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

Covering theorems for Artinian rings

The covering properties of Artinian rings which depend on their additive structure only, are investigated

Ionization of atoms by few-cycle EUV laser pulses: carrier-envelope phase dependence of the intra-pulse interference effects

We have investigated the ionization of the H atom by intense few-cycle laser pulses, in particular the intra-pulse interference effects, and their dependence on the carrier-envelope phase (CEP) of the laser pulse. In the final momentum distribution of the continuum electrons the imprint of two types of intra-pulse interference effects can be observed, namely the temporal and spatial interference. During the spatial interference electronic wave packets emitted at the same time, but following different paths interfere leading to an interference pattern measurable in the electron spectra. This can be also interpreted as the interference between a direct and a scattered wave, and the spatial interference pattern as the holographic mapping (HM) of the target. This HM pattern is strongly influenced by the carrier-envelope phase through the shape of the laser pulse. Here, we have studied how the shape of the HM pattern is modified by the CEP, and we have found an optimal CEP for the observation of HM