Thanks to fundamental advances, coupled with the development of efficient algorithms and fast compu­ters, the PF technique has become a very powerful and versatile tool for simulating phase transforma­tions and microstructural evolution in materials, as illustrated in this chapter. This technique provides simulation tools that are complementary to atomistic models, such as molecular dynamics and lattice Monte Carlo simulations, and to larger scale approaches, such as finite element models. With some modifications, it can also be employed for mate­rials subjected to irradiation.

In the case of materials subjected to irradiation, specific issues need to be addressed to fully realize the potential of PF modeling. First, a proper descrip­tion of point defects and atom transport requires mobility matrices (or tensors) that capture the kinetic coupling between these different species. In particu­lar, the models reviewed in this chapter do not account for the correlated motion of point defects and atoms, thus leading to unphysical correlation factors in the mobility coefficients. These correlation effects, however, play an essential role in phenomena

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Figure 15 Defect concentration fields corresponding to Figure 14: (a) free vacancies CV, (b) free interstitials Cfnt A + CP, t B (A and B atoms), (c) clustered vacancies Cc;V, and (d) clustered interstitials Cc;A + Cc;B (A and B atoms). Reproduced from Badillo, A.; Bellon, P.; Averback, R. S. to be submitted.

such as irradiation-induced segregation and precipi­tation and are thus required in PFMs aiming for system-specific predictive power. Second, it remains challenging to include in a PFM all the elements of the microstructure relevant to evolution under irra­diation, namely point-defect clusters, dislocations, grain boundaries, and surfaces, although it has been shown here that models handling adequately a subset of these microstructural elements are now becoming available. Third, the numerical integration of the evolution equations is more challenging than for conventional PFMs in the sense that the continuous defect production, as well as the large difference in vacancy and interstitial mobility, usually prevents the use of long integration time steps, even in coarse microstructures. Finally, materials under irradiation constitute nonequilibrium systems that are quite sensitive to the amplitude and the structure of fluc­tuations, in particular the fluctuations resulting from

point defect and point-defect cluster production, and from ballistic mixing of species. A self-consistent and tractable PFM that would include both ther­mal and irradiation-induced fluctuations is still miss­ing. Such a model would be very beneficial for the study of microstructural evolution under irradiation, especially that involving the nucleation of new phases, defect clusters, or gas bubbles see Chapter 1.13, Radiation Damage Theory; Chapter 1.14, Kinetic Monte Carlo Simulations of Irradiation Effects; and Chapter 1.09, Molecular Dynamics.