| Abstract:
Following up on the talk this morning by Alberto Pimpinelli, I discuss here some issues that arise when analyzing actual experimental or numerical data using the formalism he described [1]. Experimental data is far less extensive, by orders of magnitude, than that achieved in recent simulations[2,3]. There are insufficient realizations in such cases to allow scrutinizing the distribution for very small or large capture zone areas. Often it is difficult to ascertain whether the generalized Wigner surmise (GWS) or the gamma distribution account better for the data. However, both can be used to make predictions about the critical nucleus size, the key microscopic parameter that GWS analysis extracts from data. We discuss explicit experimental applications to pentacenequinone impurities in pentacene island nucleation [4], to self-assembled Ge islands on Si(001) [5], to submonolayer C60 on SiO2 [6], and to para-sexiphenyl islands on SiO2 [7]. In kinetic Monte Carlo simulations of growth it has been applied explicitly to faceted islands in heteroepitaxy [8] and to homoepitaxy of Cu, both pure and with codeposited impurities of various kinds [9]. While theory predicts scant dependence of this parameter on coverage below the coalescence regime, some experiments and simulations of growth systems find significant changes with coverage. This suggests that one might better view this parameter as effective
We discuss some possible refinements of the distribution [10]. We also discuss attempts to describe the areas of secondary administrative units (counties in the original colonies, départements in France, provinces in Italy, Landkreise in Germany, powiat in Poland, etc.) in this context [11]. In many cases, the GWS or the Gamma distribution provide very a very good description. We discuss these and the conditions when the description is not so good.
Joint work with Alberto Pimpinelli, Rajesh Sathiyanarayan, Ajmi BH. Hammouda, Diego Luis González Cabrera, Brad Conrad, Michelle Groce, William Cullen, and Ellen Williams.
This work was supported by the NSF-MRSEC at the University of Maryland, DMR 05-20471, with ancillary support from CNAM.
1. A. Pimpinelli, T.L. Einstein, Phys. Rev. Lett. 99, 226102 (2007); 104, 149602 (2010).
2. F. Shi, Y. Shim, J.G. Amar, Phys. Rev. E 79, 011602 (2009).
3. M. Li, Y. Han, J.W. Evans, Phys. Rev. Lett. 104, 149601 (2010).
4. B.R. Conrad, Elba Gomar-Nadal, W.G. Cullen, A. Pimpinelli, T.L. Einstein, and E.D. Williams, Phys. Rev. B 77, 205328 (2008)
5. S. Miyamoto, O. Moutanabbir, E. E. Haller, and K. M. Itoh, Phys. Rev. B 79, 165415 (2009)
6. M.A. Groce, B.R. Conrad, W.G. Cullen, E.D. Williams, and T.L. Einstein, "Submonolayer C60 films on ultrathin SiO2," preprint.
7. S. Lorbek, G. Hlawacek and C. Teichert, "Determination of critical island size in para-sexiphenyl islands on SiO2 using capture-zone scaling," submitted
8. Chi-Hang Lam, Phys. Rev. E 81, 021607 (2010)
9. R. Sathiyanarayanan, A. BH. Hamouda, A. Pimpinelli, TLE, "Role of Codeposited Impurities During Growth: II. Dependence of Morphology on Binding and Barrier Energies," submitted.
10. Diego Luis González, Alberto Pimpinelli, and T. L. Einstein, "Mean-Field Approximation for Spacing Distribution Functions in Classical Systems," preprint; also "Spacing Distributions Functions for the One-Dimensional Point Island Model with Irreversible Attachment"
11. Rajesh Sathiyanarayan, Ph.D. dissertation (UMD, 2009), and to be published.
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