Elastic fields, dipole tensors, and interaction between self-interstitial atom defects in bcc transition metals

Abstract

Density functional theory (DFT) calculations show that self-interstitial atom (SIA) defects in nonmagnetic body-centered-cubic (bcc) metals adopt strongly anisotropic configurations, elongated in the $\ensuremath{\langle}111\ensuremath{\rangle}$ direction [S. Han et al., Phys. Rev. B 66, 220101 (2002); D. Nguyen-Manh et al., Phys. Rev. B 73, 020101 (2006); P. M. Derlet et al., Phys. Rev. B 76, 054107 (2007); S. L. Dudarev, Annu. Rev. Mater. Res. 43, 35 (2013)]. Elastic distortions, associated with such anisotropic atomic structures, appear similar to distortions around small prismatic dislocation loops, although the extent of this similarity has never been quantified. We derive analytical formulas for the dipole tensors of SIA defects, which show that, in addition to the prismatic dislocation looplike character, the elastic field of a SIA defect also has a significant isotropic dilatation component. Using empirical potentials and DFT calculations, we parametrize dipole tensors of $\ensuremath{\langle}111\ensuremath{\rangle}$ defects for all the nonmagnetic bcc transition metals. This enables a quantitative evaluation of the energy of elastic interaction between the defects, which also shows that in a periodic three-dimensional simple cubic arrangement of crowdions, long-range elastic interactions between a defect and all its images favor a $\ensuremath{\langle}111\ensuremath{\rangle}$ orientation of the defect.