Construction of radiation-modified phase diagrams under cascade-producing irradiation: application to Zr–Nb alloy

Formation of steady state size distribution of precipitates in alloys under cascade-producing irradiation

“…Using results of [22,24], one can show that in the absence of segregation effects the diffusion-controlled growth rate of coherent and incoherent precipitates is given by…”

“…where D mix is the diffusion coefficient due to cascade mixing, which is proportional to the mixing efficiency d mix and the generation rate of freely migrating PD K [23,24].…”

“…at temperatures below 600 K. In our opinion, this indicates that incoherent precipitates are unstable under irradiation and therefore cannot form. At the same time, stability of small platelet or needlelike precipitates under irradiation can be understood if we note that these precipitates are in a more coherent state with the a-Zr matrix [24]. In reality, b-Nb particles cannot be fully coherent with the a-matrix because of different crystal lattices.…”

“…The results of phase stability studies have been presented in the form of radiation-modified phase diagram [21][22][23][24]. This diagram contains a low temperature boundary for precipitate stability, the location of which depends on displacement rate and mixing efficiency of irradiation.…”

“…1). The existence of two thresholds for stability of precipitates suggests that in alloys under irradiation at temperatures T coh < T < T inc a quasi-stationary distribution of semicoherent precipitates may form [24]. The mechanism is connected with competition of (i) the nucleation and growth of coherent precipitates in a supersaturated solid solution and (ii) the cascade-induced dissolution of large precipitates that lose coherency upon reaching, during growth, some critical range of sizes.…”