Stability of β-Nb phase in Zr–Nb alloys under neutron irradiation: Phase field modeling

Abstract

A phase field approach to study stability of β-Nb precipitates in Zr–Nb alloys is extended by taking into account local rearrangement of point defects and misfit dislocations. Kinetic properties of β-Nb phase formation are discussed at a heat treatment stage. Stability of secondary phase precipitates is studied at different irradiation temperatures and dose rates. It is shown that processes of dissolution/growth of precipitates are governed by the competition of ballistic mixing and thermal diffusion. It is found that at large values of dose rates and low temperatures, precipitates are dissolved due to a major role of ballistic mixing, whereas at low dose rate and elevated temperatures, β-niobium particles grow slowly by an Ostwald ripening scenario up to 1–2 nm due to the dominant role of thermal diffusion. Misfit dislocations sustain the existence of Nb-enriched domains of mixed symmetry. It is shown that growing dislocation loops and dissolving/growing precipitates result in the hardening change up to 0.01% at a dose rate of 10−5dpa/s and temperatures of 550–575 K. Obtained theoretical results are verified by experimental data.

Phase stability and precipitation modeling in neutron irradiated Zr–2% Nb alloy

“…To describe incoherent interface a misfit dislocation density is included into the corresponding phase field model. In our recent work [32] we have used such combined phase field approach allowing us to distinguish β-phase precipitates from α-Zr matrix with segregation of vacancies around incoherent interface. It was shown that the phase field follows a spatial distribution of Nb-concentration, where all Nb-enriched domains belong to β-phase.…”

“…Moreover, by assuming that atoms in this kind of alloys diffuse by vacancy (dominant) mechanism a contribution of interstitials into thermodynamics is neglected. The system is considered in a fixed volume V. The model used next is based on statements discussed in references [25,[30][31][32], rate theory assumptions discussed in references [33,34] and radiation induced ballistic mixing shown in references [35][36][37][38][39].…”

“…takes into account interactions of vacancies through elastic deformation of the lattice [18,25,32,45,46]. Here r v0 ≈ (2-3)a denotes the mean square distance between produced defect and atom of the matrix.…”

“…Phase field modeling concerning Zr-Nb alloys reported in literature is addressed to thermal treatment [30,31]. Radiation induced precipitation was studied for zirconium alloys with elevated concentration of Nb [25,32]. At the same time, a problem of modeling the precipitation in alloys with low content of doping under thermal treatment and irradiation remains opened.…”

Study of Dislocation Loops Growth in Zr–Sn–Alloys Under Neutron Irradiation by Rate Theory Modelling

“…Cluster dynamics is used to receive data for cluster number density dynamics, mean cluster size and cluster growth speed at different irradiation regimes [27][28][29]. Phase field modelling allows one to describe defects rearrangement and phase stability based on thermodynamic approaches and reaction rate theory [6,25,[30][31][32][33][34][35][36][37][38].…”