Analysis of spinodal decomposition in Fe-32 and 40 at.% Cr alloys using phase field method based on linear and nonlinear Cahn-Hilliard equations

Authors

  • Orlando Soriano-Vargas Instituto Politécnico Nacional (ESIQIE) - Tecnológico de Estudios Superiores de Jocotitlan
  • Víctor M. López-Hirata Instituto Politécnico Nacional (ESIQIE)
  • Erika O. Ávila-Dávila Instituto Tecnológico de Pachuca
  • Maribel L. Saucedo-Muñoz Instituto Politécnico Nacional (ESIQIE)
  • Nicolás Cayetano-Castro Centro de Nanociencias y Micro y Nanotecnologías

DOI:

https://doi.org/10.3989/revmetalm.078

Keywords:

Cahn-Hilliard equations, Fe-Cr alloys, Phase field method, Spinodal decomposition

Abstract


Spinodal decomposition was studied during aging of Fe-Cr alloys by means of the numerical solution of the linear and nonlinear Cahn-Hilliard differential partial equations using the explicit finite difference method. Results of the numerical simulation permitted to describe appropriately the mechanism, morphology and kinetics of phase decomposition during the isothermal aging of these alloys. The growth kinetics of phase decomposition was observed to occur very slowly during the early stages of aging and it increased considerably as the aging progressed. The nonlinear equation was observed to be more suitable for describing the early stages of spinodal decomposition than the linear one.

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References

Bonny, G., Terentyev, D., Malerba, L. (2008). On the Éø-ÉøÅL miscibility gap of Fe-Cr alloys. Scripta Mater. 59 (11), 1193-1196. https://doi.org/10.1016/j.scriptamat.2008.08.008

Brenner, S.S, Miller, M.K., Soffa, W.A. (1982). Spinodal decomposition of iron-32at.% chromiun at 470°C. Scripta Metall. Mater. 16 (7), 831-836. https://doi.org/10.1016/0036-9748(82)90239-3

Cahn, J.W. (1966). The later stages of spinodal decomposition and the beginnings of particle coarsening. Acta Metall. Mater. 14 (12), 1685-1692. https://doi.org/10.1016/0001-6160(66)90021-6

Cahn, J.W., Hilliard, J.E. (1958). Free energy of a nonuniform system. I. interfacial free energy. J. Chem. Phys. 28 (2), 258-267. https://doi.org/10.1063/1.1744102

Cahn, J.W., Hilliard, J.E. (1971). Spinodal decomposition: A reprise. Acta Metall. Mater. 19 (2), 151-161. https://doi.org/10.1016/0001-6160(71)90127-1

Danoix, F., Auger, P. (2000). Atom probe studies of the Fe-Cr system and stainless steels aged at intermediate temperature: A review. Mater. Charact. 44 (1-2), 177 -201. https://doi.org/10.1016/S1044-5803(99)00048-0

Dieter, G.E. (1988). Mechanical Metallurgy: SI Metric Edition, McGraw-Hill, London. pp. 17-68.

Dongsheng, C., Akihiko, K., Wentuo, H. (2014). Correlation of Fe/Cr phase decomposition process and age-hardening in Fe-15Cr ferritic alloys. J. Nucl. Mater. 455 (1-3), 436-439. https://doi.org/10.1016/j.jnucmat.2014.07.069

Dubiel, S.M., Zukrowski, J. (2013). Fe-rich border and activation energy of phase decomposition in a Fe-Cr alloy. Mater. Chem. Phys. 141 (1), 18-21. https://doi.org/10.1016/j.matchemphys.2013.05.023

Hilliard, J.E. (1970). Spinodal Decomposition. In: Phase transformations. ASM, USA, pp. 497-539.

Honjo, M., Saito, Y. (2000). Numerical simulation of phase separation in Fe-Cr binary and Fe-Cr-Mo ternary alloys with use of the Cahn-Hilliard equation. ISIJ Int. 40 (9), 914-919. https://doi.org/10.2355/isijinternational.40.914

Hyde, J.M., Miller, M.K., Hetherington, M.G., Cerezo, A., Smith, G.D.W., Elliott, C.M. (1995). Spinodal decomposition in Fe-Cr alloys: experimental study at the atomic level and comparison with computer models-II. Development of domain size and composition amplitude. Acta Metall. Mater. 43 (9), 3403-3413. https://doi.org/10.1016/0956-7151(95)00042-t

Jing, Z., Joakim, O., Mattias, T., Peter, H. (2013). Quantitative evaluation of spinodal decomposition in Fe-Cr by atom probe tomography and radial distribution function analysis. Microsc. Microanal. 19 (3), 665-675. https://doi.org/10.1017/S1431927613000470 PMid:23642804

Kostorz, G. (2001). Phase Transformations in Materials, Spinodal Decomposition. Wiley-VCH, Germany, pp. 409-480. https://doi.org/10.1002/352760264X

La Salle, J.C., Schwartz, L.H. (1986). Further studies of spinodal decomposition in Fe-Cr. Acta Metall. Mater. 34 (6), 989-1000. https://doi.org/10.1016/0001-6160(86)90208-7

Malerba, L., Bonny, G., Terentyev, D., Zhurkin, E.E., Hou, M., Vörtler, K., Nordlund, K. (2013). Microchemical effects in irradiated Fe-Cr alloys as revealed by atomistic simulation. J. Nucl. Mater. 442 (1-3), 486-498. https://doi.org/10.1016/j.jnucmat.2012.12.038

Martínez, E., Senninger, O., Fu, Ch., Soisson, F. (2012). Decomposition kinetics of Fe-Cr solid solutions during thermal aging. Phys. Rev. B 86 (12), Id. 224109. https://doi.org/10.1103/physrevb.86.224109

Mehrer, H. (1990). Diffusion in Solid Metals and Alloys. Landolt-Bornstein, Numerical Data and Functional Relationships in Science and Technology. Group III: Crystal and Solid State Physics. Vol. 26, Springer-Verlag, Germany, pp. 32-80. https://doi.org/10.1007/b37801

Pearson, W.B. (1958). A Handbook of Lattice Spacings and Structures of Metals and Alloys. Pergamon, London. https://doi.org/10.1063/1.3062734

Senninger, O., Martínez, E., Soisson, F., Nastar, M., Bréchet, Y. (2014). Atomistic simulations of the decomposition kinetics in Fe-Cr alloys: Influence of magnetism. Acta Mater. 73, 97-106. https://doi.org/10.1016/j.actamat.2014.03.019

Soriano, V.O., Avila, D.E.O., López-Hirata, V.M, Dorantes- Rosales, H.J., González, V.J.L. (2009). Spinodal Decomposition in an Fe-32 at% Cr Alloy during Isothermal Aging. Mater. Trans. 50 (7), 1753-1757. https://doi.org/10.2320/matertrans.M2009029

Soriano, V.O., Avila, D.E.O., López-Hirata, V.M., Cayetano, C.N., González, V.J.L. (2010). Effect of spinodal decomposition on the mechanical behavior of Fe-Cr alloys. Mat. Sci. Eng. A-Struct 527 (12), 2910-2914. https://doi.org/10.1016/j.msea.2010.01.020

Terentyev, D.A., Bonny, G., Malerba, L. (2008). Strengthening due to coherent Cr precipitates in Fe-Cr alloys: Atomistic simulations and theoretical models. Acta Mater. 56 (13), 3229-3235. https://doi.org/10.1016/j.actamat.2008.03.004

Tomoaki, S., Yasuyoshi, N., Daniel, S., Alfredo, C. (2015). Hardening in thermally-aged Fe-Cr binary alloys: Statistical parameters of atomistic configuration. Acta Mater. 89, 116-122. https://doi.org/10.1016/j.actamat.2015.02.013

Voorhees, P.W. (1992). Ostwald ripening of two-phase mixtures. Annu. Rev. Mater. Sci. 22, 197-215. https://doi.org/10.1146/annurev.ms.22.080192.001213

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Published

2016-12-30

How to Cite

Soriano-Vargas, O., López-Hirata, V. M., Ávila-Dávila, E. O., Saucedo-Muñoz, M. L., & Cayetano-Castro, N. (2016). Analysis of spinodal decomposition in Fe-32 and 40 at.% Cr alloys using phase field method based on linear and nonlinear Cahn-Hilliard equations. Revista De Metalurgia, 52(4), e078. https://doi.org/10.3989/revmetalm.078

Issue

Vol. 52 No. 4 (2016)

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Articles

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