Research Activities > Programs > Nonequilibrium Interface and Surface Dynamics 2007

Morphometric Multi-scale Surface Science

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Morphometric Multi-scale Surface Science

Dr. Stephen Watson

University of Glasgow


Abstract:   The characterization of self-assembled faceted surfaces is a central theoretical challenge in surface science, since the ensuing morphological statistics (morphometrics) impact applications in diverse areas. I'll discuss the morphometrics emerging from the attachment kinetics limited coarsening of a thermodynamically unstable crystalline surface. One commonly used model is a dissipative ("steepest descent") singularly perturbed fourth-order partial differential equation. We first show that its singular limit is naturally characterized through the asymptotic expansion of an Onsager-Raleigh-type Principle of Maximal Dissipation (PMD) [1]. The resulting limiting faceted surface is then characterized by an intrinsic dynamical system. The properties of the resulting Piecewise-Affine Dynamic Surface (PADS) predict the scaling law L_M t^1/3, for the growth in time t of a characteristic morphological length scale L_M. We then introduce a novel computational geometry tool which directly simulates the coarsening dynamics of million-facet PADS. We conclude by presenting data consistent with the dynamic scaling hypothesis, and report a variety of associated morphometric scaling-functions.

[1] S.J. Watson & S.A. Norris, Scaling theory and morphometrics for a coarsening multiscale surface, via a principle of maximal dissipation, Physical Review Letters 96 (17), Art. No. 176103 (2006).


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