The study of the crystalline phosphates of kosnarite type structure containing different alkali metals

The incorporation possibilities of different alkali elements into crystalline phosphates A_1−xA′_xHf₂(PO₄)₃ (A=Li, Na, K, Rb, Cs) were studied, the formation regions of kosnarite solid solutions were determined. Na_0.5K_0.5Hf₂(PO₄)₃ crystal structure was studied by powder X-ray diffraction, and the distribution of alkali metals in kosnarite structure was found out. The phosphate crystallizes in the space group R3?c, with a=8.7295(1) Å, c=23.2023(4) Å, V=1531.24(4) Å³, Z=6; R_wp=6.15, R_p=4.43. The concentration region knowledge of the kosnarite phase existence and peculiarities of their phase formation in the A_1−xA′_xM₂(PO₄)₃ (M=Ti, Zr, Hf) systems allow us to choose phosphate matrice compositions suitable for solidification of reprocessing wastes of spent U-Pu nuclear fuels.     

Asymptotic theory of the asymmetry parameters of a weak shock wave

A theory of the asymmetry parameters of a weak shock wave in a binary gas mixture, based on the expansion of the solutions of the Burnett equations in series in a small parameter of the shock wave intensity, that ensures the asymptotic accuracy of the required data, is given. The dependence of the solution on the characteristics of the mixture is examined. The known results for a polyatomic gas are refined and supplemented.     

Chaos and order in stateless societies: Intercommunity exchange as a factor impacting the population dynamical patterns

The once abstract notions of dynamical chaos now appear naturally in various systems [Kaplan D, Glass L. Understanding nonlinear dynamics. New York: Springer; 1995]. As a result, future trajectories of the systems may be difficult to predict. In this paper, we demonstrate the appearance of chaotic dynamics in model human communities, which consist of producers of agricultural product and producers of agricultural equipment. In the case of a solitary community, the horizon of predictability of the human population dynamics is shown to be dependent on both intrinsic instability of the dynamics and the chaotic attractor sizes. Since a separate community is usually a part of a larger commonality, we study the dynamics of social systems consisting of two interacting communities. We show that intercommunity barter can lead to stabilization of the dynamics in one of the communities, which implies persistence of stable equilibrium under changes of the maximum value of the human population growth rate. However, in the neighboring community, the equilibrium turns into a stable limit cycle as the maximum value of the human population growth rate increases. Following an increase in the maximum value of the human population growth rate leads to period-doubling bifurcations resulting in chaotic dynamics. The horizon of predictability of the chaotic oscillations is found to be limited by 5 years. We demonstrate that the intercommunity interaction can lead to the appearance of long-period harmonics in the chaotic time series. The period of the harmonics is of order 100 and 1000 years. Hence the long-period changes in the population size may be considered as an intrinsic feature of the human population dynamics.     

Mössbauer study of tektites

Room temperature ⁵⁷Fe Mössbauer spectroscopy has been used to investigate the structural and oxidation state of Fe in tektites from different strewn fields. Spectra have been analyzed in terms of two quadrupole splitting distributions corresponding to Fe^3?+? and Fe^2?+?. All tektites show similar distribution of quadrupole splitting. Each distribution has one peak. The Fe^2?+? sites show a narrow region of Mössbauer line shift (δ) and quadrupole splitting (ε), δ?= 1.02–1.10 mm/s and ε?= 0.85–1.00 mm/s relative to α-Fe. These values have been assigned to intermediate coordination between tetrahedral and octahedral. The Fe^3?+? sites show wider regions of hyperfine parameters: δ?= 0.25–0.45 mm/s and ε?= 0.65–0.90 mm/s. The Fe^3?+?/Fe^2?+? ratio was found to be 0.05–0.15.     

Relation between the intensity of ir absorption bands of stretching vibrations of nitrogroups and their number in aromatic nitrocompounds

Yaroslavl' State University, 9 Matrosov Ave., Yaroslavl', 150023, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 62, No. 6, pp. 30–37, November–December, 1995.     

On the long‐range relativistic effects in the 15N NMR chemical shifts of halogenated azines

Long‐range β‐ and γ‐relativistic effects of halogens in ¹⁵N NMR chemical shifts of 20 halogenated azines (pyridines, pyrimidines, pyrazines, and 1,3,5‐triazines) are shown to be unessential for fluoro‐, chloro‐, and bromo‐derivatives (1–2 ppm in average). However, for iodocontaining compounds, β‐ and γ‐relativistic effects are important contributors to the accuracy of the ¹⁵N calculation. Taking into account long‐range relativistic effects slightly improves the agreement of calculation with experiment. Thus, mean average errors (MAE) of ¹⁵N NMR chemical shifts of the title compounds calculated at the non‐relativistic and full 4‐component relativistic levels in gas phase are accordingly 7.8 and 5.5 ppm for the range of about 150 ppm. Taking into account solvent effects within the polarizable continuum model scheme marginally improves agreement of computational results with experiment decreasing MAEs from 7.8 to 7.4 ppm and from 5.5 to 5.3 ppm at the non‐relativistic and relativistic levels, respectively. The best result (MAE: 5.3 ppm) is achieved at the 4‐component relativistic level using Keal and Tozer's KT3 functional used in combination with Dyall's relativistic basis set dyall.av3z with taking into account solvent effects within the polarizable continuum solvation model. The long‐range relativistic effects play a major role (of up to dozen of parts per million) in ¹⁵N NMR chemical shifts of halogenated nitrogen‐containing heterocycles, which is especially crucial for iodine derivatives. This effect should apparently be taken into account for practical purposes.     

Dipropadienyl telluride

Russian Chemical Bulletin -     

Structural trends of 77Se?1H spin–spin coupling constants and conformational behavior of 2‐substituted selenophenes

Experimental measurements and second‐order polarization propagator approach (SOPPA) calculations of ⁷⁷Se? ¹H spin–spin coupling constants together with theoretical energy‐based conformational analysis in the series of 2‐substituted selenophenes have been carried out. A new basis set optimized for the calculation of ⁷⁷Se? ¹H spin–spin coupling constants has been introduced by extending the aug‐cc‐pVTZ‐J basis for selenium. Most of the spin–spin coupling constants under study, especially vicinal ⁷⁷Se? ¹H couplings, demonstrated a remarkable stereochemical behavior with respect to the internal rotation of the substituent in the 2‐position of the selenophene ring, which is of major importance in the stereochemical studies of the related organoselenium compounds. Copyright © 2009 John Wiley & Sons, Ltd.