Designing next-generation negative compressibility materials.

Negative compressibility is a rare but desirable property whereby a material's crystal structure actually expands in one (negative linear compressibility, NLC) or two (negative area compressibility, NAC) principal directions against application of increasing hydrostatic pressure. The performance of such materials-for use in, for e.g., sensitive interferometric or ferroelectric pressure sensing devices, advanced actuators, or prototype artificial muscle-critically depends on the magnitude of intrinsic negative response. NLC and NAC have been previously reported in a diverse range of materials: from the elemental forms of selenium and tellurium, to transition metal oxides, halides and chalcogenides [1], to more recent reports of NLC in molecular materials, and metal-organic and metal-cyanide frameworks. We explore, using examples from our work [2,3] as well as that of others, how understanding known NLC and NAC materials can inform material design, and how the versatile chemistry of molecular frameworks-the connecting of cationic metal nodes with anionic molecular linkers in one or more dimensions-allows for the targeting, enhancing and coupling of functionalities. By analysis of the negative response across all known NLC and NAC materials we develop new understanding into the underlying mechanisms of these unusual responses. Structural motifs identified point towards strategies for designing the next-generation of these materials, including the simple "wine-rack," "honeycomb" and "spring" mechanisms, where hinging about nodes requires volume reduction by simultaneous expansion and contraction in perpendicular directions (Figure 1). We discuss the first report of "giant" NLC in zinc(II) dicyanoaurate(I), Zn[Au(CN)₂]₂, where the crystal structure expands >10% over 1.8 GPa [2], the unprecedented prolonged NAC in silver (I) tricyanomethanide, Ag(C₄N₃) [3], and conclude with our perspective on the challenges and opportunities that remain in the quest for even more extreme responses.

Contrasting compressibility trends in layered structures Ag(tcm) and Ni(CN)₂

Ag(tcm) (tcm = tricyanomethanide) and Ni(CN)2 are layered structures. Both these materials exhibit area negative thermal expansion (area-NTE) due to 'rippling' of the layers - a displacement pattern that causes the interlayer separation to increase and the effective layer area to decrease (Fig. 1a). We have shown that Ag(tcm) shows negative area compressibility (NAC) under hydrostatic pressure. The latter can be attributed to the rippling phenomenon: when hydrostatic pressure is applied, the effective layer area increases (Fig. 1a). On the contrary, Ni(CN)2 shows shows positive linear compressibility in all directions, albeit much more strongly along the stacking axis than in any direction parallel to the square-grid sheets. This is attributed to transverse phonon modes within the Ni(CN)2 sheets, which can be visualised as 'tilting' of the rigid unit modes (RUMs) (Fig. 1b). A discussion of relating such behaviour to the Grüneisen parameters is undertaken in this study.