Importance of inclusion of the effect of s electrons into bond-order potentials for transition bcc metals with d-band mediated bonding

Abstract

In bond-order potentials (BOPs) for transition metals only the bonding mediated by the d electrons is included explicitly and the covalent part of the cohesive energy is evaluated using Slater–Koster dd bond integrals. However, the effect of s electrons with orbitals centered on atoms neighboring the corresponding dd bond is not necessarily negligible. As shown in Nguyen-Manh et al (2000 Phys. Rev. Lett. 85 4136) this can be taken into account via screening of the dd bond integrals. In a recent paper (Lin et al 2014 Model. Simul. Mater. Sci. Eng. 22 034002) the dd bond integrals were determined using a projection scheme utilizing atomic orbitals that give the best representation of the electronic wave functions in the calculations based on the density functional theory (DFT) (Madsen et al 2011 Phys. Rev. B 83 4119) and it was inferred that in this case the effect of s electrons was already included. In this paper we analyze this hypothesis by comparing studies employing BOPs with both unscreened and screened dd bond integrals. In all cases results are compared with calculations based on DFT and/or experiments. Studies of structures alternate to the bcc lattice, transformation paths that connect the bcc structure with fcc, simple cubic (sc), body centered tetragonal (bct) and hcp structures via continuously distorted configurations and calculations of γ-surfaces were all found to be insensitive to the screening of bond integrals. On the other hand, when the bond integrals are screened, formation energies of vacancies are improved and calculated phonon dispersion spectra reproduce the experimentally observed ones much better. Most importantly, dislocation core structure and dislocation glide are significantly different without and with screening of dd bond integrals. The latter lead to a much better agreement with available experiments. These findings suggest that the effect of s electrons on dd bonds, emulated by the screening of corresponding bond integrals, is the least significant when the lattice is distorted away from the ideal bcc structure homogeneously even if such distortion is large. On the other hand, when the distortion is local and inhomogeneous the impact of screening of the dd bond integrals is significant. In the studies presented in this paper such local inhomogeneities occur when phonons propagate through the lattice, at point defects and in the cores of dislocations.