Computer simulation of epitaxial nucleation of a crystal on a crystalline surface

Abstract

We present results of computer simulations of crystal nucleation on a crystalline surface, in the Lennard-Jones model. Motivated by the pioneering work of Turnbull and Vonnegut [Ind. Eng. Chem. 44, 1292 (1952)], we investigate the effects of a mismatch between the surface lattice constant and that of the bulk nucleating crystal. We find that the nucleation rate is maximum close to, but not exactly at, zero mismatch. The offset is due to the finite size of the nucleus. In agreement with a number of experiments, we find that even for large mismatches of 10% or more, the formation of the crystal can be epitaxial, meaning that the crystals that nucleate have a fixed orientation with respect to the surface lattice. However, nucleation is not always epitaxial, and loss of epitaxy does affect how the rate varies with mismatch. The surface lattice strongly influences the nucleation rate. We show that the epitaxy observed in our simulations can be predicted using calculations of the potential energy between the surface and the first layer of the nucleating crystal, in the spirit of simple approaches such as that of Hillier and Ward [Phys. Rev. B 54, 14037 (1996)

Contact efflorescence as a pathway for crystallization of atmospherically relevant particles

“…Small lattice mismatches (δ < 0.12) generally indicate an effective heterogeneous nucleus [i.e., low σ(RH) and high CERH]. Notably, the high K 2 SO 4(CN) −(NH 4 ) 2 SO 4(aq) CERH of 77% (δ AS = 0.03) clearly demonstrates that a low δ can lead to a profound effect and offers experimental support for simulations that suggest a small lattice mismatch may be more favorable than a perfect lattice match for nucleation on a heterochemical surface because the crystal nucleus does not necessarily have the same lattice constants as the bulk crystal (23). Larger lattice mismatches (δ J 0.12) generally indicate a less effective heterogeneous nucleus.…”

“…Similarity in crystal lattice structure between the heterogeneous surface and the crystallizing compound has long been recognized as an important factor in heterogeneous nucleation (16,(22)(23)(24). Here, we explore the strength of this relationship by comparing crystal lattice structure and σ(RH).…”

“…4A, with values for the unit cell constants a, b, and c given in Table S1. The standard expression for lattice mismatch (δ) between a substrate (i.e., the CN) and a crystalizing overlayer (i.e., the aqueous component) is given by δ = (a CN -a aq )/a aq , where a aq is the lattice constant of the crystalline phase of the droplet component and a CN is the lattice constant of the CN (22)(23)(24). This equation was valid for cases where both species were cubic crystals.…”

Nucleation of crystals that are mixed composites of all three polymorphs in the Gaussian core model

“…Here, we are defining a critical nucleus as a nucleus at the FFS critical interface, which is the first interface at which the probability of the nucleus reaching the final phase exceeds 0.5, as is conventional. 29,30 We denote the size of the critical nucleus as n crit and the fraction of particles of each crystal phase in the nucleus as f fcc = n fcc /n, f hcp = n hcp /n, and f bcc = n bcc /n. The nucleus in Fig.…”

“…Although this scheme is usually used for computing static equilibrium properties (e.g., as we use it here for US simulations), it is also frequently used for dynamical evolution, especially in nucleation studies. 29,30 Time in our FFS simulations is measured in "cycles," with one MC cycle corresponding to (on average) a single attempted displacement move per particle and a single attempted volume change, accepted or rejected in the normal way. 20 At the beginning of the simulation, we initialize the positions of the particles in a random liquid-like configuration.…”