Backlund transformations and exact solutions for a nonlinear elliptic equation modelling isothermal magnetostatic atmosphere

The equations of magnetostatic equilibria for a plasma in agravitational field are investigated analytically. For equilibriawith an ignorable spatial coordinate, the equations reduce toa single nonlinear elliptic equation for the magnetic potentialu known as the Grad-Shafranov equation. By specifying the arbitraryfunctions in this equation, a Liouville equation is obtained.Bäcklund transformations are described and applied to obtainexact solutions for the Liouville equation modelling an isothermalmagnetostatic atmosphere, in which the current density J isproportional to the exponential of the magnetic potential andmoveover falls off exponentially with distance vertical to thebase with an e-folding distance equal to the gravitational scaleheight.     

In situ investigation of the formation of Cu(In,Ga)Se2 from selenised metallic precursors by X-ray diffraction—The impact of Gallium, Sodium and Selenium excess

The chemical reactions during rapid thermal processing of stacked elemental layers were investigated by angle-dispersive in situ X-ray diffraction. With a time resolution of 5 diffractograms per minute four different solid state reactions resulting in ternary chalcopyrites were identified: (A) CuSe+InSe→CuInSe₂, (B) Cu₂Se+2InSe+Se→2CuInSe₂, (C) Cu₂Se+In2Se₃→2CuInSe₂, (D) Cu₂Se+Ga2Se₃→2CuGaSe₂. All these reactions form pure tenary chalcopyrites. The reaction resulting in the mixed crystal Cu(In,Ga)Se₂ starts not before (B) has begun. The reaction speed of (A) and the fraction of CuInSe₂ formed by (B) depend on Na-doping and Se-pressure, (C) takes place only, if the reaction paths (A) and (B) are suppressed. Reaction (D) is observed only, if 25% In is replaced by Ga in the precursor. The diffractograms were evaluated by Rietveld refinement to give the phase contents of the samples as a function of reaction time.     

Ferroelectric poly(vinylidene fluoride) PVDF films derived from the solutions with retainable water and controlled water loss

To obtain β‐phase dominant ferroelectric poly(vinylidene fluoride) (PVDF) homopolymer thin films on aluminum‐coated silicon substrates, the retaining and loss of water were manipulated by introducing several hydrated and hygroscopic chemicals in the precursor solutions, including aluminum nitrate nonahydrate, aluminum chloride hexahydrate, chromium nitrate nonahydrate, tetra‐n‐butylammonium chloride, and one hygroscopic but nonhydrated chemical, ammonium acetate. Their ability of retaining water during the thermal annealing of the films and the relationship between water retaining and the effects on promoting the β phase were investigated. The results showed an ideal scenario was that the added hydrated salts should be able to retain substantial amount of water during the PVDF crystallization to effectively promote the β phase but completely dehydrate or decompose at the further elevated annealing temperature in order to obtain β‐phase dominant PVDF film without substantially incorporating water and deteriorating the electrical properties. As one of the hydrated chemicals well satisfying the above requirements, Al(NO₃)₃·9H₂O, of different amounts was introduced to the PVDF precursor solutions and the optimal resulting β‐phase dominant ferroelectric PVDF thin films exhibited smooth morphology, low dielectric loss, high remnant polarization of 89 mC/m², and large effective piezoelectric coefficient d₃₃ of ?14.5 pm/V (under the clamping of the substrate). © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2410–2418, 2009     

Smoothing filters in phase-shifting interferometry

The images used in phase-shifting interferometry are usually noisy and smoothing filters are frequently used. Filtering can be done on the fringe patterns before phase retrieving or on the phase map after phase retrieving. Filtering fringe patterns—a form of preprocessing, requires the same processing to be done on at least three patterns. Filtering phase map, on the other hand, needs processing of only one pattern. Preprocessing prevents noise from being carried through while post-processing might clip parts of the signal. Thus there is a need to evaluate which one is better. A theoretical analysis was carried out for this basic problem, followed by computer simulations and a real experiment for verification. The comparison was also extended to phase difference measurement which uses similar but slightly different phase retrieval algorithms.     

Morphology of polypropylene crystallized from the melt

Polypropylene was oxidized with nitric acid in a manner contrived to remove its amorphous component. Concurrent with the loss in weight there was an increase in crystallinity, a decrease in molecular weight, a drop in melting point, and a change in visible structure. The crystalline component, which survived from polymer which had orginally crystallized isothermally, consisted of separated spherulites. These spherulites could be broken apart into lamellae which gave electron diffraction patterns like those now associated with a variety of solution-grown single crystals. As opposed to the high molecular weight of the unoxidized parents, the lamellae which survived the acid treatment consisted of short chains whose length depended on the temperature at which the parents had crystallized. If, as diffraction studies indicate, these short molecules are lined up in rank and file, then the length of the molecules and the height of the lamellae should correspond. The heights of the lamellae could not be measured precisely enough to establish an exact correlation, but the variations in average chain length calculated from viscosity data at least approximated the heights of the lamellae which were observed visually.     

1H NMR spectra and ring shapes of the 4,5,8-trimethyl and 4-methyl derivatives of 1-tetralone

The 220 MHz spectra of the title compounds are reported and values for the internal ring dihedral angle, Ψ, formed between the C-2? C-1 and C-3? C-4 bonds, calculated using the R-value method. The trimethyltetralone exists in a conformer having Ψ = 51° and the 4-methyl group in the axial position. 4-Methyl-1-tetralone exists in a conformational equilibrium where the mean value of Ψ for the conformers adopted is 56°.     

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K-shell ionization by protons for Cr,Cu, In and by alpha-particles for Cr,Cu

K-shell ionization cross sections have been determined for Cr, Cu and In at proton bombardment in the energy region from 0.9 to 2.5 MeV. The same cross sections were determined for Cr and Cu at alpha bombardment in the 0.9–4.0 MeV region. The experimental results are compared with five different theoretical calculations.