Predicting Nonequilibrium Patterns beyond Thermodynamic Concepts: Application to Radiation-Induced Microstructures

Convection-Induced Compositional Patterning at Grain Boundaries in Irradiated Alloys

We consider the stability of precipitates formed at grain boundaries (GBs) by radiation-induced segregation in dilute alloys subjected to irradiation. The effects of grain size and misorientation of symmetric-tilt GBs are quantified using phase field modeling. A novel regime is identified where, at long times, GBs are decorated by precipitate patterns that resist coarsening. Maps of the chemical Péclet number indicate that arrested coarsening takes place when solute advection dominates over thermal diffusion right up to the precipitate-matrix interface, preventing interfacial local equilibrium and overriding capillary effects. This contrasts with liquid-solid mixtures where convection always accelerates coarsening.

Radiation-Induced Patterning at the Nanometric Scale: A Phase Field Approach

The phase field approach was developed in the last 20 years to handle radiation damage in materials. This approach bridges the gap between atomistic simulations extensively used to model first step of radiation damage at short time and continuum approach at large time. The main advantage of such an approach lies in its ability to compute not only the microstructure at the nanometric scale but also to calculate generalized susceptibilities such as elastic constants under irradiation. After a brief description of the rate theory, used to model the microstructure induced by irradiation, we briefly discuss the foundation of the phase field method, highlighting not only its advantages, but also its limitations in comparison with the rate theory. We conclude this presentation by proposing future orientations for computing the microstructure in irradiated materials.

Nano-Structured Materials under Irradiation: Oxide Dispersion-Strengthened Steels

Oxide dispersion-strengthened materials are reinforced by a (Y, Ti, O) nano-oxide dispersion and thus can be considered as nanostructured materials. In this alloy, most of the nanoprecipitates are (Y, Ti, O) nano-oxides exhibiting a Y₂Ti₂O₇ pyrochlore-like structure. However, the lattice structure of the smallest oxides is difficult to determine, but it is likely to be close to the atomic structure of the host matrix. Designed to serve in extreme environments—i.e., a nuclear power plant—the challenge for ODS steels is to preserve the nano-oxide dispersion under irradiation in order to maintain the excellent creep properties of the alloy in the reactor. Under irradiation, the nano-oxides exhibit different behaviour as a function of the temperature. At low temperature, the nano-oxides tend to dissolve owing to the frequent ballistic ejection of the solute atoms. At medium temperature, the thermal diffusion balances the ballistic dissolution, and the nano-oxides display an apparent stability. At high temperature, the nano-oxides start to coarsen, resulting in an increase in their size and a decrease in their number density. If the small nano-oxides coarsen through a radiation-enhanced Ostwald ripening mechanism, some large oxides disappear to the benefit of the small ones through a radiation-induced inverse Ostwald ripening. In conclusion, it is suggested that, under irradiation, the nano-oxide dispersion prevails over dislocations, grain boundaries and free surfaces to remove the point defects created by irradiation.

Symmetry Breaking Resulting from Long-Range Interactions in Out of Equilibrium Systems: Elastic Properties of Irradiated AgCu

This work presents a consistent formulation of the phase-field approach to model the behavior of nonmiscible alloys under irradiation which includes elastic strain fields, an example of a long-range interaction. Simulations show that the spatial isotropy that is characteristic of radiation-induced patterns breaks down as a result of the elastic strain energy. The consequence of this is the emergence of superlattice structures under irradiation liable to modify macroscopic material properties. This approach is assessed against the experimental study of a AgCu alloy under irradiation: we compare our simulation results to measured solubility limits and Young moduli.