Ziman theory

The resistivity of all the Er-based alloys is shown in fig. 90. It can be seen that the alloys containing Al, Ga, and Au all have positive temperature coefficients of resistivity at high temperatures whereas the alloys containing transition metals have negative temperature coefficients. Hadjipanayis et al. (1980) interpret this behaviour in terms of the Ziman theory of liquid metals. 

The atomic disorder associated with the amorphous state leads to completely different transport properties from those encountered in the crystalline state. Experimental results of the electrical resistivity, the Hall effect, magnetoresistance, thermoelectric power and the occurrence of. superconductivity are discussed in section 8. The main emphasis is placed on the electrical resistivity. The occurrence of negative temperature coefficients of the resistivity is related to models based on the extended Ziman theory. In the low temperature regime the resistivity often shows a In T... 

It was stressed by Mueller et al. (1980) that the extended Ziman theory is not the only model that can explain the negative value of a observed in many amorphous alloys. In fact, Mueller et al. showed that the negative temperature dependence in amorphous Lao.66 Alo.34 better explained in terms of the Kondo mechanism than by the extended Ziman model. We will return to this point later on, after having discussed the resistivity anomalies associated with several types of Kondo mechanisms. 

The NFE approximation is invoked explicitly in the Ziman theory of the electric resistivity of liquid metals (Ziman, 1961) in which scattering of electrons is treated using perturbation theory. The approximation is justified by the experimental fact that for many liquid metals, the average distance between scattering events, the electronic mean free path A, is... 

At temperatures above 1100 °C (p S 1.3 g cm ), the measured conductivity is clearly less than the NFE values. The gradual failure of the Ziman theory at high temperatures and low density is probably not due to the breakdown of NFE conditions at 1.3 g cm . As stated above, the evidence suggests that the NFE approximation is valid at least down to a density of about 1.1 g cm . Estimates of A from the conductivity (Winter et al., 1987) indicate that the condition A a is only reached in the density range p 0.8 g cm . The NFE breakdown is more likely to reflect the increased importance of electron correlations at low density (Sec. 3.2). Simple arguments (Mott, 1974) based on the ideas of Brinkman and Rice suggest that the Ziman conductivity should be reduced by a factor (m ) in the range where the effective mass (density of states) is enhanced by correlations. 

Most studies of disordered solids have been based on simple tight binding Hamiltonians of the kind described in Section 3.3. While this approach is of limited validity, it is at least susceptible to a certain amount of rigorous mathematical analysis. Other Hamiltonians, such as pseudopotential Hamiltonians, which might be more desirable in a given context, pose many more difficulties in a disordered system unless simple lowest-order perturbation theory happens to be adequate, as in the case of the Ziman theory of liquid metals, which is quite successful for the simple metals. 

Ziman J M 1986 Principles of the Theory of Solids 2nd edn (Cambridge Cambridge University Press)... 

J.M.ZIMAN, Principles of the theory of solids (Cambridge University Press, London, 1964). 

Band Theory of Metals, Three approaches predict the electronic band structure of metals. The first approach (Kronig-Penney), the periodic potential method, starts with free electrons and then considers nearly bound electrons. The second (Ziman) takes into account Bragg reflection as a strong disturbance in the propagation of electrons. The third approach (Feynman) starts with completely bound electrons to atoms and then considers a linear combination of atomic orbitals (LCAOs). 

Ziman, J. M. Principles of the Theory of Solids, second edition, Cambridge University Press 1972... 

The quantum-mechanical expression for the dielectric function may be written in the form (see, e.g., Ziman, 1972, Chap. 8, for an elementary discussion of the quantum theory of optical properties)... 

Our understanding of conduction in liquid metals is based on the theory put forward by Ziman (1961).This is a weak-scattering theory that has proved highly satisfactory for the description of normal metals for which l a, and proves surprisingly satisfactory in many cases even when this is not the case (see Faber 1972, Mott and Davis 1979, Chap. 5). Most metal-insulator transitions in liquids occur in. the regime where l a. They can be induced in several ways. 

The experimental evidence, then, suggests that quantum interference is absent in liquid metals. At first sight this might seem to contradict Ziman s (1961) theory of liquid metals, in which waves scattered by different atoms do interfere this, however, is not so. Following arguments of Baym (1964), Greene and Kohn (1965) and Faber (1972), one should not use in that theory the Fourier transform S(k) of the instantaneous pair-distribution function, but rather... 

C. Kittel, Solid State Physics, John Wiley Sons, New York (1956) J.M. Ziman, Principle of Theory of Solids, Cambridge Univ. Press (1964). 

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