Abstract
A new model for homogeneous nucleation of structural phase transformations, which can span the range of nucleation from classical to nonclassical, is presented. This model is extended from the classical nucleation theory by introducing driving-force dependencies into the interfacial free energy, the misfit strain energy, and the nucleus chemical free-energy change in order to capture the nonclassical nucleation phenomena. The driving-force dependencies are determined by matching the asymptotic solutions of the new model for the nucleus size and the nucleation energy barrier to the corresponding asymptotic solutions of the Landau-Ginzburg model for nucleation of solid-state phase transformations in the vicinity of lattice instability. Thus, no additional material parameters other than those of the classical nucleation theory and the Landau-Ginzburg model are required, and nonclassical nucleation behavior can be easily predicted based on the well-developed analytical solutions of the classical nucleation model. A comparison of the new model to the Landau-Ginzburg model for homogeneous nucleation of a dilatational transformation is presented as a benchmark example. An application to homogeneous nucleation of a cubic-to-tegragonal transformation is presented to illustrate the capability of this model. The nonclassical homogeneous nucleation behavior of the experimentally studied fcc → bcc transformation in the Fe-Co system is examined by the new model, which predicts a 20 pct reduction in the critical driving force for homogeneous nucleation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J.C. Fisher, J.H. Hollomon, and D. Turnbull: Trans. AIME, 1949, vol. 185, pp. 691–700.
L. Kaufman and M. Cohen: in Progress in Metal Physics, B. Chalmers and R. King, eds., Pergamon Press, New York, NY, 1958, vol. 7, pp. 165–246.
J.W. Christian: The Theory of Transformations in Metals and Alloys, 2nd ed., Pergamon, Oxford, United Kingdom, 1975.
D.A. Porter and K.E. Easterling: Phase Transformations in Metals and Alloys, 2nd ed., Chapman and Hall, London, 1992.
G.B. Olson and A.L. Roitburd: in Martensite, G.B. Olson and W.S. Owen, eds., ASM INTERNATIONAL, Materials Park, OH, 1992.
A.L. Roitburd: in Solid State Physics, H. Ehrenreich, F. Seitz, and D. Turnbull, eds., Academic Press, New York, NY, 1978, vol. 33, pp. 317–90.
G.B. Olson and M. Cohen: J. Phys., 1982, vol. 43, pp. C4-C5.
D.M. Haezebrouck: Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1987.
B. Moran, Y.A. Chu, and G.B. Olson: Int. J. Solid Structure, 1996, vol. 33 (13), pp. 1903–19.
Y.A. Chu and B. Moran: Modelling Simul. Mater. Sci. Eng., 1995, vol. 3, pp. 455–71.
T. Belytschko, Y.Y. Lu, and L. Gu: Int. J. Num. Methods Eng., 1994, vol. 37, pp. 229–56.
Y.Y. Lu, T. Belytschko, and L. Gu: Comput. Methods Appl. Mech. Eng., 1994, vol. 113, pp. 397–414.
G.R. Barsch and J.A. Krumhansl: Phys. Rev. Lett., 1984, vol. 53(11), pp. 1069–72.
G.R. Barsch and J.A. Krumhansl: Metall. Trans. A, 1988, vol. 19A, pp. 761–75.
M. Lin, G.B. Olson, and M. Cohen: Acta Metall. Mater., 1993, vol. 41(1), pp. 253–63.
J.D. Eshelby: Proc. R. Soc., 1957, vol. A241, pp. 376–96.
J.D. Eshelby: Proc. R. Soc., 1959, vol. A252, pp. 561–69.
T. Mura: Micromechanics of Defects in Solids, 2nd ed., Academic Publishers, Hingham, MA, Kluwer, 1987.
J.W. Cahn and J.E. Hilliard: J. Chem. Phys., 1958, vol. 28, pp. 258–67.
P. Hong: Ph.D. Thesis, Northwestern University, Evanston, IL, 1994.
P. Hong and G.B. Olson: Solid State Commun., 1993, vol. 85(8), pp. 681–83.
S.H. Wen, E. Kostlan, M. Hong, A.G. Khachaturyan, and J.W. Morris, Jr.: Acta Metall., 1981, vol. 29, pp. 1247–54.
Y.A. Chu: Ph.D. Thesis, Northwestern University, Evanston, IL, 1996.
G.L. Krasko and G.B. Olson: Phys. Rev. B, 1989, vol. 40(17), pp. 11536–11545.
A.G. Khachaturyan: Theory of Structural Phase Transformations in Solids, John Wiley and Sons Inc., New York, 1983.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chu, Y.A., Moran, B., Olson, G.B. et al. A model for nonclassical nucleation of solid-solid structural phase transformations. Metall Mater Trans A 31, 1321–1331 (2000). https://doi.org/10.1007/s11661-000-0251-7
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11661-000-0251-7