Diffuse x-ray scattering study of the formation of microdefects in heat-treated dislocation-free large-diameter silicon wafers

Diffuse x-ray scattering (DXS) is used to study the formation of microdefects (MDs) in heat-treated dislocation-free large-diameter silicon wafers with vacancies. The DXS method is shown to be efficient for investigating MDs in silicon single crystals. Specific defects, such as impurity clouds, are found to form in the silicon wafers during low-temperature annealing at 450°C. These defects are oxygen-rich regions in the solid solution with diffuse coherent interfaces. In the following stages of decomposition of the supersaturated solid solution, oxide precipitates form inside these regions and the impurity clouds disappear. As a result of the decomposition of the supersaturated solid solution of oxygen, interstitial MDs form in the silicon wafers during multistep heat treatment. These MDs lie in the {110} planes and have nonspherical displacement fields. The volume density and size of MDs forming in the silicon wafers at various stages of the decomposition are determined.     

A numerical study of time-dependent schr?dinger equation for multiphoton vibrational interaction of NO molecule, modelled as Morse oscillator, with intense far-infrared femtosecond lasers

For the NO molecule, modelled as a Morse oscillator, time-dependent (TD) nuclear Schr?dinger equation has been numerically solved for the multiphoton vibrational dynamics of the molecule under a far-infrared laser of wavelength 10503 nm, and four different intensities,I = 1 × 10⁸, 1 × 10¹³, 5 × 10¹⁶, and 5 × 10¹⁸ W cm⁻² respectively. Starting from the vibrational ground state at zero time, various TD quantities such as the norm, dissociation probability, potential energy curve and dipole moment are examined. Rich high-harmonics generation (HHG) spectra and above-threshold dissociation (ATD) spectra, due to the multiphoton interaction of vibrational motions with the laser field, and consequent elevation to the vibrational continuum, have been obtained and analysed. Dedicated to Professor C N R Rao on his 70th birthday An erratum to this article is available at .     

Two observations about free graded hopf algebras

This paper records two results about graded Hopf algebras that do not appear to be stated explicitly in the literature. Let B be a graded set, graded by the positive integers. Let V be the graded vector space with basis B over a field K of characteristic zero and V^'=K⊕V, where K is in grading zero. Let L ne the free graded Lie algebra on B over K and let T be the free graded tensor algebra on B. The first result is the "graded Witt formula" giving the dimension of the subspace of L in each grading. The second result is the observation that any graded coassociative, co-commutative comultiplication Δ:V^'→V^'⊗V^', with co-unit the projection V¹→K. extends to a graded Hopf algebra structure on T that is in fact isomorphic to the natural graded Hopf algebra structure on T. In the ungraded case the statement analogous to the second result is false.     

Partition of Euclidean space into polyhedra induced by a small deformation of the densest lattice sphere packing

The number of combinatorially nonequivalent Dirichlet-Voronoi diagrams constructed for the centers of balls in the packing obtained from the densest lattice packing of equal spheres by a small displacement of the spheres is estimated. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 5, pp. 79–84, 2005.     

Convergence of optimal controls in some optimization problems

We consider the behavior of bundles of optimal controls when the initial state of the system goes to some given vector. We investigate three types of optimization problems: problems with fixed process length and a free right endpoint; problems with fixed process length and a fixed right endpoint; time-optimal problems. The article is a review of recent results obtained by the author. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 301–314, 2004.     

Colorings of spaces,and random graphs

This work deals with some problems on the embeddings of finite geometric graphs into the random ones. In particular, we study here applications of the random graph theory to the Nelson-Erdös-Hadwiger problem on coloring spaces.     

Gas solubility of carbon dioxide in poly(lactic acid) at high pressures: Thermal treatment effect

The sorption of carbon dioxide in glassy Poly(lactic acid) (PLA) films was studied by quartz crystal microbalance (QCM) at high pressures. Two thermal treatments, melted and quenched, were performed in PLA with two different L:D contents, 80:20 and 98:2, films and compared with a third thermal protocol, annealed, and used in a previous work. The results obtained show that for pressures higher than 2 MPa, the carbon dioxide solubility is larger in PLA 80:20 than in PLA 98:2, indicating that the L:D plays a dominant role on this property. The thermal treatments only affect the gas solubility in PLA 98:2. Sorption isotherms at temperatures 303, 313, and 323 K, below the glass transition temperature of the polymer, and pressures up to 5 MPa were measured and analyzed with three different models, the dual‐mode sorption model, the Flory–Huggins equation, and a modified dual‐mode sorption model where the Henry's law term was substituted by the Flory–Huggins equation. This last model performs especially well for CO₂ in PLA 80:20, due to the convex upward curvature of the solubility isotherms for that system. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 616–625, 2007     

On the law of corresponding states for thermodynamic properties of a crystal

To study thermodynamic similarity of the properties of crystalline substances, we propose an approach connected with engaging of the metastable state region. Internal pressure and specific volume on the crystal’s stability boundary at T = 0 K are used as characteristic scales of thermodynamic variables. A semiempirical method of calculation of the stability boundary by the thermodynamic data related to the stable states region of a solid body is described. In the cases of argon and natrium, the stability boundary is calculated for a wide range of temperatures and pressures. Analysis of the properties of neon, argon, krypton, and xenon crystals in these variables indicates that the law of corresponding states holds for these substances.