Towards a quantitative description of nanostructured order in amorphous diamond-like carbon

Our knowledge of crystals rests on precisely measured structural models, which are lacking for amorphous matter. Without long-range order, the available experimental evidence matches competing structural models, including paracrystalline and random network models, limiting our understanding of formation mechanisms and properties. This impedes discovery of new amorphous materials, including high-density sp³-rich carbons, among the hardest known. We show that the pair-angle distribution function (PADF) overcomes these limitations, applying it to a non-crystalline sp³-rich carbon produced by compression of fullerenes at room temperature. The PADF reveals that this phase contains nanostructures with distinct short-range (4^th-5^th neighbours, < 5 Å) and medium-range (5-10 Å) order. The nanostructure planes and angles relate to diamond, suggesting coordinated diamond-like tetrahedra too disordered to be nanodiamonds. The characterisation of nanoscale disorder via the PADF thus offers insight into the nature of structural order in amorphous materials and the formation pathways of diamond-like materials.