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Phase Field Approach to Transformations Involving Concurrent Nucleation and Growth

Published online by Cambridge University Press:  15 February 2011

J.P. Simmons ,
C. Shen  and
Y. Wang
J.P. Simmons
Affiliation:
Air Force Research Laboratory, Materials and Manufacturing Directorate, Processing Science Group, AFRL/MLLM, Wright-Patterson AFB, Dayton, OH 45433.
C. Shen
Affiliation:
Department of Materials Science and Engineering, The Ohio State University, 2041 College Rd, Columbus, OH 43210.
Y. Wang
Affiliation:
Department of Materials Science and Engineering, The Ohio State University, 2041 College Rd, Columbus, OH 43210.
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Abstract

A model is developed that is capable of simulating simultaneous nucleation, growth, and coarsening. Growth and coarsening are simulated with a 2-D Phase Field model and nucleation is simulated by a stochastic algorithm. The actual nucleation events are simulated by placing ordered particles in the matrix, according to the local supersaturation, with the mean rate of introduction matching that of the nucleation rate. The nucleation rates are input parameters that could, for example, be supplied by experiment or atomistic modeling. Isothermal results for this model under conditions approaching constant nucleation show excellent agreement with the Johnson-Mehl- Avrami-Kolmogorov (JMAK) theory of isothermal transformations involving nucleation and growth. Because the Phase Field simulation is interrupted in order to put particles in, problems can arise due to the mismatch of the assumed diffusion field about the nucleating particles and that would be obtained as a result of growth. This can lead to numerical instabilities as the simulation parameters are adjusted to approach the site saturation extreme as well as underestimating the transformation rate by a small transient time. Preliminary step quench results showed the method to be stable enough to simulate non-isothermal transformations with a series of step quench operations.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 580: Symposium E – Nucleation & Growth Processes in Materials , 1999 , 417
Copyright
Copyright © Materials Research Society 2000

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References

1. Wei, D.Y., Russel, E.S., and Backman, D.G.: Modeling Across Length Scales for Materials Development, MRS Fall 1997, MRS, Boston, MA, 1997.Google Scholar
2. Rohrer, C.L., Asta, M.D., Foiles, S.M., and Hyland, R.W.: Thermodynamic and Kinetics of Phase Transformations, Im, J.S., Park, , and Stevenson, , eds., MRS, Boston, MA, 1995, vol. 398.Google Scholar
3. Hohenberg, P.C. and Halperin, B.I.: Rev. Mod. Phys., 1977, vol. 49, p. 435.Google Scholar
4. Gunton, J.D., Miguel, M.S., and Sahni, P.S.: Phase Transitions and Critical Phenomena, Domb, C. and Lebowitz, J.L., ed., Academic Press, New York, 1983, p. 267.Google Scholar
5. Elder, K.: Computers in Physics, 1993, vol. 7, p. 27.Google Scholar
6. Chen, L.-Q.: Scripta Metall. Mater, 1995, vol. 22, p. 115.Google Scholar
7. Chen, L.-Q. and Wang, Y.: JOM, 1996, vol. 48, p. 13.Google Scholar
8. Wang, Y, Chen, L.-Q., and Khachaturyan, A.G.: Computer Simulation in Materials Science, Kirchner, H.O., Kubin, K.P., and Pontikis, V., ed., Kluwer Academic Publishers, 1996, p. 325.Google Scholar
9. Tikare, V., Holm, E.A., Fan, D., and Chen, L.-Q.: Acta Mater, 1999, vol. 47, p. 363.Google Scholar
10. Wang, Y., Banerjee, D., Su, C.C., and Khachaturyan, A.G.: Acta Mater, 1998, vol. 46, p. 2983.Google Scholar
11. Banerjee, D., Banerjee, R., and Wang, Y.: Scripta Mater, 1999, vol. 41, p. 1023.Google Scholar
12. Landau, L.D. and Lifshitz, E.M.: Statistical Physics, Pergamon, Oxford, 1980, p. 363.Google Scholar
13. Wang, Y, Wang, H.-Y, Chen, L.-Q., and Khachaturyan, A.G.: J. Am. Ceram. Soc., 1995, vol. 78, p. 657.Google Scholar
14. Cahn, J.W.: Acta Metall., 1956, vol. 4, p. 449.Google Scholar
15. Swalin, R.A. and Martin, A.: Trans. AIME, 1956, vol. 206, p. 567.Google Scholar
16. Chen, L.Q. and Shen, J.: Comput. Phys. Comm., 1998, vol. 108, p. 147.Google Scholar
17. Feller, W.: An Introduction to Probability Theory and Its Applications, John Wiley and Sons, New York, 1950, p. 153.Google Scholar
18. Leonard, J.P. and Im, J.S.: paper given in this session.Google Scholar
19. Avrami, M.: J. Chem. Phys., 1940, vol. 8, p. 212.Google Scholar
20. Johnson, W.A. and Mehl, R.F.: Trans. AIME, 1939, vol. 135, p. 416.Google Scholar
21. Kolmogorov, A.E.: Akad. Nauk. SSR. ISV Ser Mat., 1937, vol. 1, p. 355.Google Scholar
22. Aaronson, H.I. and Lee, J.K.: Lectures on the Theory of Phase Transformations, Aaronson, H.I., ed., TMS, New York, 1975, p. 83.Google Scholar
23. Simmons, J.P., Shen, C., and Wang, Y: Scripta Mater et Metall., submitted for publication.Google Scholar
24. Avrami, M.: J. Chem. Phys., 1940, vol. 8, p. 212.Google Scholar
25. Christian, J.W.: The Theory of Phase Transformations in Metals and Alloys: Part I, 2nd ed., Pergamon Press, New York, 1975, p. 586.Google Scholar
26. Gottstein, G., Marx, V., and Sebald, R.: The Fourth International Conference on Recrystallization and Related Phenomena, Sakai, T. and Suzuki, H.G., eds., Japan Institute of Metals, 1999, p. 15.Google Scholar
27. Jou, H.-J. and Lusk, M.T.: Phys. Rev. B, 1997, vol. 55, p. 8114.Google Scholar
28. Khachaturyan, A.G.: Theory of Structural Transformations in Solids, John Wiley and Sons, New York, 1983, p. 198.Google Scholar