Analysis of Local and Global Segregation Occurring in Grain Boundary Diffusion

Abstract:

It is generally well recognized that in the course of a grain boundary (GB) diffusion experiment the diffusion of solute atoms in grain boundaries must exhibit a strong time-dependent segregation. But there has been no clear understanding of exactly how this time dependence develops. In this chapter, we review and analyse transient solute GB diffusion by means of the computer simulation technique of Lattice Monte Carlo (LMC). This technique has been successfully used on numerous occasions for the purposes of systematically studying the GB transition regimes that occur between the principal well-defined Harrison GB kinetics regimes (A, B and C-Types). Recently, the analysis using LMC has been extended to the case of solute GB diffusion when the segregation factor is independent of time. In the present paper, we analyse two cases of solute segregation in GB diffusion: first, where the solute atoms are homogeneously distributed along the tracer source plane but their mobility is not high at this plane; and the second, where the mobility of the solute atoms along the tracer source plane is comparable to their mobility along the GB. It is shown that the time dependence of the segregation can contribute significantly into the resulting values of the triple-product that is usually obtained experimentally in the Harrison Type-B kinetics regime.

• Periodical: Diffusion Foundations (Volume 5)
• Pages: 3-18
• DOI: https://doi.org/10.4028/www.scientific.net/DF.5.3
• Online since: July 2015
• Authors: Irina V. Belova*, Graeme E. Murch
• Keywords: Grain Boundary Diffusion, Monte Carlo, Solute Segregation

References

[1] I. Kaur, Y. Mishin and W. Gust: Fundamentals of Grain and Interphase Boundary Diffusion, Wiley, Chichester (1995).

[2] I. Kaur, W. Gust and I. Kozma: Handbook of Grain and Interphase Boundary Diffusion Data, Ziegler Press, Stuttgart (1989).

[3] Y. Mishin: Def. Diff. Forum, 194/199, (2001), 1113.

[4] B. Bokstein: Def. and Diff. Forum, 297/301, (2010). 1268.

[5] Y. Mishin et al.: Acta Materialia, 58, (2010), 1117.

[6] B. Bokstein and A. Rodin, Chapter VI, Grain Boundary Diffusion and Grain Boundary Segregation in Metals and Alloys, in: Diffusion Foundations, 1, (2014), p.99.

DOI: 10.4028/www.scientific.net/df.1.99

[7] S. V. Divinski and Chr. Herzig, J. Mater. Sci. 43, (2008) 3900.

[8] S. V. Divinski and B. S. Bokstein, Defect Diffus. Forum 309/310, (2011) 1.

[9] T. Surholt and Chr. Herzig, Acta Mater. 45, (1997) 3817.

[10] T. Surholt, Yu. Mishin, Chr. Herzig, Phys. Rev, 50 B, (1994) 3577.

[11] S. V. Divinski, M. Lohmann, Chr. Herzig, Acta Mat. 49, (2001) 249.

[12] S. V. Divinski, J. Ribbe, G. Scmitz, Chr. Herzig, Acta Mat. 55, (2007) 3337.

[13] S. Divinski, M. Lohmann, Chr. Herzig, Acta Mat. 52, (2004) 3973.

[14] M. Lohmann, S. Divinski, Chr. Herzig, Z. Metallkde., 93, (2003) 1172.

[15] M. Pinneau, B. Aufray, F. Cabane-Brouty and J. Cabane, Acta Mat., 31, (1983), 1047.

DOI: 10.1016/0001-6160(83)90200-6

[16] S. V. Divinski, M. Lohmann, Chr. Herzig, Interface science, 11, (2003), 21.

[17] Z. B. Wang, K. Lu, G. Wilde and S. Divinski, Appl. Phys. Let., 93 (2008), 131904.

[18] L. G. Harrison, Trans. Faraday Soc. 57, (1961), 1191.

[19] P. Neuhaus, Chr. Herzig, W. Gust, Acta Met., 37, (1989), 587.

[20] A.R. Paul, R.P. Agarwala, Metal. Trans. 2, (1971), 2691.

[21] A. Chaterjee, D.J. Fabian, Acta Met. 16, (1968), 789.

[22] A. Wazzan, J. Appl. Phys, 36, (1965), 3596.

[23] N. Dolgopolov, A. Rodin, A. Simanov, I. Gontar', Mat. Let., 62, (2008), 4477.

[24] M. Lohmann, S. V. Divinski, Chr. Herzig, Z. Metallkunde, 96, (2005), 532.

[25] M. Astahov, B. Bokstein, A. Rodin, M. Sinyaev: Izv. Vuzov, Non-ferr. Met. 4, (1998), 1.

[26] A. Habner, Krist. Tech., 9, (1974), 1374.

[27] H. Edelhoff, S. I. Prokofjev, S. V. Divinski, Scripta Mat, 64, (2011), 374.

[28] S.J. Rothman, Chapter 1, in Diffusion in Crystalline Solids, G.E. Murch and A.S. Nowick, eds., Academic Press, Orlando (1984).

[29] H. Mehrer, Diffusion in Solids: Fundamentals, Methods. Materials, Diffusion-Controlled Processes, Springer-Verlag, Berlin (2007).

[30] I.V. Belova and G.E. Murch, Phil. Mag., 81, (2001), 2447.

[31] S.V. Divinski, F. Hisker, Y. -S. Kang, J. -S. Lee and Chr. Herzig., Z. Metallk., 93, (2002), 256.

[32] I.V. Belova and G.E. Murch, Def. Diff. Forum, 258/260, (2006), 483.

[33] I.V. Belova and G.E. Murch, Def. Diff. Forum, 273/276, (2008), 425.

[34] I.V. Belova and G.E. Murch, Def. Diff. Forum, 283/286, (2009), 697.

[35] I.V. Belova and G.E. Murch, Phil. Mag. 89, (2009), 665.

[36] S.V. Divinski, and L.N. Larikov, Def. Diff. Forum, 143/147 (1997), 1469.

[37] I V Belova, T Fiedler, N Kulkarni and G E Murch, The Philosophical Magazine, 92, (2012), 1748.

[38] I.V. Belova and G.E. Murch, Phil. Mag. 81, (2001), 2447.

[39] I.V. Belova and G.E. Murch, Defect and Diffusion Forum, 218, (2003), 79.

[40] E.W. Hart, Acta Metall. 5, (1957), 597.

[41] J.R. Kalnin, E.A. Kotomin and J. Maier, J. Phys. Chem. Solids, 63, (2002), 449.

[42] J.C. Maxwell-Garnett, Phil. Trans. Roy. Soc. London, 203, (1904), 386.

[43] B.S. Bokshtein, I.A. Magidson and I.L. Svetlov, Phys. Met. Metallogr., 6(6), (1958), 81.

[44] G.B. Gibbs, Phys. Stat. Solidi (a), 16, (1966), K27.

[45] T. Suzuoka, Trans. Jap. Inst. Metals, 2, (1961), 25.

[46] H.S. Levine and C.J. MacCallum, J. Appl. Phys., 31, (1960), 595.

[47] I.V. Belova, G.E. Murch, T. Fiedler and A. Öchsner, Def. Diff. Forum, 283/286, (2009), 13.

[48] I.V. Belova, G.E. Murch, T. Fiedler and A. Öchsner, Def. Diff. Forum, 279, (2008), 13.