Metals lattice theory

Attempts were made to quantitatively treat the elementary process in electrode reactions since the 1920s by J. A. V. Butler (the transfer of a metal ion from the solution into a metal lattice) and by J. Horiuti and M. Polanyi (the reduction of the oxonium ion with formation of a hydrogen atom adsorbed on the electrode). In its initial form, the theory of the elementary process of electron transfer was presented by R. Gurney, J. B. E. Randles, and H. Gerischer. Fundamental work on electron transfer in polar media, namely, in a homogeneous redox reaction as well as in the elementary step in the electrode reaction was made by R. A. Marcus (Nobel Prize for Chemistry, 1992), R. R. Dogonadze, and V. G. Levich. 

This view is really an oversimplification that fails to explain metals in a quantitative way, nor can it account for the differences in the properties of individual metals. A more detailed treatment, known as the bond theory of metals, applies the idea of resonance hybrids to metallic lattices. In the case of an alkali metal, for example, this would involve a large number of hybrid structures in which a given Na atom shares its electron with its various neighbors. 

According to the modem quantum electronic theory [1,88,89], electrical resistivity of a metal results from the scattering of electrons by the lattice. In a perfect lattice, electrons experience no scattering, and they can carry current without any attenuation. A real metal lattice departs from perfect long-range order, and electrons are... 

In the previous section we have seen how metal bond can be described according to the band theory. The valence electrons can freely move through the metal lattice in empty anti-bond orbitals. But how are the single atoms arranged relative to each other We are going to look at the answer to this question in this section. Generally two t q)es of structures in solid compounds can be distinguished ... 

The Modern Theory of Alloys. We thus find that electrical conduetionindicates that, in a metallic lattice, the cloud electrons are/rcc, while specific heat suggests, since they do not normally take part in the absorption of heat energy, that they are fixed. 

The theory of Mott and Cabrera for the growth of very thin oxide films did not satisfactorily explain the results. The governing kinetic factor was found to be the increase in oxide thickness rather than the total oxide-film thickness. A mechanism based on the formation of metal lattice vacancies and their elimination by heating is proposed. 

In the framework of the so-called mean-field theory, in which the fluctuations in the 1-d metal lattice are neglected, the energy gap 2A = 0 for T > Tp. Below the energy gap opens continuously with decreasing temperature, analogously to the BCS theory of superconductivity, and at T - 0, it has the value... 

Correlation of the observed onset of Wagner s passivity on alloys like Ni-Cu, Nl-Zn-Cu, and Cu-Ni-Al to the occupancy of the d levels of the alloys is given in support of the theory. According to the theory, the same type of passive film (l.e., M-O-O ) is formed in solutions, interposing a stable barrier between metal and electrolyte, displacing adsorbed H2O and increasing the activation energy for the hydration and dissolution of the metal lattice. Such films... 

The results obtained on the first two subjects were used by me to calculate the optimal geometry and multiplication constant for oxide lattices and to obtain estimates for the same quantity in metal lattices. I arrived at the conclusion - around the middle of November - that the multiplication constant in Fermi s Columbia pile could be increased by about 5% by going over to a lattice with a considerably smaller lattice constant. I expected a further increase of another 5% if one could replace the oxide by metal. This last increase was not really based on the measurements of Creutz and Wilson, but on a theory of the resonance absorption which I developed around this time. On the basis of these calculations and because it became evident that a very considerable improvement in the multiplication constant can be achieved by using materials of a higher purity, I became convinced that a chain reaction is possible in a graphite-uranium mixture and estimated the multiplication constant obtainable with an oxide-graphite lattice as 1.02, with a metal-graphite lattice as 1.07. 

When metals are heated, their electrical conductivity decreases. Lower conductivity at higher temperatures can be explained if the movement of the valence electrons is considered to be limited by rapidly vibrating atoms in the metal lattice. The kinetic molecular theory says that higher temperatures... 

Davisson and Germer (1927) used a metal lattice to show that interference between matter waves takes place. De Broglie s theory was confirmed. 

It is postulated that specific ions are absorbed and interact with strained bonds at the surface of the crack tip, thus reducing the bond strength, and permitting continued brittle fi acture. This theory has been supported by observations in SCC. By chemisorption of the environmental species on the crack tip, the local fracture stress of the metal lattice is reduced. The theory has been applied to hydrogen embrittlement and liquid metal embrittlement. The adsorption phenomenon may be used to interpret the crack propagation mechanism of alloys which fail by hydrogen embrittlement, such as aluminum alloy 7075. 

There is a generally accepted theory of superconductivity in metals.This theory is based on the notion that under certain conditions the electrons interact with the lattice of the solid in such a way that two electrons form a pair with opposite spins having a lower energy than two single uncorrelated electrons. The pair of electrons is called a Cooper pair. Unless the pair is broken up, it is not possible for one of the electrons to be scattered by a nucleus. Below a temperature called the transition temperature, there is not enough thermal energy to break up the pair, so that scattering does not occur and an electrical current can flow without observable resistance. 

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