Polydispersity during the Formation and Growth of the Stöber Silica Particles from Small-Angle X-Ray Scattering Measurements.

The early stages of formation of Stöber silica particles have been investigated in situ during the hydrolysis and condensation of tetraethylorthosilicate under base-ammonia conditions in different alcoholic solvents. Time-resolved ultra-small-angle X-ray scattering by the entities produced in the solutions is used for structural characterization and monitoring of the growth kinetics of the particles. Our primary focus is to assess the polydispersity of the formed colloidal particles and its evolution as a function of time. We first applied a maximum entropy analysis of the scattering data to determine the size distribution and the time evolution of the size distribution of the colloidal particles. Second, we extended the cumulant method to analyze our earlier small-angle X-ray scattering data (H. Boukari, J. S. Lin, and M. T. Harris, J. Colloid Interface Sci. 194, 311, 1997; Chem. Mater. 9, 2376, 1997) and search for the presence of a distribution of fractal particles. The maximum entropy analysis indicates that there is a continuous nucleation of particles during the synthesis, and that this takes place within a relatively narrow size distribution. The cumulant analysis shows that, except at later times, the data are not adequate to confirm conclusively the presence of a distribution of fractal dimension at any time during the experiment. We discuss the impact of these results on growth kinetic models proposed for this system. Copyright 2000 Academic Press.

Small-angle scattering by dislocations.

It is shown that the small-angle scattering of X-rays or neutrons by dislocations within a deformed metal, which are partially ordered into wall-like structures, is characterized by several factors. Principally these are associated with: (i) a single dislocation or dipole; (ii) the dislocation configuration in the plane of the wall; and (iii) the distribution of dislocations across the wall thickness. With the assumption of isotropic elasticity, small-angle scattering will be sensitive only to the edge components of the dislocations. The scattered intensity is dominated by scattering from dislocations that lie perpendicular to the scattering vector, q, and reaches a maximum when q is normal to the slip plane of these dislocations. Above a particular |q|, the scattered intensity is sensitive only to the total edge dislocation content of the scattering dislocations (i.e. scattering is incoherent), while, below this value, the scattering is dominated by how the dislocations are distributed in walls. For walls normal to their slip planes, the configuration factor will reflect the dislocation distribution in the plane of the wall, while, for walls parallel to their slip planes, the distribution in the thickness direction will be visible. Therefore, even though a deformed material is composed of complicated dislocation structures, only those segments conforming to these rather strict prescriptions will be singled out for scattering, and, by adjusting the beam/slip system geometry, many parameters of the microstructure can be determined experimentally.