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Kashchenko M.P.,Ural State Forestry University | Chashchina V.G.,Ural Federal University
Materials Science Forum | Year: 2013

Basic directions in the theory of martensitic transformations are specified. Instances of solving several important problems in the context of dynamic theory of reconstructive martensitic transformations are reviewed. An fcc-bcc (bct) transformation in iron alloys is referred to as example. Much attention is given to certain concept-affiliated aspects. In particular, the key role of the concept of initial exited state in conceiving transformations with crystal growth at supersonic speed is shown. An additional emphasis is made at showing that this concept is of primary importance in both calculating critical rates of austenite cooling and evaluating the scale of incubation-period-related times at bainitic transformation. © (2013) Trans Tech Publications, Switzerland.


Kashchenko M.P.,Ural State Forestry University | Chashchina V.G.,Ural Federal University
Physics of Metals and Metallography | Year: 2012

The existence of critical cooling rates for the beginning of rapid growth of lamellar crystals in alloy steels is considered as a consequence of the suppression of diffusion on spatial scale d corresponding to the transverse size of the initial excited state that appears in the elastic field of a dislocation center of nucleation. Theoretical estimates agree with the experimental results obtained for polycrystals with calibrated grain sizes. © Pleiades Publishing, Ltd., 2012.


Kashchenko M.P.,Ural Federal University | Chashchina V.G.,Ural State Forestry University
Metal Science and Heat Treatment | Year: 2014

It is shown that the concept of phase B19 as an intermediate one in the course of the B2∈→∈B19transformation in alloys based on titanium nickelide is helpful for describing the observed morphological features. The {78 39 48}B2 habits of phase B19 can be compared to standard dislocation of centers of nucleation. A brief discussion of the results is suggested. © 2014 Springer Science+Business Media New York.


Kashchenko M.P.,Ural Federal University | Chashchina V.G.,Ural State Forestry University
Metal Science and Heat Treatment | Year: 2016

Variants of initiation of growth of crystals of α-martensite by couples of elastic waves propagating in directions <001>γ and <110>γ in singles crystals of Fe31Ni are suggested. The dynamic theory is used to show that the expected orientations of habit planes {110}γ, {001}γ and {559}γ differ from the typical {31015}γ. Possible features of tetragonality of martensite crystals are discussed. The power of the sources of ultrasound required for initiation of γ – α martensitic transformation is estimated. © 2016 Springer Science+Business Media New York


Chashchin N.I.,Ural State Forestry University
Physics of Metals and Metallography | Year: 2016

We investigate the ground state (T = 0 K) of the one-dimensional symmetrical (n = 1) Hubbard model formalized in terms of the system of integral equations, which we previously obtained using the method of the generating functional of Green’s functions with the subsequent Legendre transformation. In a wide range of variations in the parameter of Coulomb interaction U, the following characteristics of the system have been calculated: the electron density of states, the electron band spectrum, the number of doubly occupied lattice sites, the localized magnetic moment, the correlator of the square of the longitudinal component of spin at a site,, and the internal energy of the system. It has been shown that, for all U > 0, the model yields two solutions, i.e., an antiferromagnetic insulator and a paramagnetic insulator, in which there are no single-electron quasi-particles at the Fermi level. The energy of the paramagnetic solution in the region of U < 1.1 is considerably less than that of the antiferromagnetic solution for the case of U > 1.1, we have the opposite situation. © 2016, Pleiades Publishing, Ltd.


Chashchin N.I.,Ural State Forestry University
Physics of Metals and Metallography | Year: 2012

Based on the previously obtained equations, a paramagnetic solution to the symmetrical Hubbard model for the case of d = ∞, T = 0 K has been investigated. The solutions obtained are represented in the form of graphs of the density of electron states, number of doubly occupied lattice sites D, internal energy of the system E, and static paramagnetic susceptibility X as functions of electron interaction U. The calculation results show that the stable regimes of the formation of local moments at 0 < U < 1.8 and of the strong Kondo scattering in the region of 2.8 < U < 6.0 are separated by a region (1.8 < U < 2.8) where the behavior of the system becomes irregular. The parameter D randomly takes positive and negative magnitudes, whereas the susceptibility is positive (X > 0) and the average energy E is approximately const; this indicates the occurrence of a structural rearrangement, which is accompanied by phase separation. © Pleiades Publishing, Ltd., 2012.


Chashchin N.I.,Ural State Forestry University
Physics of Metals and Metallography | Year: 2011

The method of a generating functional of Green's functions was further developed within the framework of the Hubbard model and single-impurity Anderson model. In contrast to the earlier proposed works, the equations in the variational derivatives for the partition functions are presented here in the closed form, i.e. the role of variables is played by the physical matrix parameters of the systems rather than by the external local fluctuating fields. The solutions to these equations are the generating functionals of different Green's functions. It is shown that the simplest iterative solutions in terms of the parameters U/W and W/U in the case of the Hubbard model or U/Δ and Δ/U for the Anderson model, where U is the Coulomb repulsion on a site, W is the width of a free electron zone, and Δ is the width of an impurity level, lead to the well-known results of the weak and strong coupling limits. © Pleiades Publishing, Ltd., 2011.


Chashchin N.I.,Ural State Forestry University
Physics of Metals and Metallography | Year: 2011

The previously derived variational-derivative equations for the Hubbard model and for the single-impurity Anderson model after the Legendre transformation are represented in the form of a set of two nonlinear integral equations. The one-particle propagators of the number of particles and of the momentum that are defined by these equations exhibit a regular behavior in three limiting cases. First, for both models in the limit of the zero width of the conduction band (W/U = 0) there is obtained a result known as the atomic limit. Second, it has been shown that in the limit of U/W < 1 the Pauli principle in the form of an additional coupling equation excludes from the perturbation-theory series some class of diagrams that are present in the standard expansion. Finally, for the case of U = ∞ and N e = N at - 1 in the framework of the Hubbard model there has been obtained an equation that agrees with the exact Nagaoka statement on the saturated ferromagnetism. A calculation has been performed of the density of impurity electron states in the symmetrical Anderson model in the paramagnetic phase for various values of the parameters of the Coulomb interaction U/πΓ and temperature T/Γ, where Γ is the width of the localized impurity level. The calculation results are in good agreement with the results obtained by other methods. © 2011 Pleiades Publishing, Ltd.


Kashchenko M.P.,Ural State Forestry University | Chashchina V.G.,Ural State Forestry University | Vikharev S.V.,Ural State Forestry University
Physics of Metals and Metallography | Year: 2010

Dynamic models of the pretransition state of austenite that are compatible with the supersonic formation of internally twinned martensite crystals due to the concerted action of short-wavelength and long-wavelength displacements have been considered. The preference has been given to the model of a single starting dynamic cell capable of being periodically replicated in the region of the front of a control wave process. For the level of threshold deformations, an algorithm of determining fractions of the main and additional (twin) components has been put forward. © 2010 Pleiades Publishing, Ltd.


Mikhailov Yu.E.,Ural State Forestry University
Zoologicheskii Zhurnal | Year: 2013

Four subspecies of Cystocnemis discoidea were identified; two subspecies are described as new for science, and ssp. gebleri was resurrected from synonymy. Pathways of speciation in highland-hollow landscapes are discussed. The alpine subspecies oreas ssp. n. has an altibiome disjunction with the nominotypic subspecies. A similarity of the alpine C. discoidea subspecies with species of the subgenus Entomomela was found to be a result of permanent confusion of these taxa representatives. The subgenus Entomomela is transferred from the genus Oreomela to the genus Cystocnemis. A key for the identification of species and subspecies of the enlarged genus Cystocnemis is given.

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