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تسجيل مستخدم جديدA facet is not an island: step-step interactions and the fluctuations of the boundary of a crystal facet
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In a recent paper [Ferrari et al., Phys. Rev. E 69, 035102(R) (2004)], the scaling law of the fluctuations of the step limiting a crystal facet has been computed as a function of the facet size. Ferrari et al. use rigorous, but physically rather obscure, arguments. Approaching the problem from a different perspective, we rederive more transparently the scaling behavior of facet edge fluctuations as a function of time. Such behavior can be scrutinized with STM experiments and with numerical simulations.
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Time dependent STM has been used to evaluate step fluctuations as a function of temperature (300-450 K) on Ag(111) films grown on mica. The temporal correlation function scales as a power law in time, t^1/n with measured values of 1/n varying over a
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The effects of sampling rate and total measurement time have been determined for single-point measurements of step fluctuations within the context of first-passage properties. Time dependent STM has been used to evaluate step fluctuations on Ag(111)
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Spurred by theoretical predictions from Spohn and coworkers [Phys. Rev. E {bf 69}, 035102(R) (2004)], we rederived and extended their result heuristically as well as investigated the scaling properties of the associated Langevin equation in curved ge
ometry with an asymmetric potential. With experimental colleagues we used STM line scans to corroborate their prediction that the fluctuations of the step bounding a facet exhibit scaling properties distinct from those of isolated steps or steps on vicinal surfaces. The correlation functions was shown to go as $t^{0.15(3)}$ decidedly different from the $t^{0.26(2)}$ behavior for fluctuations of isolated steps. From the exponents, we were able to categorize the universality, confirming the prediction that the non-linear term of the KPZ equation, long known to play a central role in non-equilibrium phenomena, can also arise from the curvature or potential-asymmetry contribution to the step free energy. We also considered, with modest Monte Carlo simulations, a toy model to show that confinement of a step by another nearby step can modify as predicted the scaling exponents of the steps fluctuations. This paper is an expansion of a celebratory talk at the 95$^{rm th}$ Rutgers Statistical Mechanics Conference, May 2006.
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