Solid/Liquid Cluster Recognition in Heterogeneous Systems

The kinetics of crystal growth and dissolution from the melt in Lennard-Jones systems

“…Our method takes into account all the angles that an atom forms with pairs of its neighbors and, from this, calculates a single parameter that is used to classify the atoms as solid ͑fcc͒-like or liquidlike, as explained in detail in a previous paper. 12 We have now extended the method to recognize hcp-like atoms ͑more cor-rectly, we should say that we can recognize atoms having a solidlike environment corresponding to that in a bulk hcp structure͒. At Tϭ0.45 and zero pressure, the method recognized 99.9% of the bulk phases correctly.…”

“…An explanation for this decision is given in Ref. 12. No other interfacial ''shells'' were included as part of the solid following our observation that the atoms in the first ''shell'' occupy fcc or hcp lattice sites exhibit a large degree of order, whereas more distant ''shells'' show increasing disorder.…”

“…A similar study that followed the dissolution dynamics of Stillinger-Weber crystals 12 showed that the probability of a crystal changing from one size, say i, to another does not depend on its previous history ͑i.e., the path forms a Markovian chain͒. Knowing this, the process of dissolution or growth can be analyzed using a transition probability matrix, P. Under this formalism, the element P i j represents the probability that a cluster of size i will change to size j after some predetermined time.…”

“…12 it was explained how to distinguish the extent of an fcc crystal in the melt, but no values were given for the parameters we called F C . In the following we present the parameters used for the Lennard-Jones system at a reduced temperature of 0.45 and zero pressure.…”

“…The region near Ϫ0.833 presents a minimum for the fcc lattice and a maximum for the hcp lattice in the cosines distribution. Following the same steps used to obtain the criteria to distinguish fcc crystals from the melt, 12 an angular order parameter for the hcp lattice can be calculated. We called this parameter G, to distinguish it from the fcc angular order parameter F. G and F are calculated as The critical values that distinguish the appropriate solid from the liquid, the F Cn and G Cn values, depend on n, the number of atoms in the first shell.…”