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

The atomistic study of kink pairs on screw dislocations in body-centered cubic (bcc) metals is challenging because interatomic potentials in bcc metals still lack accuracy and kink pairs require too many atoms to be modeled by first principles. Here, we circumvent this difficulty using a one-dimensional line tension model whose parameters, namely the line tension and Peierls barrier, are reachable to density functional theory calculations. The model parameterized in V, Nb, Ta, Mo, W, and Fe, is used to study the kink-pair activation enthalpy and spatial extension. Interestingly, we find that the atomistic line tension is more than twice the usual elastic estimates. The calculations also show interesting group tendencies with the line tension and kink-pair width larger in group V than in group VI elements. Finally, the present kink-pair activation energies are shown to compare qualitatively with experimental data and potential origins of quantitative discrepancies are discussed.

Figure 1

Minimum energy path between two Peierls valleys per unit of $b$ for a straight screw dislocation computed with DFT for different bcc metals: (a) Fe, (b) group V elements: V, Nb, Ta, and (c) group VI elements: Mo, W. The lines are the cubic splines used to define the function $V_P\left(Y\right)$ in Eq. (2).

Figure 2

Elastic energy of the dislocation computed from DFT in the $2b$ slab cell (symbols) and from a LT model (lines) for (a) Fe, (b) group V elements, and (c) group VI elements. On the $X$ axis, $Y_1$ and $Y_2$ correspond to the position of the dislocation segments in the first and second $1b$ slab, respectively. $L_P$ is the distance between two Peierls valleys. The adjusted values of the line tension ${\Gamma }_{\mathrm{DFT}}$ are reported in Table 1.

Figure 3

Normalized line tension computed from DFT and from isotropic (iso) and anisotropic (aniso) continuous elasticity. ${\Gamma }_{\mathrm{tot}}^{\mathrm{aniso}}$ takes into account the dislocation core energy and dilatation field contributions.

Figure 4

Kink-pair activation enthalpy computed from the LT model, parametrized with DFT for (a) Fe, (b) group V elements, and (c) group VI elements.

Figure 5

Profiles of the dislocation with a critical kink pair at $\sigma =40\mathrm{MPa}$, computed from the LT model with parameters deduced from DFT calculations in (a) Fe, (b) group V elements, and (c) group VI elements.

Figure 6

Kink-pair formation energy as a function of $\Delta E_{FK}=4\sqrt{2}/\pi \times L_P\sqrt{\Gamma V_P}$ for all investigated elements. The orange symbols correspond to the values obtained previously in Fe[30] with either the siesta code, the interatomic potential MCM2011 [16] or the interatomic potential M03 [62]. The solid line has a slope of 1, as predicted from the LT model based on a cosine function for the Peierls potential.