The effect of the heat capacity of the liquid phase on the heat of fusion liquidus equation of compound semiconductors

We have critically examined the assumptions involved in the derivation of Vieland's widely used heat of fusion liquidus equation for binary compounds and conclude that the thermodynamic form of this equation ignores the relative partial molar heat capacity of the liquid solution. Taking into account this quantity, we obtain the generalized heat of fusion equation which is exact and show its complete equivalence to its alternative, the heat of formation equation. The generalized result provides a correction term to Vieland's equation which can be expressed as a function of the activity coefficients at the compound composition. Applying the correction term to the activity coefficients derived for a number of useful solution models, we find that the regular solution form of Vieland's equation is exact, as shown previously, if α (interchange energy) is a constant or a linear function of temperature. But when α is expanded as an nth order polynomial in temperature (simple solution), Vieland's equation is inexact for n ? 2. In addition, it is demonstrated that for a regular associated solution and for Darken's quadratic representation, Vieland's thermodynamic equation is exact only with certain restrictions, while for a quasi-chemical solution it is invalid.     

Class of Hamiltonians with one degree-of-freedom allowing application of Kruskal's asymptotic theory in closed form. I

In this paper, apart from a small restriction, all time-dependent Hamiltonians with one degree-of-freedom are determined, for which Kruskal's nice variables can be found by a sort of partial separation of the variables in the equations in question. These Hamiltonians allow an application of Kruskal's perturbation method in closed form, in a way similar to Lewis' treatment of the time-dependent harmonic oscillator. For those “appropriate” Hamiltonians, a connection is further established, between the invariant J following from Kruskal's theory, and an invariant that can be calculated equivalently from Hamilton-Jacobi theory.     

Evolution of Wigner's phase-space density under a nonintegrable quantum map

A nonintegrable area-preserving map for a system with one freedom is quantized, and the evolution of Wigner's function W(q,p) illustrated by contour plots of W in the paase plane. In the classical limit, propagation is governed by Liouville's equation and the contours of W rapidly develop an intricate structure of whorls and tendrils. When Planck's constant ? is not zero, the quantum map smooths out classical detail in phase-space areas smaller than ?. The quantum-mechanical distributions spread more slowly than their classical counterparts.     

Determination of ionicity in zinc chalcogenides by X-ray absorption study

K-absorption edges and associated extended fine structure is recorded for zinc and zinc chalcogenides using a 40 cm, automatic scanning, Cauchois type X-ray spectrometer. It is observed that there is a correlation between the positive X-ray K-absorption edge chemical shift and Phillips' electronegativity difference C for zinc chalcogenides. The bond lengths for these compounds are determined using Lytle, Chivate et al. and Levy's methods. These bond lengths are observed to tally well with X-ray crystallographic data. The covalent energy gaps in Phillips' theory are determined using bond lengths determined by Chivate et al.'s method. Values of ionicities are obtained from X-ray spectroscopically determined values of C and E_h and are compared with Phillips' spectroscopically determined ionicities for zinc chalcogenides. It is shown that X-ray spectroscopically determined values of ionicities for these compounds show a more correct chemical trend.     

Modified expression for permeability tensor in partially magnetised ferrites

Green and Sandy's experimental results [IEEE Trans Microwave Theory Tech.MTT-22 641 (1974)] for μ', the permeability tensor element of the partially magnetised ferrites, show systematic discrepancies with the values computed by them from their formula for large values of the normalised average magnetisation. It has been shown that a good agreement is possible if Schlömann's expression for μ'₀ occuring in this formula is replaced by another expression originally given by Sandy provided the average demagnetisation factor N of the domains is taken as a linear function of the magnetisation. This modification is also able to interpret the author's experimental results on Magneto-Microwave Kerr Effect successfully, which are not at all explained by the original Green and Sandy formula.     

Determination of ionicity in zinc phosphide and zinc arsenide by X-ray absorption method

K-absorption edges and associated extended fine structure is recorded using a 40 cm, automatic scanning X-ray spectrometer for zinc in zinc phosphide and zinc arsenide. The bond lengths for these compounds are determined using Lytle and Chivate et al.'s method. The convalent energy gaps in Phillips' theory are evaluated on the basis of Levine's extension to Phillips theory for these complex compounds. The X-ray absorption edge shifts for zinc in both of these compounds and the ionic energy gap determined using Levine's method are in good agreement. Hence, ionicities for these compounds were determined. The ionicity value for zinc phosphide comes out to be 0.17 and for zinc arsenide 0.16.     

Interpretation of apparent chemical shifts in XP spectra from oxide—GaP interfaces

The cause of the apparent chemical shifts (ACS's) of XPS peaks between oxide and substrate GaP has been studied. The ACS's for Ga 3d, P 2p and GaLMM change significantly depending on the conditions of oxidation. The changes in the ACS's are considered in terms of not only the chemical structure of the oxide, but also other possible causes, such as charging effects, electric dipole moment, extra-atomic relaxation energy, Fermi-level pinning position, etc. The change of the Fermi-level position at the surface of substrate GaP is revealed to be a dominant factor causing the changes in the ACS's.     

Linked cluster expansions in the equations of motion method II: Kinetic equations for the single-particle density matrix

The general method of paper I of this series is applied to derive kinetic equations (KE's), i.e. closed exact equations governing the time evolution of the single-particle density matrix. The short-memory approximation of these non-Markowian equations is formulated in such a way that it is valid even in strongly inhomogeneous systems. The c-number diagram expansion of the integral kernels of the KE's is obtained from the general rules of paper I. It is shown that certain secular divergent terms cancel each other. The diagrams decay into dynamic and correlational parts, the latter being given by cluster functions describing the correlations of the particles in the local equilibrium ensemble σ(t) which is formulated in terms of the single-particle density matrix and of the Hamiltonian. The appearance of the cluster functions is the most pronounced difference of our KE's in comparison with other KE's which are formulated in terms of the dynamics of isolated clusters of particles. It is argued that our KE's may be viewed as a highly summed version of these latter KE's and that the ultimate reason for this difference lies in the fact that in our theory the conservation of the average macroscopic energy is taken into account explicitly.     

UV photoelectron spectra and sum rule consideration: Out-of-plane orbitals of unsaturated compounds with planar-skeleton structure

He(l) photoelectron spectra are presented for various planar unsaturated aliphatic compounds such as mono- and di-methyl substituted ethylenes, alkyl aldehydes, chloro-substituted aldehydes, ketones and alkyl acids. Each photoelectron spectrum is resolved into individual bands by considering the band shape, the relative intensity and the number of p-type localized MO's (LO's). The sum rule previously proposed on vertical ionization energies by the present authors is applied to the photoelectron bands associated with out-of-plane LO's. In each compound, a partial sum P(a″) is obtained over all the out-of-plane LO's and it is shown that the calculated P(a″) value is in good agreement with the experimental one which may be obtained by an appropriate sum of vertical ionization energies with negative signs.     

Large-N lattice gauge theory without third-order phase transition

Two-dimensional lattice QCD with Manton's action is solved in the N = ∞ limit. Contrary to the case when Wilson's action is used, no phase transition appears. Possible implications for higher dimensions are briefly discussed.     

Λ production in K−p interactions at 32 GeV/c

Lambda production is studied in K^?p interactions at 32 GeV/c. The total Λ cross section is 2.31±0.03 mb. Using the measured Λγ combinations we find that (31±4)% of all Λ's are produced via the Σ⁰→Λγ decay. About 60% of the Λ's are associated with either a $\text{N}\text{N}\text{or K}\text{K}$ pair; about 40% of the Λ's are produced through the hypercharge annihiltion reaction K^?p→Λ+π'a. The two-peak structure of the invariant x distribution can be related to fragmentation processes. The Λ is found to be unpolarized in the target fragmentation region, whereas a transverse polarization is observed for forward produced Λ's. As a function of p⊥, a polarization effect is measured at medium p⊥.     

X-ray photoelectron spectroscopy of rare-earth compounds

A variety of rare-earth (RE) compounds (oxides, sulfates and oxalates) have been studied by X-ray photoelectron spectroscopy. Except for Eu, the binding energies (BE's) of the RE 3d and 4d peaks for the sulfates and oxalates are respectively almost equal to and 1.3–3.1 eV higher than those for the oxides. In the Eu 3d spectrum of europium(II) oxalate, distinct shake-down satellite peaks are present, and the BE's of these peaks are 1̃0 eV lower than the parent ones. For the oxides, appreciable differences are found in the BE's of the O 1s peaks, and a specific “inclined W” form is observed in plots of BE versus 1/R (where R is the mean distance from the oxygen atom to the neighboring RE atom) and versus the RE oxidation-reduction potential (ORP). No characteristic differences are seen in the BE's (C 1s, S 2s and S 2p) of the other ligands.     

Wilson-Zimmermann expansions and the normal-product algorithm for the Ward identity of the axial-vector current in meson-nucleon dynamics

Zimmermann's normal-product algorithm is developed for the renormalizable γ₅ interaction of meson-nucleon dynamics. With the help of Zimmermann's algebraic identities Wilson's short-distance expansion and the Zimmermann identity are verified in perturbation theory for a fermion-fermion operator product. We demonstrate the power of this method in clarifying problems which seemed to appear in earlier, less rigorous, treatments of a generalized Ward-identity for the axial vector in such a field theory.     

Slavnov-Taylor identities in Weinberg's renormalization scheme

Weinberg's renormalization scheme, although more cumbersome from the computational point of view, has a more immediate physical interpretation than 't Hooft's minimal renormalization scheme. It is expected to lead to smaller higher-order coefficients in a perturbative approach to QCD. However, it a priori violates the Slavnov-Taylor identities. A complete study of this problem is performed, both theoretically and for the practitioner's sake. The ambiguities in the choice of the tensorial basis of some of the QCD vertices, as well as the dependence in the gauge parameter are used for substantiating, eventually, the Slavnov-Taylor identities in this renormalization scheme.     

On Λ-type doubling in multiplet states of diatomic molecules

Explicit expressions valid in the neighborhood of Hund's case (a) and (b) are obtained for the width of Λ-type doubling of multiplet Π terms up to septet multiplicity. Moreover, a relation between the constants occurring in the expressions of Hund's cases (a) and (b) is given.     

On coherent scattering in stellar atmospheres

An exact solution of the transfer equation for coherent scattering in stellar atmospheres with Planck's function as a sum of elementary functions, is obtained in a simple form with the help of the author's new representation of H-functions of Radiative Transfer.     

Spontaneous symmetry breaking and Higgs' mechanism in the nonsymmetric Kaluza-Klein theory

The nonsymmetric Kaluza-Klein theory unifying Moffat's theory of gravitation, the Yang-Mills' field and the Higgs' fields are constructed in a geometric manner. Spontaneous symmetry breaking, the Higgs' mechanism and mass generation in the theory are discussed. The connection between R₊ invariance (dilatation on the space-time) from Moffat's theory of gravitation and U(1)_F from GUTs, is proposed within the framework of fermion number conservation.     

A comment on functional integrals and many-body systems

Green's functions for systems of non-interacting particles at T=0 are obtained through ab initio calculations using functional integral algorithms. It is shown in detail how the correct Green's functions are computed and how one recovers the structure of the ground state (which in the usual derivations is the starting point).     

Relation between the Grüneisen ratio and the pressure dependence of Poisson's ratio for metals

The Grüneisen ratio of crystalline solids is shown to be dependent on a parameter n whose values are characteristic of each solid, and can be determined by two independent ways: from experimental shock data and from the pressure derivative of Poisson's ratio. The determinations are made for several metals, using data on the pressure derivatives of polycrystalline elastic moduli or of the second order elastic constants measured on single crystals, and giving the pressure derivatives of Poisson's ratio by means of the Voigt-Reuss-Hill averaging procedure. The values of the parameter n deduced from shock data are found to be in good agreement with those deduced from the pressure derivatives of Poisson's ratio. Positive and negative values of parameter n correspond respectively to increasing and decreasing Poisson's ratio with increasing pressure. Discussion of the results is made using the linear and the quadratic relationships between shock velocity and particle velocity. It is shown that shock wave data cannot yield directly an accurate estimation of the derivative of the initial slope of the Hugoniot.     

First order green-function theory of isotropic Heisenberg ferromagnet

The Heisenberg ferromagnet with general spin S is considered within Green-function theory and spectral density method. New difference equations of the first order determining one- and two-particle correlation functions are derived and solved. The spectral density method is used to close Oguchi's variational theory without additional decoupling assumptions. The temperature renormalized spectrum is found to be a series expansion in that the first term coincide with RPA result and the first two terms correspond essentially to Callen's result. Low temperature expansions for the renormalization factor and the magnetization are given and shown to coincide with Callen's result.