Determination of the concentration profile of interfaces in multilayered nanostructures according to the angular dependence of X-ray photoelectron spectra: A new approach

The possibility of determining the concentration profile of interfaces in multilayered nanoheterostructures according to the data of the angular dependence of X-ray photoelectron spectra was shown. To solve this ill-posed inverse problem, we used Tikhonov’s regularization method with iterative refinement. To determine the optimum parameter of regularization, we used the L curve technique. The programs used for this study allowed high accuracy of calculations. All this made it possible to obtain information about the distribution of atoms of a definite sort with a resolution of 0.1–0.15 nm in depth. The results of numerical simulation of XPS spectra are given for a three-layered Cr/Fe structure. Solving the inverse problem for the initial data distorted by the statistical noise afforded a concentration distribution over depth for Cr and Fe atoms. The stability of the solution against experimental errors was determined.     

Electron gas induced in SrTiO<Subscript>3</Subscript>

This mini-review is dedicated to the 85th birthday of Prof. L.V. Keldysh, from whom we have learned so much. In this paper, we study the potential and electron density depth profiles in surface accumulation layers in crystals with a large and nonlinear dielectric response such as SrTiO₃ (STO) in the cases of planar, spherical, and cylindrical geometries. The electron gas can be created by applying an induction D₀ to the STO surface. We describe the lattice dielectric response of STO using the Landau–Ginzburg free energy expansion and employ the Thomas–Fermi (TF) approximation for the electron gas. For the planar geometry, we arrive at the electron density profile n(x) ∝ (x + d)^–12/7, where d ∝ D₀^–12/7. We extend our results to overlapping electron gases in GTO/STO/GTO heterojunctions and electron gases created by spill-out from NSTO (heavily n-type doped STO) layers into STO. Generalization of our approach to a spherical donor cluster creating a big TF atom with electrons in STO brings us to the problem of supercharged nuclei. It is known that for an atom with a nuclear charge Ze where Z > 170, electrons collapse onto the nucleus, resulting in a net charge Zn < Z. Here, instead of relativistic physics, the collapse is caused by the nonlinear dielectric response. Electrons collapse into the charged spherical donor cluster with radius R when its total charge number Z exceeds the critical value Z_c ≈ R/a, where a is the lattice constant. The net charge eZ_n grows with Z until Z exceeds Z* ≈ (R/a)^9/7. After this point, the charge number of the compact core Z_n remains ≈ Z*, with the rest Z* electrons forming a sparse TF atom with it. We extend our studies of collapse to the case of long cylindrical clusters as well.     

An approximation condition and extremal quasiconformal extensions

The possibility that the extremal dilatation of quasiconformal extensions from the circle is determined by quadrilaterals with vertices on the circle is related to an approximation question for holomorphic functions. This allows an alternative demonstration of a result of Anderson and Hinkkanen.

     

237Np separation from environmental matrices by extraction chromatography method

Aliquat-336 anchored on hydrophobized silica gel was used for effective separation of ²³⁷Np from soil matrices and from model solutions. Alpha spectrometry for ²³⁷Np determination was used. The interfering radionuclides present in environmental samples such as ²³⁴U, ²³²Th, ²³¹Pa and ^239+240Pu were removed by separation with nitric acid solutions containing formic acid and ferrous sulfamate as reducing agents. Spiking samples with ^238,234U, ²³²Th and ²³⁸Pu were used to check separation effectiveness. A separation yield of ²³⁷Np from soil matrices was checked by measuring of added known amount activity and was found to be about 15%. The yield of separation for model solutions was about 56%. Different parameters of eluant on recovery of ²³⁷Np from column were studied.     

Über Dialkylidensulfamide

Aldehydes and ketones containing no α-hydrogen atoms yield the corresponding dialkylidene sulfamides both by reacting with sulfamide in presence of a proton acid or of SOCl₂ and by reacting with bis(trichlorphosphazo)-sulfone. The dialkylidene sulfamides of ketones also were obtained by treating ketone imines with sulfamide. Chloral did not react with sulfamide in this way but yielded 3,7-bis-(trichloromethyl)-perhydro-1,5,2,4,6,8-dithiatetrazocine-1,1,5,5-tetroxide.     

Gamma-ray emission from 134Ce and levels in 134La

The decay of ¹³⁴Ce to doubly odd ¹³⁴La has been studied using Ge(Li) and Si(Li) photon detectors. Samples of the ¹³⁴Ce(75.9 h)- ¹³⁴La(6.67 min) have been produced by ≈ 800 MeV proton bombardment of Pr foils in LAMPF, followed by chemical and mass separation. To increase the sensitivity (by up to a factor ≈ 50) for detection of ¹³⁴Ce γ-rays in the presence of the interfering ¹³⁴La activity, the ¹³⁴Ce-¹³⁴La samples were loaded onto a HDEHP column and the ¹³⁴La eluted off continuously. Gamma-ray singles and γ-γ coincidence measurements were made using the ¹³⁴Ce activity remaining on the column as the source. Some 32 γ-rays, ranging in energy up to 355 keV, are observed to be associated with this decay. Approximately 30 of these have been fitted into a level scheme for ¹³⁴La with excited states at energies of 31, 54, 93, 136 or 148, 162, 187, 150 or 205, 252, 294 and 355 keV. Only limits can be set for the spin and parity values of each of these states. The observation of γ-rays with energies up to 355 keV indicates that the previously reported values of ≈ 0.1 MeV for the ¹³⁴Ce electron-capture decay energy, inferred from the K-electron capture probability, are incorrect.     

Werteverteilung von Zetafunktionen

Ohne Zusammenfassung     

The asymptotics of nonexpansive iterations

Let D be a closed subset of a Banach space X and T: D → D a nonexpansive mapping. Conditions are given (on the space X) for T to satisfy the following property of ergodic type: $\text{{T}{}^{\mathrm{n}}\text{x}\text{n}\text{}}$ converges (either weakly or strongly) to a vector v. Rather unexpectedly, D is not assumed to be convex, nor is I – T assumed to satisfy any range condition. In addition, it is shown that ?v is the unique point of least norm in the closure of R(I – T) if and only if I – T satisfies a certain range condition at infinity. Several interesting applications to accretive operator and nonlinear semigroup theory are also included.