Theory of the mixed valent state

After briefly discussing the question of a distinct mixed valent state and theoretical models for it, the area of greatest theoretical success, namely the mixed valent impurity, is reviewed. Applications to spectroscopy, energetics and Hall effect are then putlined. The independent impurity approximation is inadequate for many properties of the bulk system, which depend on lattice coherence. A recent auxiliary or slave boson approach with a simple mean field limit and fluctuation corrections is summarized. Finally the mixed valent semiconductor is discussed as an outstanding problem.

On anomalous U(1) gauge theory in four dimensions

We discuss the consistency, unitarity and Lorentz invariance of an anomalous U(1) gauge theory in four dimensions. Our analysis is based on an effective low-energy action valid in the chiral symmetry broken phase. The allegedly bad properties of anomalous theories (except non-renormalizability) are examined. It is shown that, in the low-energy context, the theory can be consistently and unitarily quantised, and is formally Lorentz covariant.

Note on the one-parameter scaling theory of localisation

The necessary and sufficient condition for the existence of the one-parameter scale function, the /Munction, is obtained exactly. The analysis reveals certain inconsistency inherent in the scaling theory, and tends to support Motts’ idea of minimum metallic conductivity.

Thermodynamic scaling theory for impurities in metals

A perturbative scaling theory for calculating static thermodynamic properties of arbitrary local impurity degrees of freedom interacting with the conduction electrons of a metal is presented. The basic features are developments of the ideas of Anderson and Wilson, but the precise formulation is new and is capable of taking into account band-edge effects which cannot be neglected in certain problems. Recursion relations are derived for arbitrary interaction Hamiltonians up to third order in perturbation theory. A generalized impurity Hamiltonian is defined and its scaling equations are derived up to third order. The strategy of using such perturbative scaling equations is delineated and the renormalization-group aspects are discussed. The method is illustrated by applying it to the single-impurity Kondo problem whose static properties are well understood.

Note on the one-parameter scaling theory of localisation

The necessary and sufficient condition for the existence of the one-parameter scale function, the /Munction, is obtained exactly. The analysis reveals certain inconsistency inherent in the scaling theory, and tends to support Motts’ idea of minimum metallic conductivity.

Nondeactivating Nanosized Ionic Catalysts for Water-Gas Shift Reaction

The water-gas shift reaction (WGS) is an important reaction to produce hydrogen. In this study, we have synthesized nanosized catalysts where Pt ion is substituted in the +2 state in TiO2, CeO2, and Ce1-xTixO2-delta. These catalysts have been characterized by X-ray diffraction and X-ray photoelectron spectroscopy (XPS), and it has been shown that Pt2+ in these reducible oxides result in solid solutions like Ti0.99Pt0.01O2-delta, Ce0.8Ti0.15Pt0.02O2-delta, and Ce0.98Pt0.02O2-delta. These catalysts were tested for the water gas shift reaction both ill the presence and absence of hydrogen. It was shown that Ti0.99Pt0.01O2-delta exhibited higher catalytic activity than Ce0.83Ti0.15Pt0.02O2-delta and Ce0.98Pt0.02O2-delta. Further, experiments were conducted to determine the deactivation of these catalysts. There was no sintering of Pt and no carbonate formation; therefore, the catalyst did not deactivate even after prolonged reaction. There was no carbonate formation because of the highly acidic nature of Ti4+ ions in the catalysts.

Fluctuation Theory Of The Specific-Heat Of Normal Liquid-3He

The measured specific heat of normal liquid 3He shows a plateau for 0.15<1 K; below 0.15 K and above 1 K, it rises linearly with temperature. However, the slope on the high-temperature side is very much reduced compared with the free-Fermi-gas value. We explain these features through a microscopic, thermal spin- and density-fluctuation model. The plateau is due to spin fluctuations which have a low characteristic energy in 3He. Because of the low compressibility, the density fluctuations are highly suppressed; this leads to a reduced slope for CV(T) for high temperatures.

Information theory and resistance fluctuations in one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. For the probability distribution of the transfer matrix R of the conductor we propose a distribution of maximum information entropy, constrained by the following physical requirements: (1) flux conservation, (2) time-reversal invariance, and (3) scaling with the length of the conductor of the two lowest cumulants of ω, where R=exp(iω→⋅Jbhat). The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

Theory of freezing in simple systems

The transition parameters for the freezing of two one-component liquids into crystalline solids are evaluated by two theoretical approaches. The first system considered is liquid sodium which crystallizes into a body-centered-cubic (bcc) lattice; the second system is the freezing of adhesive hard spheres into a face-centered-cubic (fcc) lattice. Two related theoretical techniques are used in this evaluation: One is based upon a recently developed bifurcation analysis; the other is based upon the theory of freezing developed by Ramakrishnan and Yussouff. For liquid sodium, where experimental information is available, the predictions of the two theories agree well with experiment and each other. The adhesive-hard-sphere system, which displays a triple point and can be used to fit some liquids accurately, shows a temperature dependence of the freezing parameters which is similar to Lennard-Jones systems. At very low temperature, the fractional density change on freezing shows a dramatic increase as a function of temperature indicating the importance of all the contributions due to the triplet direction correlation function. Also, we consider the freezing of a one-component liquid into a simple-cubic (sc) lattice by bifurcation analysis and show that this transition is highly unfavorable, independent of interatomic potential choice. The bifurcation diagrams for the three lattices considered are compared and found to be strikingly different. Finally, a new stability analysis of the bifurcation diagrams is presented.

Reaction of Hexachlorocyclotriphosphazene with Sodium p-Cresoxide

The reaction of hexachlorocyclotriphosphazene (N3P3Cl6) with sodium p-cresoxide proceeds by a predominantly nongeminal pathway. The presence of geminal isomers at the bis- and tris-stages of substitution in tiny quantities (< 5%) has also been observed. All the chloro(p-cresoxy)cyclotriphosphazenes and their dimethylamino derivatives have been characterized by 1H-, 13C{1H}-, and 31P{1H}-NMR spectroscopy. The reaction of N3P3Cl6 with sodium phenoxide has been reinvestigated. The relative yields of the products at various stages of substitution and their isomeric compositions are almost the same for both phenoxy and p-cresoxy systems. Possible mechanisms to explain the observed isomeric compositions are discussed. A through-space interaction involving oxygen-2p and phosphorus-3d orbitals is invoked to explain the greater yield of the cis isomer of N3P3Cl4(OAr)2 than that of its trans isomer.

Reaction of thiophosphoryl fluoride with sulphur trioxide

Thiophosphoryl fluoride is observed to undergo a facile reaction with sulphur trioxide forming phosphoryl fluoride, sulphur dioxide and elemental sulphur in quantitative yields. In the presence of excess of sulphur trioxide, however, the elemental sulphur released combines with it to form sulphur sesquioxide which subsequently decomposes and gives off sulphur dioxide. Similar observations are made with oleum.

Thermodynamic scaling theory for the two-impurity Anderson model

We present results of a study of the two-impurity Anderson model using a thermodynamic scaling theory developed recently. The model is characterized by the Coulomb energy U, the orbital energy epsilond, the d-level width Gamma, and the separation between impurities R. If Gamma<<−epsilond<~Gamma. Here we find that the single-impurity physics dominates the low-temperature behavior, and impurity-impurity interactions are perturbative. The qualitative features of the temperature-dependent susceptibility are discussed. Journal of Applied Physics is copyrighted by The American Institute of Physics.

Critical-point Properties of Liquids and the Born-Green Theory

Recent work of Jones et al. giving the long-range behaviour of the pair correlation function is used to confirm that the critical ratio Pc/nckBTc = 1/2 in the Born-Green theory. This deviates from experimental results on simple insulating liquids by more than the predictions of the van der Waals equation of state. A brief discussion of conditions for thermodynamic consistency, which the Born-Green theory violates, is then given. Finally, the approach of the Ornstein-Zernike correlation function to its critical point behaviour is discussed within the Born-Green theory.