Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Nanoscale percolation in doped BaZrO3 for high proton mobility

Nature Materials volume 19, pages 338–346 (2020)Cite this article

Subjects

A Publisher Correction to this article was published on 09 March 2020

This article has been updated

Abstract

Acceptor-doped barium zirconate is a promising proton-conducting oxide for various applications, for example, electrolysers, fuel cells or methane-conversion cells. Despite many experimental and theoretical investigations there is, however, only a limited understanding as to how to connect the complex microscopic proton motion and the macroscopic proton conductivity for the full range of acceptor levels, from diluted acceptors to concentrated solid solutions. Here we show that a combination of density functional theory calculations and kinetic Monte Carlo simulations enables this connection. At low concentrations, acceptors trap protons, which results in a decrease of the average proton mobility. With increasing concentration, however, acceptors form nanoscale percolation pathways with low proton migration energies, which leads to a strong increase of the proton mobility and conductivity. Comparing our simulated proton conductivities with experimental values for yttrium-doped barium zirconate yields excellent agreement. We then predict that ordered dopant structures would not only strongly enhance the proton conductivities, but would also enable one- or two-dimensional proton conduction in barium zirconate. Finally, we show how the properties of other dopants influence the proton conductivity.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Unit cell of BaZrO3 and all the proton jumps that are taken into account in the energy model of yttrium-doped BaZrO3.
Fig. 2: Interaction energies between different species from DFT and their adaption in the energy model.
Fig. 3: Proton conductivities and mobilities in yttrium-doped BaZrO3—simulation and experiment.
Fig. 4: Visualization of simulated percolation pathways in the 16 × 16 × 16 supercell for different dopant fractions.
Fig. 5: Calculated proton mobilities for different 1D, 2D and 3D dopant superstructures in comparison to a random dopant distribution and two 2D cuts showing two dopant superstructures in detail.
Fig. 6: Simulated proton conductivities and average mobilities for varied radii (Rtrap) and depths (Etrap) of the trapping zone.

Similar content being viewed by others

Data availability

The data that support the findings of this study are available from M.M. upon reasonable request.

Code availability

The self-written codes iCon and MOCASSIN for the KMC simulations are available from M.M. upon reasonable request.

Change history

References

  1. Iwahara, H., Yajima, T., Hibino, T., Ozaki, K. & Suzuki, H. Protonic conduction in calcium, strontium and barium zirconates. Solid State Ionics 61, 65–69 (1993).

    CAS  Google Scholar 

  2. Kreuer, K. D. Proton-conducting oxides. Annu. Rev. Mater. Res. 33, 333–359 (2003).

    CAS  Google Scholar 

  3. Bi, L., Boulfrad, S. & Traversa, E. Steam electrolysis by solid oxide electrolysis cells (SOECs) with proton-conducting oxides. Chem. Soc. Rev. 43, 8255–8270 (2014).

    CAS  Google Scholar 

  4. Bae, K. et al. Demonstrating the potential of yttrium-doped barium zirconate electrolyte for high-performance fuel cells. Nat. Commun. 8, 14553 (2017).

    CAS  Google Scholar 

  5. Malerød-Fjeld, H. et al. Thermo-electrochemical production of compressed hydrogen from methane with near-zero energy loss. Nat. Energy 2, 923–931 (2017).

    Google Scholar 

  6. Yamazaki, Y. et al. Proton trapping in yttrium-doped barium zirconate. Nat. Mater. 12, 647–651 (2013).

    CAS  Google Scholar 

  7. Kim, D. Y., Miyoshi, S., Tsuchiya, T. & Yamaguchi, S. Defect chemistry and electrochemical properties of BaZrO3 heavily doped with Fe. ECS Trans. 45, 161–170 (2012).

    Google Scholar 

  8. Tsidilkovski, V., Kuzmin, A., Putilov, L. & Balakireva, V. H/D isotope effect for hydrogen solubility in BaZr0.9Y0.1O3–δ: chemical expansion studies. Solid State Ionics 301, 170–175 (2017).

    CAS  Google Scholar 

  9. Toyoura, K., Meng, W., Han, D. & Uda, T. Preferential proton conduction along a three-dimensional dopant network in yttrium-doped barium zirconate: a first-principles study. J. Mater. Chem. A 6, 22721–22730 (2018).

    CAS  Google Scholar 

  10. Imai, G., Nakamura, T. & Amezawa, K. Defect chemistry and thermodynamic properties of proton dissolution into BaZr0.9Y0.1O3−δ. Solid State Ionics 303, 12–15 (2017).

    CAS  Google Scholar 

  11. Buannic, L., Sperrin, L., Dervişoğlu, R., Blanc, F. & Grey, C. P. Proton distribution in Sc-doped BaZrO3: a solid state NMR and first principle calculations analysis. Phys. Chem. Chem. Phys. 20, 4317–4328 (2018).

    CAS  Google Scholar 

  12. Gomez, M. A. et al. Ordered yttrium concentration effects on barium zirconate structure, proton binding sites and transition states. Solid State Ionics 304, 126–134 (2017).

    CAS  Google Scholar 

  13. Takahashi, H. et al. First-principles calculations for the energetics of the hydration reaction of acceptor-doped BaZrO3. Chem. Mater. 29, 1518–1526 (2017).

    CAS  Google Scholar 

  14. Bork, N., Bonanos, N., Rossmeisl, J. & Vegge, T. Simple descriptors for proton-conducting perovskites from density functional theory. Phys. Rev. B 82, 014103 (2010).

    Google Scholar 

  15. Sundell, P. G., Björketun, M. E. & Wahnström, G. Density-functional calculations of prefactors and activation energies for H diffusion in BaZrO3. Phys. Rev. B 76, 94301 (2007).

    Google Scholar 

  16. Gomez, M. A., Griffin, M. A., Jindal, S., Rule, K. D. & Cooper, V. R. The effect of octahedral tilting on proton binding sites and transition states in pseudo-cubic perovskite oxides. J. Chem. Phys. 123, 94703 (2005).

    Google Scholar 

  17. Björketun, M. E., Sundell, P. G., Wahnström, G. & Engberg, D. A kinetic Monte Carlo study of proton diffusion in disordered perovskite structured lattices based on first-principles calculations. Solid State Ionics 176, 3035–3040 (2005).

    Google Scholar 

  18. Ahmed, I. et al. Structural study and proton conductivity in Yb-doped BaZrO3. Solid State Ionics 178, 515–520 (2007).

    CAS  Google Scholar 

  19. Ahmed, I. et al. Crystal structure and proton conductivity of BaZr0.9Sc0.1O3−δ. J. Am. Ceram. Soc. 91, 3039–3044 (2008).

    CAS  Google Scholar 

  20. Shirpour, M., Merkle, R., Lin, C. T. & Maier, J. Nonlinear electrical grain boundary properties in proton conducting Y-BaZrO3 supporting the space charge depletion model. Phys. Chem. Chem. Phys. 14, 730–740 (2012).

    CAS  Google Scholar 

  21. Pornprasertsuk, R., Kosasang, O., Somroop, K., Jinawath, S. & Prinz, F. B. Proton conductivity studies of Y-doped barium zirconate: theoretical and experimental approaches. ECS Trans. 25, 367–381 (2010).

    CAS  Google Scholar 

  22. Kreuer, K.-D. et al. Proton conducting alkaline earth zirconates and titanates for high drain electrochemical applications. Solid State Ionics 145, 295–306 (2001).

    CAS  Google Scholar 

  23. Kosasang, O., Somroop, K., Chindaudom, P. & Pornprasertsuk, R. Effect of doping concentration on the proton conductivity of Y-doped BaZrO3 thin films. ECS Trans. 19, 145–151 (2009).

    CAS  Google Scholar 

  24. Cervera, R. B. et al. Structural study and proton transport of bulk nanograined Y-doped BaZrO3 oxide protonics materials. Solid State Ionics 179, 236–242 (2008).

    CAS  Google Scholar 

  25. Pornprasertsuk, R., Ramanarayanan, P., Musgrave, C. B. & Prinz, F. B. Predicting ionic conductivity of solid oxide fuel cell electrolyte from first principles. J. Appl. Phys. 98, 3340–3348 (2005).

    Google Scholar 

  26. Merinov, B. & Goddard, W. Proton diffusion pathways and rates in Y-doped BaZrO3 solid oxide electrolyte from quantum mechanics. J. Chem. Phys. 130, 194707 (2009).

    Google Scholar 

  27. Gomez, M. A. & Liu, F.-J. Protons in Al doped BaZrO3 escape dopant traps to access long range proton conduction highways. Solid State Ionics 252, 40–47 (2013).

    CAS  Google Scholar 

  28. Kochetova, N., Animitsa, I., Medvedev, D., Demin, A. & Tsiakaras, P. Recent activity in the development of proton-conducting oxides for high-temperature applications. RSC Adv. 6, 73222–73268 (2016).

    CAS  Google Scholar 

  29. Kreuer, K. D. On the complexity of proton conduction phenomena. Solid State Ionics 136, 149–160 (2000).

    Google Scholar 

  30. Gomez, M. A., Shepardson, D., Nguyen, L. T. & Kehinde, T. Periodic long range proton conduction pathways in pseudo-cubic and orthorhombic perovskites. Solid State Ionics 213, 8–13 (2012).

    CAS  Google Scholar 

  31. Gomez, M. A. et al. The effect of yttrium dopant on the proton conduction pathways of BaZrO3, a cubic perovskite. J. Chem. Phys. 132, 214709 (2010).

    Google Scholar 

  32. Kim, D., Miyoshi, S., Tsuchiya, T. & Yamaguchi, S. Percolation conductivity in BaZrO3-BaFeO3 solid solutions. Solid State Ionics 262, 875–878 (2014).

    CAS  Google Scholar 

  33. Grieshammer, S., Grope, B. O. H., Köttgen, J. & Martin, M. A combined DFT+U and Monte Carlo study on rare earth doped ceria. Phys. Chem. Chem. Phys. 16, 9974–9986 (2014).

    CAS  Google Scholar 

  34. Ostwald, W. Zur Theorie der Lösungen. Z. Phys. Chem. 2, 36–37 (1888).

    Google Scholar 

  35. Bjerrum, N. Investigations on association of ions. I. Kgl. Dansk. Vidensk. Selsk. Math.-fys. Medd. 7, 1–48 (1926).

    CAS  Google Scholar 

  36. Dieterich, W., Dürr, O., Pendzig, P., Bunde, A. & Nitzan, A. Percolation concepts in solid state ionics. Physica A 266, 229–237 (1999).

    CAS  Google Scholar 

  37. Kreuer, K. D. Aspects of the formation and mobility of protonic charge carriers and the stability of perovskite-type oxides. Solid State Ionics 125, 285–302 (1999).

    CAS  Google Scholar 

  38. Tao, S. & Irvine, J. T. S. Conductivity studies of dense yttrium-doped BaZrO3 sintered at 1325 °C. J. Solid State Chem. 180, 3493–3503 (2007).

    CAS  Google Scholar 

  39. Essam, J. W. Percolation theory. Rep. Prog. Phys. 43, 833–912 (1980).

    CAS  Google Scholar 

  40. Björketun, M. E., Sundell, P. G. & Wahnström, G. Effect of acceptor dopants on the proton mobility in BaZrO3: a density functional investigation. Phys. Rev. B 76, 54307 (2007).

    Google Scholar 

  41. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    CAS  Google Scholar 

  42. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

    Google Scholar 

  43. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

    CAS  Google Scholar 

  44. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).

    CAS  Google Scholar 

  45. Henkelman, G., Uberuaga, B. P. & Jonsson, H. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys. 113, 9901–9904 (2000).

    CAS  Google Scholar 

  46. Sheppard, D., Xiao, P., Chemelewski, W., Johnson, D. D. & Henkelman, G. A generalized solid-state nudged elastic band method. J. Chem. Phys. 136, 74103 (2012).

    Google Scholar 

  47. Henkelman, G. & Jónsson, H. A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J. Chem. Phys. 111, 7010–7022 (1999).

    CAS  Google Scholar 

  48. Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976).

    Google Scholar 

  49. iCon (RWTH Aachen University, 2014).

  50. MOCASSIN (RWTH Aachen University, 2018).

  51. Murch, G. E. Monte Carlo calculation as an aid in teaching solid state diffusion. Am. J. Phys. 47, 78–80 (1979).

    CAS  Google Scholar 

  52. Matsumoto, M. & Nishimura, T. Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. 8, 3–30 (1998).

    Google Scholar 

  53. O’Neill, M. E. PCG: A Family of Simple Fast Space-Efficient Statistically Good Algorithms for Random Number Generation HMC-CS-2014-0905 (2014).

  54. Grope, B. O. H., Zacherle, T., Nakayama, M. & Martin, M. Oxygen ion conductivity of doped ceria: a kinetic Monte Carlo study. Solid State Ionics 225, 476–483 (2012).

    CAS  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the computing time granted by the JARA Vergabegremium and provided on the JARA Partition part of the supercomputer CLAIX at RWTH Aachen University within the projects jara0141 and rwth0189.

Author information

Authors and Affiliations

  1. Institute of Physical Chemistry, RWTH Aachen University, Aachen, Germany

    Fabian M. Draber, Christiane Ader, John P. Arnold, Sebastian Eisele, Steffen Grieshammer & Manfred Martin

  2. Helmholtz-Institut Münster (IEK-12) and Forschungszentrum Jülich GmbH, Münster, Germany

    Sebastian Eisele, Steffen Grieshammer & Manfred Martin

  3. National Institute for Accreditation of Degrees and Quality Enhancement of Higher Education (NIAD-QE), Tokyo, Japan

    Shu Yamaguchi

  4. JARA-HPC, Forschungszentrum Jülich GmbH and RWTH Aachen University, Aachen, Germany

    Manfred Martin

  5. JARA-Energy, Forschungszentrum Jülich GmbH and RWTH Aachen University, Aachen, Germany

    Manfred Martin

Authors
  1. Fabian M. Draber
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christiane Ader
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. John P. Arnold
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sebastian Eisele
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Steffen Grieshammer
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Shu Yamaguchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Manfred Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

M.M. led the development of the concept and supervised the research. F.M.D. performed the DFT and KMC calculations, collected the data and analysed them. C.A. also performed DFT calculations and contributed data. J.P.A., S.E. and S.G. developed the program MOCASSIN and delivered technical support. J.P.A. also created the simulation cells for the superstructures. S.Y. provided critical suggestions concerning the analytical procedure. M.M. and F.M.D. wrote the paper with contributions from all the authors.

Corresponding author

Correspondence to Manfred Martin.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary discussion and Figs. 1 and 2.

Source data

Source Data Fig. 2

Numerical data used to generate Fig. 2

Source Data Fig. 3

Numerical data used to generate Fig. 3

Source Data Fig. 5

Numerical data used to generate Fig. 5

Source Data Fig. 6

Numerical data used to generate Fig. 6

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Draber, F.M., Ader, C., Arnold, J.P. et al. Nanoscale percolation in doped BaZrO3 for high proton mobility. Nat. Mater. 19, 338–346 (2020). https://doi.org/10.1038/s41563-019-0561-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41563-019-0561-7

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing