Many dynamic growth processes are shown to involve changes in more than one of the nine geometric variable that describe the geometry of a planar interface between crystals. Even simple examples illustrating changes in each one of the nine are found to involve some of the others. A generalized concept of crystal-crystal interface motion, using all nine variables, is suggested.

The critical behavior of interfaces is discussed from a theoretical point of view. Two classes of critical phenomena will be considered: (i) Roughening phenomena related to changes in the interfacial morphology; and (ii) Wetting phenomena related to changes in the interfacial structure. In two dimensions, the critical behavior can be determined exactly for a variety of models. As a result, one obtains different universality classes depending on the nature of the inter molecular forces.

We present a method for simulation of crystal growth using completely facetted interfaces and the definition of curvature appropriate to such interfaces. The representation of these surfaces, as facets with fixed normal directions, variable distances, and semi-fixed adjacencies, is quite different from that in other methods. It is flexible as to possible growth rules, it appears to avoid the problems involved in measuring curvature and in detecting and making topological changes, and it runs relatively fast. We expect it to be a valid method to approximate growth with any isotropie or anisotropie surface energy and kinetics. The use of the method is demonstrated in dendritic crystal growth and in Ostwald ripening.

In the first part Monte Carlo studies of the kinetics of multilayer adsorption (without screening) are described. The approach to the jamming coverage in each layer is asymptotically exponential. The jamming coverages approach the infinite-layer limit value according to a power law. In the second part, studies of phase transitions in two dimensional fluids are reviewed. With a combination of Monte Carlo and finite size scaling block analysis techniques, accurate values are obtained for the critical temperatures, coexistence densities and the compressibilities of an adsorbed fluid layer in an NVT ensemble.

Recent advances in high–resolution low–energy electron diffraction (HRLEED) techniques have led to a new capability which provides both very high spatial and temporal resolutions to probe quantitatively the equilibrium and dynamical processes that occur on surfaces and growth fronts. These techniques are especially powerful when the surface or growth front contains atomic steps. Different distributions of steps give different surface atomic pair correlation functions and therefore different angular profile shapes in the diffraction pattern. Recent examples of quantitative HRLEED study of low index plane equilibrium roughening and preroughening transitions are presented. In the growth dynamics, both two–level and multilevel step structures are considered. Examples of the measurements of growth exponents and dynamics scaling are presented.

In the absence of surface tension and external force fields, the equilibrium between a hydrostatically stressed crystal and its melt is neutral with respect to the perturbations associated with particle transfer from one region of the boundary into another. However, under the action of arbitrary small nonhydrostatic components of the stress field in the elastic crystal, the neutral equilibrium is transformed to an unstable equilibrium [1]. This instability is very general in nature; for example, for it to be seen the liquid media need only to be able to dissolve the solid phase or in some way to assist the transport of particles along the crystal's surface. In contrast, the surface tension, roughly speaking, stabilizes the shape of the interphase boundary but it cannot suppress the instability generated by the nonhydrostatic components of the stress field in the region of sufficiently long perturbations. Until now the basic instability mechanism discussed here seems to have escaped the attention of theorists. This mechanism allows one to look in a completely new way at a broad range of phenomena. We discuss tentative manifestations and role of this instability in low temperature physics, in materials science, in theory of crystal growth, and, in particular, in theory of epitaxy and of the Stranski-Krastanow pattern of growth of thin crystalline films.

Results are reported for the surface tension, the surface free energy, the surface stiffness coefficient, and the single-step free energy for the Ising model in two and three dimensions. These are obtained by numerical transfer-matrix calculations, testing detailed predictions for the scaling of the largest eigenvalues of the transfer-matrix.

We report on a molecular dynamics (MD) study of the wetting state of a system of hard spheres near a smooth planar hard wall. A direct simulation at the melting point of a two-phase system between two walls develops all the way from complete wetting by fluid (cos(θ) = 0) via partial wetting state to a final arrangement of complete wetting by crystal (cos(θ) = 1). This implies that a hard sphere fluid spontaneously crystallizes at a smooth hard wall, contrary to existing beliefs.

The interfacial properties of the solid-liquid interface of 4He have been studied at temperatures below 0.5 K using crystallization waves. From the dispersion and damping of the crystallization waves, one can determine the interfacial stiffness, ᾶ, and the interfacial growth resistance, (Km)−1, respectively. Our measured values for ᾶ are consistently smaller than previously published values. At the lowest temperatures, the measured (Km)−1 increases as T4 which is consistent with the prediction that the growth velocity is limited by the scattering of ballistic phonons by the moving interface. We also observe that above 0.25 K the phonon damping is dramatically reduced.

Cell dynamics computer simulation method is used to investigate effects of hydro-dynamic interaction as well as effects of added surfactants on phase separation kinetics. In the former the obtained scattering structure function for 3-dimensional system reproduces the experimental results for polymer blends remarkably well. In the latter we display self-assembling process in two-dimensional system on computer.

We present the results of phase-separation experiments performed on the pseudo-binary fluid system guaiacol-glycerol-water. Elastic light scattering and optical microscopy were used to follow the phase-separation after quenches into the coexistence region of the phase diagram. For critical quenches, we observed the well known bicontinuous infinite cluster morphology normally associated with spinodal decomposition, but with two distinct growth modes. In the bulk, at early times we observed L(t) ∼ t1/3 consistent with diffusion driven dynamics, crossing over to L(t) ∼ t1 at later times, as hydrodynamics became important. Near the sample walls, there obtained a novel fast growth with L(t) ∼ t3/2, just as in the case of recent studies with polymer blends, inconsistent with either diffusion or interface driven dynamics. We attribute this large exponent to wetting effects, and the observation of the same phenomenon in such disparate systems as polymer blends and polar organic solvents is strong evidence that the phenomenon is generic to binary systems.

A detailed comparison between the experimental evolution of a two-dimensional soap froth and the large Q state Potts model is presented. The pattern evolution starting from identical initial conditions will be compared as well as a variety of distribution functions and correlations of the two systems. Simulations on different lattices show that the discrete lattice of the Potts model causes deviations from universal domain growth by weakening the vertex angle boundary conditions that form the basis of von Neumann's law. We show that the anisotropy inherent in a discrete lattice simulation, which masks the underlying ‘universal’ grain growth, can be overcome by increasing the range of the interaction between spins or increasing the temperature. Excellent overall agreement between the kinetics, topological distributions and domain size distributions between the low lattice anisotropy Potts-model simulations and the soap froth suggests that the Potts model is useful for studying domain growth in a wide variety of physical systems.

Understanding the kinetics of domain growth in quenched systems is a significant fundamental problem with particular relevance to materials science. The temperature dependence of domain growth has interesting manifestations which lie outside current theoretical developments. In a series of Monte Carlo studies, we have investigated and obtained a detailed resolution of the temperature dependencies of domain growth in a model of a two-dimensional, quenched, chemisorbed overlayer with a nonconserved order parameter. We discuss our findings.

The characteristics of ledge growth of precipitates are investigated by a previously developed finite-difference computer model. The plate lengthening simulation results which incorporate measured ledge heights and spacings are in reasonable agreement with the observed lengthening behavior of plates in Fe-C alloys. The simulation which takes into account the diffusion field interaction among multiple precipitates shows that a variety of precipitate morphologies actually observed can possibly be formed solely by the change in the extent of diffusion field overlap among ledges and/or neighboring precipitates. This overlap is in turn caused by changes in the solute supersaturation, distribution of ledge nucleation sites and ledge nucleation rates. A brief discussion is made of the relative growth kinetics of ledged and disordered interfaces.

The growth velocity and morphology of crystals growing in a supercooled aqueous solution of ammonium chloride (28 wt%) with small amounts of copper sulfate (0.05 to-1 wt%) have been examined. For the [100] growth direction at low supercooling and for the [110] direction at greater supercooling the crystals start to grow slowly with a faceted interface. As the supercooling is continuously increased, the growth direction becomes [111]. Dendrites with pointed tips develop but continue to grow slowly. With further increase in supercooling, the velocity increases 20- to 40-fold and the tip shape changes from a cusp to a thin and almost paraboloid interface while the growth direction remains [111]. The velocity transition is gradual when the concentration is below 0.1 wt% but is sharper at higher concentrations. The transition temperature decreases with increasing copper sulfate concentration.

We postulate that the observed transition indicates a dynamic roughening phenomenon, where the supercooling; is sufficiently high to create many nucleation islands on the faceted interface. In this case the interface behaves as an atomically rough surface and dendrite growth occurs at an interface temperature that is below the equilibrium temperature.

This paper presents a new experimental method to investigate solid-liquid interface morphologies during Zone-Melting-Recrystallization at lower than the typical processing temperatures. Gallium films were used as a substitute for silicon films. In situ preliminary investigation identified three phenomena typically occurring during ZMR of silicon films: a) Transition from planar to dendritic to cellular morphologies was observed for different processing conditions; b) cell period proved to be dependant on scanning velocity; c) instabilities at the solidification interface at low heating strip temperatures were caused by supercooling and optical property variations as the material changed phase.

Morphological instabilities of surfaces with respect to faceting in deposition of microelectronic materials and etching of semiconductors and catalysts are of great technological importance. Macroscopic theories fail in predicting correctly the time and size dependence of microstructures observed.

We have examined the temporal and spatial evolution of unstable interfaces in zero net flux, growth, and etching of crystals as functions of temperature and degree of irreversibility using the Monte Carlo method. In addition to faceting, thermal or kinetic roughening transitions are also observed under some conditions. We have found that the type of transition and the surface structures depend strongly on the irreversibility of the process and the surface temperature. It is demonstrated that surface diffusion has a profound influence on the transitions and surface morphologies.

Shape evolution of rod-shaped precipitates due to surface diffusion has been studied under the conditions of constant volume and isotropie interfacial free energy. The shape evolution depends strongly on both the initial aspect ratio and the grain boundary groove angle. For a finite rod with one grain boundary, the morphology evolves into an equilibrium shape made of spherical portions if its aspect ratio and the groove angle are small. Increase in the aspect ratio causes a boundary splitting. For an infinite rod with periodic boundaries, three types of morphological evolutions are observed. When the relationship between the aspect ratio and the groove angle satisfies a certain critical condition, the shape evolves into an equilibrium. If the relationship deviates significantly from this condition, an ovulation process takes place at each location of the internal grain boundaries. When the deviation is intermediate, the morphology undergoes an oscillation in a quasi-dynamic state between the process toward an equilibrium shape and the ovulation process. The ovulation process due to internal grain boundaries is found to precede the Rayleigh spheroidization process.

Using a millisecond time-resolved x-ray scattering technique at the National Synchrotron Light Source, we have simultaneously obtained in situ both large-angle (LAXS) and small-angle (SAXS) diffraction patterns for isothermal crystallization of amorphous Fe1−xBx (0.16 < x < 0.21) and Co1−xZrx (0.08 < x < 0.11). The large-angle x-ray data are analyzed to determine which of the two crystalline products nucleate first in each compound, and also to assess the evidence for eutectic growth as shown by a time-independent ratio of volume fractions of these product phases. The small-angle data give the length scales of the eutectic structure as well as information about its time evolution. Combining our x-ray results with TEM studies, we examine the effects of changes in temperature and composition on the structural evolution of both the amorphous and crystalline phases.

Systematic relations are shown between the parameters controlling explosive crystallization in silicon (temperature, width of a liquid zone, and gradient of melt undercooling), the kinetics of the crystallization process, the predominance of preferential growth directions, and the crystal structure observed. Three typical regions of crystallization are found: (a) cellular growth of a laminated crystalline layer controlled by the formation of high densities of twins at a nearly plane liquid/solid interface, (b) cellular-dendritic growth of crystal lamellae characterized by branching of a curved interface, and (c) formation of a diffuse “slush zone” due to random nucleation in a-Si and grain growth in the liquid zone.