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Dr. Willi Pabst
University of Chemistry and Technology, Prague (UCT Prague), Czech Republic
Cross-Property Relations between the Elastic and Thermal Properties of Porous Ceramics

Cross-property relations are relations (in the form of equations or inequalities) between different effective (or relative) properties of two-phase materials (e.g. porous materials). Famous examples are the Levin relation between the thermal expansion coefficient and the bulk modulus, as well as the Milton-Torquato (MT) and Berryman-Milton-Gibiansky-Torquato (BMGT) cross-property bounds (elementary and translational cross-property bounds) between the elastic moduli (primarily the bulk modulus) and the (thermal) conductivity. Other very useful, albeit only approximate, cross-property relations between the relative Young‘s modulus and the relative conductivity of porous materials are the Sevostianov-Kováčik-Simančík (SKS) cross-property relation and the Pabst-Gregorová (PG) cross-property relation, apart from the trivial identity valid for porous materials with translational symmetry in certain directions (in-plane or axial). In this contribution all these cross-property relations between the Young’s modulus and thermal conductivity are reviewed and their respective range of validity is explained. It is recalled that, in contrast to the identity valid for certain directions of anisotropic materials, both the SKS cross-property relation and the PG cross-property relation obey the MT and BMGT bounds and are therefore admissible candidates for property prediction. It is shown that the SKS cross-property relation can be approximated (and thus in practice replaced) by a very simple cross-property relation (based on the Maxwell model or, equivalently, the Hashin-Shtrikman upper bounds) and that, although both the SKS and PG cross-property relations are principally admissible for isotropic porous ceramics, the latter seems to be more realistic for a wide range of microstructures and thus more universal. Finally it is shown that the existence and success of cross-property relations is incompatible with so-called minimum solid area models (which are still very popular in ceramic science today) and that, therefore, the latter have to be abandoned. 

Acknowledgement: This work is part of the project P108/15-18513S (GAČR). Support by the Czech Science Foundation is gratefully acknowledged.

Willi Pabst is Associate Professor of Chemistry and Technology of Inorganic Materials at the University of Chemistry and Technology, Prague (UCT Prague), Czech Republic. He received his M.Sc. degree (Dipl.-Min.) in Mineralogy at the University of Tübingen, Germany, in 1993 and his Ph.D. degree (Dr.) in 1998 at the Institute of Chemical Technology, Prague (ICT Prague), Czech Republic, followed by a habilitation degree (Doc.) in 2005. He is an author or coauthor of more than 65 full-text papers in impacted journals (96contributions on WOS, H-index 22, > 500 non-auto citations) and 5 book chapters. He is a member of several international societies and co-editor of the impacted journal Ceramics-Silikáty. His fields of teaching and research concern materials theory (rational thermomechanics and theory of heterogeneous materials), disperse systems (particle size and shape characterization, rheology), advanced ceramic shaping processes (including new casting and foaming techniques), microstructural characterization (especially stereology-based image analysis), microstructure-property relations (especially elastic and thermal properties of porous ceramics) and the history of chemistry and materials.
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