Conductivity of metals

Metals are fiindamentally different from insulators as they possess no gap in the excitation spectra. Under the influence of an external field, electrons can respond by readily changing from one k state to another. The ease by which the ground-state configuration is changed accounts for the high conductivity of metals. 

The rate of heat-transfer q through the jacket or cod heat-transfer areaM is estimated from log mean temperature difference AT by = UAAT The overall heat-transfer coefficient U depends on thermal conductivity of metal, fouling factors, and heat-transfer coefficients on service and process sides. The process side heat-transfer coefficient depends on the mixing system design (17) and can be calculated from the correlations for turbines in Figure 35a. 

The temperature coefficients of conductivity of metallic systems are characteristically negative because of the increased scattering of the electrons brought about by the increasing amplitude of vibration of die ion cores. 

As described above, quantum restrictions limit tire contribution of tire free electrons in metals to the heat capacity to a vety small effect. These same electrons dominate the thermal conduction of metals acting as efficient energy transfer media in metallic materials. The contribution of free electrons to thermal transport is very closely related to their role in the transport of electric current tlrrough a metal, and this major effect is described through the Wiedemann-Franz ratio which, in the Lorenz modification, states that... 

The easy movement of the electrons gives the high electrical conductivity of metals. The metallic bond has no directionality, so that metal ions tend to pack to give simple, high-density structures, like ball-bearings shaken down in a box. 

The availability of large quantities of liquid helium as well as an excellent support staff led to the undertaking of many experiments at 8 K (the boiling temperature of helium) as well as the lower temperatures obtained by pumping. One subset was the measurement of the resistivity (conductivity) of metals, since this property was useful as a secondaiy thermometer. Although a linear decline was obseived, various speculations were made as to what the result would be when zero absolute temperature was reached. In April 1911 came the surprising discoveiy that the resistivity in mercury disappeared. At first the sur-... 

The high electrical conductivity of metals as well as the high electron (and hole) mobility of inorganic covalently bound semiconductors have both been clarified by the band theory [I9, which slates that the discrele energy levels of individual atoms widen in the solid stale into alternatively allowed and forbidden bands. The... 

The excellent heat conductivity of metals is also due to the mobile electrons. Electrons which... 

One clue to understanding the nature of metallic bonds comes from their high electrical conductivity. Like most substances held together by ionic or covalent bonds, pure water and pure salt do not conduct electricity well. But pure copper does. Electrical conductivity is a measure of how free the electrons are to move. The high conductivity of metals indicates that their electrons are freer to move than the electrons are in salt or water. 

The metallic structure essentially consists of atomic nuclei and associated core electrons, surrounded by a sea of free electrons. The high electrical conductivity of metals is derived from the presence of these free electrons. In addition to high electrical conductivity, the free electrons provide the metals with good thermal conductivity as well. The electrical resistivity of a metal increases with temperature. 

The electronic conductivity of metal oxides varies from values typical for insulators up to those for semiconductors and metals. Simple classification of solid electronic conductors is possible in terms of the band model, i.e. according to the relative positions of the Fermi level and the conduction/valence bands (see Section 2.4.1). 

R.L. Powell, W.A. Blaupied Thermal Conductivity of Metal and Alloys at Low Temperatures, Nat. Bureau of Standards Circular 556, US Govt. Print. Office, Washington, DC (1954)... 

Super-pure water has been distilled several times, and is indeed an insulator its conductivity k is low at 6.2 x 10-8 S cm 1 at 298 K, and lies midway between classic insulators such as Teflon, with a conductivity of about 10 15 Scm-1, and semiconductors such as doped silicon, for which k = 1O-2 Scm-1. The conductivity of metallic copper is as high as 106 Scm-1. 

No attempt will be made here to extend our results beyond the simple lowest-order limiting laws the often ad hoc modifications of these laws to higher concentrations are discussed in many excellent books,8 11 14 but we shall not try to justify them here. As a matter of fact, for equilibrium as well as for nonequilibrium properties, the rigorous extension of the microscopic calculation beyond the first term seems outside the present power of statistical mechanics, because of the rather formidable mathematical difficulties which arise. The main interests of a microscopic theory lie both in the justification qf the assumptions which are involved in the phenomenological approach and in the possibility of extending the mathematical techniques to other problems where a microscopic approach seems necessary in the particular case of the limiting laws, obvious extensions are in the direction of other transport coefficients of electrolytes (viscosity, thermal conductivity, questions involving polyelectrolytes) and of plasma physics, as well as of quantum phenomena where similar effects may be expected (conductivity of metals and semi-... 

Y. Zhao, J. Wei, R. Vajtai, P. M. Ajayan, E. V. Barrera, Iodine doped carbon nanotube cables exceeding specific electrical conductivity of metals, Scientific Reports 1 83, 2011. 

Y. Miyata, K. Yanagi, Y. Maniwa, H. Kataura, Highly stabilized conductivity of metallic single wall carbon nanotube thin films, J. Phys. Chem. C., vol. 112, pp. 3591-3596, 2008. 

Look up, for example, in Reference [1], the conductivities of metallic platinum, gold, silver, mercury and tungsten, and hence explain why graphite is not the best choice of electrode material. 

Classical Free-Electron Theory, Classical free-electron theory assumes the valence electrons to be virtually free everywhere in the metal. The periodic lattice field of the positively charged ions is evened out into a uniform potential inside the metal. The major assumptions of this model are that (1) an electron can pass from one atom to another, and (2) in the absence of an electric field, electrons move randomly in all directions and their movements obey the laws of classical mechanics and the kinetic theory of gases. In an electric field, electrons drift toward the positive direction of the field, producing an electric current in the metal. The two main successes of classical free-electron theory are that (1) it provides an explanation of the high electronic and thermal conductivities of metals in terms of the ease with which the free electrons could move, and (2) it provides an explanation of the Wiedemann-Franz law, which states that at a given temperature T, the ratio of the electrical (cr) to the thermal (k) conductivities should be the same for all metals, in near agreement with experiment ... 

Interest in the electrical conductivity of metal-chain complexes is increasing. Several studies have been made of the mixed valence complex K2Pt(CN)4BtQ 3 -2.3H2O. One reports that the conductivity in the direction of the Pt-atom chain is 100 times greater than at right angles to the chain. However, another study indicated considerable experimental scatter, which was attributed to variable water content from sample to sample. Small amounts of water were shown to increase the conductivity by a factor of up to It has also... 

The conductive properties of SWCNTs were predicted to depend on the helicity and the diameter of the nanotube [112, 145]. Nanotubes can behave either as metals or semiconductors depending upon how the tube is rolled up. The armchair nanotubes are metallic whereas the rest of them are semiconductive. The conductance through carbon nanotube junctions is highly dependent on the CNT/metal contact [146]. The first measurement of conductance on CNTs was made on a metallic nanotube connected between two Pt electrodes on top of a Si/Si02 substrate and it was observed that individual metallic SWCNTs behave as quantum wires [147]. A third electrode placed nearby was used as a gate electrode, but the conductance had a minor dependence on the gate voltage for metallic nanotubes at room temperature. The conductance of metallic nanotubes surpasses the best known metals because the... 

Polymers that display electronic conductivity are usually insulators in the pure state but, when reacted with an oxidizing or reducing agent, can be converted into polymer salts with electrical conductivities comparable to metals. Some of these polymers are listed in Figure 6.38, along with the conductivities of metals and ceramics for... 

Metals consist of a regular array of metal cations surrounded by a sea of electrons. These electrons occupy the space between the cations, binding them together, but are able to move under the influence of an external field, thus accounting for the electrical conductivity of metals. 

Extensions of this model in which the atomic nuclei and core electrons are included by representing them by a potential function, V, in Equation (4.1) (plane wave methods) can account for the density of states in Figure 4.3 and can be used for semiconductors and insulators as well. We shall however use a different model to describe these solids, one based on the molecular orbital theory of molecules. We describe this in the next section. We end this section by using our simple model to explain the electrical conductivity of metals. 

The conductivity of metallic conductors decreases with temperature. As the temperature rises the phonons gain energy the lattice vibrations have larger amplitudes. The displacement of the ionic cores from their lattice sites is thus greater and the electrons are scattered more, reducing the net current by reducing the mobility, //, of the electrons. 

When discussing the electrical conductivity of metals, we described them in terms of ionic cores and delocalised valence electrons. The core electrons contribute a diamagnetic term to the magnetic susceptibility, but the valence electrons can give rise to paramagnetism or one of the cooperative effects we have described. 

The sp-valent metals such as sodium, magnesium and aluminium constitute the simplest form of condensed matter. They are archetypal of the textbook metallic bond in which the outer shell of electrons form a gas of free particles that are only very weakly perturbed by the underlying ionic lattice. The classical free-electron gas model of Drude accounted very well for the electrical and thermal conductivities of metals, linking their ratio in the very simple form of the Wiedemann-Franz law. However, we shall now see that a proper quantum mechanical treatment is required in order to explain not only the binding properties of a free-electron gas at zero temperature but also the observed linear temperature dependence of its heat capacity. According to classical mechanics the heat capacity should be temperature-independent, taking the constant value of kB per free particle. 

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