The transition from dynamics to statics in the electron-spin-resonance spectra of impurity Mn2+ ions in strontium titanate

The electron-spin-resonance (ESR) spectra of SrTiO₃:Mn single crystals have been investigated. Results unambiguously indicate that the impurity center formed by an Mn²⁺ ion has a dynamic nature. In the high temperature range (T > 100 K), ESR spectra of Mn²⁺ ions reveal cubic symmetry; the spectrum is found to broaden significantly with a decrease in temperature. Upon cooling to T < 10 K, low-symmetry centers of Mn²⁺ ions with a strong orientational dependence emerge in the spectra. Temperature evolution of the ESR spectrum can be described within the model of a dynamic off-center Mn²⁺ ion substituting for the Sr²⁺ ion, with a transition to the static regime at low temperatures with an average localization energy of ～2.4 ± 0.4 meV for Mn²⁺ centers due to random deformations.     

EPR spectroscopy of weak exchange interactions between Co2+ ions in ZnO

Electron paramagnetic resonance (EPR) is used to identify the next nearest neighbour Co²⁺ pairs coupled by spin–spin interaction in Co‐doped ZnO single crystals grown by the hydrothermal technique. These dimer centers are described by a spin Hamiltonian with exchange coupling terms written as interaction between identical effective spins S^eff = 1/2 of the lowest ground state Kramers doublets of the two Co²⁺ ions. The exchange parameters of weakly ferromagnetically coupled next nearest neighbor Co²⁺ pairs are estimated. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sharp Estimates of the Constants of Equivalence Between Integral Moduli of Smoothness and K-functionals in the Multivariate Case

The equivalence between various types of moduli of smoothness and respective Peetre K-functionals has been actively explored since the 1960s, in view of the importance of this topic for revealing connections among approximation theory, functional analysis and operator theory. The existence of the embedding constants in this equivalence relation (together with one-sided estimates for these constants) has been established in great generality, but the derived one-sided bounds are rather coarse (see, e.g., Johnen and Scherer, in Constructive Theory of Functions of Several Variables. Proc. Conf., Math. Res. Inst. Oberwolfach, 1976, pp. 119–140, Springer, Berlin, 1977 and the references therein). The problem of finding the sharp embedding constants for this equivalence was posed in Dechevsky, C. R. Acad. Bulg. 42(2), 21–24, 1989 and Int. J. Pure Appl. Math. 33(2), 157–186, 2006, where this problem was solved in the particular case of L ₂-metric, for real-valued and complex-valued functions of one real variable, with definition domain Ω=ℝ or \varOmega = \mathbbT\varOmega =\mathbb{T} (the periodic case). In the present paper we extend the results of Dechevsky to the case of several real variables: Ω=ℝ ⁿ or \varOmega = \mathbbTⁿ\varOmega =\mathbb{T}^{n} , n∈ℕ. We consider two different types of equivalent norms for the Sobolev spaces involved in the K-functional (with and without intermediate mixed partial derivatives) and obtain a separate set of sharp two-sided bounds for the embedding constants in each of these two cases. We also briefly outline how the approach of the present study can be extended to the case of n-dimensional Lie (semi)groups.     

Diffusion of particles over triangular inhomogeneous lattice with two non-equivalent sites

We investigate the diffusion of particles adsorbed on a triangular lattice with deep and shallow sites. It is shown that the character of the particle migration depends substantially on the relative jump rates from the deep and shallow sites. The site inhomogeneity imposes specific correlation betweeen successive jumps: particles perform pairs of slow and fast jumps. General analytical expressions have been derived for the chemical and jump diffusion coefficients. We have calculated coverage dependencies of the diffusion coefficients and some thermodynamic quantities for different lateral interactions between the particles. The analytical data have been compared with the numerical data obtained by kinetic Monte Carlo simulations. The agreement between the results obtained by these quite different approaches is found to be very satisfactory.     

Mössbauer spectroscopy and additional study of neutron irradiated Cr-doped metallic glasses

Concentration and fluence dependent tendency of FeNiCrMoSiB metallic glass towards disordering as well as a decrease of the Curie temperature were revealed by Mössbauer and electron-positron annihilation spectroscopies and initial permeability measurements, respectively. The observed changes can be assigned to irradiation-induced defects resulting in fluctuations in chemical and/or topological short-range order.     

Flame atomic-absorption spectrometric determination of traces of copper, iron, lead and manganese in nitric acid by injection dosation of concentrated solutions neutralized with ammonia

Summary The dosation system MS-11T working in the solvent-sample-solvent mode was used for the flame atomic-absorption spectrometric determination of copper, lead, iron and manganese in concentrated nitric acid. The acid was neutralized with gaseous ammonia. The resulting concentrated solution of ammonium nitrate (corresponding to 46.4% HNO₃) was thermostatted at 75°C and 250 l-portions were injected into the flame. The effect of the temperature of sample and washing solvent was studied. The precision of the analysis was improved by ensemble summation of the signals. The trace element concentrations, determined by the method of standard addition, were at 0.1 mg/l level.Dedicated to Prof. Dr. Ing. Bernhard Schrader on the occasion of his 60th birthday     

Generalized Jacobians of spectral curves and completely integrable systems

Consider an ordinary differential equation which has a Lax pair representation , where A(x) is a matrix polynomial with a fixed regular leading coefficient and the matrix B(x) depends only on A(x). Such an equation can be considered as a completely integrable complex Hamiltonian system. We show that the generic complex invariant manifold of this Lax pair is an affine part of a non-compact commutative algebraic group – the generalized Jacobian of the spectral curve with its points at “infinity” identified. Moreover, for suitable B(x), the Hamiltonian vector field defined by the Lax pair on the generalized Jacobian is translation-invariant. Received April 29, 1997; in final form September 22, 1997     

Diffusion in heterogeneous lattices

We present here the results of our investigations of particle diffusion over different heterogeneous lattices with deep and shallow adsorption sites. A general analytical expression for chemical diffusion coefficient has been derived for a number of inhomogeneous lattices of different dimensionality and symmetry. We have calculated coverage dependencies of diffusion coefficients. The analytical data have been compared with the numerical data obtained by the kinetic Monte Carlo simulations. Almost perfect agreement between the respective results has been found.     

EPR investigation of the trivalent chromium complexes in SrTiO3

The trivalent chromium centers were investigated by means of electron paramagnetic resonance (EPR) in SrTiO₃ single crystals grown using the Verneuil technique. It was shown that the charge compensation of the Cr³⁺-V_O dominant centers in octahedral environment is due to the remote oxygen vacancy located on the axial axis of the center. In order to provide insight into spin-phonon relaxation processes the studies of axial distortion of Cr³⁺-V_O centers have been performed as function of temperature. The analysis of the trigonal Cr³⁺ centers found in SrTiO₃ indicates the presence of the nearest-neighbor strontium vacancy. The next-nearest-neighbor exchange-coupled pairs of Cr³⁺ in SrTiO₃ has been analyzed from the angular variation of the total electron spin of S=2 resonance lines.