Within the field of engineering, it is well known that geometry—i.e. the angles between struts in a network structure—plays an essential role in determining beam mechanics. For instance, specific beam structures—such as the “honeycomb”, “re-entrant honeycomb” and “wine-rack” networks—have known calculated responses to temperature or pressure change, and can be predicted to show negative thermal expansion, negative linear compressibility or auxetic behaviour based upon the beam structure geometry. These calculations rely on the variation in angles within the structure to obtain the different responses, while the beam length itself remains unchanged.
What we have been asking is: do the same rules work on the atomic scale? In particular, can we use the same predictive tools to design materials with specific (and perhaps highly unusual) mechanical properties?
In a recent study of two metal–organic frameworks (MOFs; zinc isonicotinate, Zn(ISN)2, and indium deuterium terephthalate, InD(BDC)2) we measured their mechanical behaviour as a function of temperature (i.e. their thermal expansion). Both MOFs have the same quartz topology, but display contrasting c/a ratios. We find that both frameworks exhibit hinging mechanisms as a function of temperature, which gives rise to both positive and negative thermal expansion (PTE and NTE). Yet the key interest in this study lies in the fact that this anisotropy is switched between the two materials: while Zn(ISN)2 displays area-NTE in the hexagonal a,b-plane, and PTE along the c-axis, InD(BDC)2 shows the reverse with area-PTE in the same a,b-plane, and NTE along the c-axis. We show that this switch in anisotropic mechanical response has nothing to do with the different chemistry of the two frameworks, but is a result purely of their different framework geometries. That geometry plays such a crucial role in these systems is a consequence of the dominant mechnical response involving changes in network angles rather than variation in metal–linker bond lengths.
What’s great is that the geometric formalism derived for the two MOFs at the heart of our study can be applied equally well to completely different framework materials in order to predict the direction of their anisotropic mechanical response. The prediction will work best with materials which exhibit hingeing mechanism (i.e. framework angle variation) as the dominant form of structural change to the external stimuli. As framework hingeing may also occur upon application of pressure, we also show the candidates most likely of displaying negative area compressibility (NAC)—a property highly sought after for signal amplification in piezoelectric or pressure sensors.