Analysis of compositional distributions for exploring the phase space by the single sample concept in ceramic combinatorial chemistry

Different components forming part of a local configuration of it >= 2 grains constitute a phase system in which the locally available masses define a working point in the corresponding phase diagram. Because the number of configurations can be larger than the number of possible phase diagrams, a basic issue of the single sample concept (SSC) may be addressed by a statistical analysis: is the large phase space of possible compounds efficiently explored by the SSC? In the present study, the compositional distribution functions p(X-E) were calculated for some of the N components comprising a sample. Broad p(XE) distributions were obtained using reasonable assumptions for the distributions describing the grain size and the local coordination number of grains. p(X-E) functions were calculated both analytically and using a fully numerical procedure. Application of the method to cuprate superconductors revealed that the observed stoichiometries conformed well with the corresponding p(X-E) distributions. From the present analysis we conclude that the SSC can provide starting compositions for compounds expected to be present in phase systems for given reaction conditions T and p.