Growth exponent

The growth exponents a are most readily eonfirmed by plotting direetly the number of blobs L)/l against redueed density The data eol-lapse onto a single master eurve, seen in Fig. 7, whieh is indeed remarkable and a eentral result of the simulation [65,66]. The two indieated slopes mateh exaetly the predieted exponents 0.46, 0.60 (note that in... 

The kinetics of the nonconserved order parameter is determined by local curvature of the phase interface. Lifshitz [137] and Allen and Cahn [138] showed that in the late kinetics, when the order parameter saturates inside the domains, the coarsening is driven by local displacements of the domain walls, which move with the velocity v proportional to the local mean curvature H of the interface. According to the Lifshitz-Cahn-Allen (LCA) theory, typical time t needed to close the domain of size L(t) is t L(t)/v = L(t)/H(t), where H(t) is the characteristic curvature of the system. Thus, under the assumption that H(t) 1 /L(t), the LCA theory predicts the growth law L(t) r1 /2. The late scaling with the growth exponent n = 0.5 has been confirmed for the nonconserved systems in many 2D simulations [139-141]. 

Using atomic force microscopy (AFM), the kinetic surface roughening in electrochemical dissolution of nickel films at a low constant current density was studied in order to reveal the scaling laws [33]. The surface measurements of AFM exhibited the oscillatory variation of the interface width with time, which made it impossible to determine the growth exponent p. The oscillatory behavior of surface... 

FIGURE 16.21 Relative density versus time for the grain growth exponent (a) = 2 (with KlfJCi = 1) and (b) = 3 (with R/Cj = 1) for various side distribution width parameters, Taken from Chappell et al. [47]. 

FIGURE 16.22 (a) Relative grain size versus relative density for a grain growth exponent g = 2 as a function of the log-normal size distribution width parameter, cr. Taken from Chappell et al. [47]. (b) Experimental grain size (GS) divided by initial particle size (PS() 0.3 pm) versus relative density for — monodisperse T1O2 [53] (cr = 0.1), — TiOj [54] ([Pg.817]

Figure 3. Recursive replacement of the zigzag motif over four decades in length scale (dash-dot-dot, coarse dash, fine dash, solid largest scale shown only partially). This generates a self-affined surface with a growth exponent equal to one-half Modified from Barabasi and Stanley (1995).

Thus, from measuring the aluminium oxide roughness for different film thicknesses the growth exponent ji can be determined as the slope of a linear fit to a log-log plot of the aluminium oxide roughness versus its film thickness. To account for the roughness of the underlying substrate we used a renormalisation according to the relation [10]... 

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