Characterization of the chemical homogeneity of solid-state materials by chemometric methods. Multivariate aspects and general recommendations

Data from milliprobe analysis of a copper standard material by spark source mass spectrometry have been investigated using multivariate methods in addition to earlier — predominantly univariate — treatment in order to derive some general recommendations for characterizing the chemical homogeneity of solids. A “disarmed” MANOVA test with the locations as effect variables and the normalized concentration data of the diverse chemical elements as replicates provided a highly rigorous Yes-No decision on homogeneity from an overall point of view. For more detailed information, data visualization by raster graphics combined with cluster analysis, principal components analysis, and non-linear mapping proved a useful explorative tool, particularly in the (here assumed) case without any preinformation. Dependent on how these methods are used, information on locations of inhomogeneities or on correlations between the analytes results. It has been shown that seeking for correlations should be the first explorative step. Employing the further steps to correlating elements increases the rigour of detecting element-specific inhomogeneities. On the other hand, including all the determined elements enables a more critical judgment of “collective homogeneity”. To confirm multivariate results on inhomogeneity by statistical means, the revealed groups of sub-samples should be tested by linear discriminant analysis. Deviations from a homogeneous distribution can be detected and/or characterized for any single element (or correlating elements) individually by univariate methods based on models of the spatial distributions, if these can be presumed a-priori or after preliminary investigations.