Characterization of relative homogeneity in particulate mixtures

Abstract

Procedures for evaluating the relative homogeneity of complex particle systems are discussed. The discrete nature of particle systems leads to an inherent heterogeneity corresponding to the situation where all particles are arranged completely at random. Theoretical relationships, based on simple statistical considerations, are available for predicting the expected variance among samples taken from random binary mixtures. It is shown that these can be applied to any particulate system by considering it as a series of binary mixtures of appropriately defined critical components with a second, composite component consisting of the remainder of the material. The critical components can also be composites provided they have some common feature and their concentration in the mixture can be measured. Criteria for the definition of critical components are discussed. Characterization of relative homogeneity is based on comparison of observed sample variances with those predicted for the random state. The importance of correct sampling is emphasized and some special constraints on the application of standard sampling procedures to evaluating relative homogeneity are described. Guidelines for the choice of appropriate sample size for specific applications are presented. It is demonstrated that a reasonable estimate of the variance associated with sampling and assaying errors can be a critical requirement for identifying relatively minor inhomogeneities. A brief discussion of procedures for characterizing the magnitude and scale of inhomogeneities is also included.