2023-Sustainable Industrial Processing Summit
Intl. Symp on Physics, Mathematics and Multiscale Mechanics
| Editors: | F. Kongoli, A. B. Bhattacharya, A.C. Pandey, G. Sandhu, F. Quattrocchi, L. Sajo-Bohus, S. Singh, H.S. Virk, R.M. Santilli, M. Mikalajunas, E. Aifantis, T. Vougiouklis, P. Mandell, E. Suhir, D. Bammann, J. Baumgardner, M. Horstemeyer, N. Morgan, R. Prabhu, A. Rajendran |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2023 |
| Pages: | 298 pages |
| ISBN: | 978-1-989820-96-4 (CD) |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
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DYNAMICS FRENKEL-KONTOROVA MODEL
Alexander Filonov1; Lyudmila Kveglis2; Artur Abkaryan2; Evgeniy Artemyev2;1INSTITUTE OF NONFERROUS METALS AND MATERIALS SCIENCE SIBERIAN FEDERAL UNIVERSITY KRASNOYARSK PR. IMENI GAZETY KRASNOYARSKII RABOCHII 95 RUSSIAN FEDERATION, Красноярск, Russian Federation; 2INSTITUTE OF ENGINEERING PHYSICS AND RADIOELECTRONICS, SIBERIAN FEDERAL UNIVERSITY, Krasnoyarsk, Russian Federation;
Type of Paper: Regular
Id Paper: 481
Topic: 38
Abstract:
In order to develop the FK model, the DFK model (Developed Frenkel-Kontorova model) is put forward: - two one-dimensional sequences of N and L point atoms, masses m and M; with coordinates {xi} and {yj}, connected by elastic springs with the laws of elastic dispersion 
and 
. Chains CH1 and CH2 interact with each other by potential Vi,j.
The Hamiltonian of the DFK model has the form:
From the analysis of the ground state of the DFK model (N = L) [1], the following conclusion follows: - when one of the Hooke’s chains is stretched by force F, an abrupt transition to the incommensurate phase occurs (F>Fc), in which part of the atoms of the stretched chain CH1 leaves the interaction with CH2. The number of atoms falling out of the Vi,j interaction space 
, where V0 = max Vi,j.
With strong interaction (V0 ~ 1) and strong stretching (F>Fc ~1), the size of the dislocation is 2, and the number of precipitated atoms is N/2. In this case, the incommensurate phase will be a periodic chain of hole dislocations, i.e., commensurate crystal with doubled period.