On a free group of transformations defined by an automaton

We prove that three automorphisms of the rooted binary tree defined by a certain 3-state automaton generate a free non-Abelian group of rank 3. Both authors are supported by the NSF grants DMS-0308985 and DMS-0456185. Yaroslav Vorobets is supported by a Clay Research Scholarship.     

RE3Ga9Ge (RE=Y, Ce, Sm, Gd and Yb): compounds with an open three-dimensional polygallide framework synthesized from liquid gallium

The RE₃Ga₉Ge compounds (RE=Y, Ce, Sm, Gd and Yb) were synthesized at 850°C in quantitative yield from reactions containing excess liquid Ga. The orthorhombic crystal structure is characterized by a unique three-dimensional open Ga framework with parallel straight tunnels. In the tunnels, inserted are arrays of the RE atoms together with interpenetrated monoatomic RE-Ga-Ge planes. A complex disordered arrangement of the RE and Ga atoms is observed in the monoatomic plane. Depending on the extent of disorder, the crystal structure could be presented either in a sub-cell (no ordering) or in a super-cell (partial ordering). Single-crystal X-ray data for Ce₃Ga₉Ge sub-structure: space group Immm, Z=2, cell parameters a=4.3400(12) Å; b=10.836(3) Å; and c=11.545(3) Å; super-structure: space group Cmma, Z=8, cell parameters a=8.680(3) Å; b=23.090(7) Å; and c=10.836(3) Å. The refinement based on the full-matrix least squares on F_o²[I>2σ(I)] converged to final residuals R₁/wR₂=0.0226/0.0528 and 0.0729/0.1569 for the sub- and super-structures, respectively. The relationship between the disordered sub-structure and partially ordered super-structure is discussed. Magnetic susceptibility measurements show Curie-Weiss behavior at the temperatures above 30 K with the negative Weiss constants Θ=−49(1) and−7.7 K for Gd and Ce analogs, respectively. An antiferromagnetic transition is observed in the Gd analog at T_N=26.1 K. The μ_eff obtained for both analogs is close to the RE³⁺ free-ion value.     

Polyparaxylylene-CdS nanocomposite films: Optical spectra, photoluminescence, and surface topography

For polyparaxylylene-CdS nanocomposite films prepared by solid-phase cryochemical synthesis, the dependences of the optical absorption spectra, photoluminescence intensity, and surface topography on the CdS concentration were examined. It was revealed that the most significant changes, such as the shift of the position of the exciton absorption band by ～1 eV and the increase of the surface roughness (the magnitude of variation of heights h _max ? h _min along a surface profile) occur within a CdS concentration range of from ～5 to ～8 vol %. The average size of the nanoparticles was determined from the position of the exciton absorption maximum: 2R _np ? ? 3 nm at c ≤ 5 vol % and 2R _np ≥ 5?7 nm at c ≥ 10 vol %. The formation of 3-nm particles at low CdS concentrations was confirmed by the existence of exciton photoluminescence with maximum at 370 nm. Exciton luminescence was not observed at c ≥ 10 vol %. By contrast, at all c values, photoluminescence with maxima at ～520 and ～570 nm, which is usually assigned to interstitial S and Cd atoms, correspondingly, and a the weak emission of unknown nature with a maximum at 545 nm were observed.     

Determination of thermodynamic functions of sorption for cyclohexyl-, piperidyl-, morpholyl-, and thiomorpholyl-n-alkanes by capillary gas-liquid chromatography

The values of partial molar free energy (G), enthalpy (H), and entropy (S) of sorption in the homologous series ofN-alkylpiperidines,N-alkylmorpholines,N-alkyl thiomorpholines, and alkylcyclohexanes were determined. It was found that the free energy of sorption is determined to a greater extent by the enthalpy term than by the entropy one. The free energy of sorption of the first homolog decreases when then-alkyl chain is attached directly to the carbon atom of the cycle and increases in the case ofN-alkylsubstituted heterocycles. The influence of the heteroatom nature on intermolecular interactions of homologs with the nonpolar stationary phase was quantitatively estimated on the basis of thermodynamic data.Dead time necessary for calculation of the retention factor was determined by the retention of methane injected into the column simultaneously with the sample.Translated from Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 2030–2032, August, 1996.     

Chemical bond in alkali metal sulfates

In the context of the density functional theory of the local electron density the valence and differential density distribution in crystalline sulfates of M₂SO₄ (M is Li, Rb, and Cs) and double sulfates of MLiSO₄ were calculated using the pseudopotential method in the basis set of numerical atomic pseudo-orbitals. It is shown that in lithium sulfate crystallographically inequivalent oxygen atoms are in different charge states and have a different force of chemical bonding with sulfur. Anions are bonded to each other through lithium atoms that form tetrahedral complexes with oxygen. In rubidium sulfates the electron clouds of the anions overlap and chain structures form. Chemical bonding between the anion and the cation has an ionic nature. These features of the electron structure manifest themselves in double sulfates, where LiO₄ complexes that link the anionic chains also form, and heavy metals serve as cations.     

Determination of gold in geological samples by x-ray fluorescence spectrometry after extraction with tributyl phosphate

The behaviour of gold and elements impeding its x-ray fluorescence spectrometric (XRF) determination, namely zinc, lead and arsenic, was studied during their extraction from hydrochloric acid, nitric acid, and aqua regia solutions using tributyl phosphate as a solid extractant [SE(TBP)]. Extraction of gold from pulps after aqua regia leaching was found to be the most favourable approach for the quantitative and selective recovery of gold. The gold distribution ratio, D_Au, is ca. 10⁴ ml g^?1. For extraction from hydrochloric acid solutions the D_Au value also exceeds 10⁴ in the whole range of gold concentrations studied (10^?8?10^?4 M), but it decreases substantially with increasing extraction temperature, from 5 × 10⁵ ml g^?1 at 20°C to 9 × 10³ ml g^?1 at 70°C. An anomalously high distribution ratio of lead, D_Pb ≈ 10³ ml g^?1, was observed during extraction from hydrochloric solutions in the presence of chlorine. This could be explained by the formation of the chloro complexes of lead(IV). An XRF method for the determination of gold in natural samples was developed, which includes back-extraction of gold from SE(TBP) using a hot 0.025 M thiourea solution, providing a thin sample layer for secondary XRF. For 25 g of sample material the limit of determination is 10 ng g^?1 (10^?6%). The accuracy of the technique was checked using different reference materials. The results agreed within 10%.     

Calculation of the thermondynamic values of alkylthiazoles from the Kovats retention indices on the basis of the non-linear additivity principle

Summary Retention indices and their energy equivalents were determined for ten alkylthiazoles analysed on the stationary phases Apiezon L, Triton X-305 and Carbowax 1000. It was found that the energy contributions of identical alkyl groups to the partial molar free energy of sorption of a molecule are not equivalent. Smaller energy contribututions are due to the α-position of alkyl groups with respect to the heteroatoms in the thiazole ring (α-effect). This effect was most pronounced for 2-alkylthiazoles. Higher sorption energies were found for dimethylthiazoles with two methylgroups in a vicinal position. The retention indices were predicted for ten other di- and tri-substituted methyl, ethyl and propyl thiazoles on the basis of the so-called α- and ortho-effects. The predicted values are in good agreement with the experimentally determined values. Dedicated to Prof. Dr. E. sz. Kováts (Ecole Polytechnique Fédérale de Lausanne) on the occasion of his sixtieth birthday.