Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Niobium hydride formation in superconducting qubit thin films

Tyler J. Leibengood1,*, Pierre-Clément A. Simon2, P. Graham Pritchard1, James M. Rondinelli1, and Peter W. Voorhees1,†

  • *Contact author: tjleibengood42@gmail.com
  • †Contact author: p-voorhees@northwestern.edu

Phys. Rev. Materials 9, 074803 – Published 17 July, 2025

DOI: https://doi.org/10.1103/v27k-y5fb

Abstract

The formation of nonsuperconducting hydrides in 160–170-nm-thick films of niobium is examined. We identify six elastically distinct orientation relationships ɛ−Nb4H3 takes within the matrix, solid-solution α−NbHx phase. We employ a phase field model to assess the impact of elastic energy induced by the strain of phase transformation on the morphology and transformation dynamics of ɛ precipitates within a thin film. We consider the dimensions of the thin film, crystallographic growth direction, and diffusion rates to predict the timescale of hydride evolution. Leveraging the finite element method, we predict two-dimensional and three-dimensional equilibrium shapes of ɛ-hydrides within a bulk sample and in a thin film that has a traction-free surface. Our results suggest that niobium hydrides migrate to the free surface of the film. Precipitates which reach the free surface coarsen, while precipitates within the film dissolve. Precipitates in both two dimensions and three dimensions experience a repulsive interaction force at the free surface, that is attractive in the bulk, shown in experiment and theory of previous studies.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (41)

  1. M. Bal, A. A. Murthy, S. Zhu, F. Crisa, X. You, Z. Huang, T. Roy, J. Lee, D. v. Zanten, R. Pilipenko, I. Nekrashevich, A. Lunin, D. Bafia, Y. Krasnikova, C. J. Kopas, E. O. Lachman, D. Miller, J. Y. Mutus, M. J. Reagor, H. Cansizoglu, J. Marshall, D. P. Pappas, K. Vu, K. Yadavalli, J.-S. Oh, L. Zhou, M. J. Kramer, F. Lecocq, D. P. Goronzy, C. G. Torres-Castanedo, P. G. Pritchard, V. P. Dravid, J. M. Rondinelli, M. J. Bedzyk, M. C. Hersam, J. Zasadzinski, J. Koch, J. A. Sauls, A. Romanenko, and A. Grassellino, Systematic improvements in transmon qubit coherence enabled by niobium surface encapsulation, npj Quantum Inf. 10, 43 (2024).
  2. K. R. Joshi, S. Ghimire, M. A. Tanatar, A. Datta, J.-S. Oh, L. Zhou, C. J. Kopas, J. Marshall, J. Y. Mutus, J. Slaughter, M. J. Kramer, J. A. Sauls, and R. Prozorov, Quasiparticle spectroscopy, transport, and magnetic properties of Nb films used in superconducting qubits, Phys. Rev. Appl. 20, 024031 (2023).
  3. A. A. Murthy, P. Masih Das, S. M. Ribet, C. Kopas, J. Lee, M. J. Reagor, L. Zhou, M. J. Kramer, M. C. Hersam, M. Checchin, A. Grassellino, R. d. Reis, V. P. Dravid, and A. Romanenko, Developing a chemical and structural understanding of the surface oxide in a niobium superconducting qubit, ACS Nano 16, 17257 (2022).
  4. A. A. Murthy, J. Lee, C. Kopas, M. J. Reagor, A. P. McFadden, D. P. Pappas, M. Checchin, A. Grassellino, and A. Romanenko, TOF-SIMS analysis of decoherence sources in superconducting qubits, Appl. Phys. Lett. 120, 044002 (2022).
  5. H. Okamoto, H-Nb (hydrogen-niobium), J. Phase Equilib. Diffus. 34, 163 (2013).
  6. J. Knobloch, The “Q disease” in superconducting niobium RF cavities, AIP Conf. Proc. 671, 133 (2003).
  7. C. G. Torres-Castanedo, D. P. Goronzy, T. Pham, A. McFadden, N. Materise, P. Masih Das, M. Cheng, D. Lebedev, S. M. Ribet, M. J. Walker, D. A. Garcia-Wetten, C. J. Kopas, J. Marshall, E. Lachman, N. Zhelev, J. A. Sauls, J. Y. Mutus, C. R. H. McRae, V. P. Dravid, M. J. Bedzyk, and M. C. Hersam, Formation and microwave losses of hydrides in superconducting niobium thin films resulting from fluoride chemical processing, Adv. Funct. Mater. 34, 2401365 (2024).
  8. A. Romanenko, F. Barkov, L. Cooley, and A. Grassellino, Proximity breakdown of hydrides in superconducting niobium cavities, Supercond. Sci. Technol. 26, 035003 (2013).
  9. F. Barkov, A. Romanenko, Y. Trenikhina, and A. Grassellino, Precipitation of hydrides in high purity niobium after different treatments, J. Appl. Phys. 114, 164904 (2013).
  10. J. Lee, Z. Sung, A. A. Murthy, M. Reagor, A. Grassellino, and A. Romanenko, Discovery of Nb hydride precipitates in superconducting qubits, arXiv:2108.10385.
  11. K. Nörthemann and A. Pundt, Coherent-to-semi-coherent transition of precipitates in niobium-hydrogen thin films, Phys. Rev. B 78, 014105 (2008).
  12. S. Wagner, P. Klose, V. Burlaka, K. Nörthemann, M. Hamm, and A. Pundt, Structural phase transitions in niobium hydrogen thin films: Mechanical stress, phase equilibria and critical temperatures, ChemPhysChem 20, 1890 (2019).
  13. W. M. Albrecht, M. W. Mallett, and W. D. Goode, Equilibria in the niobium-hydrogen system, J. Electrochem. Soc. 105, 219 (1958).
  14. H. Birnbaum, M. Grossbecr, and M. Amano, Hydride precipitation in Nb and some properties of NbH, J. Less-Common Met. 49, 357 (1976).
  15. F. Manchester and A. International, Phase Diagrams of Binary Hydrogen Alloys, Monograph Series on Alloy Phase Diagrams (ASM International, Metals Park Ohio, 2000).
  16. A. Kumar, G. Kaur, and A. Subramaniam, Critical sizes for coherent to semicoherent transition in precipitates, Int. J. Mater. Res. 104, 1171 (2013).
  17. P.-C. Simon, L. K. Aagesen, A. M. Jokisaari, L.-Q. Chen, M. R. Daymond, A. T. Motta, and M. R. Tonks, Investigation of δ zirconium hydride morphology in a single crystal using quantitative phase field simulations supported by experiments, J. Nucl. Mater. 557, 153303 (2021).
  18. A. Jokisaari, S. Naghavi, C. Wolverton, P. Voorhees, and O. Heinonen, Predicting the morphologies of γ′ precipitates in cobalt-based superalloys, Acta Mater. 141, 273 (2017).
  19. C. Su and P. Voorhees, The dynamics of precipitate evolution in elastically stressed solids—I. Inverse coarsening, Acta Mater. 44, 1987 (1996).
  20. C. Su and P. Voorhees, The dynamics of precipitate evolution in elastically stressed solids—II. Particle alignment, Acta Mater. 44, 2001 (1996).
  21. M. Thompson, C. Su, and P. Voorhees, The equilibrium shape of a misfitting precipitate, Acta Metall. Mater. 42, 2107 (1994).
  22. S. G. Kim, W. T. Kim, and T. Suzuki, Phase-field model for binary alloys, Phys. Rev. E 60, 7186 (1999).
  23. J. W. Cahn and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys. 28, 258 (1958).
  24. N. Moelans, B. Blanpain, and P. Wollants, Quantitative analysis of grain boundary properties in a generalized phase field model for grain growth in anisotropic systems, Phys. Rev. B 78, 024113 (2008).
  25. N. Moelans, A quantitative and thermodynamically consistent phase-field interpolation function for multi-phase systems, Acta Mater. 59, 1077 (2011).
  26. A. Magerl, B. Berre, and G. Alefeld, Changes of the elastic constants of V, Nb, and Ta by hydrogen and deuterium, Phys. Stat. Sol. (a) 36, 161 (1976).
  27. K. J. Carroll, Elastic constants of niobium from 4.2∘ to 300∘K, J. Appl. Phys. 36, 3689 (1965).
  28. J. Engelhard, The diffusion of H and D in Nb and Ta at low temperatures, J. Phys. F 9, 2217 (1979).
  29. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  30. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  31. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  32. A. Ramachandran, H. Zhuang, and K. S. Lackner, Probing the interactions between interstitial hydrogen atoms in niobium through density functional theory calculations, Mater. Today Commun. 25, 101415 (2020).
  33. G. Giudicelli, A. Lindsay, L. Harbour, C. Icenhour, M. Li, J. E. Hansel, P. German, P. Behne, O. Marin, R. H. Stogner, J. M. Miller, D. Schwen, Y. Wang, L. Munday, S. Schunert, B. W. Spencer, D. Yushu, A. Recuero, Z. M. Prince, M. Nezdyur, T. Hu, Y. Miao, Y. S. Jung, C. Matthews, A. Novak, B. Langley, T. Truster, N. Nobre, B. Alger, D. Andrš, F. Kong, R. Carlsen, A. E. Slaughter, J. W. Peterson, D. Gaston, and C. Permann, 3.0 - MOOSE: Enabling massively parallel multiphysics simulations, SoftwareX 26, 101690 (2024).
  34. M. R. Tonks, D. Gaston, P. C. Millett, D. Andrs, and P. Talbot, An object-oriented finite element framework for multiphysics phase field simulations, Comput. Mater. Sci. 51, 20 (2012).
  35. D. Schwen, L. K. Aagesen, J. W. Peterson, and M. R. Tonks, Rapid multiphase-field model development using a modular free energy based approach with automatic differentiation in MOOSE/MARMOT, Comput. Mater. Sci. 132, 36 (2017).
  36. M. Doi, Elasticity effects on the microstructure of alloys containing coherent precipitates, Prog. Mater. Sci. 40, 79 (1996).
  37. M. V. Eremin and K. V. Vasin, Interaction of spherically symmetric particles in cubic crystals, J. Exp. Theor. Phys. 127, 1112 (2018).
  38. Z.-H. Sung, M. Wang, A. A. Polyanskii, C. Santosh, S. Balachandran, C. Compton, D. C. Larbalestier, T. R. Bieler, and P. J. Lee, Development of low angle grain boundaries in lightly deformed superconducting niobium and their influence on hydride distribution and flux perturbation, J. Appl. Phys. 121, 193903 (2017).
  39. B. Hauer, R. Hempelmann, T. J. Udovic, J. J. Rush, E. Jansen, W. Kockelmann, W. Schäfer, and D. Richter, Neutron-scattering studies on the vibrational excitations and the structure of ordered niobium hydrides: The ɛ phase, Phys. Rev. B 57, 11115 (1998).
  40. G. V. Khaldeev and V. K. Gogel', Physical and corrosion-electrochemical properties of the niobium–hydrogen system, Russ. Chem. Rev. 56, 605 (1987).
  41. R. Roberge, Lattice parameter of niobium between 4.2 and 300 K, J. Less-Common Met. 40, 161 (1975).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation