Smooth approximation of convex bodies

We describe a general approximation procedure for convex bodies which shows, in particular, that a body of constant width can be approximated, in the Hausdorff metric, by bodies of constant width with analytic boundaries (in fact, with algebraic support functions). Moreover, the approximating bodies have (at least) the same symmetries as the original one.     

Calculated elastic properties of M2AlC (M=Ti, V, Cr, Nb and Ta)

M₂AlC phases, where M is a transition metal, are layered ternary compounds that possess unusual properties. In this paper, we have calculated the elastic properties of M₂AlC, with M=Ti, V, Cr, Nb and Ta, by means of ab initio total energy calculations using the projector augmented-wave method. We have derived the bulk and shear moduli, Young's moduli and Poisson's ratio for ideal polycrystalline M₂AlC aggregates. We have estimated the elastic modulus of Cr₂AlC with 357.7 GPa while the values of all other phases are in the range 309±10 GPa. We suggest that this can be understood based on the calculated bond energies for the M-C bonds. Furthermore, our results indicate a profound elastic anisotropy of M₂AlC even compared to materials with a well-established anisotropic character such as α-alumina. Finally, we have estimated the Debye temperatures of M₂AlC from the average sound velocity.     

Zur Beleuchtung der Scala bei Polarisationsapparaten

Ohne Zusammenfassung     

Quantitative XPS of NiO, CoO and MnO. The effects of elastic and inelastic electron scattering

In order to check whether the method for background correction developed by Tougaard can be applied to oxides we measured XPS spectra of single crystalline NiO, MnO and CoO samples. The materials for which background treatment was developed and tested originally were metals and alloys. In contrast to that, the oxides we study in the present work are insulators. We have chosen these compounds because their structure is simple and by cleaving them in vacuo it is possible to obtain surfaces with well-defined stoichiometry.

The inelastic background for these oxides is likewise described well by the above mentioned model. The ratio of metal to oxygen concentration calculated from the XPS intensities so obtained oscillates around 1.0 with a maximum deviation of about ±20% in the worst case. These deviations originate from elastic electron scattering, namely forward focusing (X-ray photoelectron diffraction). Taking this into account, the perfect stoichiometry is obtained within a few percent.     

Non-destructive evaluation of the mechanical behaviour of TiN-coated steels by laser-induced ultrasonic surface waves

Measuring the propagation velocity of ultrasonic surface waves has been used to determine the Young's modulus of TiN films on steel. Wide-band surface-wave pulses are generated by a pulsed nitrogen laser and detected by a piezoelectric PVDF-foil transducer. A spectrum of the surface-wave phase velocity is obtained from the Fourier transformation of the surface-wave signals. The TiN films were deposited after different presputtering times with argon ions to vary the adhesion on the steel substrate. The adhesion behaviour of the films was investigated with the scratch tester. A correlation was found between the Young's modulus of the film material and the acoustic emission activity in the scratch test, which has been shown to be a suitable measure for adhesion.     

Memory effects in polymers. V. Processing history versus thermally induced self-orientation of unoriented poly(chlorotrifluoroethylene) films

A peculiar phenomenon is reported whereby a melt-extruded, low-crystallinity, unoriented film of poly(chlorotrifluoroethylene) upon unconstrained thermal treatment, self-extends in the machine direction (MD) while shrinking along the transverse (TD) and normal/thickness (ND) directions. In addition to the expected increase in crystallinity, the annealing process leads to an unexpected development of crystalline orientation along the MD. This phenomenon is an example of “processing-induced memory effects” since it depends on the processing history of the starting film, e.g., melt-extrusion leads to the subject behavior whereas compression molding does not. We must mention that the melt-extruded films of poly(chlorotrifluoroethylene) are isotropic to start with, that is, MD and TD are indistinguishable prior to the annealing process. Furthermore, this phenomenon has not been observed for any other semicrystalline polymer and is believed to be the first citation for poly(chlorotrifluoroethylene) since its commercialization in 1957. Thermomechanical analysis (TMA) is the analytical technique that led to this novel phenomenon which was later substantiated by x-ray diffraction (XRD). ©1995 John Wiley & Sons, Inc.     

Convergence results for multistep Runge-Kutta methods

Summary. Recently Ch. Lubich proved convergence results for Runge-Kutta methods applied to stiff mechanical systems. The present paper discusses the new ideas necessary to extend these results to general linear methods, in particular BDF and multistep Runge-Kutta methods. Received August 9, 1993 / Revised version received May 3, 1994