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Extracting the Grain Boundary Character/Free Energy Relationship from the Microstructure: Pure <100> and <111> Tilt Boundaries

Published online by Cambridge University Press:  10 February 2011

B. Adams ,
D. Kinderlehrer ,
S. Ta'asan ,
W.W. Mullins  and
S. Costiner
B. Adams
Affiliation:
Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213–3890
D. Kinderlehrer
Affiliation:
Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213–3890
S. Ta'asan
Affiliation:
Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213–3890
W.W. Mullins
Affiliation:
Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213–3890
S. Costiner
Affiliation:
Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213–3890
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Abstract

Analysis is described to extract the excess free energy of grain boundaries from the mesotexture of well-equilibrated polycrystalline samples. The approach is based upon the force and torque balances at triple junctions described in the classical work of Herring [1]. The main advantage of the approach is that the free energy function is obtained over the full fundamental zone of grain boundary types. For the purposes of exposition, the method is described for specified two-parameter hypersurfaces in the fundamental zone for cubic polycrystals (the sets of pure <100> and <111> tilt boundaries) and the free energy is assumed to depend only upon the lattice misorientation. Results from testbed simulations are presented.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 472: Symposium I – Polycrystalline Thin Films - Structure, Texture, Properties..III , 1997 , 105
Copyright
Copyright © Materials Research Society 1997

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References

REFERENCES

1. Herring, C., in Structure and Properties of Solid Surfaces, Gomer, R. and Smith, C. S., eds., 1952, Chicago: University of Chicago Press.Google Scholar
2. Adams, B. L., Wright, S. I. and Kunze, K., Metallurgical Transactions, 24A (1993), 819.Google Scholar
3. Lejcek, P. and Hofmann, S., CRC Critical Reviews in Solid State and Materials Science, 20 (1995), 1.Google Scholar
4. Gibbs, J. W., The Scientific Papers of J. Willard Gibbs, Vol. 1: Thermodynamics, 1962, New York: Dover Publications.Google Scholar
5. Mullins, W. W., in Metal Surfaces: Structure, Energetics and Kinetics, Robertson, W. D. and Gjostein, N. A., eds., 1963, p. 17, Metals Park: The American Society for Metals.Google Scholar