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

Abstract

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.

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

“…In a more precise way, the appearance of radiationinduced nano-structures may modify the response of the materials to external perturbation such as constraints or temperature gradients. By its ability to compute generalized susceptibilities [23], the phase field method then offers the unique opportunity to compute for instance variations of elastic constant induced by the formation of B-rich precipitates under irradiation [46]. As irradiation stops the coarsening of B-rich precipitates in non miscible alloys [39], the characteristic size of nano-structured B-rich precipitates is about few nanometers in agreement with experimental results [46,47] in AgCu and are always in coherence with the underlying atomic lattice.…”

“…By its ability to compute generalized susceptibilities [23], the phase field method then offers the unique opportunity to compute for instance variations of elastic constant induced by the formation of B-rich precipitates under irradiation [46]. As irradiation stops the coarsening of B-rich precipitates in non miscible alloys [39], the characteristic size of nano-structured B-rich precipitates is about few nanometers in agreement with experimental results [46,47] in AgCu and are always in coherence with the underlying atomic lattice. Applying the formalism developed by Katchaturyan [48] for computing elastic constants, variation of elastic constants resulting from the radiation-induced microstructure has been computed.…”

“…Applying the formalism developed by Katchaturyan [48] for computing elastic constants, variation of elastic constants resulting from the radiation-induced microstructure has been computed. Figure 4 displays the comparison between Young moduli computed from the application of the Katchaturyan's methods [46] and extracted from nano-indentation [49] experiments performed in Ag 0.42 Cu 0.58 thin films irradiated at different temperatures (for all experiments, the Poisson ratio is equal to 0.24 in agreement with numerical simulations). The experimental increasing of about 10% of the Young modulus with the temperature (navy triangle on Figure 4) can only be modeled taking into account the precipitate-precipitate dipoles elastic interactions (blue stars on Figure 4) highlighting the impact of infinite range on the elastic properties of irradiated alloys.…”