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The kinetics of CaCO3 precipitation from model solutions formed by preliminary saturating deionized water with CO2 and by adding NaHCO3 and CaCl2 has been considered. The characteristic feature of the method is the almost simultaneous measurement of the activities of major components of the aqueuos calcium hydrocarbonate system (ACHCS): Ca 2+ , CO2, HCO − 3 , as well as pH and the temperature. CaCO3 crystallization was provided with the help of the CO2 degassing by air. The processes running in the ACHCS during the degassing can be divided into four stages: dissociation of CaHCO + 3 complexes; formation of crystal nuclei in the solution; a transitive stage, which includes the final phase of crystal nucleation and the initial growth of newly formed crystals; and intensive growth of crystal nuclei, which gives rise to the mass CaCO3 precipitation. The product (Ca 2+)•(CO 2− 3) is a reaction coordinate for the second stage of CaCO3 precipitation, whereas (Ca 2+)•(HCO − 3) for the third and fourth stages. The kinetics of growth of crystal nuclei and their concentration are calculated for the second stage, by using the concept of CaCO3 dissolution product that depends on the crystal nucleus size. During the process of crystal nucleation, the crystal size remains practically stable (≈8 × 10 −8 m), and the concentration reaches 1.5 × 10 −15 m −3. The mass CaCO3 precipitation (the fourth stage) starts when the crystal nuclei reach dimensions of about 3 × 10 −7 m. K e y w o r d s: calcium carbonate crystallization, reaction coordinate, crystal nuclei, CaCO3 precipitation stages.

ABSTRACT. A three-parametric model of a massive degenerate dwarf was proposed. Unlike paramagnetic state of electron system in the standard Chandrasekhar model electrons are considered in a partially spin-polarized state. The parameters of the model are: x 0 -the relativism parameter at stellar centre, µ e = ⟨ Z A ⟩ -the average chemical composition parameter and ζ -the degree of spin polarization of the electron system. The macroscopic characteristics (e.g. mass, radius, energy) as functions of the model parameters were obtained from the solution of the mechanical equilibrium equation. The electron spin polarization was shown to lead to the increase of stellar radius and especially to mass compared with the corresponding characteristics of the standard model. The application of the proposed model to interpreting the stability of massive dwarfs in binary system was discused.

The study proposes a new method for the calculation of the equilibrium conguration of polytropes with rigid-body axial rotation. Self-consistency is based on the simultaneous use of dierential and integral forms of the mechanical equilibrium equation and a new variant of the perturbation theory, which is relative to the rotation inuence. The solutions are shown in the form of expansions for the Legendre polynomials and the functions of radial coordinate. The integral form of the equilibrium equation allows us to correctly dene the set of the integration constants (the expansion coecients, which depend on the angular velocity). The geometrical parameters of the stellar surface as well as the mass, volume and the moment of inertia were calculated as the functions of the angular velocity at xed values of the polytropic index n = 0; 1.0; 1.5; 2.0; 2.5; 3.0. A comparison with the results of other authors was performed.

Reference system approach of non-relativistic electron fluid theory was adapted for calculation of characteristics of the electron-nuclear model at the densities typical of degenerate dwarfs. Two-and three correlation functions of degenerate relativistic electron gas have been calculated in the momentum-frequency representation in the local field approximation. Main contributions of the Coulomb interactions to the energy and equation of state of the model at T = 0 K have been calculated in the adiabatic approximation.

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The two-and three-particle correlation functions of degenerate relativistic model of homogeneous electron gas with Coulomb interactions at T = 0 K in the momentum-frequency presentation in the local field approximation are investigated. These functions are sufficient for a correct calculation of the equation of state for the electron-nuclear model with the densities that correspond to the degenerate dwarfs.