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Analysis of Compositional Distributions for Exploring the Phase Space by the Single Sample Concept in Ceramic Combinatorial Chemistry
Author(s) -
Hulliger Jürg,
Dessauges Luc,
Samtleben Till A.
Publication year - 2006
Publication title -
journal of the american ceramic society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.9
H-Index - 196
eISSN - 1551-2916
pISSN - 0002-7820
DOI - 10.1111/j.1551-2916.2005.00855.x
Subject(s) - phase diagram , stoichiometry , cuprate , sample (material) , ceramic , distribution (mathematics) , point (geometry) , phase (matter) , space (punctuation) , statistical physics , sample space , diagram , phase space , thermodynamics , superconductivity , mathematics , materials science , mineralogy , chemistry , physics , mathematical analysis , statistics , computer science , geometry , condensed matter physics , metallurgy , quantum mechanics , operating system
Different components forming part of a local configuration of n ≥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 ( X E ) 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 .