A generalised scale-independent mechanism for tailoring of thermal expansivity: Positive and negative

Negative thermal expansivity (NTE) is uncommon and naturally occurs in few solids, including metal oxides, e.g. zirconium tungstate, and some polymers and zeolites. A generalised mechanism for NTE has not been described, i.e. it is currently difficult to design microstructures or molecular networks with NTE. Here we report a procedure for designing NTE structures from positive thermal expansivity units.We consider a triangular structure consisting of corner-hinged beam-like elements, all with intrinsically positive coefficients of thermal expansivity (CTE), but one of which has a relatively larger thermal expansivity. This unit may be tessellated into more complex structures. Temperature change leads to dissimilar element expansions within the triangles, resulting in the effective CTE of the tessellated structures being different from that of the constituent elements. This effect is unbounded and can be tuned via the triangle geometry and ratio of element CTEs using the relationships given.