The influence of the segregation effects on the motion of interphase boundaries at a cellular decomposition in Pb-Sn system
Main Article Content
Abstract
Stability of polycrystalline binary and multicomponent metallic systems at low homologous temperatures depends on the mobility of the interphase boundaries and segregation kinetics of components at these boundaries. If the interphase boundaries move with sufficiently high velocity, the segregation process starts to depend on the magnitude of their velocity. In this case a dynamic coefficient of segregation should be used for the description of the process. Furthermore, a concentration distribution that corresponds to the non-equilibrium segregation appears within the interphase boundaries. Presence of the nonequilibrium segregation may cause additional dissipation of energy, which reduces the driving force of the thermodynamic reaction and changes the magnitude of the interphase boundary velocity. The main kinetic mechanism responsible for the dissipation of energy within the interphase boundaries is the process of the drag of these boundaries by the segregated atoms (i.e. solute drag effect). This process occurs in case of deviation of the concentration distribution of the segregated atoms from the equilibrium one, which is mediately linked to the change of the interfacial energy. In its turn a change of the surface energy may also change the value of the diffusion coefficient of atoms across the interphase boundary.
The concentration profiles inside the grain boundary were built and analyzed at different values of the boundary velocity. The rate of the Gibbs free energy dissipation, which appears due to the attraction of the segregated atoms by a boundary, was found as a function of the velocity of the cellular decomposition front. In this work the law of motion of the grain boundaries was investigated by applying the diffusion model of the phase separation interface. The developed model of the interphase boundary drag by segregated atoms was used for the description of the peculiarities of the grain boundary motion during cellular decomposition. During this process the high-angle grain boundary moves toward the region of the supersaturated and elastically deformed binary solid solution leaving behind the region of depleted and less thermodynamically unstable solid solution. The generalized Miedema model was used for the description of the thermodynamic properties of adjacent phases and for the estimation of the segregation energy. According to this model the surface enthalpies, enthalpies of mixing of solid solution in Pb-Sn system and segregation energies were found at different concentration of Sn. It was shown that dissipation rate of the Gibbs free energy decreases with increase of velocity of the cellular decomposition front.
Article Details
References
1. Cahn J. W. (1962). The impurity-drag effect in grain boundary motion. Acta metallurgica. 10(9), 789-794.
2. Hillert M. (1999). Solute drag, solute trapping and diffusional dissipation of gibbs energy. Acta metallurgica. 47(18), 4481.
3. Lyashenko Yu. O., Gladka L. I., Shmatko I. O. (2012). Modelyuvannya vplyvu segregatsiyi na rukh mezhi zerna na prykladi komirkovoho rozpadu. Metallofyzyka y noveyshye tekhnolohyy, 12, 1693-1713.
4. Kaur I., Hust V. (1991). Dyfuziya po mezhakh zeren i faz M.: Mashynobuduvannya, p. 448 (in Rus).
5. Larikov L. N., Shmatko O. A., (1976). Nizdryuvatyy rozpad peresychenykh tverdykh rozchyniv. K.: Naukova Dumka, p. 259 (in Rus.).
6. Cahn J. W. (1959). The Kinetics of Cellular Segregation Reactions. Acta. Met. 7, 18-27.
7. Lyashenko Yu. O., Gusak A. M., Shmatko O. A., (2005). Metalofizyka i novitni tekhnolohiyi. 27, 873-894.
8. Lyashenko Yu. A., Zaitzeva N. V., Shmatko O. A. (2007). Peculiarities of Discontinuous Precipitation in the Pb-Sn Alloy. Defect and Diffusion Forum. 261 – 262, 61- 68.
9. Gusak A. M., Zaporozhets T. V., Lyashenko Yu. O., Kornienko S. V., Pasichnyy M. O., Shirinyan A. S. (2010). Diffusion-controlled solid state reactions: in alloys, thin-films, and nanosystems. Berlin: Wiley-VCH.
10. Cahn J. W., Hilliard J. E. (1958). Free Energy of a Nonuniform System. The Journal of Chemical Physics. 28, 258-269.
11. Wang H., Liu F., Yang W., Chen Z., Yang G., Zhou Y. (2008). Solute trapping model incorporating diffusive interface. Acta Mater. 56, 746-753.
12. Li Sh., Zhang J., Wu P. (2010). Numerical solution and comparison to experiment of solute drag models for binary alloy solidification with a planar phase interface. Scripta Materialia. 62(9), 716.
13. Miedema A. R. (1976). On the heat of formation of solid alloys II. Less Common Metals. 46, 67-83.
14. Bakker H. (1998). Enthalpies in Alloys – Miedema`s Semi Empirical Model. Switzerland: Trans Tech Publications Ltd.
15. Kim S. G., Park Y. B. (2008). Grain boundary segregation, solute drag and abnormal grain growth. Acta Materialia. 56, 3739-3753.
16. Strandlund H., Odqvist J., Agren J. (2008). An effective mobility approach to solute drag in computer simulations of migrating grain boundaries. Computational materials science. 44, 265-273.
17. Hillert M. (1983). On the driving force for diffusion induced grain boundary migration. Scripta Metallica. 17, 237-240.
18. Brechet Y. J. M., Purdy G. R. (1990). Elastic energy and the solute drag effect. Scripta Metall. Mater. 24, 1831-1835.
19. Denton A. R., Ashcroft N. W. (1991). Vegard`s law. Phys. Rev. 43, 3161.
20. McLean D. (1957) Grain Boundaries in Metals. London: Oxford Univ.
21. Koval Yu. M., Bezuhlyy A. M., Didyk M. I., Zaytseva N. V., Shmatko O. A., (2004) Dopovidi NANU, 2: 102-104.
22. Liashenko Yu., Derev’ianko S. I., Shmatko O. A. (2015). Rozrakhunok vplyvu sehrehatsiinykh efektiv na rukh mizhfaznykh mezh za komirkovoho rozpadu. Metal Physics and Advanced Technology (Metalofizyka i novitni tekhnolohii), 37(13), 1619–1632.