The calculation influence addition of the third component to system Сu-Ti on segregation energy in processes of the cellular decomposition
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Abstract
Analysis of the influence of the third component addition on grain boundary mobility in alloys is one of the impotant problems of the phase transformation kinetics. Segregation of atoms on grains and interfacial boundaries is an important factor that influences the thermodynamic stability of polycrystalline structures. We consider the influence of the addition of the third element (Ni, In, Ga, Mn, Co, Cr, Fe, Sn and Zr) on the values of the segregation energies in the volume of the grains and on segregation energies at the interphase boundaries of the metallic polycrystalline systems. We treat the Cu-Ti system at the low homologous temperature as a model system. For description of the experimental data about influence of the third component addition on the rate of the grain boundary velocity at the cellular decomposition the Miedema thermodynamic approach is used. In such case the enthalpy of formation of solid solution from the pure components is the sum of three terms: interatomic interaction energy, structural energy and elastic energy. Calculation of the enthalpy of the grain boundary segregation includes both the calculation of the chemical enthalpy of mixing of components and enthalpy of elastic interaction depending on the different size of atoms.
We evaluated of the enthalpies of segregation taking into account the energies of interatomic and elastic interaction of atoms of different kind. It was found that Ni addition enhances the cellular decomposition rate of Cu-4.35at%Ti alloy whereas Co addition reduces this rate. We estimated the enthalpies of mixing in the bulk of grains and in the grain boundary interphases and found that with addition of Ni or Co in the Cu-4.35at%Ti alloy the enthalpies of mixing in the bulk of grains differ significantly. The peculiarities revealed in this study are important for construction of the model of the dynamic segregation and its influence on the cellular decomposition rate in the ternary systems.
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References
1. Лариков Л. Н. Ячеистый распад пересыщенных твердых растворов / Л. Н. Лариков, О. А. Шматко. – К. : Наукова Думка, 1976. – 259 с.
2. Zieba P. Local Characterization of Chemistry and Kinetics in Discontinuous Solid State Reactions / P. Zieba. – Cracow : Polish Academy of Sciences, Institute of Metallurgy and Material Science, 2001. – 368 p.
3. Kirchheim R. Grain coarsening inhibited by solute segregation / R. Kirchheim // Acta Mater. – 2002. – Vol. 50. – P. 413–419.
4. Darling K. A. Thermal stability of nanocrystalline Fe–Zr alloys / K. A. Darlind, B. K. van Leeuwen, C. C. Koch, R. O. Scattergood // Mater. Sci. Eng., A – 2010. – Vol. 527. – P. 3572–3580.
5. Lejcek P. Grain Boundary Segregation in Metals / P. Lejcek. – Springer : Heidelberg, Germany, 2010. – 252 p.
6. McLean D. Grain Boundaries in Metals / D. McLean. – London : Oxford Univ., 1957. – 346 p.
7. Wynblatt P. Anisotropy of Segregation at Grain Boundaries and Surfaces / P. Wynblatt, D. Chatain // Metall. and Mat. Trans. A, – 2007. – Vol. 38, №2. – P. 438–439.
8. Wynblatt P. Surface energy and solute strain energy effects in surface segregation / P. Wynblatt, R. C. Ku // Surface Science, – 1977. – Vol. 65. – P. 511–523.
9. Guttman М. Grain boundary segregation, two dimensional compound formation and precipitation / M. Guttman // Met. Trans. – 1977. – Vol. 8A. – P. 1383–1393.
10. Cahn J. W. The Impurity-Drag Effect in Grain Boundary Motion / J. W. Cahn // Acta metallurgica, – 1962. – Vol. 10, № 9. – P. 789–794.
11. Hillert M. A treatment of the solute drag on moving grain boundaries and phase interfaces in binary alloys / M. Hillert, B. Sundman // Acta Metall. – 1976. – Vol. 24. – P. 731.
12. Rabkin E. On dynamic segregation in the discontinuous precipitation reaction / E. Rabkin, W. Gust, Y. Estrin // Scripta Mater. – 1997. – Vol. 37. – P. 119–124.
13. Каур И. Диффузия по границам зерен и фаз / И. Каур, В. Густ – М. : Машиностроение, 1991. – 448 с.
14. Cahn J. W. The Kinetics of Cellular Segregation Reactions / J. W. Cahn // Acta. Met. – 1959.– Vol. 7. – P. 18–27.
15. Ляшенко Ю. А. Модель ячеистого распада сплавов на основе баланса и максимума производства энтропии / Ю. А. Ляшенко // Письма в ЖТФ, – 2004. – Vol. 30, № 3. – P. 54–63.
16. Aaronson H. I. On the turnbull and the cahn theories of the cellural precipitation / H. I. Aaronson, Y. C. Liu // Scr. Met. – 1968. – Vol. 2., № 1. – P. 1–17.
17. Гаценко Т. С. Вплив третього елементу на швидкість коміркового розпаду в сплаві Cu-4,35 ат.%Ti / Т. С. Гаценко, Ю. О. Ляшенко, О. А. Шматко // Вісник Черкаського національного університету. – 2013. – Вип. 269. – C. 31–37.
18. Афанасьев Н. И Влияние примесей на скорость прерывистого распада сплавов Pb-Sn / Н. И. Афанасьев, Т. Ф. Елсукова // ФММ. – 1984. – Вып. 57, № 1. – С. 96–102.
19. Bakker H. Enthalpies in Alloys – Miedema`s Semi-Empirical Model / H. Bakker // Switzerland : Trans Tech Publications Ltd, 1998. – 78 p.
20. Murdoch A. Design of a Stable Nanocrystalline Alloy / A. Murdoch – Cambridge, Massachusetts : Massachusetts Institute of Technology, 2013. – 216 p.
21. Benedictus R. Thermodynamic model for solid-state amorphization in binary systems at interfaces and grain boundaries / R. Benedictus // Lab. of Mat. Sci., Delft University of Technology. – Rotterdamseweg, 1996. – P. 17.
22. Ляшенко Ю. О. Моделювання впливу сеґреґації на рух межі зерна на прикладі коміркового розпаду / Ю. О. Ляшенко, Л. І. Гладка, І. О. Шматко // Металлофизика и новейшие технологии. – 2012. – Vol. 12. – С. 1693–1713.