Determination of Percolation Threshold for Random Boundary Network on the Basis of EBSD/OIM Observations


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Grain boundary engineering through the control of grain boundary character distribution (GBCD) has been extensively employed as a powerful tool for achieving enhanced properties and for development of high performance both structural and functional polycrystalline materials. Many efforts were made firstly to increase the frequency of low-energy CSL boundaries of polycrystalline materials in grain boundary engineering. However, the connectivity of grain boundaries can be an important microstructural parameter governing bulk properties of polycrystalline materials as well as the GBCD. In the present work, the connectivity of random grain boundaries was quantitatively evaluated using both the triple junction distribution and random boundary cluster length on the basis of SEM-EBSD/OIM observations, and then these evaluated parameters were linked to intergranular corrosion of SUS304 stainless steel. We have found that the length of the maximum random boundary cluster drastically decrease with increasing CSL boundaries in the fraction ranging 60 – 80% CSL boundaries, which leads to percolation threshold occurring at approximately 70±5% CSL boundary fraction (at 30±5% random boundary fraction). The experimentally observed percolation threshold is much higher than theoretically obtained one based on randomly assembled network (at 35% resistant bonds for a 2D hexagonal lattice). In addition, the fraction of resistant triple junctions is found to increase with increasing the the CSL boundary fraction. An increase in the frequency of resistant triple junctions can enhance intergranular corrosion resistance of polycrystalline austenitic stainless steel even if the GBCD is the same.



Materials Science Forum (Volumes 539-543)

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Edited by:

T. Chandra, K. Tsuzaki, M. Militzer , C. Ravindran




S. Tsurekawa et al., "Determination of Percolation Threshold for Random Boundary Network on the Basis of EBSD/OIM Observations", Materials Science Forum, Vols. 539-543, pp. 2371-2376, 2007

Online since:

March 2007




[1] H. Gleiter and B. Chalmers: Prog. Mater. Sci. Vol. 16 (1972), p.1.

[2] G.A. Chadwick and D.A. Smith (ed): Grain Boundary Structure and Properties (Academic Press 1976) Fig. 5 SEM micrographs of the cross-sections in the samples A (a) and B (b) after the ferric sulfate-sulfuric acid test for 48h, showing the influence of grain boundary connectivity on corrosion percolation. The frequency of resistant triple junction is twice as high in the sample B (0. 19) than in the sample A (0. 10) but both of samples have the same frequency of CSL boundaries (0. 5).

[3] Y. Ishida (ed): Grain Boundary Structure and Related Phenomena (Trans. JIM suppl. 27 (1986).

[4] A.P. Sutton, R.W. Balluffi: Interfaces in Crystalline Materials (Oxford Sci Pub 1995).

[5] T. Watanabe: Res Mechanica Vol. 11 (1984), p.47.

[6] E.M. Lehockey, G. Palumbo P. Lin and A.M. Brennenstuhl: Scripta Mater Vol. 36 (1997), p.1211.

[7] S. Tsurekawa and T. Watanabe: Mat. Res. Soc. Symp. Proc. Vol. 586 (2000), p.237.

[8] S. Yamaura, S. Tsurekawa and T. Watanabe: Mater. Trans. Vol. 44 (2003), p.1494.

[9] T. Watanabe, H. Fujii, H. Oikawa and K.I. Arai: Acta Metall Vol. 37 (1989), p.941.

[10] T. Hirano: Acta Metall Mater Vol. 38 (1990), p.2667.

[11] D.C. Crawford and G.S. Was: Metall Trans Vol. 23A (1992), p.1195.

[12] T. Watanabe, T. Hirano, T. Ochiai and H. Oikawa: Mater Sci Forum Vol. 157-162 (1994), p.1103.

[13] P. Lin, G. Palumbo, U. Erb and K.T. Aust: Scripta Metall Mater Vol. 33 (1995), p.1387.

[14] G. Palumbo, E.M. Lehockey, P. Lin, U. Erb and K.T. Aust: Mat. Res. Soc. Symp. Proc. Vol. 458 (1997), p.273.

[15] E.M. Lehockey and G. Palumbo: Mater Sci Eng Vol. A237 (1997), p.168.

[16] V. Thaveeprungsriporn and G.S. Was: Metall Mater Trans Vol. 28A (1997), p.2101.

[17] E.M. Lehockey, G. Palumbo, P. Lin and A. Brennenstuhl: Metall Mater Trans Vol. 29A (1998), p.387.

[18] E. M. Lehockey, D. Limoges, G. Palumbo, J. Sklarchuk, K. Tomantschger and A. Vincze: J. Power Sources Vol. 78 (1999), p.79.


[19] M. Shimada, H. Kokawa, Z.J. Wang, Y.S. Sato and I. Karibe: Acta Mater Vol. 50 (2002), p.2331.

[20] S. Kobayashi, T. Yoshimura, S. Tsurekawa and T. Watanabe: Mater Trans Vol. 44 (2003), p.1469.

[21] R. Ishibashi, T. Horiuchi, J. Kuniya, M. Yamamoto, S. Tsurekawa, H. Kokawa, T. Watanabe and T. Shoji: Mater Sci Forum Vol. 475-479 (2005), p.3863.

[22] Y. Furuya, N.W. Hagood, H. Kimura and T. Watanabe: Mater Trans JIM Vol. 39 (1998), p.1248.

[23] C.A. Schuh, R.W. Minich, M. Kumar: Phil. Mag. Vol. 83 (2003), p.711.

[24] M. Frary and C.A. Schuh: Phil Mag Vol. 85 (2005), p.1123.

[25] D. Stauffer and A. Aharony: Introduction to percolation theory (London, Taylor and Francis 1992).

[26] P. Fortier, K.T. Aust and W.A. Miller: Acta Metall. Mater. Vol. 43 (1995), p.339.

[27] P. Fortier, W.A. Miller, K.T. Aust: Acta Mater. Vol. 45 (1997), p.3459.

[28] M. Kumar, W.E. King and A.J. Schwartz: Acta Mater. Vol. 48 (2000), p. (2081).

[29] T. Watanabe: Textures and Microstructures Vol. 20 (1993), p.195.

[30] S. Tsurekawa, S. Nakamichi and T. Watanabe: Acta Mater. (Submitted).

[31] D.B. Wells, J. Stewart, A.W. Herbert, P.M. Scott and D.E. Williams: Corrosion Vol. 45 (1989), p.649.

[32] E.S. McGarrity, P.M. Duxbury and E.A. Holm: Phys. Rev. E Vol. 71 (2005), p.026102.