Investigation of Al diffusion in different oxide thin-film layers by SNMS/HFM method

Depth profiles of Ga₂O₃/a-SiO₂/Al₂O₃- substrate, Ga₂O₃/a-Si₃N₄/Al₂O₃- substrate, and Ga₂O₃/Al₂O₃ substrate thin layers were determined by the SNMS/HFM method. Al diffusion from the Al₂O₃ substrate was investigated after 50, and in some cases after 600 hours of heat treatment time at different temperatures (600 °C,850 °C,950 °C,1050 °C and 1150 °C). The diffusion coefficient of Al at 850 °C was found to be D _Al=8.7 * 10^–18 cm²/s in amorphous SiO₂; D _Al=1.5*10^–17 cm²/s in amorphous Si₃N₄ and D _Al=5.5* 10^–16 cm²/s in Ga₂O₃ at 600 °C, respectively. The possible diffusion mechanism is explained in terms of the metal-oxygen bond-strengths. Although the studied materials have high resistivity at room temperature, the applied SNMS/HFM method has proven to be an efficient surface analytical tool even in these cases.Dedicated to Professor Dr. rer. nat. Dr. h.c. Hubertus Nickel on the occasion of his 65th birthday     

An additive analysis of multiplicative Schwarz methods

We present an analysis of multiplicative Schwarz methods for symmetric positive definite problems that is based on the theory of additive Schwarz preconditioners and discuss applications to multigrid methods and domain decomposition methods.     

Vertices, sources and Green correspondents of the simple modules for the large Mathieu groups

We investigate the simple modules for the sporadic simple Mathieu groups M₂₂, M₂₃ and M₂₄ as well as those of the automorphism group, the covering groups and the bicyclic extensions of M₂₂ in characteristics 2 and 3. We determine the vertices and sources as well as the Green correspondents of these simple modules. We also find two 3-blocks with elementary abelian defect groups of order 9 in these groups which are Morita equivalent to their Brauer correspondents.     

Boundedness of solutions of a system of integro-differential equations

Let b: [?1, 0] →$\text{R}$ be a nondecreasing, strictly convex C²-function with b(? 1) = 0, and let g: $\text{R}$ⁿ → $\text{R}$ⁿ be a locally Lipschitzian mapping, which is the gradient of a function G: $\text{R}$ⁿ → $\text{R}$. Consider the following vector-valued integro-differential equation of the Levin-Nohel type

$\text{x}\text{?}\text{(t)=?∝}{}_{\mathrm{?1}}{}^0\text{b(θ)g(x(t + θ))dθ}$

. (E) This equation is used in applications to model various viscoelastic phenomena. By LaSalle's invariance principle, every bounded solution x(t) goes to a connected set of zeros of g, as time t goes to infinity. It is the purpose of this paper to give several geometric criteria assuring the boundedness of solutions of (E) or some of its components.     

Convergence of nonconforming multigrid methods without full elliptic regularity

We consider nonconforming multigrid methods for symmetric positive definite second and fourth order elliptic boundary value problems which do not have full elliptic regularity. We prove that there is a bound () for the contraction number of the -cycle algorithm which is independent of mesh level, provided that the number of smoothing steps is sufficiently large. We also show that the symmetric variable -cycle algorithm is an optimal preconditioner.

     

Saturation of the all-optical Kerr effect in solids

We discuss the influence of the higher-order Kerr effect (HOKE) in wide bandgap solids at extreme intensities below the onset of optically induced damage. Using different theoretical models, we employ multiphoton absorption rates to compute the nonlinear refractive index by a Kramers-Kronig transform. Within this theoretical framework we provide an estimate for the appearance of significant deviations from the standard optical Kerr effect predicting a linear index change with intensity. We discuss the role of the observed saturation behavior in practically relevant situations, including Kerr lens mode-locking and supercontinuum generation in photonic crystal fibers. Furthermore, we present experimental data from a multiwave mixing experiment in BaF2, which can be explained by the appearance of the HOKE.     

High-sensitivity microchip electrophoresis determination of inorganic anions and oxalate in atmospheric aerosols with adjustable selectivity and conductivity detection

A sensitive and selective separation of common anionic constituents of atmospheric aerosols, sulfate, nitrate, chloride, and oxalate, is presented using microchip electrophoresis. The optimized separation is achieved in under 1 min and at low background electrolyte ionic strength (2.9 mM) by combining a metal-binding electrolyte anion (17 mM picolinic acid), a sulfate-binding electrolyte cation (19 mM HEPBS), a zwitterionic surfactant with affinity towards weakly solvated anions (19 mM N-tetradecyl,N,N-dimethyl-3-ammonio-1-propansulfonate), and operation in counter-electroosmotic flow (EOF) mode. The separation is performed at pH 4.7, permitting pH manipulation of oxalate's mobility. The majority of low-concentration organic acids are not observed at these conditions, allowing for rapid subsequent injections without the presence of interfering peaks. Because the mobilities of sulfate, nitrate, and oxalate are independently controlled, other minor constituents of aerosols can be analyzed, including nitrite, fluoride, and formate if desired using similar separation conditions. Contact conductivity detection is utilized, and the limit of detection for oxalate (S/N = 3) is 180 nM without stacking. Sensitivity can be increased with field-amplified sample stacking by injecting from dilute electrolyte with a detection limit of 19 nM achieved. The high-sensitivity, counter-EOF operation, and short analysis time make this separation well-suited to continuous online monitoring of aerosol composition.