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Read-Shockley Grain Boundaries and the Herring Equation

Published online by Cambridge University Press:  01 February 2011

Shashank Shekhar  and
Alexander H. King
Shashank Shekhar
Affiliation:
[email protected], Purdue University, School of Materials Engineering, 701 Northwestern Avenue, Neil Armstrong Hall of Engineering, West Lafayette, IN, 47907, United States
Alexander H. King
Affiliation:
[email protected], The Ames Laboratory, Office of the Director, 311 TASF, Iowa State University, Ames, IA, 50014-3020, United States
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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.

Keywords

grain boundariesdislocationselastic properties
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 1090: Symposium Z – Materials Structures–The Nabarro Legacy , 2008 , 1090-Z05-18
Copyright
Copyright © Materials Research Society 2008

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