Formulas and numerical table for the radial part of overlap integrals with the same screening parameters of Slater-type orbitals

 The numerical properties of the radial part of overlap integrals with the same screening parameters in the form of polynomials in p = ξR over Slater-type orbitals have been studied and obtained by using three different methods. For that purpose, the characteristics of auxiliary functions were used first, then Fourier transform convolution theorem, and recurrence relations for the basic coefficients of A ^s _{n l λ, n ′ l ′λ} were used. The calculations of the radial part of overlap integrals with the same screening parameters were made in the range 1 ≤ n ≤ 75, 1 ≤ n′ ≤ 75, and 10⁻⁶ ≤ p. Received: 18 January 2001 / Accepted: 5 April 2001 / Published online: 27 June 2001     

Crystal Structures of Na3PO2S2 · 11H2O and Na3POS3 · 11H2O

Summary.  Single crystals of sodium dithiophosphate undecahydrate (Na₃PO₂S₂ · 11H₂O) and sodium trithiophosphate undecahydrate (Na₃POS₃ · 11H₂O) were grown from aqueous solution. The crystal structures of Na₃PO₂S₂ · 11H₂O (P2₁2₁2₁; a = 1248.1(1), b = 945.2(1), c = 1383.1(1) pm; R ₁ = 0.0202, wR ₂ = 0.0502) and Na₃POS₃ · 11H₂O (Pna2₁; a = 1262.0(2), b = 947.6(2), c = 1431.5(2) pm; R ₁ = 0.0720, wR ₂ = 0.1371) are related to each other in a sense that all constituting units are arranged in similar positions and with similar orientations. The geometries of the anions were determined with high accuracy; thus, the structural parameters of the POS³⁻ ₃ anion were measured for the first time. Received September 25, 2001. Accepted January 21, 2002     

Reactivity of C<Subscript>3</Subscript>-C<Subscript>8</Subscript> alkanes with nitronium ions in sulfuric acid

We have determined the parameters of the Arrhenius equation (E, log A) for reactions between \textNO₂⁺ {\text{NO}}_2^{+} ions and C₃-C₈ alkanes in HNO₃–93 wt.% H₂SO₄ solutions at 277–353 K, and we have also estimated the activation parameters E _j , log A _j for secondary and tertiary C—H bonds of these alkanes. We show that the following compensation relations are satisfied: E = 2.3R βlog A + C with isokinetic temperature β = 360 ± 65 K, and also E _j =2.3Rβ _j log A _j  + C _j , for secondary C—H bonds, β₂ =300 ± 60, and for tertiary C—H bonds, β₃ =310 ± 50.     

High-frequency dielectric permittivity of water and its components

The values of electron polarizability of water molecules in a medium and the values of water deformational dielectric permittivity (ɛ_∞) and its components (electron (n _v), nuclear (Δn _nuc), and vibrational intermolecular (Δn _inter)) are calculated. It is shown that T → T _cr, ɛ_∞^inter and Δn _inter approach zero, while Δn _nuc in the range (T _melt − T _cr) has a maximum located at around T = 0.785T _cr.     

Ionic conduction of lithium for Perovskite-type compounds, Li x La(1− x )/3NbO3 and (Li0.25La0.25)1− x Sr0.5 x NbO3

Perovskite-type compounds, Li _x La_{(1− x )/3}NbO₃ and (Li_0.25La_0.25)_{1− x} Sr_{0.5 x} NbO₃ as lithium ionic conductors, were synthesized by a solid-state reaction. From powder X-ray diffraction, the solid solution ranges of the two compounds were determined to be 0≤x≤0.25 and 0≤x≤0.125, respectively. In the Li _x La_{(1− x )/3}NbO₃ system, the ionic conductivity of lithium at room temperature, σ₂₅, exhibited a maximum value of 4.7 × 10⁻⁵ S · cm⁻¹ at x = 0.10. However, because of the decrease in the lattice parameters with increasing Li concentration x˙, σ₂₅ of the samples decreased with increasing x from 0.10 to 0.25. Also, in the (Li_0.25La_0.25)_{1− x} Sr_{0.5 x} NbO₃ system, the lattice parameter increased with the increase of Sr concentration and the σ₂₅ achieved a maximum (7.3 × 10⁻⁵ S · cm⁻¹ at 25 °C) at x = 0.125. Received: 12 September 1997 / Accepted: 15 November 1997     

Quasielastic light scattering study of chemically crosslinked gelatin solutions and gels

Quasielastic light scattering measurements are reported for experiments performed on mixtures of gelatin and glutaraldehyde (GA) in the aqueous phase, where the gelatin concentration was fixed at 5 (w/v) and the GA concentration was varied from 1×10⁻⁵ to 1×10⁻³ (w/v). The dynamic structure factor, S(q,t), was deduced from the measured intensity autocorrelation function, g ₂(τ), with appropriate allowance for heterodyning detection in the gel phase. The S(q,t) data could be fitted to S(q,t)=Aexp(−D _f q ² t)+Bexp(−t/τ_c)^β, both in the sol (50 and 60 ^∘C) and gel states (25 and 40 ^∘C). The fast-mode diffusion coefficient, D _f showed almost negligible dependence on the concentration of the crosslinker GA; however, the resultant mesh size, ξ, of the crosslinked network exhibited strong temperature dependence, ξ∼(0.5−χ)^1/5exp(−A/RT) implying shrinkage of the network as the gel phase was approached. The slow-mode relaxation was characterized by the stretched exponential factor exp(−t/τ_c)^β. β was found to be independent of GA concentration but strongly dependent on the temperature as β=β₀+β₁ T+β₂ T ². The slow-mode relaxation time, τ_c, exhibited a maximum GA concentration dependence in the gel phase and at a given temperature we found τ_c(c)=τ₀+τ₁ c+τ₂ c ². Our results agree with the predictions of the Zimm model in the gel case but differ significantly for the sol state. Received: 25 May 1999 /Accepted in revised form: 27 July 1999     

Development of a non-invasive method for the determination of the macroscopic neutron cross sections of a sample matrix in large-sample prompt-gamma neutron activation analysis

In order to correct for neutron self-shielding in large-sample prompt gamma NAA, a method has been developed to determine the macroscopic scattering and absorption cross sections, i.e., Σ _a and Σ _s, using four Cu flux monitors placed around the sample. With Monte Carlo computations, the neutron densities throughout the sample and the resulting and the corresponding self-shielding factor as calculated from the Σ _a and Σ _s as obtained through the Cu monitors were compared to the true values. The derived Σ _a and Σ _s were found to be sufficiently accurate as long as Σ _t = Σ _a + Σ _s was less than 0.6 cm⁻¹ and Σ _s/Σ _t was greater than 0.1.     

Electronic absorption spectra of charge-transfer complexes and effects of substituents in radical cations

The effects of X substituents on the energies of charge-transfer bandshv _CT in electronic absorption spectra of charge-transfer complexes of π-, n-, or σ-donors (DX) with π- or σ-acceptors (A) as well as on the ionization potentialsI _D of individual DX molecules are described by the equationhv _CT(l _D)=a +bσ₁ +cσ _R ⁺ +dσ_α. When DX and A are fixed, the inductive (bσ₁), resonance (cσ _R ⁺ ), and polarization (dσ_α) contributions tohv _CT andI _D are virtually identical. The electronic structure of the D^.+X donor component of the compact [A^.−, D^.+X] radical-ionic pair in a solution is similar to that of the radical cation generated upon photoionization of the individual DX molecule in the gaseous phase. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1002–1006, June, 2000.     

Thermodynamic properties of molybdenum-transition metal-hydrogen (nitrogen) solid solutions

Using the experimental values ΔH _H^exc and ΔS _H^exc (ΔH _N^exc and ΔS _N^exc) for solid solutions of hydrogen and nitrogen in molybdenum, we calculate the parameters ɛ_H^Mand ɛ_N^M of interaction between hydrogen (nitrogen) and molybdenum lattice doped with small additives of transition metals M; the values of the activity coefficients on hydrogen and nitrogen γ_H^M and γ_N^M, ΔH _H, ΔH _N, ΔS _H, ΔS _N; enthalpy (η_H^M and η_N^M) and entropy (σ_H^M and σ_N^M) parameters of interaction over the 1100–1300 K range for alloys of Mo_{1 − y} M _y H _x and Mo_{1 − y} M _y N _x types (y = 0.01 and 0.02; x = 0.01 and 0.02).     

Mixed conductivity and stability of A-site-deficient Sr(Fe,Ti)O<Subscript>3–δ</Subscript> perovskites

Deficiency in the A sublattice of perovskite-type Sr_{1– y} Fe_0.8Ti_0.2O_3–δ (y=0–0.06) leads to suppression of oxygen-vacancy ordering and to increasing oxygen ionic conductivity, unit cell volume, thermal expansion, and stability in CO₂-containing atmospheres. The total electrical conductivity, predominantly p-type electronic in air, decreases with increasing A-site deficiency at 300–700 K and is essentially independent of the cation vacancy concentration at higher temperatures. Oxygen ion transference numbers for Sr_{1– y} Fe_0.8Ti_0.2O_3–δ in air, estimated from the faradaic efficiency and oxygen permeation data, vary in the range from 0.002 to 0.015 at 1073–1223 K, increasing with temperature. The maximum ionic conductivity was observed for Sr_0.97Fe_0.8Ti_0.2O_3–δ ceramics. In the system Sr_0.97Fe_{1– x} Ti _x O_3–δ (x=0.1–0.6), thermal expansion and electron-hole conductivity both decrease with x. Moderate additions of titanium (up to 20%) in Sr_0.97(Fe,Ti)O_3–δ result in higher ionic conductivity and lower activation energy for ionic transport, owing to disordering in the oxygen sublattice; further doping decreases the ionic conduction. It was shown that time degradation of the oxygen permeability, characteristic of Sr(Fe,Ti)O_3–δ membranes and resulting from partial ordering processes, can be reduced by cycling of the oxygen pressure at the membrane permeate side. Thermal expansion coefficients of Sr_{1– y} Ti_{1– x} Fe _x O_3–δ (x=0.10–0.60, y=0–0.06) in air are in the range (11.7–16.5)×10^–6 K^–1 at 350–750 K and (16.6–31.1)×10^–6 K^–1 at 750–1050 K. Electronic Publication     

Small-angle neutron-scattering study of bis(quaternaryammonium bromide) surfactant micelles in water. Effect of the long spacer chain on micellar structure

The microstructure of the normal micelles formed by dimeric surfactants with long spacers, [Br⁻(CH₃)₂N⁺(C _m H_{2 m +1})-(CH₂) _S  -(C _m H_{2 m +1})N⁺(CH₃)₂Br⁻, m = 10 and s = 8, 10 and 12], has been investigated by small-angle neutron scattering and compared with previously reported results for micelles of the same dimeric surfactants with shorter spacers (m = 10 and s = 2, 3, 4 and 6). It was found that for dimeric surfactants with long spacers (s = 8 and 10), both micellar growth and variation in shape occur to only a small extent, if at all, compared with dimeric surfactants with short spacers. However, for the dimeric surfactant with the longest spacer, s = 12, the extent of micellar growth and shape variation is also large. These results are due to the differences in conformation of dimeric surfactants with short spacers (s = 2–6) compared with that of the surfactants with long spacers (s = 8–12). Received: 15 June 1998 Accepted: 22 July 1998     

Thermophysical Investigations of the Polymorphous Phases of Calcium Carbonate

1. Results of thermodynamic and kinetic investigations for the different crystalline calcium carbonate phases and their phase transition data are reported and summarized (vaterite: V; aragonite: A; calcite: C). A→C: T _tr=455±10°C, Δ_tr H=403±8 J mol^–1 at T _tr, V→C: T _tr=320–460°C, depending on the way of preparation,Δ_tr H=–3.2±0.1 kJ mol^–1 at T _tr,Δ_tr H=–3.4±0.9 kJ mol^–1 at 40°C, S _V ^Θ= 93.6±0.5 J (K mol)^–1, A→C: E _A=370±10 kJ mol^–1; XRD only, V→C: E _A=250±10 kJ mol^–1; thermally activated, iso- and non-isothermal, XRD 2. Preliminary results on the preparation and investigation of inhibitor-free non-crystalline calcium carbonate (NCC) are presented. NCC→C: T _tr=276±10°C,Δ_tr H=–15.0±3 kJ mol^–1 at T _tr, T _tr – transition temperature, Δ_tr H – transition enthalpy, S ^Θ – standard entropy, E _A – activation energy. 3. Biologically formed internal shell of Sepia officinalis seems to be composed of ca 96% aragonite and 4% non-crystalline calcium carbonate. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Thermal Dehydration of Magnesium Aluminum Pentafluoride Dihydrate: Crystal Structures of MgAlF5(H2O)2 and MgAlF5

Summary.  Small plate-like single crystals of MgAlF₅(H₂O)₂ have been obtained during hydrothermal treatment (270°C) of microcrystalline material prepared by precipitation of stoichiometric solutions of Al₂(SO₄)₃ ·  18H₂O and Mg(NO₃)₂ · 6H₂O with diluted hydrofluoric acid. The crystal structure of MgAlF₅(H₂O)₂ has been refined from single crystal data (Imma (# 74), Z = 4, a = 7.0637(7), b = 10.1308(10), c = 6.7745(7) ?, 398 structure factors, 33 parameters, R(F² > σ(F ²)) = 0.0245, wR(F² all) = 0.0525). Main features of the inverse weberite type structure are infinite chains of trans-bridged [AlF₆] octahedra which are connected via common fluorine atoms by isolated [MgF₄(H₂O)₂] octahedra. MgAlF₅(H₂O)₂ dehydrates at temperatures above 300°C to give MgAlF₅. XRPD analysis of this phase has revealed isotypism with FeAlF₅. The crystal structure of MgAlF₅ (Immm (# 71), Z = 2, a = 7.268(1), b = 6.123(2), c = 3.543(1) ?) is built of infinite chains of edge-sharing [MgF₆] octahedra and chains of corner-sharing [AlF₆] octahedra along [001]. Upon further heating to temperatures above 500°C, MgAlF₅ decomposes to MgF₂ and α − AlF₃. Received January 15, 2001. Accepted February 12, 2001     

A short review and an empirical method for estimating the absorbed enthalpy of formation and the absolute enthalpy of dried microbial biomass for use in studies on the thermodynamics of microbial growth

Calculations are made using the equations Δ_r G = Δ_r H − TΔ_r S and Δ_r X = Δ_r H − Δ_r Q where Δ_r X represents the free energy change when the exchange of absorbed thermal energy with the environment is represented by Δ_r Q. The symbol Q has traditionally represented absorbed heat. However, here it is used specifically to represent the enthalpy listed in tabulations of thermodynamic properties as (H _T  − H ₀) at T = 298.15 K, the reason being that for a given substance TS equals 2.0 Q for solid substances, with the difference being greater for liquids, and especially gases. Since Δ_r H can be measured, and is tangibly the same no matter what thermodynamics are used to describe a reaction equation, a change in the absorbed heat of a biochemical growth process system as represented by either Δ_r Q or TΔ_r S would be expected to result in a different calculated value for the free energy change. Calculations of changes in thermodynamic properties are made which accompany anabolism; the formation of anabolic, organic by-products; catabolism; metabolism; and their respective non-conservative reactions; for the growth of Saccharomyces cerevisiae using four growth process systems. The result is that there is only about a 1% difference in the average quantity of free energy conserved during growth using either Eq. 1 or 2. This is because although values of TΔ_r S and Δ_r Q can be markedly different when compared to one another, these differences are small when compared to the value for Δ_r G or Δ_r X.     

Phenomenological theory of the kinetics of ultrasonic emulsification

Summary A working model is given for the rate of ultrasonic emulsification, considering the dispersion at the interface (areaA) and the coagulations in the volumeV of the emulsion. A bimolecular coagulation leads to the equationc=c _∞tanhbt;c _∞=(Aα/Vβ)^1/2;b=(Aαβ/V)^1/2 while a monomolecular coagulation givesc=c _∞{1−exp (−at)};c _∞=Aα/Vβ;a=β. The experiments on the dependence of c_∞,a andb uponA andV favour the bimolecular coagulation. The results are satisfactorily explained on general theoretical grounds.

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Zusammenfassung Ein Arbeitsmodell für die Geschwindigkeit der Ultraschallemulgierung wird entwickelt, das Dispersion in der Grenzfl?che (Fl?cheA) und Koagulation im Volumen (V) der Emulsion annimmt. Eine bimolekulare Koagulation führt zu der Gleichung:c=c _∞ tanhbt;c _∞=(Aα/Vβ)^1/2;b=(Aαβ/V)^1/2, eine monomolekulare dagegen zu:c=c _∞{1−exp (at−)};c _∞=Aα/Vβ;α=β. Die Versuche über die Abh?ngigkeit vonc _∞,a undb vonA undV scheinen für bimolekulare Koagulation zu sprechen. Die Ergebnisse werden auf der Basis dieser einfachen theoretischen Grundlagen befriedigend erkl?rt.

     

A note on overpotential dependence of AC impedance data

Charge-transfer resistance [R _ct = (dη/di)_{η = 0}] and Tafel plots of current density (i) versus overpotential (η) data are generally known to yield values of the energy-transfer coefficient (α) and exchange current density (i _o) of an electrochemical reaction. In the present investigation, the resistance (dη/di)_η≠0 that could be calculated by differentiating a wide range of i−η curves was also shown to provide the values of α and i _o, by plotting ln(dη/di)_η≠0 against η. Since α and i _o could also be evaluated directly from the experimental DC polarization data, the procedure was not of significant importance. Nevertheless, it was considered important in evaluating α and i _o from AC impedance data, because the procedure was based on data analysis, which was much simpler than that reported in the literature. A cobalt electrode prepared from fine metal powder was used in 1 M KOH electrolyte and the hydrogen evolution reaction was studied by AC impedance at several potentials. The resistance values measured from the complex plane impedance diagram were plotted against the potential, and the values of α and i _o were evaluated. Received: 8 October 1998 / Accepted: 11 January 1999     

Steric effects on the singlet-triplet energy gaps of five-membered ring R<Subscript>2</Subscript>C<Subscript>4</Subscript>H<Subscript>2</Subscript>M

Thermal internal energy gaps, ΔE _s−t; enthalpy gaps, ΔH _s−t; Gibbs free energy gaps, ΔD _s−t, between singlet (s) and triplet (t) states of R₂C₄H₂M (M = C, Si, and Ge) were calculated at B3LYP/6-311++G** level of theory. The ΔG _s−t of R₂C₄H₂C was increased in the order (in kcal/mol): R = −CH₃ (−10.51) > −H (−9.59) > i-Pr (−9.51) > t-Bu (−8.98). While, the ΔG _s−t of R₂C₄H₂Si and R₂C₄H₂Ge were increased in the order (in kcal/mol): −CH₃ (17.01) > i-Pr (15.30) > −H (15.26) > t-Bu (14.35) and -H (22.79) > −CH₃ (22.69) > i-Pr (21.66) > t-Bu (21.01), respectively.     

Synthesis and Reactivity of Stannyloligosilanes IV [1]: From Hydrido Substituted Stannasilanes Towards Stannasiloxanes

Summary.  Hydrido substituted stannasilanes of the type or (Z = H, Me, Ph; R, R′ = alkyl, Ph) are accessible by reaction of either alkali metal stannides (MSn(Z)R ₂; M = Li, Na) with halogen substituted silanes (; X = F, Cl) or chlorostannanes (R ₂SnCl₂, Ph₃SnCl) and fluorosilanes in the presence of magnesium. Stannasilanes with halogen substituents at the silicon as well as the tin atom are formed by treatment of the hydrido substituted stannasilanes with CHCl₃ or CCl₄. The hydrido substituted stannasilanes decompose in contact with air to distannanes and siloxanes or to the linear ( ^t Bu₂Sn(–O– ^t Bu₂Si–OH)₂) and cyclic ((– ^t Bu₂Sn–O– ⁱ Pr₂Si–O–)₂) stannasiloxanes. Received November 29, 2001. Accepted (revised) January 16, 2002     

Effect of oxygen nonstoichiometry on kinetics of oxygen exchange and diffusion in lanthanum-strontium cobaltites

The method of isotopic exchange was used to study the kinetics of oxygen exchange and diffusion in complex oxides of La_{1 − x} Sr _x Co_{1 − y} Fe _y O_{3 − δ} (x = 0.0, y = 0.0; x = 0.6, y = 0.2, 0.4). The rates of oxygen interfacial exchange and its diffusion coefficient were determined for LaCoO_{3 − δ} at the pressure of 5 torr in the temperature range of 600–850°C and at the temperature of 700°C in the pressure range of 1–70 torr. The contributions of the three exchange types were calculated. The order of the dependence of the interfacial exchange rate on the oxygen pressure was 0.51 ± 0.01. In the case of La_0.4Sr_0.6Co_{1 − y} Fe _y O_{3 − δ} (y = 0.2, 0.4) in the temperature range of 600–900°C at the oxygen pressure of 10 torr, the oxygen exchange rates and diffusion coefficients were determined in the material bulk and in the subsurface region; contributions of the three types of exchange were calculated. The paper considers the mechanism of oxygen exchange and diffusion as compared to nonstoichiometry in the oxygen sublattice of the La_{1 − x} Sr _x Co_{1 − y} Fe _y O_{3 − δ} oxides.     

Recombination of tert-butyl radicals: the role of weak van der Waals interactions

A mechanism for the recombination of tert-butyl radicals is postulated to involve the loosely bonded intermediates tert-C₄H₉⋯tert-C₄H₉. Three processes contribute to the overall recombination rate constant: tert-C₄H₉+ tert-C₄H ⇆ tert-C₄H₉⋯tert-C₄H₉ characterized by the equilibrium constant K ₁ and tert-C₄H₉⋯tert-C₄H₉ → C₈H₁₈* characterized by the rate constant k ₂, k _rec,∞(T) ≈ K ₁ k ₂. This recombination rate constant exhibits a negative temperature dependence and is proportional to T ^−3/2. The agreement with experiment is very good. Received: 2 October 2000 / Accepted: 2 May 2002 / Published online: 7 August 2002