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Surface Energy and Microstructure

Published online by Cambridge University Press:  25 February 2011

Robert V. Kohn  and
Stefan MÜtller
Robert V. Kohn
Affiliation:
Courant Institute, 251 Mercer Street, NY, NY 10012, USA
Stefan MÜtller
Affiliation:
Universität Bonn, Institut für Angewandte Mathematik, Beringstr. 4, D-5300 Bonn 1, Germany
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Abstract

Bulk energy considerations can predict the gross features of microstructures observed in martensitic phase transitions, but not finer details such as the length scale on which twinning occurs. These are determined by surface energy. A standard approach is to minimize the sum of bulk and surface energy within the class of “twinned” configurations. This leads to the conclusion that the twin width w and the twin length L should satisfy w ∼L∼. While that seems to be the rule, a different structure is sometimes observed, for example in In-Tl and Cu-Al-Ni. It involves successive coarsening of the twins away from an austenite/twinned-martensite interface.

We re-examine the minimization of bulk plus surface energy. Our analysis differs from prior ones in that it permits configurations which are not essentially “onedimensional” to compete in the minimization. We find that the global minimum of energy can be either “one-dimensional” or “branched,” depending on the relative values of the elastic moduli and surface energy density.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 246: Symposium M – Shape-Memory Materials and Phenomena--Fundamental Aspects and Applications , 1991 , 19
Copyright
Copyright © Materials Research Society 1992

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References

[1]Ball, J. M. and James, R. D., Arch. Rat. Mech. Anal. 100, 13 (1987); A. G. Khachaturyan, Theory of Structural Transformations in Solids (John Wiley & Sons, 1983); A. L. Roitburd, in Solid State Physics 33, edited by N. Ehrenreigh, R. Seitz, and D. Turnbull, (Academic Press, 1978), p. 317.Google Scholar
[2]Christian, J. W., The Theory of Transformations in Metals and Alloys (Pergamon Press, 1975); C. M. Wayman, Introduction to the Theory of Martensitic Transformations (Macmillan, 1964).Google Scholar
[3]Barsch, G. R., Horovitz, B., and Krumhansl, J. A., Phys. Rev. Lett. 59, 1251 (1987; Phys. Rev. B43, 1021 (1991).Google Scholar
[4]Basinski, Z. S. and Christian, J. W., Acta Metall. 2, 148 (1954); K. Shimizu and K. Otsuka, in Shape Memory Effects in Alloys, edited by J. Perkins (Plenum Press, 1975) p. 59; D. Schryvers (private communication).Google Scholar
[5]Lifschitz, E. M., J. of Physics 8, 337 (1944); I. Privorotskii, Thermodynamic Theory of Domain Structures (John Wiley & Sons, 1976).Google Scholar
[6]Kohn, R. V. and S. Müller, “Branching of twins near an austenite/twinnedmartensite interface,” preprint.Google Scholar
[7]Kohn, R. V. and Müller, S., “Surface energy and microstructure in coherent phase transitions,” preprint.Google Scholar