Toward Quantitative Modeling of Morphology Changes in Solids with Phase Field Theories: Atomistic Arguments for the Determination of Higher Gradient Coefficients


Article Preview



Key Engineering Materials (Volumes 240-242)

Main Theme:

Edited by:

Besim Ben-Nissan, Doron Sher, William Walsh




W. Dreyer and W. H. Müller, "Toward Quantitative Modeling of Morphology Changes in Solids with Phase Field Theories: Atomistic Arguments for the Determination of Higher Gradient Coefficients", Key Engineering Materials, Vols. 240-242, pp. 901-914, 2003

Online since:

May 2003




[1] R. Stevens: Zirconia and Zirconia Ceramics (Twickenham: Magnesium Elektron Publication 1986).

[2] W. Dreyer, W.H. Müller: A Study of the Coarsening in Tin/Lead Solders, Int. J. Sol. Struct, 37 28 (2000), pp.3841-3871.

[3] W. Dreyer, W.H. Müller: Modeling Diffusional Coarsening in Eutectic Tin/Lead Solders: A Quantitative Approach, Int. J. Sol. Struct., 38 1 (2001), pp.1433-1458.


[4] Dreyer, W., Müller, W.H.: Computer Modeling of Micromorphological Change by Phase Field Models: Applications to Metals and Ceramics. Journal of the Australasian Ceramic Society, 36 1 (2001), pp.83-94.

[5] J.W. Cahn, J.E. Hilliard: Free energy of a non-uniform system. I. Interfacial free energy. The Journal of Chemical Physics, 28 1 (1958), pp.258-267.


[6] A.G. Khachaturyan, S. Semenovskaya, T. Tsakalakos: Elastic strain energy of inhomogeneous solids. Physical Review B. 52 22 (1995), pp.15909-15919.


[7] M. McCormack, A.G. Khachaturyan, J.W. Morris Jr: A two-dimensional analysis of the evolution of coherent precipitates in elastic media. Acta metall. mater. 40 2 (1992), pp.325-336.


[8] Y. Wang, A.G. Khachaturyan: Shape instability during precipitate growth in coherent solids. Acta metall. Mater., 43 5 (1995), pp.1837-1857.


[9] T. Koyama, T. Miyazaki, M. Doi, A. E. -A. M. Mebed, T. Moriya: Computer simulation of phase decomposition in Fe-Mo alloy based on discrete type diffusion equation. J. Japan. Inst. Metals. 60 6 (1996), p.560568.


[10] T. Miyazaki, T. Koyama: Theoretical analysis of phase decomposition in real alloy systems based on the non-linear diffusion equation. Materials Transactions, JIM. 37 4 (1996), pp.684-690.


[11] MTData NPL Databank for Materials Thermochemistry. National Physical Laboratory, Queens Road, Teddington, Middlesex, TW11 0LW (1998).

[12] L. Löchte, G. Gottstein: Computer simulation of phase-transition of AlCu-alloys. Computational Materials Science 7 (1996), pp.115-117.

[13] G. Leibfried, G.: Gittertheorie der mechanischen und thermischen Eigenschaften der Kristalle, Encyclopedia of Physics, Volume VII, Part 1, Crystal Physics I, Springer Verlag, Berlin, Göttingen, Heidelberg (1955).


[14] D. de Fontaine: Clustering effect in solid solutions., In: Treatise on Solid State Chemistry. (N.B. Hannah, editor). Plenum Press, New York, London, pp.129-178 (1975).

[15] R.A. Johnson: Relationship between two-body interatomic potentials in a lattice model and elastic constants. Physical Review B, 6 6 (1972), pp.2094-2100.


[16] L.A. Girifalco, V.G. Weizer: Application of the Morse Potential Function to Cubic Metals. Phys. Rev. 114 3 (1959), pp.687-690.


[17] C. Kittel: Einführung in die Festkörperphysik, R. Oldenbourg Verlag, München, Wien (1976).

[18] M. Winter: WebElements™. University of Sheffield, http: /www. webelements. com/ index. html.

[19] H. Huang: Result: No super-modulus, effect in Ag/Cu multilayers. http: /hrl. harvard. edu/~gu/ huang/Result3. html.

[20] R. Becker: Theorie der Wärme. Springer Verlag, Berlin, Heidelberg, New York (1975).