Capillarity-Mediated Grain Growth in 3-D

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Space-filling in kinetically active 3-d network structures, such as polycrystalline solids at high temperatures, is treated using topological methods. The theory developed represents individual network elements—the polyhedral cells or grains—as a set of objects called average N-hedra, where N, the topological class, equals the number of contacting neighbors in the network. Average N-hedra satisfy network topological averages for the dihedral angles and quadrajunction vertex angles, and, most importantly, act as “proxies” for real irregular polyhedral grains with equivalent topology. The analysis provided in this paper describes the energetics and kinetics of grains represented as average N-hedra as a function of their topological class. The new approach provides a quantitative basis for constructing more accurate models of three-dimensional grain growth. As shown, the availability of rigorous mathematical relations for the curvatures, areas, volumes, free energies, and rates of volume change provides precise predictions to test simulations of the behavior 3-d networks, and to guide quantitative experiments on microstructure evolution in three-dimensional polycrystals.

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Periodical:

Materials Science Forum (Volumes 467-470)

Edited by:

B. Bacroix, J.H. Driver, R. Le Gall, Cl. Maurice, R. Penelle, H. Réglé and L. Tabourot

Pages:

1025-1032

Citation:

M. E. Glicksman, "Capillarity-Mediated Grain Growth in 3-D", Materials Science Forum, Vols. 467-470, pp. 1025-1032, 2004

Online since:

October 2004

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$38.00

[1] C.S. Smith, Grain Shapes and other Metallurgical Applications of Topology, Chapter in Metal Interfaces, American Society for Metals, Cleveland, OH, 1952, p.65.

[2] J. von Neumann, in Metal Interfaces, written discussion, American Society for Metals, Cleveland, OH, 1952, p.108.

[3] W. W. Mullins, J. Appl. Phys. 27, 1956, p.900.

[4] V. Fradkov, M. Palmer, J. Nordberg, M.E. Glicksman, and K. Rajan, Physica D 66, 1993, p.50. 7.

[5] V. E. Fradkov, M. Palmer, M.E. Glicksman, and K. Rajan, Acta Metall. Mater., 42, No. 8, 1994, p.2719.

[6] M. A. Palmer, V.E. Fradkov, M.E. Glicksman, and K. Rajan, Scripta Met. et Mat., 30, 1994, p.633.

[7] M.A. Palmer, M.E. Glicksman, K. Rajan, V. Fradkov, and J. Nordberg, Metall. and Mat. Trans. A, 26A, 1995, p.1061.

[8] E.B. Matzke, Am.J. Botany, 33, 1946, p.58.

[9] E.B. Matzke, in Metal Interfaces, written discussion, American Society for Metals, Cleveland, OH, 1952, p.110.

[10] F. Graner, Y. Jiang, E. Janiaud, and C. Flament, Phys. Rev. E., 63, 2001, p.402.

[11] M.F. Vaz and M.A. Fortes, F. Graner, Phil. Mag. Lett., 82, 2002, p.575.

[12] W.W. Mullins,J. Appl. Phys., 59, 1986, p.1341.

[13] W.W. Mullins, Acta Metall., 37, 1989, p.2979.

[14] D. Weaire and J.A. Glazier, Phil. Mag. Lett., 68, 1998, p.363.

[15] J.A. Glazier, Phys. Rev. Lett., 70, 1993, p.2170.

[16] C. Monnereau and M. Vignes-Adler, Phys. Rev. Lett., 80, 1998, p.5228.

[17] D. Wu, Private Communication, (2003).

[18] K. Brakke, Exper. Math. 1, 1992, p.141.

[19] K. Brakke, (http: /geom. umn. edu/software/evolver), (2002).

[20] C. Monnereau, N. Pittet, and D. Weaire, Europhys. Lett., 52, 2000, p.361.

[21] S. Hilgenfeldt, A.M. Kraynik, S.A. Koehler, and H.A. Stone, Phys. Rev. Lettr., 86, 2001, p.2685.

[22] S.J. Cox and M.A. Fortes, Phil. Mag. Lettr., 83, 2003, p.28.

[23] A. Rollett, Private Communication, (2003).

[24] C.P. Gonatus, J.S. Leigh, A.G. Yodh, J.A. Glazier, and B. Prause, Phys. Rev. Lettr., 75, 1995, p.573.

[25] J.A. Glazier and B. Prause, in Foams, Emulsions and Their Applications,P. Zitha et al. eds., MIT-Verlag, Bremen, 2000, p.120.

[26] S.J. Cox Private Communication, (2003).

[27] R.T. DeHoff, Acta Metall. Mater., 42, no. 8, 1994, p.2633.

[28] H.S.M. Coxeter, M.S. Longuet-Higgins, and J.C.P. Miller, Phil. Trans. Roy. Soc. London, Series A, 236, 1954, p.401. This article was processed using the LATEX macro package with TTP style.