Materials with low-dimensional structures (eg graphene, high-temperature superconductors) form an important class of material precisely because low dimensionality often leads to unusual and useful physical properties.
Nickel cyanide, Ni(CN)2, is one such material: its structure consists of square-grid-like layers that stack on top of one another. Just how they stack has remained a mystery — and despite the simple chemical formula it has taken a combination of cutting-edge neutron total scattering and X-ray diffraction experiments to determine the first complete structural model of Ni(CN)2. What emerges is that the material in fact exhibits long-range structural order in only two dimensions, with no true periodicity perpendicular to its grid-like layers.
To some extent, this lack of periodicity actually reflects the low energy of the interactions between layers. Because this energy is so low, the square-grid layers can vibrate very easily and essentially independently of one another. So both its structure and its dynamics are basically two-dimensional, and this gives rise to some very unusual mechanical properties.