Characterization of the precipitates formed during the denitration of simulated HRLW

The denitration of several chemical compositions of simulated HRLW (highly radioactive liquid waste) was performed using formic acid as reducing agent. Precipitates formed during the denitration of simulated HRLW were analyzed using X-ray diffraction and⁵⁷Fe Mössbauer spectroscopy. Goethite and amorphous fraction were the principal phases in these precipitates. It was found that the chemical composition of simulated HRLW and the experimental conditions of denitration have more influence on the crystallinity and the particle size than on the phase composition of the precipitates. Thermal treatment of denitrated precipitates caused the solid state transformation of goethite+amorphous fraction into hematite. The values of hyperfine magnetic field (HMF) of hematite were decreased, thus indicating the substitution of Fe³⁺ ions with other metal cations.     

Diagonalization of the spin part of the exchange hamiltonian in the second-quantization method for composite particles

Using the atomic second-quantization procedure an explicit expression is derived for the operator of exchange interaction between two atoms a and b in a state of any value of their atomic orbital and spin momenta, in the approximation of one and two pairs of exchanging electrons and without assuming the orthogonality between the orbitals of a and b. The obtained exchange interaction operator diagonalized in spin space is a second-order polynomial in the scalar product ?_a · ?_b. The coefficients of the polynomial are given operators operating in orbital space only. The possible physical implications are discussed.     

Preparation,structural and thermal characterization of cobalt(II) and copper(II) complexes with 3-hydroxypicolinamide

Cobalt(II) and copper(II) complexes of 3-hydroxypicolinamide (3-OHpia), namely [Co(3-OHpia)₂(H₂O)₂](NO₃)₂ (1), [Co(3-Opia)₂(H₂O)₂] (2) and [Cu(3-OHpia)₂(NO₃)₂] (3), were prepared and characterized by IR spectroscopy and TG/DTA methods. The molecular and crystal structures of 1 and 3 were determined by X-ray crystal structure analysis. Complexes 1 and 3 were obtained by reaction of 3-hydroxypicolinamide with cobalt(II) nitrate or copper(II) nitrate, respectively, in a mixture of ethanol and water. Complex 2 was prepared by reaction of cobalt(II) acetate and 3-OHpia in aqueous solution. X-ray structural analysis revealed octahedral coordination polyhedra in both 1 and 3 and the same N,O-chelated coordination mode of 3-OHpia. The coordination sphere of the cobalt(II) center in 1 is completed by two coordinated water ligands and that of the copper(II) center in 3 by two coordinated nitrate anions. There are also two uncoordinated nitrate ions in 1 which compensate the positive charge of cobalt(II). The crystal structures of 1 and 3 are dominated by intermolecular O–H···O and N–H···O hydrogen bonds. The thermogravimetric study indicated the loss of two coordinated water molecules in 1 and 2 and of one 3-OHpia ligand together with N₂ molecule in 3 at lower temperatures (up to 300 °C).     

A geometric analysis of front propagation in a family of degenerate reaction-diffusion equations with cutoff

We investigate the effects of a Heaviside cutoff on the dynamics of traveling fronts in a family of scalar reaction-diffusion equations with degenerate polynomial potential that includes the classical Zeldovich equation. We prove the existence and uniqueness of front solutions in the presence of the cutoff, and we derive the leading-order asymptotics of the corresponding propagation speed in terms of the cutoff parameter. For the Zeldovich equation, an explicit solution to the equation without cutoff is known, which allows us to calculate higher-order terms in the resulting expansion for the front speed; in particular, we prove the occurrence of logarithmic (switchback) terms in that case. Our analysis relies on geometric methods from dynamical systems theory and, in particular, on the desingularization technique known as ‘blow-up.’     

Exact Markov-Type Inequalities for Oscillating Perfect Splines

We prove the inequality for each perfect spline s of degree r with n-r knots and n zeros in [-1,1] . Here T _rn is the Tchebycheff perfect spline of degree r with n-r knots, normalized by the condition ||T _rn || _C[-1,1] := max  _{-1≤ x ≤ 1} |T _rn (x)| =1 . The constant ||T _rn ^(k) || _Lp[-1,1] in the above inequality is the best possible. June 8, 1999. Date revised: May 31, 2000. Date accepted: January 16, 2001.     

Evaluation of surface potential from single crystal electrode potential

The new method of evaluation of the point of zero potential for the metal oxide exhibiting a saddle-like surface potential function Ψ ₀(pH), as obtained by acid base potentiometric titration using Single Crystal Electrode, was proposed. The electrode potential of sapphire single crystal electrode (A crystal plane, $11\bar{2}0$ ) was measured, point of zero potential and surface potentials were evaluated, and the results were analyzed using the Surface Complexation Model. The electroneutrality point corresponding to the point of zero potential was found to be at pH_pzp=7.0. Thermodynamic protonation equilibrium constants for the first and the second step of protonation were obtained as $\lg K_{1}^{\circ} = 12.7$ ; $\lg K_{2}^{\circ} = 1.2$ .     

Influence of the pH on the Formation of the Catanionic n-Tetradecylammonium Cholate Surfactant Salt

The catanionic n-tetradecylammonium cholates, with the 1:1 and 1:2 cationic:anionic surfactant molar ratio, have been synthesized by reaction of tetradecylammonium chloride and sodium cholate. The stoichiometry of the compounds formed is strongly dependent on pH of the aqueous reaction solution. In the neutral and slightly acidic medium the isolated surfactant was detected as 1:1, at acidic medium (pH ≈ 3) as 1:2, while the cholic acid alone precipitated from the strong acidic solution (pH ≈ 2). The catanionic surfactants have been characterized by elemental and spectroscopic (IR, ¹H, and ¹³C NMR) analyses, and microscopic observations. The mole fractions of individual components in precipitate present in the heterogeneous aqueous system have been determined as a function of pH. The data interpretation in the pH regions where two different kinds of precipitates coexist pointed to the complex equilibrium in the examined systems. The evaluation of the relevant equilibrium constants was solved by the nonlinear regression analysis. In the acidic region where cholic acid and 1:2 precipitate coexisted the equilibrium constants of dissolution were K ₁ = 8.4 × 10^?10 and K ₄ = 3.7 × 10^?27, respectively. In the region where 1:2 and 1:1 precipitate coexisted the equilibrium constant of dissolution of 1:1 tetradecylammonium cholate was K ₂ = 4.2 × 10^?20.