Characterization of the chemical homogeneity of solids affected with periodical concentration fluctuations using the statistics of stochastic processes

Abstract

Application of the theory of generalized stochastic processes to periodical concentration fluctuations in solid state samples enables a comprehensive characterization of the homogeneity of materials affected by such fluctuations. From the results of only one line scan carried out by using a microprobe with a roughly known probe profile characterized by the effective probe width, for any optional probe profile a variance function is estimated which represents the dependence of the variance of the results on the effective probe width in each case. Using this function, assertions about the homogeneity of the sample can be made which are vastly independent of the conditions of the experimental investigation, but correspond to the ultimate purpose of the material. Moreover, the mathematical processing of the measuring results enables the detection of concentration fluctuations which are not visible from the original data.