INFLUENCE OF METAL GRAIN-SIZE ON SURFACE-ENHANCED RAMAN-SCATTERING

The surface roughness of nominally smooth and of randomly roughened thin silver films is characterized using scanning tunneling microscopy and the metal grain size is assessed using transmission electron microscopy. On each type of substrate used, glass or CaF2-roughened glass, the silver films are deposited either very slowly (approximately 0.15 nm s-1) or quite quickly (approximately 2.0 nm s-1). Only silver films deposited on CaF2-roughened glass yield measurable surface-enhanced Raman signals for benzoic acid; the enhancement is brought about by surface field amplification due to the excitation of delocalized surface-plasmon polaritons. However, the surface-enhanced Raman signals obtained from the slow-deposited silver films are significantly better (by about a factor of 3) than those obtained from the fast-deposited silver films on a given CaF2-roughened substrate. The explanation of this observation does not lie with different surface roughness; both types of film yield closely similar data on the scanning tunneling microscope. Rather, it is suggested that the relatively small grain size of the fast-deposited silver films leads to increased elastic scattering of surface-plasmon polaritons at the grain boundaries, with a consequent increase of internal damping. This results in a reduction of the scattered Raman signal.

SURFACE ENHANCED RAMAN-SCATTERING FROM MILDLY ROUGHENED SURFACES - VARIATION OF SIGNAL WITH METAL GRAIN-SIZE

The intensity of surface enhanced Raman scattering from benzoic acid derivatives on mildly roughened, thermally evaporated Ag films shows a remarkably strong dependence on metal grain size. Large grained (slowly deposited) films give a superior response, by up to a factor of 10, to small grained (quickly deposited) films, with films of intermediate grain size yielding intermediate results. The optical field amplification underlying the enhancement mechanism is due to the excitation of surface plasmon polaritons (SPPs). Since surface roughness characteristics, as determined by STM, remain relatively constant as a function of deposition rate, it is argued that the contrast in Raman scattering is due to differences in elastic grain boundary scattering of SPPs (leading to different degrees of internal SPP damping), rather than differences in the interaction of SPPs with surface inhomogeneities.

The size distribution of Jupiter Family comets

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The Size Distribution of US Banks and Credit Unions

This study examines the firm size distribution of US banks and credit unions. A truncated lognormal distribution describes the size distribution, measured using assets data, of a large population of small, community-based commercial banks. The size distribution of a smaller but increasingly dominant cohort of large banks, which operate a high-volume low-cost retail banking model, exhibits power-law behaviour. There is a progressive increase in skewness over time, and Zipf’s Law is rejected as a descriptor of the size distribution in the upper tail. By contrast, the asset size distribution of the population of credit unions conforms closely to the lognormal distribution.