Effect of alloying on stability of grain boundary in γ phase of the U–Mo and U–Nb systems

Abstract

U–Mo and U–Nb alloys are both extensively used in nuclear industry. γ phase in U–Mo or U–Nb alloy is a solid solution, being metastable in low temperature region. In this work, the effect of alloying on stability of grain boundary in meta-stable γ phase in U–Mo and U–Nb alloys are investigate through first-principles calculations. At first, crystal structure and elastic constants of Mo, Nb and γ-U metals are calculated and the obtain results show the mechanical unstable nature of γ phase at 0 K, no matter with GGA or GGA + U treatment, which agrees with most of the theoretical results in the literature. Furthermore, from the calculated symmetric tilt grain boundary (STGB) formation energies of Σ3[110]/(111) and Σ5[001]/(310) in Mo, Nb, and γ-U, it is found that due to the mechanical unstable character of the γ-U phase, negative GB formation energy is predicted at 0 K for Σ5[001]/(310) if the STGB model is relaxed with all degrees of freedom. Therefore, by using special quasirandom structure (SQS) method, Σ5[001]/(310) and Σ3[110]/(111) STGBs with different solute concentrations in U-rich side in U–Mo and U–Nb systems are further investigated. It is found that, when alloying with Mo or Nb, unlike Σ3[110]/(111), although the fixed-atom constraint is applied, the GB formation energy of Σ5[001]/(310) STGB is becoming negative when the solute concentration is in U-rich side. Only when the concentration of Mo or Nb is larger than 27 at.% or 30 at.%, respectively, or sufficient small, the GB formation energy is becoming positive, suggesting a cooperative effects of solute concentration, unstable character, and grain size on GB structures in γ phase. The predicted different stability of alloyed GB structures at 0 K suggest that although γ phase is metastable at low temperature, its metastability can be controlled through alloying with different solutes, or with different GBs. And grain refinement should be relatively easy in U-rich part than U-poor part of the U–Mo and U–Nb systems.