An equilibrium penny-shaped crack in an inhomogeneous elastic medium

The problem of a penny-shaped tensile crack in a continuously-inhomogeneous space is considered. The problem reduces to a dual integral equation for which an approximate analytical solution is constructed. It is proved that the approximate solution of the integral equation is asymptotically exact for both small and large values of the dimensionless geometric parameter of the problem. The accuracy of the solution obtained is investigated. Expressions are presented for the stress intensity factor, the energy of the opening of the crack, the displacements of its sides and the normal components of the stress tensor in the neighbourhood of its contour. In the numerical analysis of the solution of the problem, special attention is paid to analysing of the problem when the first derivative of the change in the elastic properties of the material changes sign.     

Solubility of α-and β-gypsum in aqueous solutions of calcium,magnesium, and sodium chlorides

The interaction of multicomponent water-salt systems including calcium, magnesium, and sodium chlorides, gypsum, air, and water were studied by the methods of thermodynamic modeling. The solubility of α-CaSO₄ · 2H₂O and β-CaSO₄ · 2H₂O were determined in aqueous solutions of calcium, magnesium, and sodium chlorides and their mixtures at 25°C and carbon dioxide partial pressure of 10^?1.53 kPa, metal chloride concentrations of 10^?4 to 1.0 mol/kg H₂O, and their molar ratio of 1: 1.     

Calculation of the formation enthalpies,standard entropies,and standard heat capacities of alkali and alkaline-earth germanates

The formation enthalpies, standard entropies, and standard heat capacities of alkali and alkaline-earth germanates were determined by regression analysis with allowance for error in the initial data (weights). The potentialities of the presented method of calculation appreciably grew due to the possibility to enhance the array of initial data independently of the crystal structure of compounds. The thermodynamic properties of alkali germanates were estimated for the first time and could be used in the physicochemical models of magmatic melts.     

Interaction of basalt with hydrochloric acid

Physicochemical modeling and experimental investigations are performed to study the interaction of basalt with hydrochloric acid. The equilibrium compositions of the liquid and solid phases of the basalt-hydrogen chloride-water system are calculated. The effects of the hydrochloric acid concentration and solid-to-liquid weight ratio on the phase composition of reaction products are quantified, and the degrees of extraction of iron, aluminum, calcium, sodium, and silicon into liquid are determined. The results of physicochemical modeling are compared with the experimental data. Conditions for selective extraction of the basalt components into solution are estimated.     

Physicochemical interaction in the system Si-Al-Ti-Ca-Mg-Fe-Na-K-O with the consideration of the formation of solid solutions

Based of a physicochemical model of basalt melting processes with the consideration of the solid solution formation, a method for determining the mineral compositions of gabbro-basalt rocks was proposed, which helps estimate the technological properties of melts for mineral fiber production and stone casting.     

Estimation of the heat capacity of individual substances on the basis of experimental enthalpy increments

A method of determination of the high-temperature (T > 298.15 K) heat capacity function of individual substances by differentiation of enthalpy increment measurements with respect to temperature has been suggested. The approach is based on approximation of enthalpy increment measurements by a polynomial without free term, which makes it possible to strictly meet the boundary conditions of differentiation determined by the properties of the enthalpy increment function. In combination with the Shomate method, the approach enables the optimal choice of the form of temperature dependence of heat capacity that is consistent best of all with the concepts of classical thermodynamics and provides the best reproducibility of enthalpy increment measurements. When low-temperature heat capacity measurements for individual substances are not available, i.e., the Shomate method is inapplicable, the suggested strategy makes it possible to obtain the heat capacity change function in the temperature range of enthalpy increment measurements and to estimate the heat capacity of the substance at standard temperature.     

Influence of the Crystallization Temperature and Atmosphere on the Equilibrium Phase Assemblage of Plutonic Rocks of the Monzonite Family

The influence of external settings on the mineral assemblage of plutonic rocks is studied. The equilibrium compositions of phases formed during melting–crystallization of quartz monzodiorite are calculated by physicochemical modeling (PCM) methods. It is shown that, by changing the temperature and atmosphere of melt formation, one can change the mineral assemblage of the crystallizing solid phase that can be used in stone casting and in the production of mineral fibers.     

The unified method for computing thermodynamic properties of natural zeolites based on their crystallochemical formulas

The standard thermodynamic potentials of natural zeolites in universal stoichiometric representation are computed. The enthalpies are estimated using linear deconvolution into chemical elements for calibration minerals. The entropies are computed using the additive scheme for oxide components; the Gibbs free energies are computed based on the calculated standard thermodynamic functions and entropies of thermochemically simple compounds.