Possible role of grain-boundary and dislocation structure for the magnetic-flux trapping behavior of niobium: A first-principles study

First-principles methods were used to understand magnetic flux trapping at vacancies, dislocations, and grain boundaries in high-purity superconducting niobium. Full-potential linear augmented plane-wave methods were applied in progressively greater complexity, starting at simple vacancies and extending to screw dislocations and tilt grain boundaries to analyze the effects of magnetic field on the superconducting state surrounding these defects. Density-functional theory calculations identified changes in electronic structure at the dislocation core and different types of symmetric tilt grain boundaries relative to bulk niobium. Electron redistribution enhanced nonparamagnetic effects and thus perturb superconductivity, resulting in local conditions suitable for premature flux penetration and subsequently flux pinning. Since the coherence length of superconducting niobium at 0 K is significantly larger than the lattice parameter, the effects of line and planar defects in niobium are predicted to be stronger for defect clusters than single defects in isolation, which is consistent with recent experimental observations. Controlling accumulation or depletion of charge at the defects, e.g., by segregation of an impurity atom, can mitigate these tendencies thus increasing the quality of superconducting niobium.

Figure 1

Grain boundary energy ($E_{\mathrm{gb}}$) represented as a function of (a) misorientation angle and (b) polar and azimuthal angles for 〈100〉, 〈110〉, and 〈111〉 STGBs in Nb. Grain boundaries with low energy are blue regions identified within the standard stereographic triangle.

Figure 2

Screw dislocation core structure on (111) plane in bcc niobium. The atoms are colored according to common neighbor analysis such that dislocation core atoms are red and bcc atoms are blue. The red atoms of the upward and downward triangles in the (111) plane represent the dislocation dipoles with opposite burgers vector. The remnant flux following removal of the magnetic field was 4.70 mT.

Figure 3

An external magnetic field (${\mathit{B}}_{\mathrm{ext}}$) was applied along the grain boundary plane of (c) Σ5 (210), (d) Σ13 (023), and (e) Σ3 (111) grain boundaries in Nb. (d) The remnant magnetic moment per unit periodic length of GB peaks near 40° GB misorientation for 〈100〉 symmetric tilt grain boundaries. Blue and red colored solid circles represent body-centered cubic and grain boundary atomic structures, respectively, obtained from the common neighbor analysis in Ovito.

Figure 4

(a) An equilibrated polycrystalline sample constructed using the Voronoi tessellation consisting of nonsymmetric tilt grain boundaries and (b) schematic of externally applied magnetic field (${\mathit{B}}_{\mathrm{ext}}$) along the grain boundary plane of a nonsymmetric tilt grain boundary in Nb. Blue and red colored solid circles represent body-centered cubic and grain boundary atomic structures, respectively, obtained from the common neighbor analysis. The $z$ axis is aligned along the [110] direction. This boundary showed a 2.5-mT residual flux.

Figure 5

Total (black) and orbital decomposed density of states curves (colored curves) for (a) bcc niobium, (b) niobium with 6.25 at% of vacancy, (c) screw dislocation dipole, [(d)−(h)] 〈100〉 family of STGBs, (i) 〈110〉 family of STGB, and (j) 〈111〉 family of STGB.

Figure 6

Bader charge analysis for (a) bcc niobium with 6.25 at% of vacancy, (b) screw dislocation dipole, (c)–(g) 〈100〉 family of STGBs, (h) 〈110〉 family, and (i) 〈111〉 family of STGB. The atoms are colored according to the Bader charge on each atom.

Figure 7

(a) Bader charge analysis for Σ3 (111) STGB in niobium. Atoms are colored according to the Bader charge on each atom. (b) Partial DOS curves for different atoms selected based on Bader charge analysis of the Σ3 (111) STGB. Orbital decomposed DOS curves for bulk atoms (c), grain boundary atoms with charge accumulation (d) and depletion (e), respectively, below the Fermi level. Note that the upward moving DOS are spin up and downward are spin down.