Towards the synthesis of MAX-phase functional coatings by pulsed laser deposition

Pulsed laser deposition with a Nd:YAG laser was used to grow thin films from a pre-synthesized Ti₃SiC₂ MAX-phase formulated ablation target on oxidized Si(1 0 0) and MgO(1 0 0) substrates. The depositions were carried out in a substrate temperature range from 300 to 900 K, and the pressure in the deposition chamber ranged from vacuum (10⁻⁵ Pa) to 0.05 Pa Argon background pressure. The properties of the films have been investigated by Rutherford backscattering spectrometry for film thickness and stoichiometric composition and X-ray diffraction for the crystallinity of the films. The silicon content of the films varied with the energy density of the laser beam. To suppress especially the silicon re-sputtering from the substrate, the energy of the incoming particles must be below a threshold of 20 eV. Therefore, the energy density of the laser beam must not be too high. At constant deposition energy density the film thickness depends strongly on the background pressure. The X-ray diffraction measurements show patterns that are typical of amorphous films, i.e. no Ti₃SiC₂ related reflections were found. Only a very weak TiC(2 0 0) reflection was seen, indicating the presence of a small amount of crystalline TiC.     

Partitioning Balls into Topologically Equivalent Pieces

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Partitioning Balls into Topologically Equivalent Pieces

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Invariants of Conformai and Projective Structures

While in Euclidean, equiaffine or centroaffine differential geometry there exists a unique, distinguished normalization of a regular hypersurface immersion x: M ⁿ → Aⁿ⁺¹, in the geometry of the general affine transformation group, there only exists a distinguished class of such normalizations, the class of relative normalizations. Thus, the appropriate invariants for speaking about affine hypersurfaces are invariants of the induced classes, e.g. the conformai class of induced metrics and the projective class of induced conormal connections. The aim of this paper is to study such invariants. As an application, we reformulate the fundamental theorem of affine differential geometry.     

Investigation of the photothermally modulated ferromagnetic resonance signal from magnetostatic modes in yttrium iron garnet films

The conventional and photothermally modulated (PM) ferromagnetic resonance (FMR) of magnetostatic modes (MSM) in yttrium iron garnet (YIG) films have been investigated as a function of temperature. Approaching the ferrimagnetic transition at T _c=560 K a strong enhancement of the PM-FMR signal amplitude is observed which is accompanied by a change of the signal shape. The observations are discussed in the framework of a model that takes into account the temperature derivatives of those quantities that contribute to the high-frequency susceptibility. At temperatures still below T _c a paramagnetic line emerges. The MSM disappear in a state of finite magnetization which is explained on the basis of damping of the MSM being important in the vicinity of the magnetic phase transition. Additionally, frequency and power dependent measurements are presented and the imaging ability of PM-FMR is demonstrated.     

On Nodal Sets for Dirac and Laplace Operators

We prove that the nodal set (zero set) of a solution of a generalized Dirac equation on a Riemannian manifold has codimension 2 at least. If the underlying manifold is a surface, then the nodal set is discrete. We obtain a quick proof of the fact that the nodal set of an eigenfunction for the Laplace-Beltrami operator on a Riemannian manifold consists of a smooth hypersurface and a singular set of lower dimension. We also see that the nodal set of a Δ-harmonic differential form on a closed manifold has codimension 2 at least; a fact which is not true if the manifold is not closed. Examples show that all bounds are optimal. Received: 28 October 1996 / Accepted: 3 March 1997     

Comments concerning the HPLC separation of acrolein from other C3 carbonyl compounds as 2,4-dinitrophenylhydrazones: A proposal for improvement

The separation of the toxicologically important aldehyde acrolein from other carbonyl compounds by high performance liquid chromatography after derivatization to 2,4-dinitrophenylhydrazones is critically discussed on the basis of a selection of published methods. A method is proposed whereby the compounds acrolein, acetone, and propanal may be reproducibly separated to baseline by a reversed phase HPLC procedure employing a ternary mixture of methanol, water, and acetonitrile as mobile phase.     

Determination of the spin-spin centrifugal distortion parameters for deuterated selenoformaldehyde in its first excited triplet state

Recently-formulated centrifugal distortion corrections to the spin-spin Hamiltonian have been used to analyse the first excited triplet state (ã³A₂) of deuterated selenoformaldehyde. By including six spin-spin centrifugal distortion parameters, it is possible to account for the energy levels of this state using a single set of three rotational constants, A, B, and C, where previously nine spin-dependent parameters were required.