Ordering of nonstoichiometric hexagonal compounds <Emphasis Type="Italic">M</Emphasis><Subscript>2</Subscript><Emphasis Type="Italic">X</Emphasis>: A sequence of special figures

An ensemble of figures required for the analysis of the atomic-vacancy ordering in nonstoichiometric compounds M ₂ X _y (M ₂ X _y ▭_{1 − y} ) with an L′3 hexagonal structure has been determined by the order-parameter functional method. It has been demonstrated reasoning from the crystal lattice geometry that, in order to describe M ₂ X _y compounds with an L′3 structure, it is necessary to use the basis cluster in the form of a trigonal prism consisting of six sites of the nonmetal lattice with a metal atom at the center. The overlapping figures that, together with the basis cluster, form a sequence of special figures uniquely describing the L′3 structure have been found. The equilibrium conditions for disorder-order transformations in nonstoichiometric compounds M ₂ X _y have been determined in the general form.     

Geometric frustrations in magnetically diluted complex oxides Li<Emphasis Type="Italic">M</Emphasis>O<Subscript>2</Subscript> (<Emphasis Type="Italic">M</Emphasis> = Sc,Ga, 3<Emphasis Type="Italic">d</Emphasis> elements)

The effect of local environment of a transition-element atom on the properties of bulk ceramics has been investigated by the example of complex oxides LiMO₂ (M = Sc, Ga, Fe, Co, Ni). It is found that the anomalies in the magnetic properties of all systems studied are due to the presence of nanoclusters of transition-element atoms and the magnetic and geometric frustrations related to the nanocluster formation.     

Low-temperature anomaly of the magnetization in alloys (Pr,Dy,<Emphasis Type="Italic">M</Emphasis>)<Subscript>2</Subscript>(Fe,Co)<Subscript>14</Subscript>B (<Emphasis Type="Italic">M</Emphasis> = Gd,Sm, Nd)

It has been found that temperature dependences of the saturation magnetization of sintered hard magnetic (Pr,Dy,M)₂(Fe,Co)₁₄B (M = Gd, Sm, Nd) alloys demonstrate an increase at a temperature lower than a critical temperature (150 K for Sm and Nd and 70 K for Gd). An additive of copper does not influence the critical temperature. It has been assumed that there is a low-temperature phase in which cobalt is replaced with boron that diffuses from the (Pr,Dy,Gd)(Fe,Co)₄B phase to the near-surface region of grains of the main magnetic (Pr,Dy,Gd)₂(Fe,Co)₁₄B phase.     

Running electromagnetic-coupling constant: Low-energy normalization and the value at <Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">Z</Emphasis></Subscript>

A numerical value for the running electromagnetic-coupling constant in the \(\overline {MS} \) scheme is calculated at a low-energy normalization scale equal to the τ-lepton mass M_τ. This low-energy boundary value is used for running the electromagnetic coupling to larger scales, where high-precision experimental measurements can be performed. Particular scales of interest are the b-quark mass for studying ?-resonance physics and the Z-boson mass M _Z for high-precision tests of the Standard Model and for the determination of the Higgs boson mass from radiative corrections. A numerical value of the running electromagnetic-coupling constant at M _Z in the on-shell renormalization scheme is also given.     

Electronic structure of the Np<Emphasis Type="Italic">MT</Emphasis> <Subscript>5</Subscript> (<Emphasis Type="Italic">M</Emphasis> = Fe,Co, Ni; <Emphasis Type="Italic">T</Emphasis> = Ga,In) series of neptunium compounds

Evolution of the electronic structure of the NpMGa₅ (M = Fe, Co, Ni) series of neptunium compounds, whose crystal structure is similar to that of the known family of Pu115 superconductors, was studied by the LDA + U + SO method. The calculations took into account both the strong electron correlations and the spin?orbit coupling in the 5f shell of neptunium. For the first time, the electronic structure was calculated for a hypothetical series of compounds in which gallium is replaced with indium. Parameters of the crystal structure of the given series were obtained using the relationship between the parameters of the crystal structure of the earlier-studied compounds PuCoGa₅ and PuCoIn₅. The analysis of the electronic structure and characteristics of neptunium ions calculated in the framework of the LDA + U + SO method showed that the neptunium ions in NpMIn₅ with M = Fe, Co, and Ni should have an electron configuration closer to f⁴, but a spin and magnetic characteristics close to those in NpMGa₅.     

<Emphasis Type="Italic">SU</Emphasis>(3)-Instantons and <Emphasis Type="Italic">G</Emphasis><Subscript>2</Subscript>,<Emphasis Type="Italic">Spin</Emphasis>(7)-Heterotic String Solitons

Necessary and sufficient conditions to the existence of a hermitian connection with totally skew-symmetric torsion and holonomy contained in SU(3) are given. A formula for the Riemannian scalar curvature is obtained. Non-compact solution to the supergravity-type I equations of motion with non-zero flux and non-constant dilaton is found in dimension 6. Non-conformally flat non-compact solutions to the supergravity-type I equations of motion with non-zero flux and non-constant dilaton are found in dimensions 7 and 8. A Riemannian metric with holonomy contained in G₂ arises from our considerations and Hitchin’s flow equations, which seems to be new. Compact examples of SU(3),G₂ and Spin(7) instanton satisfying the anomaly cancellation conditions are presented.     

Infrared spectroscopy of europium borates Eu<Emphasis Type="Italic">M</Emphasis><Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> (<Emphasis Type="Italic">M</Emphasis> = Al,Cr, Fe,Ga) with a huntite mineral type of structure

Huntite-like EuM ₃(BO₃)₄ crystals (M = Al, Cr, Fe, or Ga) are synthesized by means of spontaneous crystallization from a solution in a melt. The infrared spectra of the compounds are measured. The experimental data and the results from ab initio DFT calculations are compared. The comparison shows that the compounds have a primarily noncentrosymmetric rhomboherdal structure with the R32 space group. This indicates these compounds could exhibit magnetoelectric and nonlinear optical properties.     

Electronic structure and stability of complex hydrides Mg<Subscript>2</Subscript><Emphasis Type="Italic">M</Emphasis>H<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> (<Emphasis Type="Italic">M</Emphasis> = Fe,Co)

This paper reports on the results of theoretical investigations carried out for the hydrides Mg₂FeH₆ and Mg₂CoH₅ and the mixed hydride Mg₂(FeH₆)_0.5(CoH₅)_0.5 in terms of the full-potential linearized augmented plane wave (FLAPW) method. It has been shown that the partial substitution of the Co atoms for the Fe atoms leads to a slight increase in the stability of the hydride, but, at the same time, makes it impossible to increase the stability of the alloy. The high stability of the hydrides under investigation has been explained by the strong bonding between atoms of the transition metal and hydrogen.     

<Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">e</Emphasis>3</Subscript> decays and CKM unitarity

We present a detailed numerical study of the K_e3 decays to in chiral perturbation theory with virtual photons and leptons. We describe the extraction of the CKM matrix element |V_us| from the experimental K_e3 decay parameters. We propose a consistency check of the K ⁺ _e3 and K⁰_e3 data that is largely insensitive to the dominating theoretical uncertainties, in particular the contributions of . Our analysis is highly relevant in view of the recent high statistics measurement of the K ⁺ _e3 branching ratio by E865 at Brookhaven which does not indicate any significant deviation from CKM unitarity but rather a discrepancy with the present K⁰_e3 data.Received: 22 January 2004, Published online: 30 April 2004Work supported in part by IHP-RTN, Contract No. HPRN-CT2002-00311 (EURIDICE) and by Acciones Integradas, Project No. 19/2003 (Austria), HU2002-0044 (MCYT, Spain)     

Magnetic properties of single crystals of ludwigites Cu<Subscript>2</Subscript><Emphasis Type="Italic">M</Emphasis>BO<Subscript>5</Subscript> (<Emphasis Type="Italic">M</Emphasis> = Fe<Superscript>3+</Superscript>, Ga<Superscript>3+</Superscript>)

High-quality single crystals of ludwigites Cu₂ MBO₅ (M = Fe³⁺, Ga³⁺) have been grown, and the magnetic, resonance, and Mössbauer studies have been performed. It is established that the Cu₂FeBO₅ and Cu₂GaBO₅ compounds are antiferromagnets with Néel temperatures of 32 and 3.4 K, respectively. A model of the magnetic structure of the compounds is proposed. It is shown that the magnetic properties of the ludwigites are substantially dependent on the degree of ion distribution over crystallographic positions.     

The Dirac Operator on <Emphasis Type="Italic">SU</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript>(2)

We construct a 3⁺-summable spectral triple over the quantum group SU_q(2) which is equivariant with respect to a left and a right action of The geometry is isospectral to the classical case since the spectrum of the operator D is the same as that of the usual Dirac operator on the 3-dimensional round sphere. The presence of an equivariant real structure J demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order.Partially supported by Polish State Committee for Scientific Research (KBN) under grant 2 P03B 022 25.Regular Associate of the Abdus Salam ICTP, Trieste.     

Polynomial Realization of <Emphasis Type="Italic">s</Emphasis>l<Subscript><Emphasis Type="Italic">q</Emphasis></Subscript>(2) and Fusion Rules at Exceptional Values of <Emphasis Type="Italic">q</Emphasis>

Representations of the sℓ_q(2) algebra are constructed in the space of polynomials of real (complex) variable for q^N=1. The spin addition rule based on eigenvalues of Casimir operator is illustrated on few simplest cases and conjecture for general case is formulated.     

Chemical and phase compositions of multilayer nanoperiodic <Emphasis Type="Italic">a</Emphasis>-SiO<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>/ZrO<Subscript>2</Subscript> structures subjected to high-temperature annealing

The chemical and the phase compositions of multilayer nanoperiodic SiO _x /ZrO₂ structures prepared by vacuum evaporation from separated sources and subjected to high-temperature annealing have been studied by X-ray photoelectron spectroscopy with a layer-by-layer etching. It is found that, under deposition conditions used, the silicon suboxide layers had the stoichiometric coefficient x ~1.8 and the zirconium-containing layers were the stoichiometric zirconium dioxide. It was found, using X-ray photoelectron spectroscopy, that annealing of the multilayer structures at 1000°C leads to mutual diffusion of the components and chemical interaction between ZrO₂ and SiO _x with predominant formation of zirconium silicate at heteroboundaries of the structures. The SiO _x layers of the annealed nanostructures contained ~5 at % elemental silicon as a result of the phase separation and the formation of fine silicon nanocrystals.     

Magnetic M<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>O<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript>@N-C as heterogeneous catalysts for the catalytic oxidation of aniline solution with sulfate radicals

Metal nanoparticles have been combined with magnet metal–organic frameworks (MOFs) to afford new materials that demonstrate an efficient catalytic degradation, high stability, and excellent reusability in areas of catalysis because of their exceptionally high surface areas and structural diversity. Magnetic M _x O _y @N-C (M = Fe, Co, Mn) nanocrystals were formed on nitrogen-doped carbon surface by using 8-hydroxyquinoline as a C/N precursor. The Co@N-C, MnO@N-C, and Fe/Fe₂O₃@N-C catalysts were characterized by X-ray diffraction (XRD), Raman, scanning electron microscopy (SEM), high-resolution transmission electron microscopy (HRTEM), N₂ adsorption/desorption, and X-ray photoelectron spectroscopy (XPS). The catalytic performances of catalysts were thoroughly investigated in the oxidation of aniline solution based on sulfate radicals (SO₄ ^?.) toward Fenton-like reaction. Magnetic M _x O _y @N-C exhibits an unexpectedly high catalytic activity in the degradation of aniline in water. A high magnetic M _x O _y @N-C catalytic activity was observed after the evaluation by aniline degradation in water. Aniline degradation was found to follow the first-order kinetics, and as a result, various metals significantly affected the structures and performances of the catalysts, and their catalytic activity followed the order of Co > Mn > Fe. The nanoparticles displayed good magnetic separation under the magnetic field.

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Graphical Abstract ?

     

Electron paramagnetic resonance of spin-variable metallomesogens [Fe<Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript>]<Emphasis Type="Italic">X</Emphasis> (<Emphasis Type="Italic">X</Emphasis> = PF<Subscript>6</Subscript>, SCN)

Significant differences in the manifestation of spin-crossover properties of the mesogen compounds [FeL ₂]X with oxysalicylidene-N′-ethyl-N-ethylenediamine ligands L and anions X = PF₆⁻ and SCH⁻ have been found by means of electron paramagnetic resonance. The electron paramagnetic resonance data and the quantum-chemical calculation within the density functional theory enables us to establish that the observed specific features are associated with the incorporation of the SCH⁻ ion into the first coordination sphere of the Fe(III) ion. The role of the transition of the material to the liquid-state phase in the formation of a low-dimensional (two-dimensional) structure with stronger intermolecular interactions has been revealed.     

Intervalley electron scattering by phonons in (GaAs)<Subscript><Emphasis Type="Italic">m</Emphasis></Subscript>(AlAs)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>(001) ultrathin superlattices

The electron scattering by short-wavelength and long-wavelength phonons in (GaAs) _m (AlAs) _n (001) superlattices with ultrathin layers (n, m = 1, 2, 3) has been investigated using the pseudopotential method and the phenomenological model of bonding forces. The deformation potentials have been found for intervalley electron transitions in the conduction bands of the superlattices and solid solutions of the corresponding compositions. It has been shown that, owing to the localization of the wave functions in the quantum wells Γ, L, and X, the intensity of intervalley electron transitions in the superlattices, as a whole, is higher than that of similar transitions in the solid solutions. As the content of light Al atoms in the superlattices increases, the deformation potentials monotonically increase for the X-X transitions and decrease for the L-L and X-L transitions. The potentials of the Γ-X and Γ-L transitions change nonmonotonically depending on the layer thickness due to the pronounced quantum-well effects in the deep Γ quantum wells of GaAs. The deformation potentials averaged over phonons and related valleys in the superlattices are close to the corresponding potentials in the solid solutions.     

Dynamics of the first-order magnetostructural transition in Gd<Subscript>5</Subscript>(Si<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ge<Subscript>1-<Emphasis Type="Italic">x</Emphasis></Subscript>)<Subscript>4</Subscript>

For a given crystal structure, say body-centred-cubic, the many-body Hamiltonian H in which nuclear and electron motions are to be treated from the outset on the same footing, has parameters, for the elements, which can be classified as (i) atomic mass M, (ii) atomic number Z, characterizing the external potential in which electrons move, and (iii) bcc lattice spacing, or equivalently one can utilize atomic volume, . Since the thermodynamic quantities can be determined from H, we conclude that T _c , the superconducting transition temperature, when it is non-zero, may be formally expressed as T _c = . One piece of evidence in support is that, in an atomic number vs. atomic volume graph, the superconducting elements lie in a well defined region. Two other relevant points are that (a) T _c is related by BCS theory, though not simply, to the Debye temperature, which in turn is calculable from the elastic constants C ₁₁, C ₁₂, and C ₄₄, the atomic weight and the atomic volume, and (b) T _c for five bcc transition metals is linear in the Cauchy deviation C ^* = (C ₁₂ - C ₄₄ )/(C ₁₂ + C ₄₄ ). Finally, via elastic constants, mass density and atomic volume, a correlation between C ^* and the Debye temperature is established for the five bcc transition elements.Received: 13 May 2004, Published online: 23 July 2004PACS: 74.62.-c Transition temperature variations - 74.70.Ad Metals; alloys and binary compounds     

<Emphasis Type="Italic">J</Emphasis><Subscript><Emphasis Type="Italic">AW,WA</Emphasis></Subscript> functions in Passarino-Veltman reduction

We continue to study a special class of Passarino-Veltman functions J arising at the reduction of infrared divergent box diagrams. We describe a procedure of separation of two types of singularities, infrared and mass singularities, which are absorbed in simple C ₀ functions. The infrared divergences of C ₀’s can be regularized then by any method: photon mass, dimensionally or by the width of an unstable particle. Functions D ₀ are represented as certain linear combinations of the standard C ₀ Passarino-Veltman functions and infrared finite functions J. Then mass singularities are extracted from J to other combinations of C ₀. The rests are free of both types of singularities and are expressed as explicit and compact linear combination of logarithms and dilogarithm functions. The extensive comparison of numerical results with those obtained with the aid of the Loop Tools package is presented.     

Shell effects for isovector <Emphasis Type="Italic">l</Emphasis>-forbidden <Emphasis Type="Italic">M</Emphasis>1 transitions in odd nuclei

It is inferred from the analysis of the experimental data that the reduced probabilities of isovector l-forbidden M1 transitions achieve maximum values in nuclei with a magic core. The minimum values are related to γ transitions in nuclei belonging to the region of stable deformation with A ≈ 25. Isovector l-forbidden M1 transitions in mirror nuclei are explored. The ratio of the reduced probabilities for proton and neutron transitions shows the maximum deviation from the theoretical evaluations for the pair of nuclei ⁴¹Ca-⁴¹Sc consisting of the even-even magic core ⁴⁰Ca and one nucleon outside the closed 1d2s shell.     

The isospin-symmetry-breaking effects in <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">e</Emphasis>4</Subscript> decays

The final-state interaction of pions in K _e4 decay allows to obtain the value of the isospin and angular-momentum-zero ππ scattering length a ₀⁰.We take into account the electromagnetic interaction of pions and isospin-symmetry-breaking effects caused by different masses of neutral and charged pions and estimate the impact of these effects on the procedure of scattering-length extraction from K _e4 decays.