Optimisation of rGO-enriched nanoceramics by combinatorial analysis

The design of new ceramic materials with specific thermo-electrical and me- chanical properties is important for a range of engineering applications. Re- cent research has demonstrated that inclusion of soft reduced graphene oxide (rGO) in hard ceramic matrix produces nano-structured ceramic composites with improved electrical conductivity and fracture toughness. The emer- gent properties of such composites are strongly related to the mass fraction and spatial distribution of rGO inclusions. Their micro-structure includes sub-structures with different dimensions - 1D, 2D and 3D - which calls for entirely new approaches to characterisation and design. In this theoretical work, a new discrete (combinatorial) strategy is proposed that allows for capturing all sub-structures, employing elements of algebraic topology and modern graph theory. It is demonstrated how this strategy can be applied to the flexible design of nano-structured ceramics with a superior balance between conductivity and resistance to fracture.