**Application of Phase-Field Method to the Analysis of Phase Decomposition of Alloys**

Erika O. Avila-Davila, Victor M. Lopez-Hirata and Maribel L. Saucedo-Muñoz

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/64153

#### **Abstract**

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This chapter is focused on the application of the phase-field method to the analysis of phase decomposition during the isothermal aging of alloys. The phase-field method is based on a numerical solution of either the nonlinear Cahn-Hilliard equation or the Cahn-Allen equation. These partial differential equations can be solved using the finite difference method among other numerical methods. The phase-field method has been applied to analyze different types of phase transformations in alloys, such as phase decomposition, precipitation, recrystallization, grain growth, solidification of pure metals and alloys, martensitic transformation, ordering reactions, and so on. One of the main advantages of phase-field method is that this method permits to follow the microstructure evolution in two or three dimensions as the time of phase transforma‐ tions progresses. Thus, the morphology, size, and size distribution could be deter‐ mined to follow their corresponding growth kinetics. Additionally, the evolution of chemical composition can also be followed during the phase transformations. Furthermore, both Allen-Cahn and Cahn-Hilliard equations can be solved simultane‐ ously to analyze the presence of ordered phases or magnetic domains in alloys.

The formation of phases in alloys usually takes place by nucleation mechanism, growth mechanism, or spinodal decomposition mechanism, which is followed by the coarsen‐ ing of phases in alloy systems. These three processes can be been analyzed using the phase-field method and their results can also be compared with the fundamental theories of phase transformations such as the Cahn-Hilliard spinodal decomposition theory and the Lifshitz-Slyozov-Wagner diffusion-controlled coarsening theory.

Therefore, this chapter first deals with the analysis of phase decomposition during the isothermal aging of hypothetical binary alloys using the nonlinear Cahn-Hilliard equation. To continue, the effect of main parameters, such as the atomic mobility interface energy and alloy composition, on the microstructure evolution and growth kinetics are discussed. To conclude, the application of phase-field method is extended

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

to the analysis of phase decomposition during isothermal aging of real binary and ternary alloy systems, such as Fe-Cr, Cu-Ni, and Cu-Ni-Fe. A comparison of simulat‐ ed results with experimental ones is also included.

**Keywords:** phase field method, phase decomposition, alloys, aging
