Step motion

Usually, experimentalists quantify step fluctuations by averaging the data to find the correlation function G(t) = 0.5 < (h(x,i) - h(x,0)Y >, where h x,t) specifies the step position at time t and the average is over many sample points, x. G(f) measures how far a position on a step wanders with time. If that position were completely free to wander, it would obey a diffusive law G(t) t. However, its motion is restricted by the fact that it is connected to the other parts of the step. For that reason G(t) is sub-diffusive. The detailed law which G(f) obeys is dependent on the atomic processes which mediate step motion. For example, if the step edge is able to freely exchange... 

At r > Tr, the relaxation of a non-equilibrium surface morphology by surface diffusion can be described by Eq. 1 the thermodynamic driving force for smoothing smoothing is the surface stiffness E and the kinetics of the smoothing is determined by the concentration and mobility of the surface point defects that provide the mass transport, e.g. adatoms. At r < Tr, on the other hand, me must consider a more microscopic description of the dynamics that is based on the thermodynamics of the interactions between steps, and the kinetics of step motion [17]. 

Assuming the width of the terrace W is much larger than the lattice constant of the crystal, we can use a continuum description of the step) motion. The problem can be simplified by using the relative separation between the tno lines. x(y, t), where y runs along the strip. The equation of motion for x is given by. 

The dynamics of the step motion leading to faceting would be very complicated if it were strongly coupled to the dynamics of reconstruction. Fortunately, in most cases the growth of a reconstructed region occurs much more rapidly than the characteristic time for step motion. Thus we will not consider the dynamics of reconstruction explicitly here, and instead use a simple two state where each terrace is either... 

We now modify the 2D continuum equations of step motion, Eqs. (7) and (8), in order to study some aspects of the dynamics of faceting. We assume the system is in the nucleation regime where the critical width Wc is much larger than the average step spacing In the simplest approximation discussed here, we incorporate the physics of the two state critical width model into the definition of the effective interaction term V(w) in Eq. (2), which in turn modifies the step chemical potential terms in Eqs. (7) and (8). Again we set V(w) = w/ l/w) as in Eq. (4) but now we use the /from Eq. (10) that takes account of reconstruction if a terrace is sufficiently wide. Note that this use of the two state model to describe an individual terrace with width w is more accurate than is the use of Eq. (10) to describe the properties of a macroscopic surface with average slope s = Mw. 

R. E. Schwoebel and E. J. Shipsey, Step motion on crystal surfaces,/. Appl. Phys., 37,1966, 3682-6... 

The electrochemical and chemical behavior of rotaxane 7 + was analyzed by CV and controlled potential electrolysis experiments.34,35 From the CV measurements at different scan rates (from 0.005 to 2 V/s) both on the copper(I) and on the copper(II) species, it could be inferred that the chemical steps (motions of the ring from the phenanthroline to the terpyridine and vice versa) are slow on the timescale of the experiments. As the two redox couples involved in these systems are separated by 0.7 V, the concentrations of the species in each environment (tetra- or pentacoor-dination) are directly deduced from the peak intensities of the redox signals. In Fig. 14.13 are displayed some voltammograms (curves a-e) obtained on different oxidation states of the rotaxane 7 and at different times. 

Fig. 3. Contour diagram for the correlated in-step motion of the two protons in a dimer-type system such as...

The observed decays for E = 0 (and at higher energies) give the rates at which the BPS is changing with time due to proton transfer. The fact that the initial tautomerization is on the femtosecond time scale, when the total vibrational energy is zero, indicates that the proton transfer motion is direct and does not involve the entire vibrational phase space of the pair. The implication is that the motion can be described as localized in the coordinate of N—H N. Furthermore, the two decay components indicate the presence of the intermediate structure, which reflects the two-step motion in the transfer. 

Figure B.2 Symmetric large-angle (113)(TlO] tilt boundary in A1 viewed along the [110] tilt axis by high-resolution electron microscopy. The tilt angle is 50.48°. The inset shows a simulated image [4], Reprinted, by permission, from K.L. Merkle, L.J. Thompson, and F. Phillipp, Thermally activated step motion observed by high-resolution electron microscopy at a (113) symmetric tilt grain-boundary in aluminum," Philosophical Magazine Letters, vol. 82. pp. 589-597. Copyright (c) 2002 by Taylor and Francis Ltd., http //www.tandf.co.uk/journals.

K. L. Merkle, L. J. Thompson, and F. Phillipp. Thermally activated step motion observed by high-resolution electron microscopy at a (113) symmetric tilt grain-boundary in aluminium. Phil. Mag. Lett., 82 589-597, 2002. 

With step-by-step motion along the stable branches 1 and 3, the relaxation time must depend on the step value AT. For example, with increasing (decreasing) AT, the distance on the phase pattern that must be passed by the... 

The transport of oxygen consists of two parts, one related to the interstitial transport of O2 through the network and the other to a step-by-step motion of network oxygen atoms.A significant part of the oxygen diffusion may be of ionic nature since an electric field is found to affect the growth of oxide. ... 

The motion of the growth steps is consistent with the hypothesis that vapour molecules are adsorbed in equilibrium concentration upon the flat basal surface and that those within some characteristic surface diffusion distance /g can migrate to the step and become incorporated in the crystal. If the step height is h -4 Ig then the rate of step motion should be... 

The theory of surface diffusion and step motion for simple crystals is well known (Burton et al. 1951). From the formula due to Einstein, the surface diffusion length 4 is given in terms of surface diffusion coefficient Z)g and surface adsorption lifetime Tg... 

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