Secondary structure of crystals

Published experimental data on the dependence of the properties of crystal substances on crystal size are discussed. The dependence is of the same form for different properties and different crystal substances. When the crystal diminishes in size, its properties remain constant until the size decreases to 10⁻⁵–10⁻⁶ cm; smaller crystals considerably change their properties. It is shown that the currently available experimental data are sufficient to substantiate the notion of an “elementary unit of a solid crystal” (“crystal quantum”). The elementary unit of a crystal is regarded as a basis for the secondary structure (macrostructure) of a solid and an elementary carrier of its “crystal” properties. Due to this notion, we can interpret the vast experimental material on the real structures and properties of solids from a single viewpoint. Institute of Inorganic Chemistry, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 4, pp. 724–730, July–August, 1995. Translated by L. Smolina     

Anomalies of the partition coefficient and properties of crystals in the region of low concentrations of an isomorphous admixture. 1. Unusual decomposition of solid solutions of the NaCl—CdCl2 system

Solid solutions NaCl—CdCl₂ were studied in an interval of CdCl₂ concentrations of 0.05—3 mol.% by Raman spectroscopy. The molecular form Na₂CdCl₄ decomposes: Na₂CdCl₄ 2Na⁺ + Cd²⁺ + 2Cl₂ ^– + 2e^–; 2Na + 2e^– 2Na⁰. Free sodium atoms form color centers of crystal (F centers) in the region of jumpwise changing the partition coefficient of CdCl₂ in NaCl (K jump).     

Two-sided bounds for the volume of right-angled hyperbolic polyhedra

For a compact right-angled polyhedron R in Lobachevskii space ?³, let vol(R) denote its volume and vert(R), the number of its vertices. Upper and lower bounds for vol(R) were recently obtained by Atkinson in terms of vert(R). In constructing a two-parameter family of polyhedra, we show that the asymptotic upper bound 5v ₃/8, where v ₃ is the volume of the ideal regular tetrahedron in ?³, is a double limit point for the ratios vol(R)/ vert(R). Moreover, we improve the lower bound in the case vert(R) ≤ 56.     

Volumes of hyperbolic Löbell 3-manifolds

In 1931 F. Löbell constructed the first example of a closed orientable three-dimensional hyperbolic manifold. In the present paper we study properties of closed hyperbolic 3-manifolds generalizing Löbell's classical example. Explicit formulas for the volumes of these manifolds in terms of the Lobachevski function are obtained.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 17–23, July, 1998.This research was partially supported by GARC-KOSEF (Global Analysis Research Center of National Seoul University) and by the Russian Foundation for Basic Research under grant No. 95-01-01410.     

Absorption spectra of benzene-isooctane mixtures in the wavelength range 1620–1820 nm

Experimental absorption spectra of benzene, isooctane, and their mixtures are obtained in the wavelength range λ = 1620–1820 nm in which the first overtones of vibrational frequencies of CH, CH₂, and CH₃ hydrocarbon groups are located. Positions of fundamental absorption bands of benzene are refined. Absorption spectra of benzene-isooctane mixtures are shown to intersect in a narrow area near λ ≈ 1695 nm. The main maximum of benzene absorption at λ = 1671.5 ± 0.5 nm, where the influence of isooctane absorption is practically absent, is proposed for determining the content of benzene in benzene-isooctane mixtures. A linear calibration curve for λ = 1671.5 nm that encompasses the full range of benzene concentrations (0–100%) is presented. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 5, pp. 631–634, September–October, 2008.     

Surgery on Small Volume Hyperbolic 3-Orbifolds

Siberian Mathematical Journal -     

A Generalization of Fibonacci Groups

We study the class of cyclically presented groups which contain Fibonacci groups and Sieradski groups. Conditions are specified for these groups to be finite, pairwise isomorphic, or aspherical. As a partial answer to the question of Cavicchioli, Hegenbarth, and Repov, it is stated that there exists a wide subclass of groups with an odd number of generators cannot appear as fundamental groups of hyperbolic three-dimensional manifolds of finite volume.