Use of Monte Carlo Methods in Characterizing Nanostructured Materials by Wide‐ and Small‐Angle X‐Ray Scattering

Abstract

In the last years, a method for recovering the size distribution of nanoparticles from both wide‐ and small‐angle x‐ray scattering curves has been developed, tested, and successfully applied to real cases. It is based on the assumption that the scattered intensity can be approximated by the sum of elementary components. In the small angle scattering regime (SAXS), the elementary components are the Rayleigh scattering functions of homogeneous spheres, whereas in wide angle regime (WAXS), according to the “column‐like” crystal model proposed by Bertaut, are the interference functions from the coherently diffracting domains inside a crystal. In all cases, the amplitude of the interference functions is related to the size of the scattering entities. A robust Monte Carlo (MC) algorithm, able to select the best set of elementary components, is used to fit the experimental diffraction profile. From the best approximating ensemble of functions, the particle size distribution (PSD) is estimated in both SAXS and WAXS and in the latter case, also information on the lattice strains, can be obtained. The method is very easy to use since it requires as input, the scattering data and the instrumental slit function. Therefore, it is suitable for “in line” automatic quality control without any skilled supervision. An additional application of the procedure to determine the size and composition distributions in graded layers of binary isomorphous mixtures is also presented. Finally, a possible further development of the MC algorithm for the deconvolution of a generic signal from the instrumental broadening effect is briefly illustrated.