Skip to main content

Thank you for visiting 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.

Variability and origins of grain boundary electric potential detected by electron holography and atom-probe tomography


A number of grain boundary phenomena in ionic materials, in particular, anomalous (either depressed or enhanced) charge transport, have been attributed to space charge effects. Developing effective strategies to manipulate transport behaviour requires deep knowledge of the origins of the interfacial charge, as well as its variability within a polycrystalline sample with millions of unique grain boundaries. Electron holography is a powerful technique uniquely suited for studying the electric potential profile at individual grain boundaries, whereas atom-probe tomography provides access to the chemical identify of essentially every atom at individual grain boundaries. Using these two techniques, we show here that the space charge potential at grain boundaries in lightly doped, high-purity ceria can vary by almost an order of magnitude. We further find that trace impurities (<25 ppm), rather than inherent thermodynamic factors, may be the ultimate source of grain boundary charge. These insights suggest chemical tunability of grain boundary transport properties.

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: High-resolution TEM (HRTEM) image of a representative grain boundary in 0.2 cation% Sm-doped ceria.
Fig. 2: Macroscopic transport properties of polycrystalline 0.2 cation% Sm-doped ceria (grain size 12.5 ± 1.2 µm) under synthetic air.
Fig. 3: Electron holographic imaging of a representative grain boundary in 0.2 cation% Sm-doped ceria.
Fig. 4: Schematics of factors affecting measured electric field associated with grain boundary space charge effects.
Fig. 5: Grain boundary space charge potentials measured in 0.2 cation% Sm-doped ceria.
Fig. 6: Elemental composition across grain boundaries in 0.2 cation% Sm-doped ceria as measured by APT.

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.


  1. Luo, J. Interfacial engineering of solid electrolytes. J. Materiomics 1, 22–32 (2015).

    Google Scholar 

  2. Zhang, T. S., Ma, J., Chan, S. H., Hing, P. & Kilner, J. A. Intermediate-temperature ionic conductivity of ceria-based solid solutions as a function of gadolinia and silica contents. Solid State Sci. 6, 565–572 (2004).

    CAS  Google Scholar 

  3. Kim, S., Kim, S. K., Khodorov, S., Maier, J. & Lubomirsky, I. On determining the height of the potential barrier at grain boundaries in ion-conducting oxides. Phys. Chem. Chem. Phys. 18, 3023–3031 (2016).

    CAS  Google Scholar 

  4. Fleig, J. & Maier, J. Finite-element calculations on the impedance of electroceramics with highly resistive grain boundaries: I, laterally inhomogeneous grain boundaries. J. Am. Ceram. Soc. 82, 3485–3493 (1999).

    CAS  Google Scholar 

  5. Lei, Y. Y., Ito, Y., Browning, N. D. & Mazanec, T. J. Segregation effects at grain boundaries in fluorite-structured ceramics. J. Am. Ceram. Soc. 85, 2359–2363 (2002).

    CAS  Google Scholar 

  6. Vikrant, K. S. N., Chueh, W. C. & Garcia, R. E. Charged interfaces: electrochemical and mechanical effects. Energy Environ. Sci. 11, 1993–2000 (2018).

    CAS  Google Scholar 

  7. Maier, J. Ionic conduction in space charge regions. Prog. Solid State Chem. 23, 171–263 (1995).

    CAS  Google Scholar 

  8. Sato, K. Probing charge-state distribution at grain boundaries varied with dopant concentration for ceria ceramics. J. Phys. Chem. C. 121, 20407–20412 (2017).

    CAS  Google Scholar 

  9. Guo, X. & Maier, J. Grain boundary blocking effect in zirconia: a Schottky barrier analysis. J. Electrochem. Soc. 148, E121–E126 (2001).

    CAS  Google Scholar 

  10. Guo, X. & Waser, R. Electrical properties of the grain boundaries of oxygen ion conductors: acceptor-doped zirconia and ceria. Prog. Mater. Sci. 51, 151–210 (2006).

    CAS  Google Scholar 

  11. Gregori, G., Merkle, R. & Maier, J. Ion conduction and redistribution at grain boundaries in oxide systems. Prog. Mater. Sci. 89, 252–305 (2017).

    CAS  Google Scholar 

  12. Kim, S., Fleig, J. & Maier, J. Space charge conduction: simple analytical solutions for ionic and mixed conductors and application to nanocrystalline ceria. Phys. Chem. Chem. Phys. 5, 2268–2273 (2003).

    CAS  Google Scholar 

  13. Rodewald, S., Fleig, J. & Maier, J. Microcontact impedance spectroscopy at single grain boundaries in Fe-doped SrTiO3 polycrystals. J. Am. Ceram. Soc. 84, 521–530 (2001).

    CAS  Google Scholar 

  14. Zhang, Z. L. et al. Comparative studies of microstructure and impedance of small-angle symmetrical and asymmetrical grain boundaries in SrTiO3. Acta Materialia 53, 5007–5015 (2005).

    CAS  Google Scholar 

  15. R. Diercks, D. et al. Three-dimensional quantification of composition and electrostatic potential at individual grain boundaries in doped ceria. J. Mater. Chem. A. 4, 5167–5175 (2016).

    Google Scholar 

  16. Eguchi, K., Setoguchi, T., Inoue, T. & Arai, H. Electrical properties of ceria-based oxides and their application to solid oxide fuel cells. Solid State Ion. 52, 165–172 (1992).

    CAS  Google Scholar 

  17. Mogensen, M., Sammes, N. M. & Tompsett, G. A. Physical, chemical and electrochemical properties of pure and doped ceria. Solid State Ion. 129, 63–94 (2000).

    CAS  Google Scholar 

  18. Rau, W. D., Schwander, P., Baumann, F. H., Höppner, W. & Ourmazd, A. Two-dimensional mapping of the electrostatic potential in transistors by electron holography. Phys. Rev. Lett. 82, 2614–2617 (1999).

    CAS  Google Scholar 

  19. Wang, Y. G. & Dravid, V. P. Determination of electrostatic characteristics at a 24°, [001] tilt grain boundary in a SrTiO3 bicrystal by electron holography. Philos. Mag. Lett. 82, 425–432 (2002).

    CAS  Google Scholar 

  20. Ravikumar, V., Rodrigues, R. P. & Dravid, V. P. Space-charge distribution across internal interfaces in electroceramics using electron holography: II, doped grain boundaries. J. Am. Ceram. Soc. 80, 1131–1138 (1997).

    CAS  Google Scholar 

  21. Ravikumar, V., Rodrigues, R. P. & Dravid, V. P. Direct imaging of spatially varying potential and charge across internal interfaces in solids. Phys. Rev. Lett. 75, 4063–4066 (1995).

    CAS  Google Scholar 

  22. Guo, X., Sigle, W. & Maier, J. Blocking grain boundaries in yttria-doped and undoped ceria ceramics of high purity. J. Am. Ceram. Soc. 86, 77–87 (2003).

    CAS  Google Scholar 

  23. Chueh, W. C., Yang, C. K., Garland, C. M., Lai, W. & Haile, S. M. Unusual decrease in conductivity upon hydration in acceptor doped, microcrystalline ceria. Phys. Chem. Chem. Phys. 13, 6442–6451 (2011).

    CAS  Google Scholar 

  24. Yeh, T. C., Perry, N. H. & Mason, T. O. Nanograin composite model studies of nanocrystalline gadolinia-doped ceria. J. Am. Ceram. Soc. 94, 1073–1078 (2011).

    CAS  Google Scholar 

  25. Haile, S. M., West, D. L. & Campbell, J. The role of microstructure and processing on the proton conducting properties of gadolinium-doped barium cerate. J. Mater. Res. 13, 1576–1595 (1998).

    CAS  Google Scholar 

  26. Tschope, A., Kilassonia, S. & Birringer, R. The grain boundary effect in heavily doped cerium oxide. Solid State Ion. 173, 57–61 (2004).

    Google Scholar 

  27. Avila-Paredes, H. J., Choi, K., Chen, C. T. & Kim, S. Dopant-concentration dependence of grain-boundary conductivity in ceria: a space-charge analysis. J. Mater. Chem. 19, 4837–4842 (2009).

    CAS  Google Scholar 

  28. Kim, S. K., Khodorov, S., Chen, C. T., Kim, S. & Lubomirsky, I. How to interpret current-voltage relationships of blocking grain boundaries in oxygen ionic conductors. Phys. Chem. Chem. Phys. 15, 8716–8721 (2013).

    CAS  Google Scholar 

  29. McCartney, M. R. & Gajdardziska-Josifovska, M. Absolute measurement of normalized thickness, t/λi, from off-axis electron holography. Ultramicroscopy 53, 283–289 (1994).

    CAS  Google Scholar 

  30. Williams, D. B. & Carter, C. B. Transmission Electron Microscopy: A Textbook for Materials Science 2nd edn (Springer, 2009).

  31. Shibata, N., Oba, F., Yamamoto, T. & Ikuhara, Y. Structure, energy and solute segregation behaviour of [110] symmetric tilt grain boundaries in yttria-stabilized cubic zirconia. Philos. Mag. 84, 2381–2415 (2004).

    CAS  Google Scholar 

  32. Bokov, A. et al. Energetic design of grain boundary networks for toughening of nanocrystalline oxides. J. Eur. Ceram. Soc. 38, 4260–4267 (2018).

    CAS  Google Scholar 

  33. Harbison, T. Anisotropic Grain Boundary Energy Function for Uranium Dioxide. BSc thesis, Brigham Young Univ. (2015).

  34. Rittner, J. D. & Seidman, D. N. <110> symmetric tilt grain-boundary structures in fcc metals with low stacking-fault energies. Phys. Rev. B. 54, 6999–7015 (1996).

    CAS  Google Scholar 

  35. Rohrer, G. S. Grain boundary energy anisotropy: a review. J. Mater. Sci. 46, 5881–5895 (2011).

    CAS  Google Scholar 

  36. Seidman, D. N. Three-dimensional atom-probe tomography: advances and applications. Annu. Rev. Mater. Res. 37, 127–158 (2007).

  37. Aggarwal, S. & Ramesh, R. Point defect chemistry of metal oxide heterostructures. Annu. Rev. Mater. Sci. 28, 463–499 (1998).

    CAS  Google Scholar 

  38. Minervini, L., Zacate, M. O. & Grimes, R. W. Defect cluster formation in M2O3-doped CeO2. Solid State Ion. 116, 339–349 (1999).

    CAS  Google Scholar 

  39. Shannon, R. D. Revised effective ionic-radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Crystallogr. A 32, 751–767 (1976).

    Google Scholar 

  40. Ge, L., Ni, Q., Cai, G. F., Sang, T. Y. & Guo, L. C. Improving SiO2 impurity tolerance of Ce0.8Sm0.2O1.9: synergy of CaO and ZnO in scavenging grain-boundary resistive phases. J. Power Sources 324, 582–588 (2016).

    CAS  Google Scholar 

  41. Cho, P. S. et al. Effect of CaO concentration on enhancement of grain-boundary conduction in gadolinia-doped ceria. J. Power Sources 183, 518–523 (2008).

    CAS  Google Scholar 

  42. Kim, D. K. et al. Mitigation of highly resistive grain-boundary phase in gadolinia-doped ceria by the addition of SrO. Electrochem. Solid State Lett. 10, B91–B95 (2007).

    CAS  Google Scholar 

  43. Cho, Y. H. et al. Enhancement of grain-boundary conduction in gadolinia-doped ceria by the scavenging of highly resistive siliceous phase. Acta Materialia 55, 4807–4815 (2007).

    CAS  Google Scholar 

  44. Lane, J. A., Neff, J. L. & Christie, G. M. Mitigation of the deleterious effect of silicon species on the conductivity of ceria electrolytes. Solid State Ion. 177, 1911–1915 (2006).

    CAS  Google Scholar 

  45. Lee, J. H. Highly resistive intergranular phases in solid electrolytes: an overview. Monatsh. Chem. 140, 1081–1094 (2009).

    CAS  Google Scholar 

  46. Sudarsan, P. & Moorthy, S. B. K. Synergistic effect of lithium and calcium for low temperature densification and grain boundary scavenging in samarium doped ceria electrolyte. Materials Chem. Phys. 238, (2019).

  47. Thompson, A. W. Calculation of true volume grain diameter. Metallography 5, 366–369 (1972).

    Google Scholar 

  48. Larson, D. J., Prosa, T. J., Ulfig, R. M., Geiser, B. P. & Kelly, T. F. Local Electrode Atom Probe Tomography: A User’s Guide (Springer, 2013).

  49. Thompson, K. et al. In situ site-specific specimen preparation for atom probe tomography. Ultramicroscopy 107, 131–139 (2007).

    CAS  Google Scholar 

Download references


This material is based on work supported in large part by the National Science Foundation under grant no. DMR-1720139 (partial support of S.M.H., partial support of X.X., support for sample fabrication and characterization by impedance spectroscopy and HRTEM). Partial support for X.X. was provided by a Northwestern-Argonne Early Career Investigator Award for Energy Research. Work by C.P. was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division. SEM and HRTEM were performed in the EPIC facility of Northwestern University’s NUANCE Center, which has received support from the Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (no. NSF ECCS-1542205); the MRSEC program (no. NSF DMR-1720139) at the Materials Research Center; the International Institute for Nanotechnology (IIN); the Keck Foundation and the State of Illinois, through the IIN. EDS and electron holography were performed at the Center for Nanoscale Materials, an Office of Science user facility, supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under contract no. DE-AC02-06CH11357. APT was performed at the Northwestern University Center for Atom-Probe Tomography (NUCAPT). The LEAP tomography instrument at NUCAPT was purchased and upgraded with grants from the NSF-MRI (no. DMR-0420532) and ONR-DURIP (nos. N00014-0400798, N00014-0610539, N00014-0910781 and N00014-1712870) programs. NUCAPT received support from the MRSEC program (no. NSF DMR-1720139) at the Materials Research Center, the SHyNE Resource (no. NSF ECCS-1542205), and the Initiative for Sustainability and Energy at Northwestern University.

Author information

Authors and Affiliations



X.X. performed most of the experiments and their analysis. Y.L. and C.P assisted with electron holography and data analysis. J.W. assisted with electron microscopy and EDS measurements. D.I. supervised and assisted with APT measurements. V.P.D. assisted with design of holography experiments. C.P and S.M.H designed the research plan, with S.M.H. providing overall guidance for the research work. X.X. and S.M.H. wrote the manuscript with input from all authors.

Corresponding author

Correspondence to Sossina M. Haile.

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 Figs. 1–16 and Tables 1 and 2 along with discussion of these figures and tables.

Supplementary Video 1

Grain boundary segregation in ceria detected by APT.

Source data

Source Data Fig. 2

Raw data of impedance and conductivity

Source Data Fig. 3

Data of electrical potential of the GB

Source Data Fig. 5

Space charge potential of 9 GBs

Source Data Fig. 6

Composition, space charge potential, and oxygen vacancy concentrations of GB1 and GB2

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Xu, X., Liu, Y., Wang, J. et al. Variability and origins of grain boundary electric potential detected by electron holography and atom-probe tomography. Nat. Mater. 19, 887–893 (2020).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


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