Computational modelling studies of ZrNb-X (X = Co, Sn) Alloys

Abstract

The ab initio density functional theory and molecular dynamics approach have been used to study the properties of Zr-based systems. In particular Zr-Nb, Zr-Nb-X (X = Co and Sn). We have calculated the structural, elastic, mechanical properties and temperature dependence particularly to determine their stabilities. These alloys are important for a wide range of technological applications, primarily in the nuclear and chemical industries due to their good irradiation stability, wear and corrosion resistance, high mechanical strength and superior neutron economy. The virtual crystal approximation was used to introduce small amounts of either Co or Sn contents on Zr-Nb system. The main idea is to advance high-temperature applications of Zr-Nb system through ternary alloying. Calculations were carried out using the ab initio DFT employing the plane-wave pseudopotential method as implemented within the CASTEP code. The influence of partial substitution for Nb concentration with either Co or Sn concentrations was investigated on the Zr-Nb-X systems of various concentrations. The resulting equilibrium lattice parameters, heats of formation, elastic properties, and the density of states were evaluated to mimic their structural, thermodynamic and mechanical stability trends. The lattice parameters of binary systems Zr99Nb1.0, Zr98.8Nb1.2, Zr98.1Nb1.9, Zr97.5Nb2.5, Zr97Nb3, Zr78Nb22, Zr78Nb22 and Zr50Nb50 gave better agreement with available experimental data to within 5 %, while those for ternary systems have shown a decrease with the introduction of the third element i.e. Co or Sn. The heats of formation were negative (stable) at smaller concentrations of ≤ 1 at. % Co. Moreover, the correlation of electronic stability using the DOS and the ∆Hf calculations has indicated that the systems are thermodynamically stable within ≤ 1 at. % Co for (Zr99Nb1-xCox, Zr98.8Nb1.2-xCox, Zr98.1Nb1.9Cox, Zr97.5Nb1.5-xCox, Zr97Nb3- xCox and Zr78Nb22-xCox) systems. It was found that the increase in Co concentration enhances the thermodynamic, elastic and mechanical stability of the systems and they are found to be stable at small concentrations of about 1 at. % Co. Furthermore, the temperature dependence was carried out using Dmol3 . In particular, the canonical ensemble (NVT) calculations were carried out at different temperatures and we observed their structural behaviour with regard to the binding energy and elastic properties at any given temperature up to 2400 K. We compare the temperature dependence of Zr, Zr50Nb50, Zr78Nb22, Zr78Nb21Co1, Zr78Nb20Co2, Zr78Nb19Co3, Zr50Nb49Sn1, Zr50Nb48Sn2 and Zr50Nb47Sn3 systems. In the case of binary system, the Zr78Nb22 was more promising, showing lower binding energy of - 6.87eV/atom. It was shown that ternary additions with small atomic percentages of Co and Sn have a significant impact on Zr-Nb alloy. Particularly, their elastic properties showed a possible enhancement on the strength and ductility at high temperature. This was observed for 1 at. % since it satisfied the requirements for ductility and strength as specified in literature. The Co and Sn addition on the Zr78Nb22 system is more promising for high-temperature applications, with Sn being more preferable.