Chr V. Christov

Thermodynamics of formation of carnallite type double salts

The solubility of the systems RbCl−MgCl2−H2O, RbBr−MgBr2−H2O and CsBr−MgBr2−H2O have been investigated by the physicochemical analysis method at 25°C and formation of carnallite type double salts was established. The Pitzer model is used to calculate the thermodynamic functions needed to plot the solubility isotherms of the systems. The results obtained are in good agreement with the experimental data. The free energies of formation of carnallite and bromcarnallite type double salts from simple salts and the standard molar energies of formation are estimated.

Investigation of the aqueous lithium and magnesium halide systems

The solubilities of the system LiBr−MgBr2−H2O have been investigated at 25°C and 50°C. It is established that the system is of a simple eutonic type. Pitzers model is used for calculating the thermodynamic functions needed for plotting the solubility isotherms of the systems LiX−MgX2−H2O (X=Cl, Br) at 25°C. According to calculations made, the Gibbs energy of formation of LiCl·MgCl2·7H2O from simple salts is ΔrG°m=−2.01 kJ-mol−1, while the value ΔfG°m=−2748 kJ-mol−1 corresponds to formation from the elements.

Effect of temperature on the solubility of carnallite type double salts

A method based on Pitzers model has been used for calculation of the solubilities of carnallite type double salts crystallizing in the systems MeX−MgX2−H2O (Me=Li, NH4, K, Rb, Cs; X=Cl, Br). The solubility of congruently soluble double salts was also determined experimentally at 25–75°C. The results from studies of the solubility diagrams of ternary carnallite type water-salt systems over a wide temperature range are summarized. It is found that the width of the crystallization region for each of the salts can be explained by the relative differences in the solubilities of the ternary solution components (MeX, MgX2·6H2O and MeX·MgX2·6H2O) and by a change of temperature, and by the effect of temperature on the solubility. A method is proposed for calculating Pitzers ternary parameters of interionic interaction (ΘMN and ΨMNX) on the basis of experimental data for the solubility in water of the double salts crystallizing in the corresponding ternary water-salt systems.

Calculation of the Gibbs energy of mixing in crystals using Pitzer's model

Pitzers model has been applied to the thermodynamic study at 25°C of a series of systems of the type MeX-Me′X-H2O, MeX-MeX′-H2O (where Me, Me′=K, NH4,Rb and Cs; X, X′=Cl, Br and I), MeSO4-Me′SO4-H2O (where Me, Me′=Mg, Ni, Zn and Co). The integral Gibbs energy of mixing Gmix and the excess Gibbs energy of mixing GE(s) are calculated, and simplified correlation equations are proposed for their calculation. The results obtained are compared with experimental data from the literature and with values calculated using various theories. The rational activity coefficients of the mixed crystal components are estimated. The energy of phase transition of one structure into another has been estimated for the isodimorphous mixed crystals in the system MgSO4−CoSO4−H2O.

Thermodynamic study of the aqueous rubidium and manganese bromide system

Crystallization of 2RbBr · MnBr2 · 2H2O, the only double salt obtained under standard conditions from saturated aqueous rubidium–manganese bromide solutions, was theoretically predicted using the “hard” and “soft” Lewis acids and bases concept and Paulings rules. The RbBr—MnBr2—H2O system was thermodynamically simulated by the Pitzer model assuming a solubility diagram of three branches only: RbBr, 2RbBr · MnBr2 · 2H2O and MnBr2 · 4H2O. The theoretical result was experimentally proved at 25°C by the physicochemical analysis method and formation of the new double salt 2RbBr · MnBr2 · 2H2O was established. It was found to crystallize in a triclinic crystal system, space group −P1, a = 5.890(1) Å, b = 6.885(1) Å, c = 7.367(2) Å, α = 66.01(1)°, β = 87.78(2)°, γ = 84.93(2)°, V = 271.8(1) Å3, Z = 1, Dx = 3.552 g-cm−3. The binary and ternary ion interaction parameters were calculated and the solubility isotherm was plotted. The standard molar Gibbs energy of the synthesis reaction, ΔrGmo, of the double salt 2RbBr · MnBr2 · 2H2O from the corresponding simple salts RbBr and MnBr2 · 4H2O, as well as the standard molar Gibbs energy of formation, ΔfGmo, and standard molar enthalpy of formation ΔfHmo of the simple and double salts were calculated.

Generator coordinate method calculations of natural orbitals and single-particle occupation numbers in4He,16O and40Ca

SummarySingle-particle occupation numbers and natural orbitals in4He,16O and40Ca are calculated diagonalizing the one-body density matrix obtained in an approach within the generator coordinate method. Square-well and harmonic-oscillator construction potentials and Skyrme-like forces are used. The natural orbitals (single-particle wave functions) are presented in both coordinate and momentum spaces. Together with the nucleon momentum distributionn(k) they are compared with results of Hartree-Fock as well as of correlation methods and with available experimental data forn(k) in4He. The realistic high-momentum behaviour ofn(k) and of the natural orbitals in the case of square-well construction potential shows that the nucleon-nucleon correlations at small distances are taken into account. It is pointed out that the correlations strongly affect the natural orbitals but not the occupation numbers.

Numerical study of the viscous flow in oscillatory spherical annuli

Abstract The method of fractional steps is applied for investigating the viscous flow field in the oscillatory spherical annuli. The numerical solution obtained enlarges the intervals of the frequency parameter M and amplitude of the torsional oscillations e in comparison with known solutions. Typical flow fields are shown graphically.

Zero-motion correlations in high-energy proton elastic scattering on40Ca with noneikonal nucleon-nucleon amplitude

Using a noneikonal expression for the two-body scattering amplitude, consistent with the proton-nucleon scattering data, the cross-section of the 1.04 GeV-proton elastic scattering on40Ca is calculated by the Glauber-Sitenko theoretical scheme in the framework of the coherent density fluctuation model (CDFM) as well as of the independent-particle model (IPM). It is shown that the use of the noneikonal amplitude in the CDFM calculation improves the agreement with the experimental data especially at larger scattering angles in contrast to the case of the independent-particle model. To that end a decisive role play the zero-motion flucton correlations taken into account in the CDFM.

Model description of direct-particle emission followed by neutron evaporation

A model including the direct and the compound phases of a nuclear reaction is applied to the analysis of particle-γ coincidences data. The model describes the shape of the exclusive particle spectra and reproduces the dependence of the entry point of the residual nucleus on the beam energy.

Analysis of the cross-sections of protons emitted at backward angles from4He-induced reactions at (11.2÷27.5) MeV/A

SummarySummed exclusive proton cross-sections at angles of 45° and 135° are obtained for the159Tb (4He, pxnγ) reactions atE(4He)=45, 75 and 110 MeV and for the209Bi (4He, pxnγ) reactions atE(4He)=45, 75 MeV from particle—γ-ray coincidence experiments. The experimental data are analyzed in the framework of the complete fusion—statistical decay model. It is shown that the summed exclusive proton spectra at backward angle of ϑ=135° with respect to the beam direction and particularly their high-energy parts cannot be explained by the model considered. A conclusion is drawn that an additional reaction mechanism intermediate with respect to both compound and direct ones should be invoked.