Nb-Zr

Abstract: We use atomistic simulations to study the structure and shape of niobium precipitates with a body-centered cubic crystallographic structure in a zirconium matrix with a hexagonal close-packed structure. We consider a Pitsch-Schrader orientation relationship, which is observed experimentally for Nb precipitates appearing under irradiation in zirconium alloys. In this regard, we have developed a Zr-Nb empirical potential using the embedded atom method. This parametrization offers a good description of the interfaces between Nb precipitates and the Zr matrix. The potential includes all the necessary physical ingredients to account for the coherency strain between both phases. The atomistic simulations reveal a significant decrease in the precipitate formation energy when they become semicoherent, with enough misfit dislocations at the interface to eliminate the lattice misfit between the Nb precipitates and the Zr matrix. The "idealized" equilibrium shape that minimizes the formation energy of these semicoherent precipitates matches the experimental shape: platelets lying in the Zr basal planes with a reduced dimension along the [0001] axis. Our simulations suggest that the platelet shape observed in zirconium for irradiation-induced Nb-enriched precipitates simply results from a minimization of their energy cost.

Abstract: We present a new classical interatomic potential for a study of the binary Zr-Nb system, taking into account a wide range of the components concentrations. The potential was developed by virtue of the force-matching method that is capable of ensuring a high accuracy at the description of the complex systems containing diverse crystal phases. At simulation of pure Zr, the potential correctly describes a relative stability of Zr phases (α-Zr, β-Zr and ω-Zr) and qualitatively reproduces the right arrangement of these phases in the phase diagram. It is remarkable that β-Zr phase is found to have a dynamically unstable structure at the low temperature, in agreement with the ab initio calculations. The potential can also play a role in considering the tasks related to the crystal defects in the Zr-Nb system. In support of this statement, we show the simulation results proving adequate representation of a number of key properties of the crystal defects in Zr-Nb system. In particular, the offered potential reproduces formation/solution energies of point defects with well accuracy. To illustrate wide application possibilities for the model, we made a prediction of atomic self-diffusion and impurity diffusion in Zr and Nb. Also, the potential ensures correct description of a screw dislocation in niobium, which is a crucial point for the investigation of plasticity.

Abstract: We report a new attempt to study properties of Zr-Nb structural alloys. For this purpose we constructed an angular-dependent many-body interatomic potential. The potential functions were fitted towards the ab initio data computed for a large set of reference structures. The fitting procedure is described, and its accuracy is discussed. We show that the structure and properties of all Nb and Zr phases existing in the Zr-Nb binary system are reproduced with good accuracy. The interatomic potential is appropriate for study of the high-pressure hexagonal ω-phase of Zr. We also estimated characteristics of the point defects in α-Zr, β-Zr and Nb; results are proven to correlate with the existing experimental and theoretical data. In case of α-Zr the model reveals anisotropy of the vacancy diffusion, in agreement with previous calculations and experiments. The potential provides an opportunity for simulation of Zr-Nb alloys based on α-Zr and β-Zr. This conclusion is illustrated by the results obtained for the alloys with different niobium concentrations: up to 7% in case of hcp alloys and up to 50% for bcc alloys.