Determination of the position of impurity atoms in yttrium-aluminum garnet by means of forbidden reflections

The possibility of determining the position of terbium impurity atoms in yttrium-aluminum garnet lattice is analyzed. It is shown that in the presence of the impurity in both aluminum and yttrium positions the tensor factors of the nearest yttrium atoms change. To determine the position of impurity atoms in the yttrium-aluminum garnet unit cell, measurements should be carried out at energies near the L-absorption edges of terbium.     

Model-theoretic properties of regular polygons

This work is devoted to results obtained in the model theory of regular polygons. We give a characterization of monoids with axiomatizable and model-complete class of regular polygons. We describe monoids with complete class of regular polygons that satisfy some additional conditions. We study monoids whose regular core is represented as a union of finitely many principal right ideals and all regular polygons over which have a stable and superstable theory. We prove the stability of the class of all regular polygons over a monoid provided this class is axiomatizable and model-complete. We also describe monoids for which the class of all regular polygons is superstable and ω-stable provided this class is axiomatizable and model-complete. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 4, pp. 107–157, 2004.     

Vibrational relaxation of diatomic hydrides in inert gases. Rate constant calculations

Systematic calculations of thermal rate constants of vibrational relaxation of diatomic hydrides (HX) in inert gases (A) have been carried out for all available potential of such pairs. The method of calculation is based on a static approximation with respect to relative motion and includes a numerical calculation of Fourier harmonics of the perturbation during rotational motion of the molecule in the potential of the pair AHX. For all systems AHX, A = He, Ne, Ar, Xe, X = HCl, HF, OH, DCl, etc. the theoretical rate constants obtained with the power-type potentials (by Lennard-Jones, or Howard and Hutson) are significantly larger than experimental data. For available exponential-type potentials of ArHCl or the ab initio potentials of Ar, He + HF there is reasonable agreement between calculated and experimental data. The mechanism of VR relaxation is specified: the large contribution of trajectories with quasi-free molecule rotation passing through the linear configuration AHX has been established. Estimates of the rate constants as a function of initial rotational energy permit us to discuss the role of VR processes in recently observed laser effects on the rotational transition of hydrides.     

Ab initio simulation of resonant forbidden reflections in Ge crystals

Forbidden reflections are observed in the case of diffraction of synchrotron radiation with wave-lengths close to the absorption edges in crystals. A new method for calculating the intensity of thermal-motion-induced (TMI) forbidden reflections is proposed in this paper. It includes two stages: simulation of instantaneous thermal atomic displacements using ab initio molecular dynamics and subsequent quantum-mechanical calculations of the resonance scattering amplitude for various configurations. This procedure is used to calculate the temperature dependence of the 600 reflection intensity for Ge. The proposed method for simulating forbidden TMI reflections is suitable for any crystal structures and can explain many results so far obtained using synchrotron.     

The impedance-characteristic method in the study of specific temperature features of dielectric anomaly suppression in triglycine sulfate

The reflection and absorption coefficients in a waveguide loaded on ferroelectric triglycine sulfate (TGS), which has a layered domain structure near the phase transition, are calculated by the impedance-characteristic method. The calculated and experimental data do not reveal any correlations with the specific temperature features in the TGS dielectric response to microwave irradiation. The mechanism of the microwave effect is discussed.     

Methods for calculating the resonant part of the atomic factor in crystals with partial filling of the crystallographic position

The resonant part of the tensor atomic factor, which is important for incident radiation energies close to the atom absorption edges, is sensitive to the local environment of a scattering atom (near-range order). In this paper, a method for mathematical modeling of the resonant part of the atomic factor is developed by taking into account crystal-lattice relaxation caused by the partial filling of a crystallographic position. It is shown that an additional contribution leading to the appearance of purely resonance “forbidden” reflections can exist in the resonant atomic factor. As examples, crystals of potassium dihydrophosphate (KDP) and rubidium dihydrophosphate (RDP) are used to calculate such a contribution to the atomic factor of potassium and rubidium, and the last is compared to the thermally induced and dipole-quadrupole contributions to the atomic factor.     

Kinetics of oxidation of β-picoline to nicotinic acid over vanadia-titania catalyst. 4. Kinetic model

A kinetic model for the β-picoline oxidation over vanadia-titania catalyst is presented. The model covers the reaction mechanism, temperature dependences and a system of kinetic equations. The activation energies and constants in these equations are calculated.     

Multicomponent sonochemical synthesis of podands

An efficient sonochemical methodology is described for the synthesis of new podands containing substituted dihydropyrimidines.