Lattice mold technique for the calculation of crystal nucleation rates

Abstract

We present a new simulation method for the calculation of crystal nucleation rates by computer simulation. The method is based on the use of molds to induce crystallization in state points where nucleation is a rare event. The mold is a cluster of potential energy wells placed in the lattice positions of the solid. The method has two distinct steps. In the first one the probability per unit volume of forming a sub-critical crystal cluster in the fluid is computed by means of thermodynamic integration. The thermodynamic route consists in gradually switching on an attractive interaction between the wells and the fluid particles. In the second step, the frequency with which such cluster becomes post-critical is computed in Molecular Dynamics simulations with the mold switched on. We validate our method with a continuous version of the hard sphere potential and with the sodium chloride Tosi–Fumi model. In all studied state points we obtain a good agreement with literature data obtained from other rare event simulation techniques. Our method is quite suitable for the study of both crystal nucleation of arbitrarily complex structures and the competition between different polymorphs in the nucleation stage.