Revealing the three-dimensional structure of liquids using four -point correlation functions

Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications, but they are also crucial for the mechanical stability of cells or the transport of chemical and biological agents in living organisms. Despite the importance of these systems, their microscopic structure is understood only on a rudimentary level, thus in stark contrast to the case of gases and crystals. Since scattering experiments and analytical calculations usually give only structural information that is spherically averaged, the three-dimensional (3D) structure of disordered systems is basically unknown. Here, we introduce a simple method that allows probing of the 3D structure of such systems. Using computer simulations, we find that hard sphere-like liquids have on intermediate and large scales a simple structural order given by alternating layers with icosahedral and dodecahedral symmetries, while open network liquids like silica have a structural order with tetrahedral symmetry. These results show that liquids have a highly nontrivial 3D structure and that this structural information is encoded in nonstandard correlation functions.