A matrix approach to grazing-incidence X-ray diffraction in multilayers

A method for computation of X-ray grazing-incidence diffraction (GID) in multilayers and superlattices is presented. The method is based on X-ray dynamical diffraction theory and a matrix from a boundary equations and provides a simple numerical solution of the problem. The application of the method to simulating GID measurements taken from A1As/GaAs superlattice (20 periods of 14.6 nm A1As and 6.8 nm GaAs) demonstrates the principal validity of the theory. A perfect matching between the theory and the experiment requires the real-structure effects of sample to be taken into account.     

On the Discrete Hardy Inequality

Necessary and sufficient conditions for the boundedness of thediscrete Hardy operator of the form , from to when 0 < q < 1 <p , is given.     

Surface Energy of Low-Index Faces of Single-Crystal Gold in Molten Sodium,Potassium, and Cesium Chlorides

The free energies of formation of gold faces (111) and (100) in molten sodium, potassium, and cesium chlorides are measured by the meniscus weighing method. The effect of the cation size, temperature, and electric potential on the electrocapillary curve and PZC is considered. A mechanism for the anion adsorption at a charged metal surface, based on the participation of valence orbitals of the electrode metal in the formation of surface compounds, is suggested.     

Decarbonylation of N-carbazolylacetyl chloride in the friedel-crafts acylation reaction

Reaction products of N-carbazolylacetyl chloride under Friedel-Crafts reaction conditions include carbon monoxide, the reaction product from carbazole and formaldehyde (CF condensate), and carbazole. It is postulated that decarbonylation of N-carbazolylacetyl chloride involves intermediate formation of a N-carbazolylmethyl cation.     

Mass-spectrometric study of permethyl compounds of group IVB elements

Russian Chemical Bulletin -     

Immobilization of carboxylic proteinases on amino-Silochrome

Summary Highly purified porcine pepsin and aspergillopepsin A immobilized on amino-Silochrome have been obtained. The enzymatic properties of these insoluble derivatives have been studied.All-Union Scientific-Research Institute of the Genetics and Breeding of Industrial Microorganisms, Moscow. Translated from Khimiya Prirodnykh Soedinenii, No. 3, pp. 373–379, May–June, 1978.     

Successive partitioning technique and Feenberg perturbation theory

Successive partitioning technique, when based on a modified bordering method for solving a system of linear equations and a relation for the inverse of a partitioned matrix leads to Feenberg's perturbation theory. This sheds light on the properties of the expansion, its bracketing properties and the nature of the “counting operators” used sometimes in this connection.     

Crystal and molecular structure of nitraminotetrazole and nitramino-1,2,4-triazole. IV. 5-nitraminotetrazole sodium salt sesquihydrate

The structure of 5-nitraminotetrazole sodium salt sesquihydrate was determined by X-ray diffraction. The crystals are monoclinic, space group P2₁/c;a = 3.551(1) Å, b = 21.834(4) Å, c = 9.075(2) Å; = 110.68(3)°; V = 658.3(2) ų; Z = 4; _calc = 1.807 g/cm³. The anion is planar and has an intramolecular hydrogen bond. The negative charge of the anion is localized on one of the oxygens of the nitro group. The sodium cation (c.n.6) is coordinated by three oxygen atoms of different anions and three oxygens of crystallization water. One of the crystallization water molecules is disordered in the unit cell. The anions are hydrogen-bonded with each other and with crystallization water molecules.Original Russian Text Copyright © 2004 by A. M. Astakhov, A. D. Vasiliev, M. S. Molokeev, L. A. Kruglyakova, A. M. Sirotinin, and R. S. StepanovTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 3, pp. 562–565, May–June 2004.     

Nonempirical estimation of the ionization conditions of water and amorphous ice

Based on the results of nonempirical dynamics simulations of the vibrationally excited water clusters combined with the data on the dynamic reorganization of water cations obtained upon the vertical ionization of neutral clusters at the additional assumptions about the general rigidity of the hydrogen-bond fragments in amorphous ice and the thermal excitation of rotational vibrations and swinging motions of molecules in liquid water, the characteristic times of structure reorganization are estimated. The possibility to evaluate the photoelectric threshold of amorphous ice from the data about the adiabatic ionization of small water clusters, whose structure reorganization upon the electron removal does not involve opening of rings and formation of chains, is founded. It is shown that the conditions of the threshold ionization of liquid water can be judged from the second intermediate ionization potentials of neutral clusters, that is, from the potentials corresponding to the appearance of cations in which H₃O and OH fragments are separated with one water molecule. Based on an analysis of the electron density distribution in the cationic and neutral water clusters, a functional dependence of the ionization potentials on the number of water molecules is derived. Approximations of the calculated full adiabatic and intermediate ionization potentials of clusters comprising up to 12 water molecules provided the photoelectric threshold estimates of water and amorphous ice in close agreement with experiments.