The aggregation-volume-bias Monte Carlo method, which has been successful in the calculation of the formation free energies of liquid clusters, is extended to solid systems. This extension is motivated by early studies where disordered clusters are observed when the original method is applied at a temperature even far below the triple point. In order to avoid the formation of disordered aggregates, the insertion of particles is targeted directly toward those crystal lattice sites. Specifically, the insertion volume used to be defined as a spherical volume centered around a given target molecule is now restricted to be around each of the crystal lattice sites near a given target molecule. The free energies obtained for both liquid and solid clusters are then used to extrapolate bulk-phase information such as the chemical potential of the liquid and solid phases at coexistence. Using the temperature and pressure dependencies of the chemical potential information obtained for both liquid and solid phases, the location of the triple point can be determined. For Lennard-Jonesium, the results were found to be in good agreement with previous simulation studies using other approaches.
A lattice-based version of the aggregation-volume-bias Monte Carlo method that was introduced recently has allowed for the extension of the calculation of the nucleation free energies from liquid clusters to solid clusters. Here, it was used to calculate the nucleation free energies of both bcc and fcc clusters formed by Lennard–Jones particles. Under the simulation conditions considered in this study, a cross-over of the thermodynamic stability from the bcc to the fcc structure was observed directly from the free energy results. In addition, the free energies obtained for both types of clusters were used to extrapolate bulk phase information, including chemical potential and surface tension, which revealed that bcc clusters are favored due to the lower surface tension. These results corroborate a recent classical density functional theory study. This work also demonstrates that this approach can be used to predict the entire thermodynamic landscape (i.e., free energies for clusters of different structures and sizes, including an infinitely large cluster, which is the bulk phase), which is important to answer fundamental questions related to crystallization such as the origin of polymorphism.
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