Tuning Ideal Tensile Strengths and Intrinsic Ductility of bcc Refractory Alloys

An important theoretical ductility criterion for group V and VI metal-based refractory alloys in body-centered cubic (bcc) lattices is the mechanical failure mode of their perfect crystals under tension along the weakest direction [100]. Pure Mo and W fail by cleavage and are deemed intrinsically brittle. However, first-principles calculations show that alloying with group IV or V transition metals can transform these materials into ones that display intrinsically ductile behavior, failing in shear under [100] tension. Remarkably, this transition can be understood as an electron filling effect with the intrinsically ductile response the manifestation of a Jahn-Teller distortion.

Figure 1

(a) Body-centered cubic structures described by two-atom cubic supercell (in blue frame with dark blue atoms) and four-atom tetragonal supercell (in red frame). (b) Shear deformation occurs ($|{\mathbf{b}}_2|\ne |{\mathbf{b}}_3|$) when ${ϵ}_{11}$ is above a critical value, then the original $[010{]}_{\mathrm{bcc}}({\mathbf{a}}_2)$ and $[001{]}_{\mathrm{bcc}}({\mathbf{a}}_3)$ are not perpendicular to each other. (c),(d) Jahn-Teller energetics for a molecule with octahedral symmetry. The $e_g$ level is shown, with an electron occupation corresponding to $d^7$ (replications of the illustrative figures in Ref. [19]).

Figure 2

(a)–(c) Stress-strain curves for different transition metal and alloys. (a) Pure Mo and MoCr in B2 structure (${\mathrm{MoCr}}_{\mathrm{B}2}$). (b) ${\mathrm{MoNb}}_{\mathrm{B}2}$ and MoNb constructed by VCA (${\mathrm{MoNb}}_{\mathrm{VCA}}$). (c) Nb and ${\mathrm{MoZr}}_{\mathrm{B}2}$. (d) Variations of lattice parameters of four-atom tetragonal supercell in the OP under different ${ϵ}_{11}$ for Mo, Nb, and ${\mathrm{MoNb}}_{\mathrm{B}2}$.

Figure 3

(a) Symmetric $\mathbf{k}$ points in the reciprocal space based on four-atom tetragonal supercells for band structure plots. (b) Band structures of Mo in four-atom tetragonal supercell at equilibrium. The 12th band is highlighted in red color with dots. (c),(d) The 12th band of Mo and ${\mathrm{MoNb}}_{\mathrm{VCA}}$ four-atom tetragonal supercells under different ${ϵ}_{11}$, respectively. The horizontal axes from different ${ϵ}_{11}$ are stretched to match the symmetry $\mathbf{k}$ points when ${ϵ}_{11}=0$. (e),(f) Density of states (DOS) for Mo and ${\mathrm{MoNb}}_{\mathrm{VCA}}$ under different ${ϵ}_{11}$.