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Read-Shockley Grain Boundaries and the Herring Equation

  • Shashank Shekhar (a1) and Alexander H. King (a2)

Abstract

We compute the strain fields and the interactions between dislocations at the junctions of classical small-angle grain boundaries. It is shown that, in contrast with the results for infinite small-angle boundaries, there are always forces acting on the dislocations in the arrays that define the grain boundaries, and that there is also an excess elastically stored energy associated with the triple junction (TJ). The forces on the dislocations and the excess stored energy of the TJ are shown to vary with the dihedral angles formed by the grain boundaries, and that the “equilibrium” dihedral angle based upon the Herring equation and the energies of the individual grain boundaries does not correspond to any kind of force or energy minimum. This relates to an unwarranted assumption in Herring's original derivation, that no interactions occur between the grain boundaries that make up a TJ.

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References

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1. Burgers, J. M., Proc. Kon. Ned. v. Wet. Amsterdam 42, 293 (1939).
2. Read, W. T. and Shockley, W., Physical Review 78, 275289 (1950).
3. King, A. H., MRS Proc. Ser. 472, 113118 (1997).
4. Herring, C., in The Physics of Powder Metallurgy, McGraw-Hill, New York, 1949, p. 143179.
5. Gjostein, N. A. and Rhines, F. N., Acta Metallurgica 7, 319330 (1959).
6. Shekhar, S., PhD Thesis, Purdue University, 2007.
7. Dougherty, L. M., Robertson, I. M. and Vetrano, J. S., Acta Mater. 51, 43674378 (2003).
8. Protasova, S. G., Gottstein, G., Molodov, D. A., Sursaeva, V. G. and Shvindlerman, L. S., Acta Mater. 49, 25192525 (2001).

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