**6. Summary**

The *phase-field method* for simulation can provide important results, qualitatively and quanti‐ tatively, about the microstructural phenomena. This is based on the solution of the Cahn-Hilliard equation and it is a powerful tool to carry out the numerical simulation of the phase decomposition in binary and ternary alloys. The numerical simulation, by mean of the explicit finite difference method, is useful not only to analyze the growth kinetics of phase decompo‐ sition but also to determine the morphology of the decomposed phases. Besides, the calculated results show, in general, a good agreement with the experimental results during the aging of these alloys. Additionally, it is interesting to notice that the simulated results enable us to analyze the effect of different parameter such as the atomic mobility and the elastic-strain energy on the growth kinetics and phase morphology of the decomposed phases. Besides, it is important to mention that the numerical simulation permits to analyze the phase decom‐ position from the early to the late stages of aging which is useful to analyze both the spinodal decomposition and coarsening processes. In the case of the Ni-30at.%Cu alloy, the application of the phase-field method to simulate the microstructural evolution confirmed that the growth kinetics of phase decomposition is very slow in Ni-Cu alloys because of the low atomic diffusive process at temperatures lower than 322°C. However, when a third alloying element, like Fe, is added to this system, the spinodal decomposition process occurs more quickly. Finally, in the case of the Fe-40at.%Cr alloy, it can be clearly observed that the coarsening process of decomposed phases takes place since several concentration fluctuations are grouped in one peak as the aging time progresses.
