Phasenbeziehungen und Natriumionenleitung im quasi-binären System Na2SiF6/Na3AlF6

Phase Relations and Sodium Ion Conductivity within the Quasi-binary System Na₂SiF₆/Na₂AIF₆ . The phase diagram of the Na₂SiF₆/Na₃AlF₆ system has been determined by means of x-ray powder diffraction, thermal analysis and conductivity measurements in the sub-solidus region. Na₃AlF₆ accomodates up to 73 mol.-% Na₂SiF₆ maintaining the crystal structure type. The sodium ion conductivity increases by about five orders of magnitude upon doping Na₃AlF₆ with Na₂SiF₆.     

On the analysis of a dynamic evolutionary algorithm

Evolutionary algorithms are applied as problem-independent optimization algorithms. They are quite efficient in many situations. However, it is difficult to analyze even the behavior of simple variants of evolutionary algorithms like the (1+1) EA on rather simple functions. Nevertheless, only the analysis of the expected run time and the success probability within a given number of steps can guide the choice of the free parameters of the algorithms. Here static (1+1) EAs with a fixed mutation probability are compared with dynamic (1+1) EAs with a simple schedule for the variation of the mutation probability. The dynamic variant is first analyzed for functions typically chosen as example-functions for evolutionary algorithms. Afterwards, it is shown that it can be essential to choose the suitable variant of the (1+1) EA. More precisely, functions are presented where each static (1+1) EA has exponential expected run time while the dynamic variant has polynomial expected run time. For other functions it is shown that the dynamic (1+1) EA has exponential expected run time while a static (1+1) EA with a good choice of the mutation probability has polynomial run time with overwhelming probability.     

Zur Synthese und Struktur von K3N

Synthesis and Structure of K₃N Two phases in the binary system K/N have been obtained via co‐deposition of potassium and nitrogen onto polished sapphire at 77 K and subsequent heating to room temperature. The powder diffraction pattern of one of these phases can be satisfactorily interpreted by assuming the composition K₃N, and the anti‐TiI₃ structure‐type, which is also adopted by Cs₃O. The resulting hexagonal lattice constants are: a = 779.8(2), c = 759.2(9) pm, Z = 2, P6₃/mcm. Comparison with possible structures of K₃N generated by computational methods and refined at Hartree‐Fock‐ and DFT level, reveals that the energetically most favoured structure has not formed (presumable Li₃P‐type), but instead one of those with very low density. In this respect, the findings for K₃N are analogous to the results on Na₃N. The thermal evolution of the deposited starting mixture has been investigated. Hexagonal K₃N transforms to another K/N phase at 233 K. Its XRD can be fully indexed resulting in an orthorhombic cell a = 1163, b = 596, c = 718 pm. Decomposition leaving elemental potassium as the only residue occurs at 263 K.     

A New Family of Binary Layered Compounds of Platinum with Alkali Metals (A = K,Rb, Cs)

By reacting platinum with alkali metals (A = K, Rb, Cs) a new family of binary alkali metal platinides has been synthesized and characterized by chemical analysis, X‐ray powder diffraction, thermal analysis (DTA and DSC), and magnetic measurements. All three compounds exhibit similar XRD‐patterns with strong reflections that can be indexed on the basis of a rhombohedral crystal system (K_xPt: a = 2.6462(1), c = 17.123(1); Rb_xPt: a = 2.6415(1) Å, c = 17.871(1) Å; Cs_xPt: a = 2.6505(1) Å, c = 18.536(1) Å; x < ½. The a lattice constant is independent on the alkali metal used and of value close to the Pt–Pt distance in NaPt₂ (2.645Å). The c parameter increases monotonically with the growing atomic radius of the alkali metal. The average structure of the alloys consists of cubic close packed layers of platinum atoms with layers of disordered alkali metals in between. For all compounds besides the strong reflections small satellites are observed which cannot be indexed together with the rhombohedral peaks in any rational 3‐dimensional lattice. However, these satellites can be indexed as incommensurate modulations within the ab plane (found propagation vectors k = (0.1011, 0.2506, 0) for Cs_xPt, and k = (0.0168, 0.2785, 0) for Rb_xPt).     

Über verallgemeinerte Momente additiver Funktionen

In this paper we give characterizations of additive functionsf, for which $$\mathop {\lim \sup }\limits_{x \to \infty } x^{ - 1} \sum\limits_{n \leqslant x} {\varphi (|f(n)|)}$$ is bounded, where φ: ?⁺ → ?⁺ is monotone and or $$\begin{array}{*{20}c} {\varphi (x) = c^x } & {(x \in \mathbb{R}).} \\ \end{array}$$ A typical example is φ (x)=x ^a (a>0) forx≥0.     

Use of solid-phase microextraction-capillary-gas chromatography (SPME-CGC) for the varietal characterization of wines by means of chemometrical methods

The extraction of wine aroma compounds was studied by direct-SPME (DI/SPME), headspace-SPME (HS/SPME) and multiple-headspace-extraction-SPME (MHE/SPME). The aromagrams obtained by HS/SPME-CGC were evaluated with chemometrical methods for the varietal classification of wines. Received: 25 July 1997 / Revised: 24 September 1997 / Accepted: 7 October 1997