First-principles determination of grain boundary strengthening in tungsten: Dependence on grain boundary structure and metallic radius of solute

The control of segregation-induced grain boundary (GB) strengthening is a strategy for improving the ductility and intergranular fracture of metals. In this work, by first-principles calculations we study the strengthening effect of transition metals on a series of tungsten GBs to uncover its dependence on the GB structures and the radius of solute itself. The results show that the GB strengthening depends strongly on the GB structures. The solutes tend to enhance cohesion for GBs with larger GB energies, while they decrease cohesion for those with smaller GB energies. In addition, it is generally found that for all GBs the strengthening energies of elements correlate positively with their metallic radii, implying that the size effect plays a major role in the GB strengthening in tungsten. By analyzing the strengthening effect of solutes at different segregated sites, we find that the oversized solutes (Zr, Nb, Hf, Ta) act as cohesion enhancers when segregated in the GB plane, while the undersized elements (Ru, Rh, Re, Os, Ir) strengthen the GBs at the nearest neighbor positions. Experimentally, we show that the presence of Zr/Ta/Re impurity, which leads to an increase of intergranular fracture, increases the theoretical tensile strength and the GB cohesion. These results suggest that the improved fracture resistance by Re, Ta and Zr originates mainly from the GB strengthening due to their segregation.