A phase field model for dislocation climb under irradiation: Formalism and applications to pure bcc iron and ferritic alloys

Abstract

A phase-field model allowing to describe dislocation climb under irradiation is presented. Whereas previous phase-field models of the literature devoted to this phenomenon only take into account vacancies, our approach includes the effect of self interstitial atoms (SIAs) as required in the context of irradiated metals. Beyond the fact that it rigorously ensures the balance between the quantity of point defects, vacancies and SIAs, absorbed or emitted by the loop and the loop evolution, the present model has several originalities. First, it is capable to quantify the climb rate for systems far from equilibrium, which is commonly the case under irradiation. This required supplemental methodological developments since we clearly show that a mere generalization of existing phase-field models is not satisfactory to tackle this specificity. Secondly, it alleviates the often adopted assumption of perfect sink through the introduction of a kinetic parameter related to the dislocation jog density. A preliminary generic study of dislocations considered as nonperfect sinks leads to nonintuitive results, since the climb rate decreases when the dislocation jog density increases. Thirdly, the possibility to consider different types of interacting microstructural defects in the model allows to show the significant role of the point defect thermal equilibrium fractions on the climb rate in pure bcc iron under irradiation conditions. Finally, the climb model is coupled to the chemical diffusion equations in the same phase-field formalism. For this purpose, a multi-time step algorithm is proposed in order to couple phenomena with different characteristic time scales by several orders of magnitude, namely climb, point defect and chemical diffusion. It allows to study the interaction between the motion of the dislocation and the well-known phenomenon of radiation induced segregation in a Fe–Cr alloy. It is shown that the shape and size of the solute atmosphere can strongly depend on the dislocation motion under irradiation.