Relaxation time, electronic conductivity

An impurity atom in a solid induces a variation in the potential acting on the host conduction electrons, which they screen by oscillations in their density. Friedel introduced such oscillations with wave vector 2kp to calculate the conductivity of dilute metallic alloys [10]. In addition to the pronounced effect on the relaxation time of conduction electrons, Friedel oscillations may also be a source of mutual interactions between impurity atoms through the fact that the binding energy of one such atom in the solid depends on the electron density into which it is embedded, and this quantity oscillates around another impurity atom. Lau and Kohn predicted such interactions to depend on distance as cos(2A pr)/r5 [11]. We note that for isotropic Fermi surfaces there is a single kp-value, whereas in the general case one has to insert the Fermi vector pointing into the direction of the interaction [12,13]. The electronic interactions are oscillatory, and their 1 /r5-decay is steeper than the monotonic 1 /r3-decay of elastic interactions [14]. Therefore elastic interactions between bulk impurities dominate the electronic ones from relatively short distances on. 

ESR can detect unpaired electrons. Therefore, the measurement has been often used for the studies of radicals. It is also useful to study metallic or semiconducting materials since unpaired electrons play an important role in electric conduction. The information from ESR measurements is the spin susceptibility, the spin relaxation time and other electronic states of a sample. It has been well known that the spin susceptibility of the conduction electrons in metallic or semimetallic samples does not depend on temperature (so called Pauli susceptibility), while that of the localised electrons is dependent on temperature as described by Curie law. 

Experimental measurement of Hall mobility produces values of the same order of magnitude as the drift mobility their ratio r = jij/l may be called the Hall ratio. If we restrict ourselves to high-mobility electrons in conducting states in which they are occasionally scattered and if we adopt a relaxation time formulation, then it can be shown that (Smith, 1978 Dekker, 1957)... 

Here n is the concentration of the electrons and is their relaxation time in the conduction band. 

Evaluation of intensities of X-ray diffraction patterns indicates that the CsCl structure is well ordered in crystalline CsAu. Excess Cs, which is the primary source for conduction electrons, is dispersed in the lattice with increase of the cell parameter (105). Cesium-133 NMR measurements (line shapes, Knight shifts, and relaxation times) confirm this result (105). The interpretation of the data for RbAu is less straightforward, however. 

The use of a bulk-like dielectric constant, such as those in Equations (2.334)-(2.336), neglects the specific contribution given by the surface to the dielectric response of the metal specimen. For metal particles, such a contribution is often introduced in the model by considering the surface as an additional source of scattering for the metal conduction electrons, which consequently affects the relaxation time r [69], Experiments indicate that the precise chemical nature of the surface also plays a role [70], The presence of a surface affects the nonlocal part of the metal response as well, giving rise to surface-assisted excitations of electron-hole pairs. The consequences of these excitations appear to be important for short molecule-metal distances [71], It is worth remarking that, when the size of the metal particle becomes very small (2-3 nm), the electron behaviour is affected by the confinement, and the metal response deviates from that of the bulk (quantum size effects) [70],... 

The conductivity increases as we see with the number of free electrons available to carry the current and with the time in which each one can be speeded up by the field before it reaches a stationary speed on account of the resistance. It is obvious that Eq. (4.8), though it gives an explanation of Ohm s law, does not lead to a calculation of the conductivity in terms of known quantities, because though we have seen how to estimate N/V, there is no way of estimating the relaxation time r. We can, of course, reverse the argument, and from known conductivities and the values of N/V, assumed in Table XXIX-1, find what values of relaxation time would be required. These times are given in Table XXIX-3, from which we see that they are very short, of the order of 10 14 sec. 

Table XXIX-3.—Relaxation Times for Electrical Conductivity, Free Electron Theory...

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