Effect of group IV content on elastic and defect properties of NbTiZr refractory medium-entropy alloys

Some refractory high- and medium-entropy alloys exhibit an exceptional combination of strength and ductility, yet the origin of this behavior remains unresolved. Here, first-principles calculations are used to investigate how group IV elements and the associated valence electron concentration (VEC) influence the defect energetics of body-centered cubic refractory alloys. Increasing the group IV concentration enhances lattice distortion and softens shear-related elastic moduli, effects that are generally associated with mechanical properties in refractory alloys. The VEC dependence of the dislocation-dipole formation energy persists after normalizing by the continuum-elastic dipole energy computed from the composition-dependent elastic constants, indicating a contribution beyond the linear-elastic response. A qualitatively similar trend is obtained in the chemically averaged VCA model, showing that such a trend can arise in the absence of explicit local chemical fluctuations. Direct electronic-structure evidence is still required to establish its microscopic origin. A Nye-tensor analysis of all dislocation configurations shows that the core broadens continuously with group IV content, with no composition threshold, while its sensitivity to the local chemical environment grows by an order of magnitude. Together, these results quantify how the defect energetics of a BCC medium-entropy alloy vary with group IV content and valence electron concentration, while showing that these quantities describe defect formation rather than dislocation mobility, strength, or ductility.