Mott temperature

This explains the phenomenon of the characteristic Mott temperature of nanocomposite with a 20 wt% particle loading decreasing and then increasing again with 50 wt% loading. 

Many metals oxidise rapidly at first when exposed to oxygen at sufficiently low temperatures, but after a few minutes, when a very thin oxide layer has been formed, the reaction virtually ceases. Oxide layers formed in this way are about 5 nm thick. Aluminium and chromium are well-known examples, showing this sort of behaviour at room temperature. A theory of the effect has been proposed by Mott . ... 

Another famous hopping model is Mott s variable range hopping [23], in which it is assumed that the localized sites are spread over the entire gap. At low temperatures, the probability to find a phonon of sufficient energy to induce a jump to the nearest neighbor is low, and hops over larger distances may be more favorable. In that case, the conductivity is given by... 

It should be mentioned that emission of oxygen atoms at initial stage of oxidation can be observed in case of oxidation of oilier metals (for instance nickel) as well. In this case due to hi rate of oxidation the emission can be observed only as a result of oxidation of freshly deposited films of nickel at a room temperature. The Cabrer-Mott loga-... 

The low-temperature thermometers based on heavily doped compensated germanium (see Section 9.6.2.1) show high stability, good reproducibility, low noise and low specific heat. Ge used for cryogenic sensors is heavily doped (1016 - 1019 atoms/cm3), with T0 of Mott s law ranging between 2 and 70K (see formula 9.6). 

The Schottky-Mott theory predicts a current / = (4 7t e m kB2/h3) T2 exp (—e A/kB 7) exp (e n V/kB T)— 1], where e is the electronic charge, m is the effective mass of the carrier, kB is Boltzmann s constant, T is the absolute temperature, n is a filling factor, A is the Schottky barrier height (see Fig. 1), and V is the applied voltage [31]. In Schottky-Mott theory, A should be the difference between the Fermi level of the metal and the conduction band minimum (for an n-type semiconductor-to-metal interface) or the valence band maximum (for a p-type semiconductor-metal interface) [32, 33]. Certain experimentally observed variations of A were for decades ascribed to pinning of states, but can now be attributed to local inhomogeneities of the interface, so the Schottky-Mott theory is secure. The opposite of a Schottky barrier is an ohmic contact, where there is only an added electrical resistance at the junction, typically between two metals. 

An important phenomenon is the Mott effect. At given temperature T and total momentum P, the binding energy of the deuteron bound state vanishes at the density n 1"" (P. T) due to the Pauli blocking. As a consequence, the... 

Calculations of the composition (112/ns) of symmetric nuclear matter (np = nn, no Coulomb interaction) are shown in Fig. 3 [7], At low densities, the contribution of bound states becomes dominant at low temperatures. At fixed temperature, the contribution of the correlated density 112 is first increasing with increasing density according to the mass action law, but above the Mott line it is sharply decreasing, so that near nuclear matter density (ns = ntot = 0.17 fm-3) the contribution of the correlated density almost vanishes. Also, the critical temperature for the pairing transition is shown. 

The modification of the three and four-particle system due to the medium can be considered in cluster-mean field approximation. Describing the medium in quasi-particle approximation, a medium-modified Faddeev equation can be derived which was already solved for the case of three-particle bound states in [9], as well as for the case of four-particle bound states in [10]. Similar to the two-particle case, due to the Pauli blocking the bound state disappears at a given temperature and total momentum at the corresponding Mott density. 

Thus, Mott-Wannier excitons can give rise to a number of absorption peaks in the pre-edge spectral region according to the different states = 1, 2, 3,... As a relevant example. Figure 4.14 shows the low-temperature absorption spectrum of cuprous oxide, CU2O, where some of those hydrogen-like peaks of the excitons are clearly observed. These peaks correspond to different excitons states denoted by the quantum numbers = 2, 3, 4, and 5. 

Temperature quenching of broad band emission is usually explained by a simple configuration coordinate model consisting of two parabolas that have been shifted with regard to each other (Fig. 6). This is called the Mott-Seitz model. Nonradiative return from the excited to the ground state is possible via the parabola crossover. Its rate can be described with an activation-energy formula Pnr = C where C is a constant of the order of 10 sec i and AE is the... 

If the c.t. state is at relatively low energies we can expect phenomena like those described above for the oxysulfides. It has been shown that the temperature quenching of the 5 )q emission of Eu3+ can occur via the c.t. state (76, 77). After >o-c.t. crossover the c.t. state relaxes nonradiatively to the ground state as in the Mott-Seitz picture. It has been found that the thermal quenching temperature of Eu + emission under c.t. excitation increases if the c.t. state is situated at higher energies [78). 

Thapar R, Rajeshwar K (1983) Mott-Schottky analyses on n- and p-GaAs/room temperature chloroaluminate molten-salt interfaces. Electrochim Acta 28 195-198... 

Fig. 4.5 Mott-Schottky plot of n-Ti02 prepared at different temperatures. AC frequency 1000 Hz. Reprinted with permission from Ref. [47].

A concept related to the localization vs. itineracy problem of electron states, and which has been very useful in providing a frame for the understanding of the actinide metallic bond, is the Mott-Hubbard transition. By this name one calls the transition from an itinerant, electrically conducting, metallic state to a localized, insulator s state in solids, under the effect of external, thermodynamic variables, such as temperature or pressure, the effect of which is to change the interatomic distances in the lattice. 

The first part of the chapter is devoted to an analysis of these correlations, as well as to the presentation of the most important experimental results. In a second part the following stage of development is reviewed, i.e. the introduction of more quantitative theories mostly based on bond structure calculations. These theories are given a thermodynamic form (equation of states at zero temperature), and explain the typical behaviour of such ground state properties as cohesive energies, atomic volumes, and bulk moduli across the series. They employ in their simplest form the Friedel model extended from the d- to the 5f-itinerant state. The Mott transition (between plutonium and americium metals) finds a good justification within this frame. 

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