Modeling of Strain Distribution in Non-Hydrostatically Pressed Nanocrystalline Sic; In-Situ X-ray Diffraction Study
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ABSTRACT Grain size and strain distribution functions of polycrystals of SiC with nanosize grains were examined based on X-ray diffraction data and ab initio calculations of scattered intensity from Debye functions. A tentative model of distribution of strain induced under high isostatic pressure in nanoparticles with different grain size is presented. Nanocrystalline SiC powders with grains down to 80A in diameter were examined. In situ high pressure diffraction experiments were performed in cubic anvil cell MAX80 (up to 6 GPa) and in Diamond Anvil Cell (DAC) (up to 45 GPa) at HASYLAB, Hamburg, Germany. Shape of the Bragg lines was analysed with the use of two methods: (i) calculation of theoretical diffraction patterns based on modeling of one-dimensional disordering and ab initio calculation of scattered intensity starting from Debye functions and, (ii) approximation of the experimental shape of Bragg reflections by a combination of two functions: Gaussian (G) and Lorentzian (L).
INTRODUCTION Due to a very large specific surface area, nanocrystalline powders exhibit unique properties which follow from different environment of the atoms at the surface, e.g. high chemical activity, strong effect of surface tension (high internal pressure), etc. [1]. This work is dedicated to a characterization of nanocrystalline SiC through in situ high pressure diffraction studies. Diffraction profiles of very small crystallites are very diffused so a determination of the compressibilities from the positions of the broad Bragg peaks is very difficult. This is particularly true in case of SiC due to one-dimensional disordering of the material which leads to diffuse scattering and strong broadening of the Bragg lines. Under isostatic conditions the presence of strains leads not only to an increase of the width of the Bragg lines but to a strong asymmetry of the reflections as well. There is no simple method which would give a quantitative interpretation of varying shape and positions of Bragg reflections of a sample subjected to high pressure. Therefore we developed a new method of modeling strains in nanocrystalline SiC polycrystals and simulating diffraction effects in such materials. The calculations of theoretical intensity profiles include: (i) modeling of one-dimensional disordering and simulation of diffuse scattering related to polytypism of SiC, (ii) ab initio calculation of powder diffraction profiles of nanosize polycrystals having different grain size distribution functions, and (iii) ab initio calculation of powder diffraction profiles of nanosize polycrystals with size-dependent lattice constants. Based on computer simulation of diffraction profiles of polycrystals with different lattice constants we present a tentative interpretation of our high pressure diffraction experiments performed for 8 nm nanocrystalline SiC. We explain the pressure behavior of SiC through non homogenous distribution of strain in nanocrystalline powder particles which due to different sizes exhibit different compressibilities. 305
Mat. Res.
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