Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-18T10:29:43.706Z Has data issue: false hasContentIssue false

Phase Separation and Elastic Fields: Three Dimensional Simulations of a Phase Field Model

Published online by Cambridge University Press:  15 February 2011

Daniel Orlikowski
Affiliation:
Department of Physics, North Carolina State University, Raleigh NC 27695
Celeste Sagui
Affiliation:
Department of Physics, North Carolina State University, Raleigh NC 27695
Andrds Somoza
Affiliation:
Departamento de Fisica, Universidad de Murcia, Apartado 4021 E-30080, Murcia, Spain
Christopher Roland
Affiliation:
Department of Physics, North Carolina State University, Raleigh NC 27695
Get access

Abstract

The effects of long-range elastic fields on the phase separation process of three- dimensional binary alloy systems was investigated with large-scale Langevin simulations. The elastic effects incorporated in the model are the result of anisotropy and dilational misfits introduced via inhomogeneities in the elastic constants of the constituents. The domain morphology obtained is readily understandable in terms of selection criterion for the shape and/or orientation of the domains, and is based on the different shear moduli that are present in the system. Coarsening mechanisms were found to be a combination of the classical Ostwald ripening mechanism and the elastically-driven coalescence of domains. Other aspects of the coarsening process such as dynamic scaling of the structure function is presented.

Type
Research Article
Copyright
Copyright © Materials Research Society 2000

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] Lifshitz, I.M. and Slyozov, V.V., J. Phys. Chem. Solids 19, 35 (1961).Google Scholar
[2] See, for example: , Landau and , Lifshitz, Theory of Elasticity, 3rd edition, Pergamon Press (New York 1986); A.G. Khatchaturyan, Theory of Structural Transformations in Solids (Wiley, New York, 1983).Google Scholar
[3] Ardell, A.J., Nicholson, R.B. and Eshelby, J.D., Acta Metall. 14, 1295 (1966);Google Scholar
Maheshwari, A. and Ardell, A.J., Phys. Rev. Lett. 70, 2305 (1993);Google Scholar
Meshkimpour, M. and Ardell, A.J., Mat. Sci. Eng. A 185, 153 (1994);Google Scholar
Wimmel, J. and Ardell, A.J., Mat. Sci. Eng. 183, 169 (1994);Google Scholar
Kamora, A.B., Ardell, A.J., and Wagner, C.N., Metall. and Mat. Trans. 27A, 2888 (1996);Google Scholar
Cho, J.H.- and Ardell, A.J., Acta Mater. 45, 1399 (1997).Google Scholar
[4] Miyasaki, T., Nakamuara, K. and Mori, H., J. Mater. Sci. 14, 1827 (1979);Google Scholar
Bendersky, L.A., Voorhees, P.W., Boettinger, W.J. and Johnson, W.C., Scripta Metall. 22, 1029 (1988);Google Scholar
Hein, W., Acta Metall. 37, 2145 (1989).Google Scholar
[5] Calderon, H. and Kostorz, G., in Neutron Scattering for Materials Science (edited by Shapiro, S.M., Moss, S.C. and Jorgensen, J.D.), Vol. 166, p. 210 Mat. Res. Soc. Symp. Proc. (1990).Google Scholar
[6] Maheshwari, A. and Ardell, A.J., Scripta Metall. Mater. 26, 347 (1992).Google Scholar
[7] Calderon, H.A., Kostorz, G., Qu, Y.Y., Dorantes, H.J., Cruz, J.J. and CabanasMoreno, J.G., Mater. Sci. Eng. A 238, 13 (1997).Google Scholar
Ges, A., Fornaro, O. and Palacio, H., J. Mater. Sci. 32, 3687 (1997).Google Scholar
[8] Cahn, J.W., Acta Metall. 9, 795 (1961); 10, 179 (1962).Google Scholar
[9] Onuki, A., J. Phys. Soc. Jpn. 58, 3065 (1989); 58, 3069 (1989);Google Scholar
Nishimori, H. and Onuki, A., Phys. Rev. B 42, 980 (1990);Google Scholar
Onuki, A. and Nishimori, H., J. Phys. Soc. Jpn. 60, 1 (1991);Google Scholar
Onuki, A. and Nishimori, H., Phys. Rev. B 43, 13649 (1991);Google Scholar
Nishimori, H. and Onuki, A., J. Phys. Soc. Jpn. 60, 1208 (1991).Google Scholar
[10] Sagui, C., Somoza, A. and Desai, R.C., Phys. Rev. E 50, 4865 (1994).Google Scholar
[11] Sagui, C., Orlikowski, D., Somoza, A. and Roland, C., Phys. Rev. E 58, R4092 (1998);Google Scholar
Orlikowski, D., Sagui, C., Somoza, A. and Roland, C., Phys. Rev. B 59, 8646 (1999).Google Scholar
[12] Fratzl, P. and Lebowitz, J.L., Acta Metall. 37, 3245 (1989);Google Scholar
Fratzl, P., Lebowitz, J.L., Penrose, O. and Amar, J., Phys. Rev. B 44, 4794 (1991).Google Scholar
[13] Yeung, C., Phys. Rev. Lett. 61, 1135 (1988);Google Scholar
Roland, C. and Grant, M., Phys. Rev. B 39, 11971 (1989).Google Scholar