Pit your wits against young minds!

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.     

Model calculations of interface segregation in dilute systems

Using a discrete model for the segregation kinetics based on the Darken theory of diffusion and on the regular solution model (RSM), one and two dimensional simulations of interface segregation in binary and ternary systems have been performed. The aim of the calculations was to investigate the kinetics of segregation sequences in ternary systems, the segregation kinetics in discrete systems during the initial phase and finally the kinetics of surface segregation in the region of a grain boundary intersected by the surface.     

Resonance ionization spectroscopy for trace analysis and fundamental research

Resonance ionization spectroscopy (RIS) and its combination with mass spectrometry (RIMS) have grown to become powerful techniques, which offer high sensitivity as well as elemental and isotopic selectivity. The principles of RIS and RIMS are introduced; they primarily concern the analysis of the optical spectra for the choice of efficient excitation schemes and the suitable design of the experimental apparatus. Recent applications span from studies of short-lived isotopes at on-line mass separators to a wide variety of trace analysis applications for radioactive isotopes, which can range from measurements of solar neutrino flux to environmental assessment.On leave from Pacific Northwest Laboratory, Richland, USA     

ARXPS-analysis and morphology of sputtered nanocrystalline TiC/SiC coatings

ARXPS (angle resolved X-ray photoelectron spectroscopy) measurements are used to obtain informations about surfaces and grain boundaries. Data acquired from nanocrystalline carbidic hard coatings have been employed to establish structural models. Magnetron-sputtered coatings of TiC, SiC and TiC/SiC were examined. In such coatings, partly defective TiC nanocrystallites are surrounded by interfacial carbide. This excess carbon shows a binding state similar to that of doped graphite or fullerenes. X-ray amorphous SiC is found in the residue. On top of sputtered SiC coatings, less oxide and graphite is found as compared to TiC/SiC or TiC coatings.     

Manifestation of biquadratic coupling in the smectic C* phase soft mode dielectric response

The soft mode dielectric response of three ferroelectric chiral smectic C* substances is studied in the vicinity of the smectic C*-smectic A* phase transition. For some substances the soft mode dielectric strength exhibits a pronounced anomaly in the C* phase just below the phase transition. We show how this anomaly can be systematically correlated with a corresponding anomaly in the experimentally determined ratio of spontaneous polarization over tilt. By comparing the experimental results with the theoretical predictions of an extended Landau model, we demonstrate how the crossover behaviour of the system can be interpreted as being the consequence of the presence of a biquadratic coupling between tilt and polarization in the Landau free-energy of the system.     

Analysis of the structure of an amorphous sediment obtained upon decomposition of potassium oxofluroniobate in water

An amorphous sediment was prepared by the decomposition of potassium oxofluoroniobate K_{2 ? x} Nb₄O₃(O, F)₃F in water. For this sediment, the atomic radial distribution function was analyzed with the use of a fragment model, which allows one to interpret expanded coordination spheres as being formed by first several strongest diffusion maxima. These spheres carry the most reliable information on the structure. It is shown that the amorphous sediment consists of the randomly packed Nb(O,F)₆-octahedra with interatomic distances close to those observed in the ordered region in the N-Nb₂O₅ structure. During decomposition in water, the initial K_{2 ? x} Nb₄O₃(O, F)₃F phase loses KF-layers, whereas Nb₆ clusters with metal bonds are destroyed.     

On complementability of certain generalized hypercenters in Artinian modules

We prove that, in an Artinian module, the upper FC-hypercenter over an infinite FC-hypercentral locally solvable group has a direct complement. Thus, we obtain a generalization of one of Zaitsev’s theorems and one of Duan’s theorems.     

Synthesis of functional polymers—Vinylidene fluoride based fluorinated copolymers and terpolymers bearing bromoaromatic side‐group

The radical co‐ and terpolymerization of 4‐[(α,β,β‐trifluorovinyl)oxy]bromo benzene (TFVOBB) with 1,1‐difluoroethylene (or vinylidene fluoride, VDF, or VF₂), hexafluoropropene (HFP), perfluoromethyl vinyl ether (PMVE), and chlorotrifluroroethylene (CTFE) is presented. Although TFVOBB could be thermocyclodimerized, it could not homopolymerize under radical initiation. TFVOBB could be copolymerized in solution under a radical initiator with VDF or CTFE comonomers, while its copolymerization with HFP or PMVE were unsuccessful. The terpolymerization of TFVOBB with VDF and HFP, or VDF and PMVE, or VDF and CTFE also led to original fluorinated terpolymers bearing bromoaromatic side‐groups. The conditions of co‐ and terpolymerization were optimized in terms of the nature of the radical initiators, and of the nature of solvents (fluorinated or nonhalogenated). Various monomer concentrations in the co‐ and terpolymers were assessed by ¹⁹F and ¹H‐NMR spectroscopy. The thermal and physico chemical properties were also studied. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5077–5097, 2004