Fig. 1

Solute-interaction energy and electronic structures of the \(\frac{1}{2}\left\langle {111} \right\rangle\) screw dislocation in bcc W. a Interaction energy between transition metal solute and the \(\frac{1}{2}\left\langle {111} \right\rangle\) screw dislocation in bcc W. The interaction energy, E_int, is defined as the difference between the total energies of the dislocation structure with a solute atom X occupying an atomic site far away from and at the dislocation core. The dislocation structure is initially fully relaxed to reach its equilibrium state in pure W and sequentially used for solute substitution. A positive value of E_int indicates an attractive binding tendency. The interaction energies were calculated under two conditions: relaxing \(\left( {E_{{\mathrm{int}}}^{{\mathrm{relax}}}} \right)\) and fixing atomic positions \(\left( {E_{{\mathrm{int}}}^{{\mathrm{fix}}}} \right)\) during the total energy calculations after the solute atom added into the supercell. The values of \(E_{{\mathrm{int}}}^{{\mathrm{relax}}}\) are taken from our recent publication⁶. b LDOS of a W atom in perfect bcc lattice (solid-blue line), perfect fcc lattice (solid-orange line), and at the \(\frac{1}{2}\left\langle {111} \right\rangle\) dislocation core site (dashed-blue line) in pure W. c, d LDOS of an Re and Ta atom occupying the bcc site (solid-blue line) and the \(\frac{1}{2}\left\langle {111} \right\rangle\) dislocation core site (dashed-blue line) in the W matrix, respectively. The bcc bulk site and core site refer to the atomic sites marked in blue and red colors in a, respectively