Kenneth A. Jackson

The Interface Kinetics of Crystal Growth Processes

A brief review of the present state of our understanding of the kinetic processes which take place on the atomic scale at the interface during crystal growth is presented in this paper. Computer simulations have played a central role in the development of this understanding. Three aspects will be discussed:(1) There are two classes of materials based on their different modes of crystallization. Molecular dynamics modeling has demonstrated that the growth rate for many simple materials is not thermally activated, but instead depends on the thermal velocity of the atoms.(2) The cooperative processes which give rise to the surface roughening transition. Kinetic Monte Carlo studies played a central role in the development of our understanding of how interface roughness dominates growth morphologies.(3) Solute trapping in alloys. Kinetic Monte Carlo simulations of alloys have led to an understanding of these kinetic effects during alloy crystallization.

Computer modeling of atomic scale crystal growth processes

The wide availability of extremely powerful computers has ushered in a new era in which simulation is the preferred method for the modeling of physical processes. The development of our understanding of the atomic scale processes involved in crystal growth, where computer simulations have played a central role, is an example of the power of these methods. It has now become apparent that computer simulations have not only been useful, but were essential for this development. Crystallization processes will be discussed in the context of the role of computer modeling in the development of our current understanding, and to illustrate how it is continuing to play a central role.

Orientation dependence of the distribution coefficient obtained from a spin-1 Ising model

The nonequilibrium distribution coefficient (k neq ) as a function of solid-liquid interface velocity and orientation was investigated for a spin-1 Ising model for binary alloys using Monte Carlo computer simulations. The crystal structure and thermodynamic properties were chosen to correspond to bismuth doped silicon with k eq = 7 x 10 -4 . Values for k neq were obtained for several orientations of the solid/liquid interface, including (111) and (001). For the same growth velocity, k neq was found to be greatest for solid/liquid interfaces parallel to the (111) plane. The orientation dependence is related to variations in the kink site density at the interface. The simulation results are compared with experimental results reported by Aziz et al.

In Situ Microscopic Observation of the Crystallization Process of Molecular Microparticles by Fluorescence Switching

To clearly understand the solid-state amorphous-to-crystalline transformation is a long-standing challenge because such crystallization occuring in confined environments is difficult to observe directly. We developed an in situ and real-time imaging procedure to record the interface evolution in a solid-state crystallization of molecular amorphous particles. The method, by employing a tetra-substituted ethene with novel morphology-dependent fluorescence, which can distinguish the interfaces between the crystalline and amorphous phase by fluorescence color, is a simple and practical method to probe the inner process of a molecular microparticle. The crystallization of amorphous microparticles in different cases was clearly recorded, where the perfect microparticles and those with defects demonstrate diverse destinies. The details disclosed in this observation will deepen the understanding for a series of solid-state crystallization that we know little about before.

Microsegregation far from equilibrium

Monte Carlo computer simulations of the crystallization of a two component mixture have been performed for crystallization conditions which are far from equilibrium in order to determine the dependence of the distribution coefficient (k-value) on the growth conditions. The simulations were based on the Ising model for a two component mixture, and the thermodynamic properties of Si doped with Bi were used as a model alloy system. At rapid crystallization rates, the k-value in the simulations differs significantly from the equilibrium value, and depends on the square of the growth rate and inversely on the diffusion coefficient in the liquid. The k-value in the simulations is found to be strongly orientation dependent, in accordance with experimental results on silicon. The simulation results are compared with experimental results which have been reported in the literature for the dependence of the k-value on growth rate in laser melted silicon which has been ion implanted with bismuth.

Non-equilibrium phase transformations

Abstract Near equilibrium, phase transformations depend primarily on the thermodynamics of the system; the redistribution of components caused by the phase transformation are predictable from the appropriate phase diagram. However, far from equilibrium, when the transformation proceeds at such a rapid rate that there is little time for diffusion, the equilibrium phase diagram seems to be no longer relevant. It is generally agreed that the thermodynamic properties of the phases involved must still play an important role in the transformation. The nature of that role has not been understood. In this paper we report the results of computer simulations which have indicated the nature of that role. These are Monte Carlo simulations of the motion of an interface through a two component mixture without diffusion in either phase. In these simulations, we find that the interface hangs up on the atoms of the species which are rejected by the growing phase, making the interface compositions different from the bulk compositions. The interface compositions depend on the thermodynamic properties of the phases at the interface. But the interface compositions do not imply corresponding changes in the bulk phases after the interface has passed, as suggested by the phase diagram. This simple yet compelling picture provides the missing link between kinetics and thermodynamics in the rapid growth regime.

Growth behavior of NH4ClH2O mixtures

A discontinuity in the growth velocity, as a function of undercooling, was reported for tin alloys by Nikonova and Temkin and also for boron doped nickel by Eckler et al. A similar discontinuity in the growth rate as a function of undercooling of ammonium-chloride-water solutions is reported. While the dendritic growth behavior of several alloys has been successfully modeled, the observed discontinuity in the growth rate of ammonium chloride crystals cannot be fit using the same equations. Since the samples used in this work have large concentrations of the second component, water, the observed discontinuity is attributed to some other mechanism.

Non-equilibrium interface of a two-dimensional low-temperature crystal

We study the interface in an Ising system with nearest-neighbor interaction on a square lattice at very low temperatures, when the Wulff shape of a nucleus is almost a perfect square. Spins are randomly flipped via Metropolis-type dynamics. At moderately strong undercoolings, the step nucleation rates can be evaluated from the first principles. This permits the description of the growth of an infinite interface using a step-on-step nucleation picture. The averaged shape of the interface is universal (i.e., it does not depend on any parameters as long as the interface remains stable), and its growth rate, in appropriate variables, also has no free parameters. For finite sizes of two-dimensional crystals their growth can be dominated by nucleation of single steps, and becomes size-dependent. For both infinite- and finite-size interfaces growth rates are in good agreement with large-scale Monte Carlo simulations. At high undercoolings the interface becomes very rough, in which case the crystals switch to circular shapes, in contrast to the equilibrium Wulff expectation.

In Situ Imaging of On-Surface, Solvent-Free Molecular Single-Crystal Growth

The formation of crystalline materials has been studied for more than a century. Recent discoveries about the self-assembly of many inorganic materials, involving aggregation of nanoparticle (NP) precursors or pre-nucleation clusters, challenge the simple assumptions of classical crystallization theory. The situation for organic materials is even more of a terra incognita due to their high complexity. Using in situ high-temperature atomic force microscopy during the solvent-free crystallization of an organic compound [Ni(quinolone-8-thiolate)2], we observe long-range migration of NPs on a silica substrate and their incorporation into larger crystals, suggesting a non-classical pathway in the growth of the molecular crystal.

Actual Concepts of Interface Kinetics

Publisher Summary The crystal growth process is reversible. The net growth rate is the difference between the arrival rate and the departure rate of atoms at the crystal surface. At equilibrium, these two rates are equal. When both phases are present, the crystal grows when the interface is below the equilibrium temperature and melts when then temperature is above the equilibrium temperature. There are atoms that belong to each phase and the transition between the two phases occurs atom by atom or molecule by molecule. The rate of crystallization is expressed as the product of four terms: a length, a frequency, a term that depends on the structure of the interface, and the free energy difference between the two phases. The atoms or molecules at the interface join and leave the crystal at rates that depend only on their local environment and on the local departure from equilibrium. Their motion depends on their individual kinetic energies and the local potentials to which they are subjected.