613 research outputs found
Towards the ab initio based theory of the phase transformations in iron and steel
Despite of the appearance of numerous new materials, the iron based alloys
and steels continue to play an essential role in modern technology. The
properties of a steel are determined by its structural state (ferrite,
cementite, pearlite, bainite, martensite, and their combination) that is formed
under thermal treatment as a result of the shear lattice reconstruction "gamma"
(fcc) -> "alpha" (bcc) and carbon diffusion redistribution. We present a review
on a recent progress in the development of a quantitative theory of the phase
transformations and microstructure formation in steel that is based on an ab
initio parameterization of the Ginzburg-Landau free energy functional. The
results of computer modeling describe the regular change of transformation
scenario under cooling from ferritic (nucleation and diffusion-controlled
growth of the "alpha" phase to martensitic (the shear lattice instability
"gamma" -> "alpha"). It has been shown that the increase in short-range
magnetic order with decreasing the temperature plays a key role in the change
of transformation scenarios. Phase-field modeling in the framework of a
discussed approach demonstrates the typical transformation patterns
On Z-graded loop Lie algebras, loop groups, and Toda equations
Toda equations associated with twisted loop groups are considered. Such
equations are specified by Z-gradations of the corresponding twisted loop Lie
algebras. The classification of Toda equations related to twisted loop Lie
algebras with integrable Z-gradations is discussed.Comment: 24 pages, talk given at the Workshop "Classical and Quantum
Integrable Systems" (Dubna, January, 2007
THE MAIN PROVISIONS OF SCIENTIFIC AND PRODUCTION ASSOCIATION’s product POLICY FORMATION
Main provisions of formation of scientific and production associations product policy are assumed. The content of the category "product policy" is clarified, This category should be considered from the point of view of the design approach, and from the point of view of process approach. The necessity of use of this item as a base to reduce the uncertainty inherent in tasks of similar complexity, the model of the problem situation is shown. The expediency of presenting such models in the form of Ishikawa diagrams is established
THE MAIN PROVISIONS OF SCIENTIFIC AND PRODUCTION ASSOCIATION’s product POLICY FORMATION
Main provisions of formation of scientific and production associations product policy are assumed. The content of the category "product policy" is clarified, This category should be considered from the point of view of the design approach, and from the point of view of process approach. The necessity of use of this item as a base to reduce the uncertainty inherent in tasks of similar complexity, the model of the problem situation is shown. The expediency of presenting such models in the form of Ishikawa diagrams is established
Autocatalytic mechanism of pearlite transformation in steel
A model of pearlite colony formation in carbon steels with ab-initio
parameterization is proposed. The model describes the process of decomposition
of austenite and cementite formation through a metastable intermediate
structure by taking into account the increase of the magnetic order under the
cooling. Autocatalytic mechanism of pearlite colony formation and the
conditions for its implementation have been analyzed. We demonstrate that
pearlite with lamellar structure is formed by autocatalytic mechanism when
thermodynamic equilibrium between the initial phase (austenite) and the
products of its decomposition (cementite and ferrite) does not take place. By
using model expression for free energy with first-principles parameterization
we find conditions of formation of both lamellar and globular structures, in
agreement with experiment. The transformation diagram is suggested and
different scenarios in the kinetics of decomposition are investigated by phase
field simulations.Comment: This work was submitted to Phys.Rev.Applie
Free Energy of the Eight Vertex Model with an Odd Number of Lattice Sites
We calculate the bulk contribution for the doubly degenerated largest
eigenvalue of the transfer matrix of the eight vertex model with an odd number
of lattice sites N in the disordered regime using the generic equation for
roots proposed by Fabricius and McCoy. We show as expected that in the
thermodynamic limit the result coincides with the one in the N even case.Comment: 11 pages LaTeX New introduction, Method change
Dependent coordinates in path integral measure factorization
The transformation of the path integral measure under the reduction procedure
in the dynamical systems with a symmetry is considered. The investigation is
carried out in the case of the Wiener--type path integrals that are used for
description of the diffusion on a smooth compact Riemannian manifold with the
given free isometric action of the compact semisimple unimodular Lie group. The
transformation of the path integral, which factorizes the path integral
measure, is based on the application of the optimal nonlinear filtering
equation from the stochastic theory. The integral relation between the kernels
of the original and reduced semigroup are obtained.Comment: LaTeX2e, 28 page
Kinetics of Ordering and Decomposition in Ti-Al-X (X = Si, Zr) Alloys: Monte Carlo Modeling
To investigate the ordering and decomposition processes in Ti-Al-X [X = Si, Zr] alloys, the Monte Carlo simulations with first-principles parametrization of interatomic interactions were employed. It was shown that the processes of ordering and the precipitation in the Ti-Al system are closely related, and the stage of homogeneous ordering precedes the formation of ordered Ti3Al particles. It was found that the duration of homogeneous ordering is very sensitive to the annealing temperature and composition of alloy, and that precipitation becomes preferable as the temperature rises. In particular, uniform ordering of alloy Ti-12 at % Al was found during long-term holding at temperature below 850 K, while annealing at 1000 K resulted in formation of ordered Ti3Al particles. The obtained results agree well with the experimental data and allow explaining the features of the microstructure formed during annealing of the Ti-Al-X alloys. © 2022 by the authors.Ministry of Education and Science of the Russian Federation, Minobrnauka: AAA-A18-118020190116-6The research was carried out within the state assignment of the Ministry of Science and Higher Education of the Russian Federation (topic Structure, No. AAA-A18-118020190116-6)
Role of magnetic degrees of freedom in a scenario of phase transformations in steel
The diversity of mesostructures formed in steel at cooling from a
high-temperature austenite ("gamma") phase is determined by the interplay of
shear reconstructions of crystal lattice and diffusion of carbon. Combining
first-principles calculations with large-scale phase-field simulations we
demonstrate a decisive role of magnetic degrees of freedom in the formation of
energy relief along the Bain path of "gamma"-"alpha" transformation and, thus,
in this interplay. We show that there is the main factor, namely, the magnetic
state of iron and its evolution with temperature which controls the change in
character of the transformation. Based on the computational results we propose
a simple model which reproduces, in good agreement with experiment, the most
important curves of the phase transformation in Fe-C, namely, the lines
relevant to a start of ferrite, bainite, and martensite transformations.
Phase-field simulations within the model describe qualitatively typical
patterns at these transformations
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