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Talanov V.M.,South Russian State Polytechnical University | Shirokov V.B.,Russian Academy of Sciences | Ivanov V.V.,South Russian State Polytechnical University | Talanov M.V.,South Federal University
Crystallography Reports | Year: 2015

A theory of phase transition in MgTi2O4 is proposed based on a study of the order-parameter symmetry, thermodynamics, and mechanisms of formation of the atomic and orbital structure of the low-symmetry MgTi2O4 phase. The critical order parameter (which induces a phase transition) is determined. It is shown that the calculated MgTi2O4 tetragonal structure is a result of displacements of magnesium, titanium, and oxygen atoms; ordering of oxygen atoms; and the participation of dxy, dxz, and dyz orbitals. The contribution of noncritical representations to ion displacements is proven to be insignificant. The existence of various metal clusters in the tetragonal phase has been established by calculation in correspondence with experimental data. It is shown (within the Landau theory of phase transitions) that phase states can be changed as a result of both first- and second-order phase transitions: the high-symmetry phase borders two low-symmetry phases by second-order transition lines, while the border between low-symmetry phases is a first-order transition line. © 2015, Pleiades Publishing, Inc.

Mukovnin A.A.,South Russian State Polytechnical University | Talanov V.M.,South Russian State Polytechnical University
Glass Physics and Chemistry | Year: 2014

Phase diagrams of oxychromites with a spinel structure are described in the context of the Landau phenomenological theory of phase transitions. As an approximation of the thermodynamic potential of the sixth degree with respect to components of the order parameter, the implementation conditions of each type of phase diagrams are found. Equations for calculation of coordinates of tricritical and triple points are obtained. A qualitative agreement of the theoretically calculated results of the phase diagrams and experimental phase diagrams of some oxychromites with a spinel structure is observed. © 2014 Pleiades Publishing, Ltd.

Nekrasov S.A.,South Russian State Polytechnical University | Volkov V.S.,South Russian State Polytechnical University
Journal of Siberian Federal University - Mathematics and Physics | Year: 2016

The article describes a mathematical model and numerical method for calculating and optimizing the speed of soil thawing using microwave energy. The main numerical method is the enthalpy method without smoothing concentrated heat. Examples of calculations and analysis of the results are presented. A series of calculations are carried out for the cases of sandstone and sandy loam thawing with the use of standard magnetrons. Nonlinear behavior of thermal parameters, phase transitions and boundary conditions significantly influence temperature distribution and electric field. The losses due to convective cooling and evaporation are negligibly small. The results can be used in research and in designing mining equipment for permafrost. © Siberian Federal University. All rights reserved.

Mukovnin A.A.,South Russian State Polytechnical University | Talanov V.M.,South Russian State Polytechnical University
Russian Journal of Physical Chemistry A | Year: 2014

Phase diagrams of crystals induced by irreducible representations with symmetry group (T d ) are constructed within the phenomenological theory of second-order phase transitions. A model of the Landau thermodynamic potential is studied, state equations of all symmetry-conditioned phases are obtained, and general conditions for their thermodynamic stability are formulated. Equations for the boundaries of phase areas and lines of phase transitions are obtained for the fourth order of expansion of the potential via components of the order parameter. Some types of the collapse of the multicritical point of the phase diagram for the eighth order of potential expansion are studied using computer calculations. The possible existence of phase diagrams that contain one or more triple points and areas of existence of three and four phases is shown for the first time for the potentials with the above symmetry. Examples are given of crystals that undergo phase transitions in the considered symmetry of the order parameter. © 2014 Pleiades Publishing, Ltd.

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