Tamás Ungár

The effect of dislocation contrast on x‐ray line broadening: A new approach to line profile analysis

The x‐ray line profiles of an ultrafine grained copper crystal, produced by equal‐channel angular pressing, were measured by a special high resolution diffractometer with negligible instrumental line broadening. The analysis of the line breadths and the Fourier coefficients have shown that taking into account the contrast caused by dislocations on line profiles gives new scaling factors in the Williamson–Hall plot and in the Warren–Averbach analysis, respectively. When strain is caused by dislocations the new procedure proposed here enables a straightforward determination of particle size and strain, the latter in terms of the dislocation density.

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.

The contrast factors of dislocations in cubic crystals: the dislocation model of strain anisotropy in practice

It has been shown recently that in many cases strain anisotropy in powder diffraction can be well accounted for by the dislocation model of the mean square strain. The practical application assumes knowledge of the individual contrast factors C of dislocations related to particular Burgers, line and diffraction vectors or to the average contrast factors C¯. A simple procedure for the experimental determination of C¯ has been worked out, enabling the determination of the character of the dislocations in terms of a simple parameter q. The values of the individual C factors were determined numerically for a wide range of elastic constants for cubic crystals. The C¯ factors and q parameters were parametrized by simple analytical functions, which can be used in a straightforward manner in numerical analyses, as e.g. in Rietveld structure refinement procedures.

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.

The effect of dislocation contrast on X-ray line profiles in untextured polycrystals

Anisotropic strain broadening in X-ray line profile analysis means that the width of diffraction profiles of Bragg reflections is not a monotonous function of the diffraction angle. The lack of a physically sound model makes the interpretation of line broadening and the structure refinement procedure of Rietveld often difficult or even impossible. A simple and straightforward procedure is presented for the rationalisation of anisotropic strain broadening in terms of the anisotropic contrast effect of dislocations or dislocation-like lattice defects. The procedure makes the evaluation of particle size or coherent domain size, and the density and arrangement of dislocations rather simple with a high precision, especially in the case of untextured polycrystals or when dislocation population on the possible slip systems is uniform. Three illustrative examples of severely deformed microcrystalline copper, the Rb 3 C 60 f.c.c. fullerite and a ball-milled iron powder show the effectiveness of the procedure.

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.

Stacking faults and twin boundaries in fcc crystals determined by x-ray diffraction profile analysis

A systematic procedure is developed to evaluate the density of planar defects together with dislocations and crystallite or subgrain size by x-ray line profile analysis in fcc crystals. Powder diffraction patterns are numerically calculated by using the DIFFAX software for intrinsic and extrinsic stacking faults, and twin boundaries for the first 15 Bragg reflections up to 20% fault density. It is found that the Bragg reflections consist of five subreflection types categorized by specific selection rules for the hkl indices in accordance with the theory of Warren [Prog. Met. Phys. 8, 147 (1959)]. It is shown that the profiles of the subreflections are Lorentzian-type functions. About 15 000 subreflections are evaluated for their full widths of half maxima and their positions relative to the exact Bragg angle. These values are parametrized as a function of the density and type of planar faults. A whole profile fitting procedure, previously worked out for determining the dislocation structure and crystallit...

An X-ray study of creep-deformation induced changes of the lattice mismatch in the γ′-hardened monocrystalline nickel-base superalloy SRR 99

Abstract X-ray line profile measurements were performed on monocrystalline specimens of the γ′-hardened nickel-base superalloy SSR 99 with axes close to the [001] direction. The aim was to measure the local lattice parameters in the γ-matrix and in the γ′-particles and to obtain information on the lattice mismatch and internal stresses. For this purpose, a special high-resolution double crystal diffractomoter with negligible instrumental line broadening was used. Measurements were performed on specimens in the initial state with cuboidal γ′-particles and on creep-deformed specimens containing the so-called γ/γ′-raft structure. In several cases the line profiles were measured as a function of the rocking angle, and the intensity distributions were mapped in reciprocal space around the (002) and (020) Bragg reflections. In the undeformed state these intensity distributionsindicate that the local lattice parameter varies spatially in the γ-phase. The line profiles of specimens in the initial state were asymmetric. A remarkable result obtained on creep-deformed specimes was that, whereas the asymmetry of the (020) line profiles was enhanced to the extent that a hump or a second peak appeared, the asymmetry of the (002) line profiles was reversed in sign. A quantitative evaluation yielded mean values of the constrained lattice mismatch which, in the case of creep-deformed specimens, differ significantly for the (001) and (010) lattice plane spacings. It is concluded that the orientation-dependent lattice spacings represent a triaxial state of residual stress which has its origin in the superposition of the originally present coherency stresses and the deformation-induced internal stresses. All observed features could be explained in detail in terms of a composite model of plastic deformation, which takes into account the dislocation networks deposited at the γ/γ′-interfaces during deformation.

Asymmetric X-ray Line Broadening of Plastically Deformed Crystals. I. Theory

X-ray diffraction line profiles of plastically deformed Cu single crystals orientated for ideal multiple slip were recently found to be markedly asymmetric. A theory is developed to interpret this kind of asymmetric line broadening in terms of the average dislocation density, the dipole polarization of the dislocation structure and the mean square fluctuation of the dislocation density.

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.