Drude formula

We showed in the preceding section that for solids with strong vibrational bands the position of features in absorption spectra can be shifted appreciably in going from the bulk to particulate states. Metallic particles can deviate even more markedly from the behavior of the bulk parent material they can have absorption features over broad frequency regions where none appear in the bulk. For a simple metal—one that is well described by the Drude formula... 

Extinction calculations for aluminum spheres and a continuous distribution of ellipsoids (CDE) are compared in Fig. 12.6 the dielectric function was approximated by the Drude formula. The sum rule (12.32) implies that integrated absorption by an aluminum particle in air is nearly independent of its shape a change of shape merely shifts the resonance to another frequency between 0 and 15 eV, the region over which e for aluminum is negative. Thus, a distribution of shapes causes the surface plasmon band to be broadened, the... 

The observed darkening of the indium slides results from a shift of the absorption peak because of the coating on the particles. Because of the cumbersomeness of the expressions for coated ellipsoids (Section 5.4) this shift can be understood most easily by appealing to (12.15), the condition for surface mode excitation in a coated sphere. For a small metallic sphere with dielectric function given by the Drude formula (9.26) and coated with a nonabsorbing material with dielectric function c2, the wavelength of maximum absorption is approximately... 

At a farther distance from the absorption region, the rotation of the molecular system is expressed as a sum of the one-term Drude formula ... 

The reflectivity initially falls rapidly and then more slowly as the photon energy increases. The vibrational modes of the polymer give rise to distinctive resonant features between 0.06 and 0.19 eV. In normal metals the optical conductivity is given by the Drude formula ... 

This expression is analogous to the general Drude formula (10), but it suggests that, in a spectral region distant from the optically active transitions of a helical polymer, the dispersion will be complex rather than simple. 

The region near the plasma edge in Id conductors /any gap uj < interband region/ is known to approximately obey the Drude formula for the dielectric function ... 

To evaluate the spectral shift of the extinction maximum, we use the Drude formula [45] along with Eq. (2.9). After some simple algebra we get [12]... 

Brewster angle ellipsometry (BAE) and surface optical second harmonic generation (SHG, see Chap. 5) were used to study the growth of 8CB films, evaporated in air onto glass (BK7) substrates, covered with a 15 nm thick film of poly(vinyl cinnamate) (PVCN) [48]. As the thickness of 8CB on PVCN layers was far below the optical wavelengths, the Drude formula for the ellipsometric coefficient at the Brewster angle, ps, (4.3), was used. The ellipticity coefficient of the 8CB adsorbate was calculated as... 

Figure 7.25. Thickness dependence of simulated ATR spectra of model organic film at galena-water interface. Simulation were performed for angle of incidence of 36°. Refractive indices for IRE, galena, and water were n-i = 2.4, 02 = 3.91, and 7)4 = 1.26, respectively, and /f4 = 0.036. Thickness of galena layer was taken as c/2 = 10 (jim. Optical constants of organic film were chosen to be close to those of lead xanthate but approximated by three-oscillator Maxwell-Helmholtz-Drude formula with fco = 2.5 yj =20 cm j = 1,2,3) vqi = 1200 cm ...

The anisotropy is also observed in the dc conductivity, with along b enhanced compared to the a-axis results (Friedmann et al. 1990, Welp et aL 1990, Rice et al. 1991). While there was considerable scatter in the data for the anisotropy in the samples studied in 1988—1992, more recent results seem to indicate that the ratio Ob/Oa is the same as o i/o>pa (Zhang et al. 1994, Basov et al. 1995a). Applying a sinqjle Drude formula to these results, suggests that the scattering rate is the same along... 

Fig. 20. Frequency dependence of the conductivity of He+-irradiated single crystals of YBa2Cu30 95. Upper curves in all panels were measured at temperatures slightly above T, while the lower curves were obtained at 10 K. The dashed curves show the fit of the narrow normal component in the superconducting conductivity to the Drude formula. After Basov et al. (1994b).

At high frequencies, o-(tB) for ordered materials is given by the Drude formula. 

But only the electrons at the surface of the Fermi sphere can move with the Fermi velocity. So instead of all of the electrons moving at the drift speed, we now have the current carried by much fewer but much faster electrons at the Fermi surface that can respond to the applied field. This new Fermi model requires a reformulation of the conductivity and it will be shown later that the Drude formula for conductivity still holds for simple metals but for wrong reason. 

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