution function. The average sizes of the crystallites obtained by X-ray diffraction agree with those estimated from Raman spectra. Applied pressure affects the magnitude of strain within the crystallites.

Densities and character of dislocations and size-distribution of subgrains in deformed metals by X-ray diffraction profile analysis

Abstract The density and the character of dislocations and the size-distribution of grains or subgrains were determined by a new procedure of X-ray diffraction (XRD) profile analysis in copper specimens deformed by equal channel angular pressing (ECA) or cold rolling. The anisotropic strain broadening of diffraction profiles was accounted for by dislocation contrast factors. The screw or edge character of dislocations was determined by analyzing the dislocation contrast factors. Three size parameters and the dislocation density were obtained by the modified Williamson–Hall and Warren–Averbach procedures. Assuming that the grain-size distribution is log-normal, the median, m, and the variance, σ, of the size distribution of grains or subgrains were obtained from these three size parameters.

Particle size distribution and dislocation density determined by high resolution X-ray diffraction in nanocrystalline silicon nitride powders

Two silicon nitride powders were investigated by high resolution X-ray diffraction. The first sample was crystallized from the powder prepared by the vapour phase reaction of silicon tetrachloride and ammonia while the second was a commercial powder produced by the direct nitridation of silicon. Their particle size and dislocation density were obtained by the recently developed modified Williamson‐Hall and Warren‐Averbach procedures from X-ray diffraction profiles. Assuming that the particle size distribution is log-normal the size distribution function was calculated from the size parameters derived from X-ray diffraction profiles. The size distributions determined from TEM micrographs were in good correlation with the X-ray results. The area-weighted average particle size calculated from nitrogen adsorption isotherms was in good agreement with that obtained from X-rays. The powder produced by silicon nitridation has a wider size distribution with a smaller average size than the powder prepared by vapour phase reaction. The dislocation densities were found to be between about 10 14 and 10 15 m 2 . Published by Elsevier Science S.A. All rights reserved.

Phase transition in nanomagnetite

Recently, the application of nanosized magnetite particles became an area of growing interest for their potential practical applications. Nanosized magnetite samples of 36 and 9nm sizes were synthesized. Special care was taken on the right stoichiometry of the magnetite particles. Mossbauer spectroscopy measurements were made in 4.2–300K temperature range. The temperature dependence of the intensities of the spectral components indicated size dependent transition taking place in a broad temperature range. For nanosized samples, the hyperfine interaction values and their relative intensities changed above the Verwey transition temperature value of bulk megnetite. The continuous transition indicated the formation of dendritelike granular assemblies formed during the preparation of the samples.

The density and the character of dislocations in cubic and hexagonal polycrystals determined by X-ray diffraction

The density and the character of dislocations in cubic and hexagonal polycrystals were determined by a new procedure of X-ray diffraction profile analysis. The anisotropic strain broadening of diffraction profiles was accounted for by dislocation contrast factors. The screw or edge character of dislocations in a severely deformed copper specimen was determined by analysing the dislocation contrast factors. Comparing the contrast effect of the possible dislocation slip systems in hexagonal crystals with that determined experimentally for a sintered tungsten carbide sample, it was found that the dominant slip system in this specimen is � 11¯�{ 0001}. The dislocation density was calculated for both samples by the modfied Warren-Averbach procedure.

A new method for hardness determination from depth sensing indentation tests

A new semiempirical formula is developed for the hardness determination of the materials from depth sensing indentation tests. The indentation works measured both during loading and unloading periods are used in the evaluation. The values of the Meyer hardness calculated in this way agree well with those obtained by conventional optical observation, where this latter is possible. While the new hardness formula characterizes well the behavior of the conventional hardness number even for the ideally elastic material, the mean contact pressure generally used in hardness determination differs significantly from the conventional hardness number when the ideally elastic limiting case is being approached.