Hubbard temperature

Figures 6 and 7 show a modem Langmuir film balance and its arrangement inside a Puffer-Hubbard temperature-controlled cabinet (63). Inside the cabinet, the film balance is protected further from circulating air currents by a Plexiglass case. At the bottom of the Teflon trough lies a serpentine glass coil through which water from a thermoregulator is circulated to help control subphase temperature.

Orientational disorder and packing irregularities in terms of a modified Anderson-Hubbard Hamiltonian [63,64] will lead to a distribution of the on-site Coulomb interaction as well as of the interaction of electrons on different (at least neighboring) sites as it was explicitly pointed out by Cuevas et al. [65]. Compared to the Coulomb-gap model of Efros and Sklovskii [66], they took into account three different states of charge of the mesoscopic particles, i.e. neutral, positively and negatively charged. The VRH behavior, which dominates the electrical properties at low temperatures, can conclusively be explained with this model. 

Lob P, Lowe H, Hessel V, Hubbard SM, Menges G, Balon-Burger M (2006b) Determination of temperature profile within continuous micromixer-tube reactor used for the exothermic addition of dimethyl amine to acrylonitrile and an exothermic ionic liquid synthesis. In Proceedings of AIChE Spring National Meeting, Orlando, 23-27 April, 2006... 

Hubbard and Miller87 used a Lewis acid catalyzed Diels-Alder reaction between y.y-disubstituted o. /i-unsaluralcd esters and cyclopentadiene in their approach toward oligomeric cyclopentanoids. In order for the reaction to proceed, they needed to add trimethylaluminum as a desiccant prior to addition of the Lewis acid catalyst aluminum trichloride. The endo/exo selectivity of the reaction with 97, depicted in equation 29, increased from 98/99 = 75/25 to 88/12 when the reaction temperature was dropped from room temperature to —20 °C. 

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. 

In materials in which a metal-insulator transition takes place the antiferromagnetic insulating state is not the only non-metallic one possible. Thus in V02 and its alloys, which in the metallic state have the rutile structure, at low temperatures the vanadium atoms form pairs along the c-axis and the moments disappear. This gives the possibility of describing the low-temperature phase by normal band theory, but this would certainly be a bad approximation the Hubbard U is still the major term in determining the band gap. One ought to describe each pair by a London-Heitler type of wave function... 

Ramirez et al (1970) discussed a metal-insulator transition as the temperature rises, which is first order with no crystal distortion. The essence of the model is—in our terminology—that a lower Hubbard band (or localized states) lies just below a conduction band. Then, as electrons are excited into the conduction band, their coupling with the moments lowers the Neel temperature. Thus the disordering of the spins with consequent increase of entropy is accelerated. Ramirez et al showed that a first-order transition to a degenerate gas in the conduction band, together with disordering of the moments, is possible. The entropy comes from the random direction of the moments, and the random positions of such atoms as have lost an electron. The results of Menth et al (1969) on the conductivity of SmB6 are discussed in these terms. 

However, we do not think that this model is applicable to V203 and its alloys, chiefly because we do not think a conduction band necessarily lies near the lower Hubbard band, and it does not describe many important features, particularly the large mass enhancement (approximately 50) in the metallic phase. In our view, to understand the behaviour of such materials as the temperature is raised, and in... 

It can be seen that e2 drops linearly at first, but has lower slope near the transition. There is no discontinuity, as would be expected for a Mott transition in a crystal (Chapter 4), and, as we believe, occurs (though broadened by temperature) in liquids such as fluid caesium (Chapter 10). The disorder here is greater than in a liquid metal because the orbitals of the electrons in the donors can overlap strongly. The present author (Mott 1978) has given conditions under which disorder can remove the discontinuity but this may not be relevant to such materials as Si P, because (Section 12) the Hubbard gap has disappeared, at any rate in many-valley semiconductors, at a concentration well below the transition,... 

The addition of 2.5% Cr02 leads at intermediate temperature to a phase i n which only half the V ions are paired the others form a zig-zag chain (Marezio et al 1972, Pouget et al 1974). At low temperatures pairing takes place, and at higher temperatures the usual transition to the metallic rutile form. This intermediate phase has high susceptibility, and the zig-zag chains are interpreted as onedimensional Mott-Hubbard insulators above their Neel temperature. Since the transition temperature is little changed, this shows that U is the most important quantity in determining the gap. 

The low-temperature phase under pressure shows a fairly high conductivity, as one would expect from increasing overlap of two Hubbard bands. 

In NaxW03-yFy Doumerc (1978) observed a transition that has all the characteristics of an Anderson transition similar phenomena are observed in NaxTayW3 y03. The results are shown in Fig. 7.14. It is unlikely that this transition is generated by the overlap of two Hubbard bands with tails (Chapter 1, Section 4) this could only occur if it took place in an uncompensated alkali-metal impurity band, which seems inconsistent with the comparatively small electron mass. We think rather that in the tungsten (or tungsten-tantalum) 5d-band an Anderson transition caused by the random positions of Na (and F or Ta) atoms occurs. The apparent occurrence of amiD must, as explained elsewhere, indicate that a at the temperature of the experiments. Work below 100 K, to look for quantum interference effects, does not seem to have been carried out. 

In the case discussed here a Mott transition is unlikely the Hubbard U deduced from the Neel temperature is not relevant if the carriers are in the s-p oxygen band, but if the carriers have their mass enhanced by spin-polaron formation then the condition B U for a Mott transition seems improbable. In those materials no compensation is expected. We suppose, then, that the metallic behaviour does not occur until the impurity band has merged with the valence band. The transition will then be of Anderson type, occurring when the random potential resulting from the dopants is no longer sufficient to produce localization at the Fermi energy. 

Schematic diagrams appropriate to NMP/TCNQ and TTF/TCNQ are shown in Fig. 30 and are based on experimental studies. Application of the one-dimensional Hubbard model to analyse low and high temperature data for NMP/TCNQ yielded consistent values of U and t. For TTF/TCNQ and HMTSF/TCNQ, the increased cation polarizability is believed to have successfully reduced the strength of the effective electron-electron interaction with the result that a true metal-semiconductor transition is observed at 58 K for TTF/TCNQ which disappears completely for HMTSF/TCNQ. At present the advantages of using complex salts as against simple salts of charge-transfer systems to produce organic metals are not clear, particularly since the...

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