In the study of crystal nucleation via computer simulations, hard spheres are arguably the most extensively explored model system. Nonetheless, even in this simple model system, the complex thermodynamics of crystal nuclei can sometimes give rise to counterintuitive results, such as the recent observation that the pressure inside a critical nucleus is lower than that of the surrounding fluid, seemingly clashing with the strictly positive Young–Laplace pressure we would expect in liquid droplets. Here, we re-derive many of the founding equations associated with crystal nucleation and use the hard-sphere model to demonstrate how they give rise to this negative pressure difference. We exploit the fact that, in the canonical ensemble, a nucleus can be in a (meta)stable equilibrium with the fluid and measure the surface stress for both flat and curved interfaces. Additionally, we explain the effect of defects on the chemical potential inside the crystal nucleus. Finally, we present a simple, fitted thermodynamic model to capture the properties of the nucleus, including the work required to form critical nuclei.
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Note that, since we consider equilibrium systems, the mechanical and thermodynamical routes for obtaining pressures are equivalent.
Note that for simplicity, we only consider hydrostatic deformations of the lattice. This is consistent with the observation that our simulations show no sign of anisotropic compression of the crystal nucleus.
Note that if interstitials are allowed as well, the true divergence is avoided, as there is a finite (but very high) chemical potential where vacancies and interstitials balance each other, resulting in a net zero flow between crystal and particle reservoir.
