Kirk M. Beatty

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.

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.

Impurity distribution in InSb single crystals

The distribution of cadmium (Cd) dopant in InSb single crystals grown by the vertical Bridgman technique has been studied. The distribution coefficient was obtained by fitting a numerical solution of the diffusion equation to the dopant profiles along growth direction. Measurement of the actual growth rate of the crystal using the Peltier demarcation technique showed a large difference between the actual growth rate of the crystal and the specimen translation rate (nominal growth rate). This difference strongly influenced the dopant distribution.

Monte Carlo simulation of non-equilibrium segregation during crystal growth

Abstract Ising model simulations of the crystallization of two component mixtures have been performed for crystallization conditions both near and far from equilibrium. These simulations reproduce the phenomenon which has been termed ‘solute trapping’, where rapid crystallization results in crystals with concentrations which are far from equilibrium concentrations. Thermodynamic properties of Si doped with Bi have been used as a model alloy system in the simulations because there are extensive experimental results for these alloys. Simulations predict that crystallization far from equilibrium follows quite different rules from crystallization near equilibrium. This has significant implications for all first order phase changes in mixtures which take place under conditions which are far from equilibrium.