2023-Sustainable Industrial Processing Summit
SIPS2023 Volume 13. 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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APPLICATION OF THE DFK MODEL TO METAL ALLOYS MODEL OF ATOMIC ORDERING IN AxB1-x ALLOYS
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: 482
Topic: 38
Abstract:
A metal alloy is a collection of crystalline grains with an average size L, the space between which is filled with impurities.
Classical theories of metal alloys are based on the idea of a “random phase”: - atoms in a crystal lattice according to chemistry. composition can be arranged randomly.
The DFK model puts forward the idea of a “commensurate phase”, which is realized by the strong interaction of crystal sublattices: - an alloy AB of equiatomic composition is considered as a commensurate crystal with AB molecules (N = L). If the main periods of the sublattices are equal, respectively: for crystal A - a, for crystal B - b, then the period of the AB alloy crystal is equal to 
. When heated (T>V0), the sublattices become independent and return to the original periods (a, b).
Having asked the question about the atomic composition of the grain of the AxB1-x alloy, we proceed from the main hypothesis - metal alloys are described by commensurate phases of the DFK structure. Let us project an alloy of cubic symmetry AxB1-x (x≥0.5) onto a one-dimensional DFK model. Assuming that the alloy is a commensurate phase of the DFK model with CH(Ax) and CH(B1-x) sublattices and strong interchain interaction, V0~1 - we will show that x can only take discretely defined values x=x0.
To the alloy grain AxB1-x (x ≥ 0.5) we associate elastically periodic chains CH(Ax) and CH(B1-x) of N and L atoms of the same size, respectively, then if the period of the chain CH(Ax) = 1, then the period of the chain CH(B1-x) is equal to 
.
Thus, x can only take discrete values x0:
The chemical composition of the AxB1-x alloy grain has the form Ax0B1-x0. We choose in (1) the first fractional-rational values 
≥ 1, with the smallest denominators, because commensurate phases [1] with strong interaction can only be realized with them. From (1) we have: x0 = 0.50; 0.70; 0.89, i.e. very limited number of options depending on V0.
The fallen atoms, with density Δx=x-x0, are located between the grains, determining their size:
L~1/ Δx. (2)
The interaction between sublattices is carried out by the potential Vij, which is significant if the temperature T 0. At T> V0 the chains are independent.