Relaxationsphänomene in Mössbauerspektren von Magnetisierten paramagnetischen Substanzen. I [(Fe x,Al1-x )NH4(SO4)2· 12H2O]

The Fe³⁺-spin in alums of type (Fe _x , A1_1-x )NH₄(SO₄)₂ · 12 H₂O interacts (i) with the crystal lattice viaLS-coupling, and (ii) with the spins of the adjacent Fe³⁺-ions via magnetic dipole-dipole interaction. These interactions lead to a time fluctuation of the spin direction, characterized by correlation times τ _c and τ′ _c of increasing order. The times may be deduced from the⁵⁷Fe-Mössbauer spectra of the alums, τ _c from the width, and τ′ _c ≈τ _c from the position of the hyperfine structure lines. The theoretical interpretation of the Mössbauer spectra is relatively simple, when (i) the spin-lattice interaction gets frozen in, and (ii) a strong applied magnetic fieldH _a decouples the spins of the Fe³⁺-ion and the⁵⁷Fe-nucleus. The spectra were taken, therefore, at 4.2 °K and 8 kOe≦H _a ≦ 54 kOe. According to the 1/r ³-dependence of the magnetic dipole-dipole interaction τ _c should be related tox, the Fe-concentration, τ _c ·x≈τ₀=const. Forx≧0.5 our experimental results are in agreement with this rule when τ₀=(1.5±0.5) · 10^?9 s. For an alum withx=0.26, however, the observed spectra cannot be explained in terms of temporal spin fluctuations, at least not in the framework of the models which are available now. Here, presumedly, the electron spins of adjacent Fe³⁺-ions are coupled to more or less isolated and, consequently, relatively stationary spin clusters of various sizes, leading to many time independent internal magnetic fields. A treatment of this proposal is in preparation.     

Reduction of hexachloroiridate (IV) by benzene-1,2-diol in aqueous perchloric acid

The kinetics of the reaction between benzene-1,2-diol(catechol) and hexachloroiridate (IV) have been measured in aqueous acidic perchlorate solutions by the stopped-flow method. The reaction is second order overall, and first order in each reactant. A reverse reaction also occurs, but it is much slower than the forward process. Observed rate constants are dependent on acidity, but the variation can be attributed to activity rather than mechanistic effects. The reaction appears to proceed predominantly by an outer sphere electron transfer mechanism, yielding o-benzoquinone and hexachloroiridate (III), although monoaquopentachloroiridate (III) is formed also at the higher [catechol]/[IrCl₆^2?]ratios.     

A superlinearly convergent method for minimization problems with linear inequality constraints

A method is described for minimizing a continuously differentiable functionF(x) ofn variables subject to linear inequality constraints. It can be applied under the same general assumptions as any method of feasible directions. IfF(x) is twice continuously differentiable and the Hessian matrix ofF(x) has certain properties, then the algorithm generates a sequence of points which converges superlinearly to the unique minimizer ofF(x). No computation of secondorder derivatives is required.Sponsored by the United States Army under Contract No. DA-31-124-ARO-D-462 and by the National Science Foundation under Research Grant GP.33033.     

Gesichtspunkte bei der Stoffauswahl für dünne Schichten in der Optik

Ohne Zusammenfassung     

Evaluation of the Fe2+/Fe3+ ratio from57Co Mössbauer emission spectra: Influence of the relaxation of Fe3+

The Fe³⁺ fraction after the EC of⁵⁷Co is usually evaluated supposing that ferric ions contribute a quadrupole doublet to Mössbauer emission spectra. It is shown that a not sufficiently fast relaxation of the electron spins may falsify the evaluated intensity even by a factor 2. Additional information can be gained from measurements performed in a large velocity span at low temperatures in high magnetic fields.     

Probabilistic clustering via Pareto solutions and significance tests

The present paper proposes a new strategy for probabilistic (often called model-based) clustering. It is well known that local maxima of mixture likelihoods can be used to partition an underlying data set. However, local maxima are rarely unique. Therefore, it remains to select the reasonable solutions, and in particular the desired one. Credible partitions are usually recognized by separation (and cohesion) of their clusters. We use here the p values provided by the classical tests of Wilks, Hotelling, and Behrens–Fisher to single out those solutions that are well separated by location. It has been shown that reasonable solutions to a clustering problem are related to Pareto points in a plot of scale balance vs. model fit of all local maxima. We briefly review this theory and propose as solutions all well-fitting Pareto points in the set of local maxima separated by location in the above sense. We also design a new iterative, parameter-free cutting plane algorithm for the multivariate Behrens–Fisher problem.     

Untersuchung von Mischvorgängen bei der Herstellung von Kohlenstoffund SiC-Werkstoffen mit Hilfe der Methodik der radioaktiven Markierung

Fūr die Herstellung von Kohlenstoff- und SiC-Werkstoffen ist eine gute Vermischung der festen und flüssigen Komponenten die notiwendige Voraussetzung. Da andere Methoden meist zu zeitaufwendig sind, wurden im VEB EKL seit mehr als 10 Jahren Versuchsreihen mit der Methodik der radioaktiven Markierung einer der Mischungskomponenten zur Untersuchung des Mischvorgangs für Maschinen bis zu 2000 kg Fülung angewandt, wobei sich die Fremdmarkierung mit ⁸²Br-Naphthalin als vorteilhaft erwiesen hat. Der Mischungszustand wird durch statistische Auswertung der Radioaktivität von Probenserien, deren γ-Strahlung gemessen wird und deren Masse in Abhängigkeit von der Mischergröβ 1 bis 100 g je Probe beträgt, charakterisiert. Zusätzlich wird die Feinverteilung durch Kontaktautoradiographie von ebenen Probenoberflächen, ebenfalls für Probenserien, bestimmt.     

Temperature dependence of Bi2O3 structural parameters close to the α–δ phase transition

This article presents the results of in situ X-ray powder diffraction, Raman spectroscopy, and electrical impedance spectroscopy of the α-phase of Bi₂O₃, at 0.1 MPa in the temperature range below and above the α–δ-phase transition. This work demonstrated subtle nonlinear temperature variations of the cell parameters, of the hard-mode Raman shift, and of the activation energy of electrical conductivity in the temperature range about 100–120°C below the α–δ phase transition temperature T _Tr ≈ 725°C in Bi₂O₃. At T < 600°C, the linear variation of the inverse dielectric susceptibility (χ ^?1) correlates well with the hard mode frequency shift Δ(ω ²) of Raman A_1g mode as Δ(χ ^?1)/Δ(ω ²) ≈ 5.5 × 10^?7 cm². A structural model describing the mechanism of O^2? anion distribution and electric dipole disordering in the vicinity of T _Tr is discussed.