Mott parameters

Table 6. A comparison of the Mott parameter Xmou in the actinide and in some lanthanides (from Ref. 61)...

Where Tq and are known as Mott parameters and depend on the type of counterion used. To understand the conduction mechanism below 100 K, the Sheng model can be applied to the analysis of the temperature dependence of polypyrrole conductivity [234]. This model takes into consideration both hopping and... 

In the expressions for the BED and BEB cross sections for each orbital the first log term represents large impact parameter collisions dominated by the dipole interaction. The remaining terms represent low-impact parameter collisions, described by the augmented Mott cross section. The second log function describes interference between direct and exchange scattering which is included in the Mott cross section. 

Their expression for a liquid interaction parameter (L) follows Mott (1968) and starts with the simple sum of an attractive term, Co, and a repulsive term, Cp,... 

These experimental facts indicate that this system can be an excellent model of band-filling control, and will be a good candidate for making a superlattice composed of Mott insulator/superconductor hetero-junctions. It should be emphasized that their lattice parameters are nearly kept constant through such an anion modification, which is the most essential feature for achieving the successful tuning of Tc in an organic superconductor. 

The f-band width was found to be about 5 eV in Ac, about 3 eV for Th-Np and around 2 eV for Pu. In Am it is down to 1 eV. The Stoner parameter, was calculated to be about 0.5 eV and almost constant throughout the series. At Am, however, the product I N(Ef) of the Stoner parameter and the f-density of states at the Fermi level exceeds one and spontaneous spin polarization occurs in the band calculation. Since Am has about 6.2 f-electrons and the moment saturates, this leads to an almost filled spin-up band and an empty spin-down band. The result is that the f-pressure all but vanishes leading to a large jump in atomic volume - in agreement with experiment. This has been interpreted as Mott-localization of the f-electrons at Am and the f-electrons of all actinides heavier than Am are Mott-localized. The trend in their atomic volumes is then similar to those of the rare earths. 

Hubbard (13) elucidated a mathematical description of the change from one situation to another for the simplest case of a half-filled s band of a solid. His result is shown in Figure 11. For ratios of W/U greater than the critical value of 2/ /3 then a Fermi surface should be found and the system can be a metal. This critical point is associated with the Mott transition from metal to insulator. At smaller values than this parameter, then, a correlation, or Hubbard, gap exists and the system is an antiferromagnetic insulator. Both the undoped 2-1 -4 compound and the nickel analog of the one dimensional platinum chain are systems of this type. At the far left-hand side of Figure 11 we show pictorially the orbital occupancy of the upper and lower Hubbard bands. 

Figure 6.52 Schematic electron addition and removal spectra representing the electronic structure of transition-metal compounds for different regimes of the parameter values (a) charge-transfer insulator with U > A (b) Mott-Hubbard insulator A> U (From Rao et al, 1992).

Anderson type (though affected of course by long-range interaction). Until recently it was supposed by the present author that the former is the case. We must now favour, however, the latter assumption for many-valley materials (e.g. Si and Ge), the Hubbard gap opening up only for a value of the concentration n below nc. The first piece of evidence comes from a calculation of Bhatt and Rice (1981), who found that for many-valley materials this must be so. The second comes from the observations of Hirsch and Holcomb (1987) that compensation in Si P leads to localization for a smaller value of nc than in its absence. As pointed out by Mott (1988), a Mott transition occurs when B = U (B is the bandwidth, U the Hubbard intra-atomic interaction), while an Anderson transition should be found when B 2 V, where V is some disorder parameter. Since U e2/jcuH, where aH is the hydrogen radius, and K e2/jca, and since at the transition a 4aH, if the transition were of Mott type then it should be the other way round. 

Figure 3. Theoretical phase diagram and doping dependence of the transition temperature predicted by our theory for the parameters D = 5, V = 0.564eV compared with the well known experimental doping Te curve shown above. The superconducting (SC), insulating (I) and metallic phases are characterised by use the Mott-Edwards-Sienko relation [23,24,28] as described in [15].

For the materials and concentration ranges we have studied, comparative batch tests have supported the use of linear isotherms (e.g., Khandelwal et al., 1998 Khandelwal and Rabideau, 2000), although the assumption of a linear isotherm may not be appropriate for all systems. In particular, Mott and Weber (1992) and Gullick (1998) have utilized nonlinear isotherms to describe the behavior of various sorbing additives, including flyash and organoclays. However, it is important to note that multi-parameter nonlinear isotherms are not easily calibrated from column data, particularly if a sorption rate constant must also be estimated. 

A fundamental question is whether the transition between localized and itinerant electronic behavior is continuous or discontinuous. Mott (1949) was the first to point out that an on-site electrostatic energy Ua > Wr, is needed to account for the fact that NiO is an antiferromagnetic insulator rather than a metal. Hubbard (1963) subsequently introduced U formally as a parameter into the Hamiltonian for band electrons his model predicted a smooth transition from a Pauli paramagnetic metal to an antiferromagnetic insulator as the ratio W/U decreased to below a critical value of order unity. This metal-insulator transition is known as the Mott-Hubbard transition. 

A in aft) provided aft is obtained directly from experimental parameters that characterize the localized electron state. The data (64, 68, 69) for metal solutions in ammonia, methylamine, and HMPA are included in Fig. 22. Inherent in the Mott picture (124) is a major change in the thermodynamic properties of the solutions in the transition region. This important feature is discussed in Section IV,B. 

It is, however, not the JTD that turn these systems into insulators but strong correlations. The nature of metal-insulator transitions in these systems is one of the most debated points at present. Experimentally, a metal-insulator transition can be induced by relatively modest pressure in Rb4C60 and in the compound with the smallest lattice parameters (Na2C60) a residual metallic character can be detected. These behaviors support the idea that these compounds lie on the border of a Mott-Hubbard transition. We still observe typical molecular excitations of JT-distorted C60 on the metallic side of the transition, suggesting a possible coexistence. 

The flat-band potential (Ufl,) is a very important parameter for a semiconductor in contact with an electrolyte. Ufl, is directly related to the conduction band (CB) level for an tt-type semiconductor or the valence band (VB) level for a p-type semiconductor. A classic method to determine Ufl, is by means of Mott-Schotky plot [99] according to ... 

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