Porosity evolution in SnO2 xerogels during sintering under isothermal conditions.

porosity and (ii) internal microporosity, respectively. The maximum of the peak increases with the sintering time in all studied samples. At 300'C the q value associated with the maximum intensity remains constant. The data analysis of the set of scattering curves for increasing time intervals at 300 C is in agreement with Cahn's theory for spinodal decomposition. At higher temperatures, 400— 600 C, the maximum of the structure function increases with time, its position shifts continuously to lower q values, and the value of the integrated intensity in reciprocal space remains constant. The structure function of microporous Sn02 under isothermal treatment in the 400— 600'C range exhibits the dynamical scaling property. The experimental results suggest that the microporosity coarsening is controlled by the coagulation mechanism. I. INTRODUCTION The kinetics aspect of phase separation has received considerable attention during recent years' due to the relevance of this phenomenon for a wide range of materials including polymers, glasses, metallic alloys, and ceramics. The small-angle x-ray scattering (SAXS) technique is useful for studying this process. It allows, for example, a direct verification of the applicability of Cahn's theory of spinodal decomposition and the statistical dynamical scaling model. Cahn's theory for phase separation assumes that the boundary between the phases is diffuse, without sharp discontinuities. This theory is based on a Fick diffusion equation with an additional term which accounts for the surface energy associated with the incipient interphases which are formed during the first stages of phase separation. The linear diffusion equation, which is valid for the first stages of the process, was solved for isotropic systems by the Fourier transform method. The result indicates that the structure function S (q, t) and also the SAXS intensity 1(q, t) (which is proportional to the structure function) exhibit an exponential growth: