MODELING RADIATION-INDUCED SEGREGATION IN BINARY ALLOYS
Keywords:
materials of nuclear engineering, radiation-induced segregation, binary metal alloys, concentration profiles, point defects, inverse Kirkendall effect, balance equations, computer simulation
Abstract
A computer code to calculate the time and space dependencies of the defect and component concentrations of a binary alloy is developed. This code is based on the theoretical model for radiation-induced segregation governed by first and second Fick’s laws with taking into account inverse Kirkendall effect. The system of three coupled partial differential equations for concentrations of one of components and point defects is converted to the system of ordinary differential equations in time by a discretization procedure. Numerical solutions of this system are obtained under appropriate initial and boundary conditions by means of the MATLAB. The modeling of radiation-induced segregation in binary Fe-Cr alloys is carried out for various initial concentrations of components, temperatures, dose rates and doses. The process of achievement of steady state at dose rising is demonstrated. The calculated concentration profiles are compared with experimental profiles published in literature. The sensitivity of model to input parameters is done and the capabilities of proposed model are estimated. This computer code for multicomponent alloys is developed.
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References
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2. Aitkaliyeva A., He L., Wen H., Miller B., Bai X.M., Allen T. Irradiation effects in Generation IV nuclear reactor materials // In Woodhead Publishing Series in Energy: N.106. Structural Materials for Generation IV Nuclear Reactors / Ed. by P. Yvon – Amsterdam: Elsevier Ltd., 2017. – P. 253-283.
3. Choudhury S., Barnard L., Tucker J.D., Allen T.R., Wirth B.D., Asta M., Morgan D. Ab-initio based modeling of diffusion in dilute bcc Fe-Ni and Fe-Cr alloys and implications for radiation induced segregation // J. Nucl. Mater. – 2011. – Vol. 411. – P. 1-14.
4. Lu Z., Faulkner R.G., Was G., Wirth B.D. Irradiation-induced grain boundary chromium microchemistry in high ferritic steels // Scr. Mater. – 2008. – Vol. 58. – P. 878-881.
5. Takahashi H., Ohnuki S., Takeyama T. Radiation-induced segregation at internal sinks in electron irradiated binary alloys // J. Nucl. Mater. – 1981. – Vol. 103-104. – P. 1415¬-1420.
6. Little E.A., Morgan T.S., Faulkner R.G. Microchemistry of neutron irradiated 12%CrMoVNb martensitic steel // Mater. Sci. Forum. – 1992. – Vol. 97-99 – P. 323-328.
7. Neklyudov I.M., Voyevodin V.N. Features of structure-phase transformations and segregation processes under irradiation of austenitic and ferritic-martensitic steels // J. Nucl. Mater. – 1994. – Vol. 212-215. – P. 39-44.
8. Schaeublin R., Spatig P., Victoria M. Chemical segregation of the low activation ferritic/martensitic steel F82H // J. Nucl. Mater. – 1998. – Vol. 263. – P. 1350-1355.
9. Gupta G., Jiao Z., Ham A.N., Busby J.T., Was G.S. Microstructural evolution of proton irradiated T91 // J. Nucl. Mater. – 2006. – Vol. 351. – P. 162-173.
10. Lu Z., Faulkner R.G., Sakaguchi N., Kinoshita H., Takahashi H., Flewitt P.E.J. Effect of hafnium on radiation-induced inter-granular segregation in ferritic steel // J. Nucl. Mater. – 2006. – Vol. 351. – P. 155-161.
11. Marquis E.A., Lozano-Perez S., de Castro V. Effects of heavy-ion irradiation on the grain boundary chemistry of an oxide-dispersion strengthened Fe-12 wt.% Cr alloy // J. Nucl. Mater. – 2011. – Vol. 417. – P. 257-261.
12. Marquis E.A., Hu R., Rousseau T., A systematic approach for the study of radiation-induced segregation/depletion at grain boundaries in steel // J. Nucl. Mater. – 2011. – Vol. 413. – P. 1-4.
13. Wharry J.P., Was G.S. A systematic study of radiation-induced segregation in ferritic-martensitic alloys // J. Nucl. Mater. – 2013. – Vol. 442. – P. 7-16.
14. Okamoto P.R., Rehn L.E. Radiation-induced segregation in binary and ternary alloys // J. Nucl. Mater. – 1979. – Vol. 83. – P. 2-23.
15. Wiedersich H., Okamoto P.R., Lam N.Q. A theory of radiation-induced segregation in concentrated alloys // J. Nucl. Mater. – 1979. – Vol. 83. – P. 98-108.
16. Watanabe S., Takahashi H. Discriminant of RIS in multi-component alloys // J. Nucl. Mater. – 1994. – Vol. 208. – P. 191-194.
17. Marwick A.D. Calculation of bias due to solute redistribution in an irradiated binary alloy: surfaces of a thin foil // J. Nucl. Mater. – 1985. – Vol. 135. – P. 68-76.
18. Voyevodin V.N., Neklyudov I.M. Evolution of the structure phase state and radiation resistance of structural materials. – Kiev: Naukova dumka, 2006. – 376 p. (in Russian)
19. Voyevodin V.N. Structural materials of nuclear power – challenge to 21 century // Problems of Atomic Science and Technology. – 2007. – Vol. 90. – P. 10-22. (in Russian)
20. Was G.S. Fundamentals of Radiation Materials Science: Metals and Alloys. – New York: University of Michigan, Springer, 2007. – 828 p.
21. Was G.S., Wharry J.P., Frisbie B., Wirth B.D., Morgan D., Tucker J.D., Allen T.R. Assessment of radiation-induced segregation mechanisms in austenitic and ferritic-martensitic alloys // J. Nucl. Mater. – 2011. – Vol. 411. – P. 41-50.
22. Xu D., Wirth B.D., Li M., Kirk M.A. Combining in situ transmission electron microscopy irradiation experiments with cluster dynamics modeling to study nanoscale defect agglomeration in structural metals // Acta Mater. – 2012. – Vol. 60. – P. 4286-4302.
23. Hairer E., Wanner G. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. – 2nd edn. – Berlin, Springer, 1996. – 614 p.
24. Shampine L.F., Reichelt M.W. The MATLAB ODE suite // SIAM J. Sci. Comput. – 1997. – Vol. 18. – No. 1. – P. 1-22.
25. Koropov O.V. Differential equations of radiation-induced segregation in five-component metal alloys // Proc. of Eighteenth International Scientific Mykhailo Kravchuk Conference, October 7-10, 2017, Kyiv: Vol. 1. – Kyiv: NTUU “KPI”, 2017. – P. 86 90. (in Ukrainian)
26. Olsson P., Domain C., Wallenius J. Ab initio study of Cr interactions with point defects in bcc Fe // Phys Rev B. – 2007. – Vol. 75. – P. 014110.
27. Schaefer H.-E., Maier K., Weller M., Herlach D., Seeger A., Diehl J. Vacancy formation in iron investigated by positron annihilation in thermal equilibrium // Scripta Metallurgica. – 1977. – Vol. 11. – P. 803–809.
28. Wharry J.P., Was G.S. The mechanism of radiation-induced segregation in ferritic-martensitic alloys // Acta Mater. – 2014. – Vol. 65. – P. 42–55.
29. Selby A.P. Modeling Radiation-Induced Segregation in Ferritic-Martensitic Steels. Master’s Thesis. – University of Tennessee, 2015.
30. Field K.G., Barnard L.M., Parish C.M., Busby J.T., Morgan D., Allen T.R. Dependence on grain boundary structure of radiation induced segregation in a 9 wt.% Cr model ferritic/martensitic stell // J. Nucl. Mater. – 2013. – Vol. 435. – P. 172-180.
31. Allen T.R., Was G.S. Modeling radiation-induced segregation in austenitic Fe-Cr-Ni alloys // Acta Mater. – 1998. – Vol. 46. – No. 10. – P. 3679-3691.
32. Terentyev D., Olsson P., Klaver T.P.C., Malerba L. On the migration and trapping of single self-interstitial atoms in dilute and concentrated Fe-Cr alloys: Atomistic study and comparison with resistivity recovery experiments // Computational Materials Science. – 2008. – Vol. 43. – P. 1183-1192.
Published
2018-04-03
Cited
How to Cite
Skorokhod, R. V., Buhay, O. M., Bilyk, V. M., Denysenko, V. L., & Koropov, O. V. (2018). MODELING RADIATION-INDUCED SEGREGATION IN BINARY ALLOYS. East European Journal of Physics, 5(1), 61-69. https://doi.org/10.26565/2312-4334-2018-1-07
Section
Original Papers
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