One method for computationally determining phase boundaries is to explicitly simulate a direct coexistence between the two phases of interest. Although this approach works very well for fluid–fluid coexistences, it is often considered to be less useful for fluid–crystal transitions, as additional care must be taken to prevent the simulation boundaries from imposing unwanted strains on the crystal phase. Here, we present a simple adaptation to the direct coexistence method that nonetheless allows us to obtain highly accurate predictions of fluid–crystal coexistence conditions, assuming that a fluid–crystal interface can be readily simulated. We test our approach on hard spheres, the screened Coulomb potential, and a 2D patchy-particle model. In all cases, we find excellent agreement between the direct coexistence approach and (much more cumbersome) free-energy calculation methods. Moreover, the method is sufficiently accurate to resolve the (tiny) free-energy difference between the face-centered cubic and hexagonally close-packed crystal of hard spheres in the thermodynamic limit. The simplicity of this method also ensures that it can be trivially implemented in essentially any simulation method or package. Hence, this approach provides an excellent alternative to free-energy based methods for the precise determination of phase boundaries.
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In principle, one could imagine shearing the crystal phase in the xz or yz plane, by moving the interfacial crystal planes tangentially to the interface, without violating the periodic boundaries. However, this would induce a tangential stress in the crystal, which would need to be balanced by an opposite stress in the fluid phase to maintain mechanical equilibrium. Since the fluid phase cannot support tangential stresses, this cannot be a stable deformation in the applied geometry.
Note that for these calculations, we also re-calculated the bulk equation of state for different crystal orientations and system sizes. However, in practice, the finite size effects on the equation of state have a negligible effect on the overall determination of the coexistence conditions: repeating our calculations with the ZS2 hard-sphere crystal equation of state by Pieprzyk et al.43 yields essentially indistinguishable results, especially for larger system sizes.
