Fig. 5: Free energy profiles for ice growth.

a Molecular dynamics simulation snapshots illustrate the growth evolution of cubic ice and hexagonal ice through monomer attachment, accompanied by the corresponding free energy surface profile, demonstrating that free energy per water molecule decreases with increasing molecular number. b MD snapshots and the corresponding free energy profile illustrate the aggregation of cubic ice 〈110〉 along the 〈111〉 direction, featuring twin boundaries that produce a stable five-fold symmetry structure. c Aggregation of hexagonal ice nuclei, showing oriented aggregation with grain rotation, ultimately achieving a zero-degree orientation angle in the final stable state. d Merging of ice Ih 〈001〉 and one smaller sized ice Ic 〈110〉, showing growth of hexagonal ice nuclei. e Merging of Ih 〈001〉 and Ic 〈111〉 nucei as a function of the size of ice Ih reveals three free energy minima and two energy barriers, indicating that one nucleus grows at the expense of the other, with one metastable state characterized by coalescence at a coherent interface between the Ih and Ic nuclei. f Summary of the free energy evolution pathways for the cooperative growth of Ih and Ic nuclei shows an initial discrete growth path, followed by interfacial-driven coalescence and ripening.