Coherence length electric

Figure 12.12. Dimensionless measure of flatness of oblate structures (S/R) as a function of dimensionless electric field strength E/Eq, Eq is chosen to be the field at which the electric coherence length equals R. The dependencies for the four oblate structures are shown RO (heavy solid line), NDO (solid), PDO I (dashed), and PDO II (dotted). Two sets of curves are shown, the upper one corresponds to qR = lOn, the lower one to qr = 40n (courtesy of J. Bajc).

TABLE 9 Experimental data for Lu(Nii xCox)2B2C (after Cheon et al., 1998) with Tc determined from electrical resistivity p(T), po—the residual resistivity, Hc2(0)—the zero-temperature upper critical field, l—the mean free path, and 0—the BCS coherence length... 

X-ray diffraction studies of these drawn films demonstrated a high degree of structural order, which improves with the draw ratio the structural coherence length perpendicular to the draw direction increases by about a factor of two as the films are drawn, from 10 nm at = 4 to 20 nm at = 15 [4]. Consistent with the chain orientation and the improved structural order, the anisotropy (a,/aj) in the electrical conductivity increased with the draw ratio, approaching 250 as X.—>15 (although cth increased dramatically as a function of X, remains... 

Electrical properties of junctions formed between superconducting material, S, and a non-superconducting metallic material, N, which may be a metal or a degenerate semiconductor, are determined by special boundary conditions. If we consider a superconductor-semiconductor (S-N) interface with high transparency, a proximity effect is observed due to injection of electron pairs (Cooper pairs) from the superconductor into the semiconductor where they decay over a characteristic length, the induced coherence length. 

Order electricity may be expected to manifest itself at the nematic-isotropic (or air) interface where, as discussed in 2.7, the order parameter changes rapidly across the transition zone from one phase to the other. Let us make the simple assumption that at the N-I interface the gradient of the order parameter sj, where is a coherence length. If is the component of the polarization normal to the interface created by the order parameter gradient, and the director at the interface is tilted at an angle 6 with respect to z, the dielectric energy due to order electricity will be proportional to ... 

Experimental [23] as well as theoretical [24-26] studies of percolation phenomena have been reported. In random and macroscopically homogeneous materials it has been demonstrated [27-29] that at concentrations of metal particles below the percolation threshold (p < Pc) a short-range percolation coherence length, exists. Electrical conductivity is probable for length scales less than Thus even if the metal-filled composite exhibits no bulk electrical conductivity, conduction can occur within domains that are smaller than As the concentration of metal particles approaches oo and the composite becomes isotropically conductive. 

To lower the probability of conduction in the X Y plane (i.e., reduce the short-range percolation coherence length ), particles are used with an aspect ratio as close to 1 as possible. In contrast, isotropically conductive systems use flakes with high aspect ratios as fillers. Particle size distributions are minimized so that each particle can potentially serve as an electrical bridge between substrate and device. 

Figure 46.22 presents [73] the low temperature dielectric constant for a series of emeraldine hydrochloride samples plotted against the square of the crystalline coherence length, (as measured by x-ray diffraction). For low temperatures, is proportional to independent of the direction of orientation of the sample with regard to the microwave frequency electric field. This demonstrates that the charge is delocalized three-dimensionally within the crystalline regions of these samples. Using a simple metallic box model [73,143],... 

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