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Yekaterinburg, Russia

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.


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.


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.


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.


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.

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