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 10¹⁴ and 10¹⁵ m⁻².     

Frequency domain analysis of acoustic wave propagation in heterogeneous media considering iterative coupling procedures between the method of fundamental solutions and Kansa's method

Acoustic wave propagation in heterogeneous media is a topic of significant interest in many areas of science and engineering, including aeroacoustics and sound propagation in oceans. In the present work, numerical frequency domain models based on the joint use of the method of fundamental solutions and of the radial basis function collocation method (also known as Kansa's method) are discussed. In this context, the method of fundamental solutions is used to model the homogeneous part of the propagation domain, while Kansa's method is employed to model the presence of heterogeneities. The coupling between the two parts of the propagation domain is performed iteratively, allowing independent spatial discretization between the different subdomains of the model (i.e. matching collocation points at common surfaces are not necessary). Additionally, an optimised algorithm, based on the use of a varying relaxation parameter, is employed to speed up and/or to ensure the convergence of the iterative coupling process. At the end of the paper, numerical results illustrate the applicability and potentialities of the proposed formulations. Copyright © 2011 John Wiley & Sons, Ltd.     

Microstructural studies on variation of defect parameters in Zr-Sn alloys and their transition with interchange of solvent and solute in Zr-Ti and Ti-Zr alloy systems by modified Rietveld method and Warren-Averbach method

The effects of deformation and the transition of microstructural defect states with the interchange of solvent and solute in Ti-Zr and Zr-Ti alloys of six different compositions and Zr-Sn alloys in three different compositions have been investigated by X-ray diffraction line profile analysis. The detailed analysis of the X-ray powder diffraction line profiles was interpreted by Fourier line shape analysis using modified Rietveld method and Warren-Averbach method taking silicon as standard. Finally the microstructural parameters such as coherent domain size, microstrains within domains, faulting probability and dislocation density were evaluated from the analysis of X-ray powder diffraction data of Zr base Sn, Ti and Ti base Zr alloys by modified Rietveld powder structure refinement. This analysis confirms that the growth fault, β, is totally absent or negligibly present in Zr-Ti, Ti-Zr and Zr-Sn alloy systems, because the growth fault, β, has been observed to be either negative or very small for these alloy systems. This analysis also revealed that the deformation fault, α, has significant presence in titanium-base zirconium alloy systems but when zirconium content in the matrix goes on increasing beyond 50%, this faulting behaviour suffers a drastic transition and faulting tendency abruptly drops to a level of negligible presence or zero. This tendency has also been observed in Zr-Sn alloys signifying high stacking fault energy. Therefore, Zr and Zr-base alloys having high stacking fault energy can be used as hard alloys in nuclear technology at high temperature.