Kinetic Roughening Transition Research Articles

Molecular dynamics determination of Two-dimensional nucleation kinetic coefficient for modeling the faceted growth of Si (1 1 1) from an undercooled melt

The discrepancies between kinetic model predictions and experimental observations of two-dimensional (2D) nucleation-mediated growth of silicon limits modeling reliability for existing and new crystal growth processes. Molecular dynamics (MD) simulations were performed to identify the mechanism of evolution of crystallites on a Si (111) facet and semi-quantitatively describe 2D nucleation kinetics using the forced-velocity solidification (FVS) and free-solidification (FS) MD simulations techniques. Both MD models predicted similar nucleation expressions but gave lesser nucleation energy barriers than predicted from Monte Carlo (MC) nucleation model. The estimated nucleation rate from MD was fitted to a polynuclear growth model to estimate a 2D kinetic model and compared to available experimentally reported growth rates. The Si (111) facet velocity model derived from the kinetic coefficient given in this work generally provided more conservative estimates of undercooling and the minimum undercooling that may result in kinetic roughening transition. In addition, the FVS model implemented in this work provided a unique opportunity for qualitatively describing the behavior of a crystal-melt interface and gave a molecular-level perspective on the interface stability criterion for the growth of single-crystal silicon during the horizontal ribbon growth (HRG) process.

Roughening of a stepped GaN grain boundary with increasing driving force for migration

High-resolution transmission electron microscopy is applied to characterize the structure of a GaN grain boundary, which is subjected to the driving force for migration arising from the surface energy anisotropy during annealing at 500 °C in a transmission electron microscope. At a low driving force for migration, the grain boundary consists of atomically flat terrace regions interrupted by steps. As the driving force increases, grain-boundary steps become more frequent and undergo meandering, which is a typical attribute of kinetic roughening transition.

Regime II–III transition in isotactic polybutene-1 tetragonal crystal growth

The lateral growth rate and growth shape morphology of isotactic polybutene-1 tetragonal crystals were investigated for crystallization from the melt at temperatures of 68–101 °C. The growth rate of tetragonal crystals shows supercooling dependence derived from the nucleation theory, and a regime II–III transition is observed at temperatures of 77–82.2 °C. The morphology of single crystals is rounded below temperatures of 77–85 °C, while the growth shape has a faceted morphology at a higher crystallization temperature of 100 °C. The kinetic roughening transition occurs between 77 and 85 °C. The regime II growth mode is observed above 82.2 °C and proceeds by multiple nucleation on the faceted growth front, while the regime III growth mode is observed below 77 °C and proceeds by rough surface growth on the kinetically roughened growth front. The observed regime II–III transition can therefore be explained by the morphology transition of crystal growth shape.

Real time observation of ZnO nanostructure formation via the solid-vapor and solid-solid-vapor mechanisms.

We report in situ transmission electron microscopy studies of the formation of ZnO nanostructures--nanoscale depressions, nanoholes, nanoribbons, and nanosheets--and the phase stability and kinetics of Au catalysts on ZnO. During annealing, the ZnO layer produces hexagonally shaped, vertical nanoscale depressions, which increase in size along the 〈 0001 〉 growth direction through preferential dissociation from the {101[combining macron]0} facet and which subsequently form hexagonal islands at their six-fold junctions. Real time observations of the annealing of Au deposited on ZnO show that the catalysts remain solid up to 900 °C, an observation that has implications regarding ZnO nanowire growth via the vapor-solid-solid mechanism (VSS). The Au also creates hexagonal nanoscale holes only at the location of solid Au catalysts, via the solid-solid-vapor (SSV) mechanism. Importantly, coarsening of the Au particles is negligible due to limited Au diffusion on the side facets of the nanoscale depressions, suggesting an approach to the growth of uniform hybrid nanowires with control over both diameter and location. Furthermore, we directly monitor the evolution of the transformation of a nanoribbon into a nanosheet with {101[combining macron]0} facets. This process takes place through a periodic, kinetic roughening transition of the surface, which is controlled by the kinetic competition between surface growth and the transfer of evaporated gases. In total, these observations give new insights into multiple growth processes occurring in this important materials system.

Kinetic roughening transition and missing regime transition of melt crystallized polybutene-1 tetragonal phase: growth kinetics analysis

The morphology and lateral growth rate of isotactic polybutene-1 (it-PB1) have been investigated for crystallization from the melt over a wide range of crystallization temperatures from 50 to 110°C. The morphology of it-PB1 crystals is a rounded shape at crystallization temperatures lower than 85°C, while lamellar single crystals possess faceted morphology at higher crystallization temperatures. The kinetic roughening transition occurs around 85°C. The nucleation and growth mechanism for crystallization does not work below 85°C, since the growth face is rough. However, the growth rate shows the supercooling dependence derived from the nucleation and growth mechanism. The nucleation theory seems still to work even for rough surface growth. Possible mechanisms for the crystal growth of this polymer are discussed.

Crystal Growth of Isotactic Poly(butene-1) in the Melt. I. Kinetic Roughening

The morphology, lateral growth rate and long spacings of isotactic poly(butene-1) (it-PB1) have been investigated for crystallization from the melt over a wide range of crystallization temperature from 50 to 111.9 °C. The morphology of it-PB1 crystals is rounded shape at crystallization temperatures lower than 85 °C, while lamellar single crystals possess faceted morphology at higher crystallization temperatures; the kinetic roughening transition occurs around 85 °C.

Melt growth rate and growth shape of Isotactic polybutene-1 tetragonal crystals

The morphology and lateral growth rate of isotactic polybutene-1 (PB1) has been investigated for crystallization from the melt over a temperature range of 50–110 °C. The morphology of the PB1 tetragonal crystals was a rounded shape at crystallization temperatures below 85 °C, whereas at higher crystallization temperatures, lamellar single crystals possessing faceted morphology were observed. The kinetic roughening transition occurred at approximately 85 °C. Regime II growth mode on faceted growth fronts does not operate below 85 °C as the growth faces are rough. The morphology was therefore indicative of regime III growth on rough surfaces. However, the growth rate showed a single temperature dependence derived from the nucleation theory and thus does not represent a regime II–III transition. Possible mechanisms for the crystal growth of PB1 are discussed.

Kinetic Roughening Transition of isotactic Polybutene-1 Tetragonal Crystals: Disagreement between Morphology and Growth Kinetics

The morphology and lateral growth rate of isotactic polybutene-1 (it-PB1) tetragonal crystals have been investigated for crystallization from the melt over a wide range of crystallization temperature from 50 to 110 °C. The morphology of it-PB1 tetragonal crystals is rounded shape at crystallization temperatures lower than 85 °C, while lamellar single crystals possess faceted morphology at higher crystallization temperatures; the kinetic roughening transition occurs around 85 °C. Regime II growth mode on faceted growth fronts does not work below 85 °C, since the growth faces are rough; the morphology is indicative of regime III growth on rough surfaces. However, the growth rate shows single temperature dependence derived from the nucleation theory; it does not present regime II-III transition. Possible mechanisms for the crystal growth of it-PB1 tetragonal phase are discussed.

Crystal Growth of Isotactic Poly(butene-1) in the Melt. I. Kinetic Roughening

The morphology, lateral growth rate and long spacings of isotactic poly(butene-1) (it-PB1) have been investigated for crystallization from the melt over a wide range of crystallization temperature from 50 to 111.9 °C. The morphology of it-PB1 crystals is rounded shape at crystallization temperatures lower than 85 °C, while lamellar single crystals possess faceted morphology at higher crystallization temperatures; the kinetic roughening transition occurs around 85 °C. The nucleation and growth mechanism for crystallization does not work below 85 °C, since the growth face is rough. However, the growth rate and the long spacings show the supercooling dependence derived from the nucleation and growth mechanism; the nucleation theory seems still to work even for rough surface growth. Taking account of a pinning model revised recently by Toda, possible mechanisms for the crystal growth of polymers are discussed.

Scaling exponents of rough surfaces generated by the Domany-Kinzel cellular automaton.

The critical behavior at the frozen-active transition in the Domany-Kinzel stochastic cellular automaton is studied via a surface growth process in (1+1) dimensions. At criticality, this process presents a kinetic roughening transition; we measure the critical exponents in simulations. Two update schemes are considered: in the symmetric scheme, the growth surfaces belong to the directed percolation (DP) universality class, except at one terminal point. At this point, the phase transition is discontinuous and the surfaces belong to the compact directed percolation universality class. The relabeling of space-time points in the nonsymmetric scheme alters significantly the surface growth, changing the values of the critical exponents. The critical behavior of rough surfaces at the nonchaotic-chaotic transition is also studied using the damage spreading technique; the exponents confirm DP values for the symmetric scheme.

Periodic instability in growth of chains of crystalline-silicon nanospheres

Chains of crystalline-silicon nanospheres were formed by a self-organized process via an extension of the vapor–liquid–solid mechanism using gold as catalyst. The diameter of nanospheres and the spacing between nanospheres were controlled by changing the growth conditions: the diameter and the spacing were small when the gold deposit was thin and the growth temperature was low. The spacing between the crystalline-silicon nanospheres was kept nearly proportional to the diameter of the chain. In order to reveal the growth mechanism of the chain, we simulated the periodic instability in chain growth, taking account of the supersaturation of silicon in vapor phase and molten catalyst, the kinetic roughening transition at the liquid–solid interface, and the interface tensions. Simulated instability was consistent with the experimental observations.

GROWTH OF SURFACES GENERATED BY A PROBABILISTIC CELLULAR AUTOMATION

A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in (1+1) dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton which is known to show a transition from an active phase to an absorbing phase at a critical probability associated with two particular components of the evolution rule. In one of these models, called Model A in this paper, the surface growth is defined in terms of the evolving front of the cellular automaton on the space-time plane. In the other model, called Model B, surface growth takes place by a solid-on-solid deposition process controlled by the cellular automaton configurations that appear in successive time-steps. Both the models show a depinning transition at the critical point of the generating cellular automaton. In addition, Model B shows a kinetic roughening transition at this point. The characteristics of the surface width in these models are derived by scaling arguments from the critical properties of the generating cellular automaton and by Monte Carlo simulations.

Curvature Effects in Alloy Dissolution

An elemental metal can dissolve at kink sites at low everpotentials producing no new interfacial area. When an ideal solid solution alloy undergoes selective dissolution, this situation is not possible owing to atomic‐scale disorder. Dissolution of the less noble constituent can proceed only by injection of regions of negative curvature into the solid surface, which increases the interfacial area. We present a thermodynamic analysis which accounts for these capillary effects in alloy dissolution. The phenomenon of the critical potential for macroscopic selective dissolution is analyzed in terms of a kinetic roughening transition. This transition results from a competition between curvature‐dependent dissolution and surface diffusion. An expression for the critical potential as a function of alloy composition is developed. The dealloying threshold corresponds to a critical composition on the line of critical potentials defining the roughening transition.

Growth of rough surfaces

The growth of objects with rough surfaces is a common phenomenon. We describe several models used in the study of the temporal evolution of fluctuating interfaces and then we explain the dynamical scaling in this class of growth models with self-affine surfaces. The recent progress in this field is reviewed. Much emphasis is put on roughness properties and in particular on a possible kinetic roughening transition — a nonequilibrium analog of the thermal roughening transition. Both analytical and numerical results for scaling exponents are summarized and indications of a phase transition in some models are discussed.

Growth kinetics of solid-liquid Ga interfaces: Part II. Theoretical

The faceted (111) and (001) Ga interfaces grow at low supercoolings with either of the lateral growth mechanisms, two-dimensional nucleation growth (2DNG) or screw dislocation-assisted growth (SDG), depending on the perfection of the interface. The classical theories regarding the growth kinetics of smooth interfaces describe the results qualitatively but not quantitatively. The latter is due to the inadequacy of the assumptions made in the classical theories, which treat the interfacial atomic migration the same as the liquid bulk diffusion process and the step edge energy as independent of the supercooling. Beyond a threshold supercooling, the results show that the faceted interfaces gradually become kinetically rough as the supercooling increases. The step energy, treated as a function of the supercooling, is shown to diverge exponentially with the supercooling at the faceted/nonfaceted transition. At supercoolings exceeding the transition value, dislocations do not affect the growth rate. Furthermore, beyond the transition, the growth rates are linearly dependent on the supercooling, which implies that the growth mode changes from lateral to normal. A generalized lateral growth equation, which includes the interfacial diffusivity and supercooling-dependent step edge free energy, is given to describe the growth kinetics of both interfaces up to supercoolings marking the kinetic roughening transition.

Kinetic roughening of interfaces in driven systems.

We study the dynamics of an interface driven far from equilibrium in three dimensions. First we derive the Kardar-Parisi-Zhang equation from the Langevin equation for a system with a nonconserved scalar order parameter, for the cases where an external field is present, and where an asymmetric coupling to a conserved variable exists. The relationship of the phenomena to self-organized critical phenomena is discussed. Numerical results are then obtained for three models that simulate the growth of an interface: the Kardar-Parisi-Zhang equation, a discrete version of that model, and a solid-on-solid model with asymmetric rates of evaporation and condensation. We first make a study of crossover effects. In particular, we propose a crossover scaling ansatz and verify it numerically. We then estimate the dynamical scaling exponents. Within the precision of our study, the Kardar-Parisi-Zhang equation and the solid-on-solid model have the same asymptotic behavior, indicating that the models share a dynamical universality class. Furthermore, the discrete models exhibit a kinetic roughening transition. We study this by monitoring the surface step energy, which shows a dramatic jump at a finite temperature for a given driving force. At the same temperature, a finite-size-scaling analysis of the bond-energy fluctuation shows a diverging peak.

Simple model of kinetic roughening of quasicrystalline surfaces.

A simple relaxational model of the dynamics of the surface of a growing quasicrystal is studied. As in a crystal, growth proceeds through the nucleation of steps on the surface. Unlike the crystal, the heights ${\mathit{h}}_{\mathit{s}}$ of these steps diverge like (\ensuremath{\Delta}\ensuremath{\mu}${)}^{\mathrm{\ensuremath{-}}1/3}$ as the driving chemical-potential difference \ensuremath{\Delta}\ensuremath{\mu} between quasicrystal and fluid goes to zero. The exponent 1/3 is universal for all quasicrystals with structures derived from quadratic irrationals. This large step size leads to unusually low growth velocities ${\mathit{V}}_{\mathit{g}}$; i.e., ${\mathit{V}}_{\mathit{g}}$\ensuremath{\propto}exp{-1/3[\ensuremath{\Delta}${\mathit{u}}_{\mathit{c}}$(T)/\ensuremath{\Delta}\ensuremath{\mu}${]}^{4/3}$}. The quantity \ensuremath{\Delta}${\mathrm{\ensuremath{\mu}}}_{\mathit{c}}$(T), which defines a rounded kinetic roughening transition, is nonuniversal. For ``perfect-tiling models'' of quasicrystal growth, I find \ensuremath{\Delta}${\mathrm{\ensuremath{\mu}}}_{\mathit{c}}$(T)\ensuremath{\propto}${\mathit{T}}^{\mathrm{\ensuremath{-}}3/2}$, which fits recent numerical simulations, while for models which allow bulk phason Debye-Waller disorder, ln(1/\ensuremath{\Delta}${\mathrm{\ensuremath{\mu}}}_{\mathit{c}}$)\ensuremath{\propto}${\mathit{T}}^{3/2}$. The growing interface is algebraically rough at all temperatures.

Kinetics of interface growth in driven systems.

We study growing interfaces by the numerical simulation of several three-dimensional systems: the Kardar-Parisi-Zhang equation, a discrete variant of that model, and a solid-on-solid model with asymmetric rates of evaporation and condensation. Growth exponents in the rough phase are calculated, and we estimate the kinetic roughening transition temperature, its dependence on driving force, and analyze the transition by finite-size scaling. We find the transition depends strongly on driving force, which could be investigated experimentally.

Anomalous roughening in three-dimensional polynucleation growth

Abstract The surface properties of the three-dimensional polynucleation growth model were studied at the kinetic roughening transition. The dependence of the surface width w on time t and linear size L of the substrate is determined by anomalous roughening: w x ∼log[ L tf( t / L z' )] where tf is a scaling function. For the exponents x = 2.8±0.2 and z ' = 1.79±0.05 were found, the latter being related to directed percolation.

Kinetic Roughening of Interfaces in Driven Systems

We study the dynamics of an interface driven far from equilibrium in three dimensions. The relationship of the phenomena to self-organized critical phenomena is discussed. Numerical results are obtained for three models which simulate the growth of an interface: the Kardar-Parisi-Zhang equation, a discrete version of that model, and a solid-on-solid model with asymmetric rates of evaporation and condensation. We show that the three models belong to the same dynamical universality class by estimating the dynamical scaling exponents and the scaling functions. We confirm the results by a careful study of the crossover effects. In particular, we propose a crossover scaling ansatz and verify it numerically. Furthermore, the discrete models exhibit a kinetic roughening transition. We study this phenomenon by monitoring the surface step energy which shows a drastic jump at a finite temperature for a given driving force. At the same temperature, a finite size scaling analysis on the bond energy fluctuation shows a diverging peak [1].