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We analyze in detail the fluctuations and correlations of the (spatial)Fourier modes of nano-scale single-layer islands on (111) fcc crystal surfaces.We analytically show that the Fourier modes of the fluctuations couple due tothe anisotropy of the crystal, changing the power spectrum of the fluctuations,and that the actual eigenmodes of the fluctuations are the appropriate linearcombinations of the Fourier modes. Using kinetic Monte Carlo simulations withbond-counting parameters that best match realistic energy barriers for hoppingrates, we deduce absolute line tensions as a function of azimuthal orientationfrom the analyses of the fluctuation of each individual mode. Theautocorrelation functions of these modes give the scaling of the correlationtimes with wavelength, providing us with the rate-limiting kinetics driving thefluctuations, here step-edge diffusion. The results for the energeticparameters are in reasonable agreement with available experimental data forPb(111) surfaces, and we compare the correlation times of island-edgefluctuations to relaxation times of quenched Pb crystallites.Comment: 11 pages, 8 figures; to appear in PRB 70, xxx (15 Dec 2004), changes  in MC and its implication

Fluctuations, line tensions, and correlation times of nanoscale islands on surfaces