Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-28T14:33:57.706Z Has data issue: false hasContentIssue false
  • English
  • Français

Equilibrium shapes of semicoherent inclusions

Published online by Cambridge University Press:  31 January 2011

Craig Rottman
Craig Rottman
Affiliation:
Department of Physics, North Dakota State University, Fargo, North Dakota 58105-5566
Get access

Abstract

The equilibrium shapes of stress free inclusions with a small mismatch and possibly a small rotation from the matrix phase are studied. The model used includes both bond-breaking and elastic contributions to the interface energy. The unrotated shape contains only facets. Rotated inclusions sometimes contain smoothly curved parts as well. Interface phase diagrams are used to characterize the stable phase behavior of flat interfaces of fixed orientation.

Type
Articles
Information
Journal of Materials Research , Volume 7 , Issue 4 , April 1992 , pp. 1029 - 1036
Copyright
Copyright © Materials Research Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. For recent reviews see Wortis, M., in Chemistry and Physics of Solid Surfaces, edited by Vanselow, R. (Springer-Verlag, Berlin, 1988), Vol. VII, pp. 367–405; C. Rottman and M. Wortis, Phys. Rep. 103, 59 (1984).Google Scholar
2.Herring, C., Phys. Rev. 82, 87 (1951); in Structure and Properties of Solid Surfaces, edited by Gomer, R. and Smith, C. S. (University of Chicago, Chicago, IL, 1953), p. 5ff.Google Scholar
3.Wang, S-W., Falicov, L. M., and Searcy, A. W., Surf. Sci. 143, 609 (1984).CrossRefGoogle Scholar
4.Porter, D. A. and Easterling, K. E., Phase Transformations in Metals and Alloys (Van Nostrand Reinhold, Wokingham, 1981), pp. 142–172.Google Scholar
5. In this more general case the shape, which now is volume dependent, has rarely if ever been investigated for a specific model.Google Scholar
6. The work here presents more details and also some corrections to a previous report. See C. Rottman, in Structure/Property Relationships for Metal/Metal Interfaces, edited by Romig, A. D., Fowler, D. E., and Bristowe, P. D. (Mater. Res. Soc. Symp. Proc. 229, Pittsburgh, PA, 1991).Google Scholar
7. Recently nonlattice models (incorporating relaxations near the interface) using pair potentials and the embedded atom method have been used to study free surfaces and grain boundaries at T = 0 K. From the values () found for surfaces it should be straightforward to find the inclusion shape. See D. Wolf, Surf. Sci. 226, 389–406 (1990); J. Mater. Res. 5, 1708 (1990).CrossRefGoogle Scholar
8. See the references in Tochov, S., in Crystal Growth: An Introduction, edited by Hartman, P. (North-Holland, Amsterdam, 1973), pp. 328–341; P. Bennema, ibid., pp. 342–357.Google Scholar
9.Dreschsler, M. and Nicholas, J. F., J. Phys. Chem. Solids 23, 185 (1962).Google Scholar
10. Temperature effects have been studied (without statistical mechanics) by incorporating a simple lattice expansion. See Ref. 9.Google Scholar
11.Read, W.T. and Shockley, W., Phys. Rev. 78, 275 (1950); A-C. Shi, C. Rottman, and Y. He, Philos. Mag. A 55, 499 (1987).CrossRefGoogle Scholar
12.Smith, D. A. and Hazzledine, P. M., Scripta Metall. 15, 393 (1981).CrossRefGoogle Scholar
13.He, Y., Jayaprakash, C., and Rottman, C., Phys. Rev. B 32, 12 (1985).CrossRefGoogle Scholar
14.DiVincenzo, D. P. and Rottman, C., Phys. Rev. B 37, 5242 (1988).CrossRefGoogle Scholar
15.Brooks, H., in Metal Interfaces (American Society for Metals, Metals Park, OH, 1952), p. 20ff.Google Scholar
16. For all relevant figures I take λ = 1.Google Scholar