Fractality and percolation in the phase transition of polycrystalline graphite

The pressure- and temperature-driven phase transition from polycrystalline graphite to diamond is investigated using molecular dynamics computer simulation. We partition the atomic coordinates into two disjoint subsets corresponding to a diminishing three-coordinate and a developing four-coordinate network. It is shown that the fractal dimension and its time evolution, as calculated from the radial distribution function “colored” for four coordinates only, tracks the transformation mechanism, capturing the growth and spatial organization of the developing domains. In particular, it reflects the increasing space-filling character and homogenization of the emerging diamondlike structure. At sufficiently high pressures and temperatures, the system consistently transforms into polycrystalline diamond, whereas at lower pressures the final structures depend sensitively on both temperature and initial microstructure, leading to greater variability in the fractal dimension. Additionally, we demonstrate that the transformation to four-coordinate sites leads to a percolation transition, which, compared to a simple hard sphere null model, occurs at a significantly lower threshold, highlighting the role of the interatomic potential in correlating network connectivity. These results demonstrate that the fractal dimension may provide a simple and robust metric for tracking topological changes during phase transitions in polycrystalline solids or other phenomena that may be characterized as domain growth.