SMALL-ANGLE X-RAY-SCATTERING SIZE PARAMETERS AND HIGHER MOMENTS OF THE PARTICLE-SIZE DISTRIBUTION FUNCTION IN THE ASYMPTOTIC STAGE OF OSTWALD RIPENING

Small-angle X-ray scattering (SAXS) is a powerful tool to study the ki netics of phase separation in materials. A simple procedure is present ed that allows one to prove if the particle-size distribution establis hed in a system in the late stages of phase separation corresponds to the predictions of the classical Lifshitz-Slyozov-Wagner (LSW) theory for the asymptotic stage of Ostwald ripening. The method is based on t he correlations between certain SAXS size parameters and the higher mo ments of the LSW size distribution functions for diffusion-limited or reaction-limited ripening. It is suggested that the use of these size parameters, which can be obtained with high accuracy from the scatteri ng curve, is frequently more advantageous than a direct comparison of the experimentally obtained size distributions with the asymptotic siz e-distribution functions predicted by the LSW theory. The method is ap plicable if the suppositions made in the LSW theory that the precipita ted particles should be homogeneous spheres with volume fraction tendi ng to zero are fulfilled. The method is applied to a photochromic glas s; although the silver-halide precipitates contained in the glass deve lop according to the power law of diffusion-limited Ostwald ripening, their size distribution is shown not to correspond to the features of the LSW size distribution. Consequently, in this case the LSW theory c annot describe quantitatively the kinetics of ripening.