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Nanoscale percolation in doped BaZrO3 for high proton mobility

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

This article has been updated


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.

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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.

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


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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




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.

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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

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Source Data Fig. 6

Numerical data used to generate Fig. 6

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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).

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