Dynamic roughening

A different kinetic realization of dynamic roughening is as follows If the rate of step-spreading is much greater than the nucleation rate, then a single layer can cover the facet before the subsequent nucleation event occurs. As the driving force is increased, this condition is more difficult to satisfy, and the facet becomes decorated with multiple supercritical nuclei simultaneously. Over a time period xs the nuclei... 

At the same time, many lattice dynamics models have been constructed from force-constant models or ab-initio methods. Recently, the technique of molecular dynamics (MD) simulation has been widely used" " to study vibrations, surface melting, roughening and disordering. In particular, it has been demonstrated " " " that the presence of adatoms modifies drastically the vibrational properties of surfaces. Lately, the dynamical properties of Cu adatoms on Cu(lOO) " and Cu(lll) faces have been calculated using MD simulations and a many-body potential based on the tight-binding (TB) second-moment aproximation (SMA). " ... 

Several recent molecular dynamics simulations (e.g. [10] and references therein) have focussed on the wetting of interfaces (Section 6.1) and, for example, the behaviour of very small droplets at the nanoscale. Such simulations are able to relate the atomistic behaviour directly to relevant macroscopic parameters such as the contact angle and are able to show the dramatic effects at this length scale of addition of surfactant molecules or roughening of the surface. 

The initial answer to this question was provided by Mullins [4], building on the work of Herring [5]. For surfaces orientations at temperatures above their thermodynamic roughening temperature Tr (the free energy for step formation becomes zero at T = Tr), the relaxation is driven by the stiffness [6] of the surface E = E + dE ldQ, where E is the surface energy and 9 is the orientation of the surface. For mass transport by surface diffusion, the dynamics of the surface at T > Tr are described by... 

The thermal healing has been studied most extensively for one-dimensional gratings. Above roughening, the gratings acquire, for small amplitude to wavelength ratios, a sinusoidal form, as predicted by the classical continuum theory of Mullins and confirmed by experimenf-s and Monte Carlo simulations. - The decay of the amplitude is, asymptotically, exponential in time. This is true for both evaporation dynamics and (experimentally more relevant) surface diffusion. 

In this paper we review some of our recent work on the dynamics of step bunching and faceting on vicinal surfaces below the roughening temperature, concentrating on several cases where interesting two dimensional (2D) step patterns form as a result of kinetic processes. We show that they can be understood from a unified point of view based on an approximate but physically motivated extension to 2D of the kind of ID step models studied by a number of workers. For some early examples, see refs. [1-5]. We have tried to make the conceptual and physical foundations of our own approach clear, but have made no attempt to provide a comprehensive review of work in this active area. More general discussions from a similar perspective and a guide to the literature can be found in recent reviews by Williams and Williams and BartelF. 

Otsuka and Iwasald [16] have employed AFM method to observe the self-affine fractal structure of the electrochemically roughened Ag electrode surfaces [17]. Later, they have described the dynamic scaling in recrystallization of this electrode surface in water. 

The balance used in the measurements presented below is a KSV 5000 with a dynamic range of 0-100 mN/m. Samples were prepared in crystallizing dishes 60 mm in diameter and 35 mm deep. The measurements were made by immersing about 1/3 of the plate in the lower phase. Measurements were made using a roughened platinum plate that had been cleaned with NoChromix solution and flamed until red hot to make it hydrophilic. 

R. Divan, N, Moldovan, and H, Camon, Roughening and smoothing dynamics during KOH silicon etching. Sensors Actuators 74, 18, 1999. 

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