Numerical calculation of the rate of crystal nucleation in a Lennard-Jones system at moderate undercooling

Abstract

We report a computer-simulation study of the rate of homogeneous crystal nucleation and the structure of crystal nuclei in a Lennard-Jones system at moderate undercooling. The height of the nucleation barrier has been determined using umbrella sampling, whereas the barrier crossing rate is calculated using molecular dynamics simulation. The simulations clearly show that the barrier crossing is a diffusive process. Nevertheless, the kinetic prefactor in the nucleation rate is found to be some two orders of magnitude larger than predicted by classical nucleation theory. The height of the barrier is in good agreement with the theoretical prediction. Although the Lennard-Jones system has a stable face-centered cubic ͑fcc͒ phase below the melting line, the precritical nuclei are found to be mainly body-centered cubic ͑bcc͒ ordered. As they grow to their critical size, they become more fcc ordered in the core. However, the critical and postcritical nuclei retain a high degree of bcc ordering in the interface. Furthermore it is found that in the interface the density falls off faster than the structural order parameter, which is in agreement with the predictions of density functional calculations.

Stabilizing colloidal crystals by leveraging void distributions

“…3b that the resulting structure is HCP. For pure colloids, the Ostwald 'rule of stages' posits that crystallization from a supernatant solution should proceed via a series of metastable intermediate states 16 , namely, a progression from a body-centred cubic (BCC) crystal to HCP and finally a very slow transition to pure FCC, during which the crystal appears to have rHCP character 4,8,31,32 . Although recent studies have challenged the ability of this principle to predict the outcome of specific nucleation events, the importance of metastable intermediates has been verified even for soft colloids [33][34][35] .…”

“…The resulting configurations were analysed using SteinhardtNelson bond order parameters to characterize crystal grains based on their local orientational symmetry (cf. Methods) 30,31 . After sufficient time, the radial distribution function between crystallized colloids was identical for all system densities above the line given in the phase diagram (Fig.…”

“…The vector connecting any two neighbours, r ij , is considered a 'bond' whose orientation is characterized by the unit vectorr ij , which defines both a polar and azimuthal angle, Following ref. 31 we focus on l ¼ 6 to quantify the degree of local ordering requisite of a solid rather than a liquid, which also exhibits non-zero local order. A normalized complex vector for each colloid, q 6 (i), can thus be defined with (2 Â 6 þ 1) orthogonal components:…”

“…In a simulation, colloids are classified as solid, liquid or gas-like based on bond-orientation order parameters 30,31 . For systems that were observed to crystallize in Fig.…”

Melting and equilibrium shape of icosahedral gold nanoparticles

“…To characterize the structure of the cluster, we measure the standard bond orientational order parameters Q 6 ,Ŵ 6 , Q 4 andŴ 4 [31] which are often used to distinguish between different phases of condensed materials [30,32]. These bond order parameters, designed to probe the degree and type of crystallinity, are sensitive to the orientational correlations of "bonds", i.e.…”