Freezing of Small SeF₆ Clusters:  Simulations, Nucleation Statistics When Events Are Few, and Effects of Laplace Pressure

Abstract

Simulations were carried out on 138-molecule clusters freezing isothermally at 130, 120, and 80 K. At 120 K, the nucleation rate was the same as in our prior simulations performed adiabatically but the final product was different. During the nanosecond period of the runs, clusters transforming adiabatically had frozen to bcc crystals while warming from 120 K to about 130 K. On the other hand, isothermal clusters at 120 and 130 K changed to monoclinic clusters after passing through the bcc phase. Clusters cooled to 80 K froze to a variety of structures. The number of molecules whose Voronoi polyhedra qualified them as being in bcc embryos grew in size erratically, and in most runs it was difficult to use the Voronoi information by itself to identify a well-characterized nucleation time. Therefore, a more discriminating criterion for the onset of nucleation was devised. The 138-molecule clusters proved to be too small to yield definitive profiles of the several order parameters characterizing the change from the liquid phase to the critical nucleus. Even though the sizes of the nuclei were not established accurately, it was clear that critical nuclei were considerably larger than the five-molecule size forecast by the classical theory of homogeneous nucleation. At the deep supercooling of the simulations, precritical and critical nuclei were extremely ramified and haphazard in molecular orientation, but the chaotically organized nuclei at 120 and 130 K quickly annealed and grew to single crystals in most clusters. Clues were found suggesting that surface molecules may participate in the formation of critical nuclei, contrary to our long-standing belief. From nucleation rates were derived the kinetic parameters σsl, the solid−liquid interfacial free energy of the classical nucleation theory, and δ, the interface thickness of Gránásy's diffuse interface theory (DIT). In addition, the effect of pressure on the DIT, a new treatment of errors, and an improved weighted least-squares analysis of nucleation data were developed.

Test of classical nucleation theory on deeply supercooled high-pressure simulated silica

“…the time required to achieve a steady state of precritical nuclei [25]. However, to take advantage of Eq.…”

“…7 we must be able to identify the time when a particular system from our ensemble of runs has nucleated. Various methods can be used to detect crystallization such as examing the Voronoi volumes or counting the number of particle neighbors [25]. In this study, we contrast three approaches: first, we employ a simple energy criterion specific to the state point studied so that the crystallization time t x for a MD run is the time at which the potential energy first reaches a value of U x = −1.81 MJ/mol.…”

“…4 may ignore effects due to transient nucleation, i.e. that R decreases smoothly at early times instead of remaining at 1 until t 0 [25], so that our estimate of the rate and lag times are strictly lower bounds. Nevertheless, the independence of our slope on the nucleation criteria suggests that our calculation of the rate is robust and any corrections would be small.…”

Analyses of Nucleation Rates from Molecular Dynamics Simulations

“…Therefore, it seemed appropriate consider the times as the uncertain "y" variable in least squares analyses and the variable ln(N n /N o ) to be the accurately known "x" variable, where N n is the number of clusters not to have experienced the formation of a critical nucleus before the n th nucleation. 1 The recommended weights and standard deviations to be expected for such an analysis were correctly determined in a previous paper, provided that the decay of unfrozen clusters obeyed the first-order law where K represents the product J s V c with J s the steady-state nucleation rate, V c the volume of the clusters, t > t o the time of nucleation, and t o the nucleation time-lag. In real processes, this analysis is wrong because the period of transient nucleation is ignored.…”

“…In a previous paper, 1 the derivation of nucleation rates from molecular dynamics (MD) simulations of freezing in sets of supercooled clusters was discussed. In particular, the statistical errors to be expected when nucleation events are few, were analyzed.…”