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Effect of the density of states at the Fermi level on defect free energies and superconductivity: A case study of Nb3Sn

Nathan S. Sitaraman, Michelle M. Kelley, Ryan D. Porter, Matthias U. Liepe, Tomás A. Arias, Jared Carlson, Alden R. Pack, Mark K. Transtrum, and Ravishankar Sundararaman
Phys. Rev. B 103, 115106 – Published 4 March 2021
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  • INTRODUCTION
  • METHODOLOGY
  • NONINTERACTING UNPAIRED ANTISITE DEFECTS
  • INTERACTING ANTISITE DEFECTS: PHASE…
  • Tc VERSUS STOICHIOMETRY
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    Although often ignored in first-principles studies of material behavior, electronic free energy can have a profound effect in systems with a high-temperature threshold for kinetics and a high Fermi-level density of states (DOS). Nb3Sn and many other members of the technologically important A15 class of superconductors meet these criteria. This is no coincidence: both electronic free energy and superconducting transition temperature Tc are closely linked to the electronic density of states at the Fermi level. Antisite defects are known to have an adverse effect on Tc in these materials because they disrupt the high Fermi-level density of states. We observe that this also locally reduces electronic free energy, giving rise to large temperature-dependent terms in antisite defect formation and interaction free energies. This work explores the effect of electronic free energy on antisite defect behavior in the case of Nb3Sn. Using ab initio techniques, we perform a comprehensive study of antisite defects in Nb3Sn, and find that their effect on the Fermi-level DOS plays a key role determining their thermodynamic behavior, their interactions, and their effect on superconductivity. Based on our findings, we calculate the A15 region of the Nb-Sn phase diagram and show that the phase boundaries depend critically the electronic free energy of antisite defects. In particular, we show that extended defects such as grain boundaries alter the local phase diagram by suppressing electronic free-energy effects, explaining experimental measurements of grain boundary antisite defect segregation. Finally, we quantify the effect of antisite defects on superconductivity with the first ab initio study of Tc in Nb3Sn as a function of composition, focusing on tin-rich compositions observed in segregation regions around grain boundaries. As tin-rich compositions are not observed in bulk, their properties cannot be directly measured experimentally; our calculations therefore enable quantitative Ginzburg-Landau simulations of grain boundary superconductivity in Nb3Sn. We discuss the implications of these results for developing new growth processes to improve the properties of Nb3Sn thin films.

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    • Received 7 February 2020
    • Revised 16 July 2020
    • Accepted 4 February 2021

    DOI:https://doi.org/10.1103/PhysRevB.103.115106

    ©2021 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Phase diagramsSuperconducting RF
    1. Techniques
    Density functional theoryWannier function methods
    Accelerators & BeamsCondensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Nathan S. Sitaraman*, Michelle M. Kelley, Ryan D. Porter, Matthias U. Liepe, and Tomás A. Arias†

    • Department of Physics, Cornell University, Ithaca, New York 14853, USA

    Jared Carlson, Alden R. Pack, and Mark K. Transtrum

    • Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA

    Ravishankar Sundararaman

    • Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA

    • *nss87@cornell.edu
    • †taa2@cornell.edu

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    Issue

    Vol. 103, Iss. 11 — 15 March 2021

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    Images

    • Figure 1
      Figure 1

      Left, atomic composition of a sample cross section showing regions of niobium segregation (1 and 3) in contrast to 25% tin regions (2), reproduced from [36] (Lee et al.). Right, atomic composition measured by atom-probe tomography near a grain boundary showing tin segregation; the 3-nm-wide segregation region is significantly wider than the region of structural disorder at the boundary core. Reproduced from [37] (Lee et al.).

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    • Figure 2
      Figure 2

      Density of states versus energy difference from Fermi level in pure Nb3Sn. The high peak at the Fermi level plays a crucial role in determining defect and superconducting behaviors.

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    • Figure 3
      Figure 3

      Fractional antisite defect concentration as a function of composition and temperature, calculated without (left) and with (right) electronic free-energy effects. Contours are at intervals of 0.005, with concentrations beyond 0.03 in dark pink.

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    • Figure 4
      Figure 4

      Change in local density of states (LDOS) at the Fermi level versus position in a 1×1×12 supercell with a NbSn defect at ∼1.8 nm and a SnNb defect at ∼4.2 nm. Both antisite defects affect the Fermi-level LDOS in a radius of just under 1 nm.

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    • Figure 5
      Figure 5

      Convex hull construction of free energy versus tin content at T=1100K: bcc phase (blue), A15 phase without (green) and with (red) NbSn−NbSn interactions, linear tangents (black), compositional limits of phases (×'s). The noninteracting approximation increasingly underestimates the A15 free energy at increasingly tin-poor compositions. The strong curvature of the A15 hull indicates that this phase favors compositional homogeneity in equilibrium.

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    • Figure 6
      Figure 6

      Nb-Sn phase diagram: this work (shaded regions reflect estimated DFT uncertainties in phase boundaries), and experiment [49] (solid curves). Hash marks indicate the region where the Nb6Sn5 phase considered in this work is unstable experimentally (see text).

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    • Figure 7
      Figure 7

      Density of states versus energy difference from Fermi level in pure Nb3Sn (black) and in a grain boundary calculation (red) [59].

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    • Figure 8
      Figure 8

      Predicted tin-rich phase limit of A15 Nb-Sn versus temperature: expected bulk dependence (black), dependence in regions where the electronic free-energy contribution to the antisite defect formation free energy is reduced by 25% (dark red) and 50% (light red).

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    • Figure 9
      Figure 9

      Phonon spectral function α2F versus energy in A15 Nb-Sn: 25% tin content (black), 26.6% (dark red), 29.2% (red), 31.3% (light red). α2F decreases with increasing tin content above 25% across all energies.

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    • Figure 10
      Figure 10

      Superconducting transition temperature Tc versus tin content of A15 Nb-Sn: experiment [54, 61, 68] (gray squares) and this work (black circles). We predict Tc to reach a minimum of about 5 K near 31% tin content in the tin-rich regime. Multiple data points at the same composition represent calculations for supercells with different antisite defect configurations.

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    • Figure 11
      Figure 11

      Predicted Tc versus Fermi-level density of states in A15 Nb-Sn of varying composition: tin-poor compositions (red circles), tin-rich compositions (red triangles), Nb3Sn stoichiometry (black circle). The data illustrate a nearly linear relationship for off-stoichiometery calculations.

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    • Figure 12
      Figure 12

      Map of the square of the superconducting order parameter |ψ|2 in a Nb3Sn layer cross section with a tin-rich grain boundary (center), adapted from [69]. Distances are measured in units of the RF penetration depth λ≈ 100 nm.

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    • Figure 13
      Figure 13

      The Cornell coating recipe [27]. The annotated steps are described in the text.

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    • Figure 14
      Figure 14

      Excess surface tin versus time for the Cornell coating recipe modeled using the temperature-dependent evaporation rates of tin and tin chloride [76] and the thickness-dependent growth rate [31] of the Nb3Sn layer. Tin-poor growth is expected when there is no excess surface tin (∼12 h and ∼15 h in this case).

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