2025 - Sustainable Industrial Processing Summit
SIPS2025 Volume 14. Intl. Symp on Multiscale, Modelling, Nanotechnology and Modelling Materials
| Editors: | F. Kongoli, D. Bammann, R. Das, J.B. Jordon, R. Prabhu, A. Rajendran, P. Trovalusci, M. de Campos |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2025 |
| Pages: | 214 pages |
| ISBN: | 978-1-998384-64-8 (CD) |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
CD shopping page
APPLICATION OF THE DFK MODEL TO METAL ALLOYS
Evgeniy Artemyev1; Lyudmila Kveglis1; Artur Abkaryan1; Alexander Filonov2;1INSTITUTE OF ENGINEERING PHYSICS AND RADIOELECTRONICS, SIBERIAN FEDERAL UNIVERSITY, Krasnoyarsk, Russian Federation; 2INSTITUTE OF NONFERROUS METALS AND MATERIALS SCIENCE, SIBERIAN FEDERAL UNIVERSITY, Krasnoyarsk, Russian Federation;
Type of Paper: Regular
Id Paper: 268
Topic: 64
Abstract:
A sublattice model of metal alloys and the hypothesis that alloys are described by commensurate phases of the DFK model are put forward. The chemical composition of its grains is predicted for the AxB1-x alloy.
A metal alloy is a collection of crystalline grains with an average size R, 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: for example - 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:
(1)
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 [1-4] 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 dropped atoms, with density Δx=x-x0, are located between the grains, determining their size R:
R~1/ Δx. (2)
It is interesting to note that the chemical composition of many metal alloys AxB1-xC, with high-temperature superconductivity (HTS), lies near the values of x0 = 0.50; 0.77; 0.89; 0.96.
This suggests that HTS should be described by a model with incommensurate phases [1-3] and a chemical density wave. In this case the variance of R is minimal.