Comparing the Mechanical and Thermodynamic Definitions of Pressure in Ice Nucleation

Crystal nucleation studies using hard-sphere and Lennard-Jones models have shown that the actual (mechanical) pressure within the nucleus is lower than that in the surrounding liquid. Here, we use the mechanical route to obtain the pressure for an ice nucleus in supercooled water (TIP4P/Ice) at 1 bar and 247 K. From this pressure, we obtain the interfacial stress using a thermodynamic definition consistent with mechanical arguments. Moreover, we compare the mechanical pressure with the thermodynamic pressure of bulk ice at an equal chemical potential and the interfacial stress with the interfacial free energy. Furthermore, we investigate these properties on the basal plane. We find that unlike in hard-sphere and Lennard-Jones systems, mechanical and thermodynamic pressures agree for the nucleus, and the interfacial stress and free energy are comparable. However, the basal interface displays an interfacial stress nearly twice its interfacial free energy, suggesting that this agreement may be dependent on the system, underscoring the limitations of mechanical routes to solid-liquid interfacial free energies.