Temperature-density dependent hidden order of amorphous carbon

The microscopic structure of amorphous carbon is inherently complex, and its underlying topological order remains poorly understood. Here, we developed a high-precision machine learning potential and performed large-scale molecular dynamics simulations of the annealing process over a wide range of temperatures and densities. Nine representative amorphous carbon structures were identified and characterized through X-ray diffraction and structure factor analysis, enabling detailed comparison of their topological differences. From these results, we constructed a temperature–density phase diagram that reveals two distinct phase boundaries associated with discontinuous structural transitions, with the critical temperature increasing approximately linearly with density. The diagram further indicates two transformation pathways, where high-density disordered graphene networks and paracrystalline diamond structures act as intermediate states. Additional pressure-controlled simulations demonstrate asymmetric nucleation during diamond formation and decomposition. These findings provide a clearer understanding of hidden order in amorphous carbon and offer a theoretical framework to guide its controlled synthesis. Carbon exhibits several known allotropes and the amorphous equivalents exhibit an even wider range of structural variations that can be difficult to identify due to their lack of crystallinity. Here, the authors report large-scale machine-learned molecular dynamics simulations that maps the hidden topological orders of amorphous carbon as a function of temperature and density.