Anomalies in the response of V, Nb, and Ta to tensile and shear loading:Ab initiodensity functional theory calculations

Abstract

Ab initio density functional calculations of the response of V, Nb, and Ta to tensile and shear loading have been performed. We find that the behavior of all three metals of the V group under large strains differs considerably from that reported for the other body-centered cubic ͑bcc͒ transition metals ͑Mo, W, and Fe͒. Under unaxial ͗100͘ tensile loading, V and Nb undergo a bifurcation from a tetragonal to an orthorhombic deformation path, associated with a shear instability, before reaching the stress maximum. The bifurcation strongly reduces the ideal tensile strengths to 11.5 GPa for V and 12.5 GPa for Nb. For Ta the bifurcation point coincides with the stress maximum of 13.6 GPa along the tetragonal path so that the metal fails under tensile strain by shear and not by cleavage. The stress-strain curves calculated for the ͕110͖͗111͘ and ͕211͖͗111͘ slip systems are strongly asymmetric; the ideal shear strengths for both slip systems are 6.5 ͑5.5͒ GPa for V and 7.8 ͑6.0͒ GPa for Nb. Hence the ideal shear strengths are only half as large as for the bcc metals Mo and W, but much larger than expected on the basis for the low shear moduli of V and Nb. Ta shows a behavior intermediate between these two groups of metals, with a calculated ideal shear strength of 7.1 ͑6.5͒ GPa, in excellent agreement with the experimental estimate from nanoindentation experiments. The saddle-point structure determining the shear strength for both slip systems is a special body-centered-tetragonal structure. This structure is identical to the saddle-point structure identified on the orthorhombic deformation path under uniaxial tension. Hence also V and Nb will fail under uniaxial tension not by cleavage, but by shear.

First-principles prediction of kink-pair activation enthalpy on screw dislocations in bcc transition metals: V, Nb, Ta, Mo, W, and Fe

“…As pointed out in Ref. [40], it is too sparse for accurate calculations of bulk properties like the C 44 elastic constants in V and Nb due to the presence of a van Hove singularity near the Fermi level [41]. However, since this singularity is smeared out by the dislocation [21], this k-point density issue should not affect the present results.…”

Lattice instabilities in metallic elements

“…42 and 43). Bifurcation was observed in several other bcc or fcc metals; e.g., by Milstein, Marschall, and Fang (1995), , and in alkali metals; Wang et al (1993) in Cu; Milstein and Farber (1980) and Milstein et al (2005) in Cu and Ni; Li and Wang (1998) and Yashiro, Oho, and Tomita (2004) in Al; Yashiro et al (2006) in Ni; Zhang et al (2008a) in Cu; Wang and Li (2009) in Au;and Nagasako et al (2010) in V, Nb, and Ta. These are only examples illustrating the complexity of the concept of ideal strength, even in straightforward model calculations for simple load geometries.…”

Peierls potential of screw dislocations in bcc transition metals: Predictions from density functional theory

“…However, for Nb and V we use 11 electrons; this formulation includes the 6 p electrons from the next lowest electron shell. The reason for using a high electron count for Nb and V is that DFT calculations tend to poorly predict C 44 for all BCC transition metals, particularly for V and Nb [29][30][31] . This inadequacy, as compared to experimental values 32 , is also observed for LDA calculations 20 .…”