Grain size, size-distribution and dislocation structure from diffraction peak profile analysis

Diffraction peak profile analysis (or Line Profile Analysis, LPA) has recently been developed to such an extent that it can be applied as a powerful method for the characterization of microstructures of crystalline materials in terms of crystallite size-distribution and dislocation structures. Physically based theoretical functions and their Fourier coefficients are available for both, the size and the strain diffraction profiles. Strain anisotropy is rationalized in terms of the contrast factors of dislocations. The Fourier coefficients of whole diffraction profiles are fitted by varying the following fundamental parameters characterizing the microstructure: (i) m and (ii) V, the median and the variance of the log-normal size distribution function, (iii) U and (iv) M, the density and the arrangement parameter of dislocations and (v) q or q1 and q2 for the average dislocation contrast factors in cubic or hexagonal materials, respectively. The method will be illustrated by showing results on ECA pressed copper and titanium

Dislocation density and graphitization of diamond crystals

Two sets of diamond specimens compressed at 2 GPa at temperatures varying between 1060 K and 1760 K were prepared; one in which graphitization was promoted by the presence of water and another in which graphitization of diamond was practically absent. X-ray diffraction peak profiles of both sets were analyzed for the microstructure by using the modified Williamson-Hall method and by fitting the Fourier coefficients of the measured profiles by theoretical functions for crystallite size and lattice strain. The procedures determined mean size and size distribution of crystallites as well as the density and the character of the dislocations. The same experimental conditions resulted in different microstructures for the two sets of samples. They were explained in terms of hydrostatic conditions present in the graphitized samples

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 micro-structural 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

Formation of nanocrystalline aluminum magnesium alloys by mechanical alloying

The effect of the nominal Mg content and the milling time on the microstructure and the hardness of mechanically alloyed Al (Mg) solid solutions is studied. The crystallite size distribution and the dislocation structure are determined by X-ray diffraction peak profile analysis and the hardness is obtained from depth sensing indentation test. Magnesium gradually goes into solid solution during ball milling and after about 3 h almost complete solid solution state is attained up to the nominal Mg content of the alloys. With increasing milling time the dislocation density, the hardness and the Mg content in solid solution are increasing, whereas the crystallite size is decreasing. A similar tendency of these parameters is observed at a particular duration of ball milling with increasing of the nominal Mg content. At the same time for long milling period the dislocation density slightly decreases together with a slight reduction of the hardness

Microstructure of a rapidly quenched nanocrystalline Hf11Ni89 alloy from X-ray diffraction

A rapidly quenched nanocrystalline Hf(11)Ni(89) alloy was produced by melt-spinning. The X-ray phase analysis shows that the as-quenched ribbon consists of mainly nanocrystalline fcc HfNi(5) although a small amount of Ni is also detected. The crystallite size distribution and the dislocation structure of the dominant HfNi(5) phase were determined by a recently developed method of diffraction profile analysis. In this procedure, by assuming spherical shape and log-normal size distribution of crystallites, the measured physical intensity profiles are fitted by the well established ab initio functions of size and strain peak profiles. The anisotropic broadening of peak profiles is accounted for by the dislocation model of the mean square strain in terms of average dislocation contrast factors. It was found that the median and the variance of the crystallite size distribution are 3.3 nm and 0.70, respectively. The dislocation density is 5.7x10(16) m(-2) and the character of dislocations is nearly pure screw

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

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

X-ray diffraction study of crystallite size-distribution and strain in carbon blacks

The crystallite size and size-distribution in the presence of strain is determined in carbon blacks by a recently developed procedure of X-ray diffraction peak profile analysis. The Fourier coefficients of the measured physical profiles are fitted by Fourier coefficients of well established ab initio functions of size and strain peak profiles. 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 modelled by ellipsoids incorporated into the size profile function. The Fourier transforme of the size profile is given as an explicite formula making the fitting procedure fast. The method is applied to carbon balcks terated at different preassures and temperatures. The microstructure is characterised in terms of crystallite size-distribution, dislocation density and crystallite shape anisotropy

Microstructure and strength of metals processed by severe plastic deformation

The microstructure of f.c.c. metals (Al, Cu, Ni) and alloys (Al-Mg) processed by severe plastic deformation (SPD) methods is studied by X-ray diffraction line profile analysis. It is shown that the crystallite size and the dislocation density saturate with increasing strain. Furthermore, the Mg addition promotes efficiently a reduction of the crystallite size and an increase of the dislocation density in Al during the SPD process. The yield strength correlates well with that calculated from the dislocation density using the Taylor equation, thereby indicating that the main strengthening mechanism in both pure metals and alloys is the interaction between dislocations