Diffusive wire

Fig. 1. A model of Andreev interferometer. A diffusive wire of the length L connects a normal reservoir (N) and short SNS junction of the length d magnetic flux (T> threads a superconducting loop (S) of the interferometer.

In this Appendix we outline, for reference purposes, the procedure and summarize the results of calculation of the CGF for a diffusive connector between normal reservoirs, by using the extended Keldysh-Green s technique. For generality, we consider a diffusive wire interrupted by tunnel barriers, which enables us to present several original results and to examine various limiting situations. 

In some limiting cases, one can obtain an analytical solution of Eq. (41). In particular, if the number M of the barriers is large, M 1, then the resistance of each barrier is small compared to the net resistance, Rk approximate solution of Eq. (41) is g = , and the CGF coincides with that for diffusive wire, Eq. (44). In the tunnel limit, when the resistance of each barrier much exceeds the net resistance of diffusive segments, Rk Rn, the first term in Eq. (41) can be neglected. Then an analytical expression for the parameter g and the CGF at arbitrary M can be obtained in the case of equivalent barriers, rk = 1/M,... 

The noble metal thermocouples, Types B, R, and S, are all platinum or platinum-rhodium thermocouples and hence share many of the same characteristics. Metallic vapor diffusion at high temperatures can readily change the platinum wire calibration, hence platinum wires should only be used inside a nonmetallic sheath such as high-purity alumina. 

Wire cords are particularly subject to degradation of their adhesion values by moisture. To combat this, halogenated butyl (HIIR) is used in tire innerliners because of its property of low air and water vapor diffusion rates. Moisture is present in most air pumps and many tires are mounted with water left in the tire on mounting. For these reasons tires and tire compounds are tested extensively at simulated aging conditions in the laboratory and on test vehicles before they are sold to the customer. 

If samples of two metals widr polished faces are placed in contact then it is clear that atomic transport must occur in both directions until finally an alloy can be formed which has a composition showing die relative numbers of gram-atoms in each section. It is vety unlikely that the diffusion coefficients, of A in B and of B in A, will be equal. Therefore there will be formation of an increasingly substantial vacancy concentration in the metal in which diffusion occurs more rapidly. In fact, if chemically inert marker wires were placed at the original interface, they would be found to move progressively in the direction of slowest diffusion widr a parabolic relationship between the displacement distance and time. 

Diffusion in the bulk crystals may sometimes be short circuited by diffusion down grain boundaries or dislocation cores. The boundary acts as a planar channel, about two atoms wide, with a local diffusion rate which can be as much as 10 times greater than in the bulk (Figs. 18.8 and 10.4). The dislocation core, too, can act as a high conductivity wire of cross-section about (2b), where b is the atom size (Fig. 18.9). Of course, their contribution to the total diffusive flux depends also on how many grain boundaries or dislocations there are when grains are small or dislocations numerous, their contribution becomes important. 

When the electrode is placed in an aqueous solution of glucose which has been suitably diluted with a phosphate buffer solution (pH 7.3), solution passes through the outer membrane into the enzyme where hydroxen peroxide is produced. Hydrogen peroxide can diffuse through the inner membrane which, however, is impermeable to other components of the solution. The electrode vessel contains phosphate buffer, a platinum wire and a silver wire which act as electrodes. A potential of 0.7 volts is applied to the electrodes (the apparatus shown in Fig. 16.17 is suitable) with the platinum wire as anode. At this electrode the reaction H202->02 + 2H+ +2e takes place, and the oxygen produced is reduced at the silver cathode ... 

In deriving the kinetic equation describing the arrival of various ionic species at the cathode, it is assumed that the primary species N2 + is formed at the central wire at a constant rate, and during its passage in the direction x perpendicular to the axis its concentration is modified by various reactions. In this treatment both ion diffusion and ion-ion or electron-ion recombination processes are neglected because the geometry of the discharge tube and the presence of an electric field would... 

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