Solubility and vacancy-mediated inter-diffusion in the Zr-Nb-Cr system

To better understand the microstructural evolution of Cr-coated Zr alloy cladding, we investigate, using density functional theory calculations, the vacancy-mediated diffusion behaviour of Zr and Nb solutes in BCC-Cr as well as Zr and Cr solutes in BCC-Nb. The calculated vacancy formation and migration energies are in good agreement with available literature, as are the self-diffusivities. We show that in BCC-Cr both Nb and Zr are faster diffusers than Cr (vacancy-mediated self-diffusion). It was also found that both Zr and Nb segregate towards vacancy sinks in BCC-Cr at normal reactor operating temperatures, but at elevated temperatures their flux is expected to be in opposite directions. In BCC-Nb, we show that Cr is a slower diffuser than Nb self-diffusion, while Zr is faster; and both Zr and Cr are expected to decorate vacancy sinks in BCC-Nb at all temperatures relevant to reactor operation. A similar behaviour is likely to occur in β-Nb phase found in Zr-Nb alloys. The implications of these findings for Cr-coated Zr alloy cladding are discussed.