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.

U-Mo和U-Nb合金均广泛用于核工业。U-Mo或U-Nb合金中的γ相是固溶体，在低温区域是亚稳态的。在这项工作中，通过第一性原理计算研究了合金化对UMo和UNb合金中亚稳态γ相中晶界稳定性的影响。首先，计算了Mo，Nb和γ-U金属的晶体结构和弹性常数，所得结果表明，无论采用GGA还是GGA + U处理，γ相在0 K时的机械不稳定性质，与大多数文献中的理论结果。此外，从计算得出的对称倾斜晶界（STGB）形成能Σ3[110] /（111）和Σ5[001] /（310）在Mo，Nb和γ-U中得出，是由于机械γ-U相的不稳定特征 如果STGB模型在所有自由度下都松弛，则对于Σ5[001] /（310），在0 K时会预测到负GB形成能。因此，通过使用特殊的准随机结构（SQS）方法，在U–Mo和U–Nb系统中，富铀侧具有不同溶质浓度的Σ5[001] /（310）和Σ3[110] /（111）STGB进一步调查。结果发现，当与Mo或Nb合金化时，与Σ3[110] /（111）不同，尽管施加了固定原子约束，但当Σ5[001] /（310）STGB的GB形成能变为负时。溶质浓度在富铀方面。仅当Mo或Nb的浓度分别大于27 at。％或30 at。％或足够小时，GB形成能才变为正，表明溶质浓度，不稳定特性和晶粒尺寸对金属的协同作用。 GB结构处于γ相。合金GB结构在0 K时预测的不同稳定性表明，尽管γ相在低温下是亚稳态的，但可以通过与不同溶质或不同GBs合金化来控制其亚稳定性。而且，富铀部分的晶粒细化应该相对于钼和铀铌系统的贫贫部分而言相对容易。