Fig. 4: The two-step crystallization mechanism of 2D ice.

a, d Temporal evolution of the largest crystal size \({L}_{{{\rm{m}}}}\) (red) and fractal dimension \({D}_{{{\rm{f}}}}\) (blue) at (a) T_sim = 100 K and (d)175 K, using one single trajectory of molecular dynamics (MD) simulation in a and averaging over five independent trajectories in d, respectively. The upper (lower) bounds of the error bars represent the maximum (minimum) values obtained from five independent measurements. b, c MD snapshots of the bilayer hexagonal ice (BHI) islands before (t = 370 ns in b) and after (t = 380 ns in c) the connection of two fractal islands at 100 K in a. The two islands are marked by red and pink in b, and the combined island is highlighted in red in c. The rest of BHI islands are colored in yellow. e, f. MD snapshots of the percolated BHI island (red) after fractal growth as \({L}_{{{\rm{m}}}}\) reaches 1 (e), and compact BHI islands after compact growth (f) at 175 K. g, h Free energy surfaces of 2D ice at 175 K, in terms of BHI molecule fraction \({n}_{{{\rm{BHI}}}}\) and ad-molecule fraction \({n}_{{{\rm{ad}}}}\), on the graphite surface without confinement (g) and confined between two parallel surfaces (h). i–n The representative structures sampled along the minimum free energy path of crystallization (black line in g). The black crosses mark the fixed BHI seeding nucleus, and the interlocked hexagons grown from the seed are marked in yellow disks. The molecules are colored from blue to red with increasing height above the substrate.