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Ceramic phases with one-dimensional long-range order


Solids are generally classified into three categories based on their atomic arrangement: crystalline, quasicrystalline and amorphous1,2,3,4. Here we report MgO and Nd2O3 ceramic phases with special atomic arrangements that should belong to a category of solids different from these three well known categories by combining state-of-the-art atomic-resolution scanning transmission electron microscopy and first-principles calculations. The reported solid structure exhibits a one-dimensional (1D) long-range order with a translational periodicity and is composed of structural units that individually have atomic arrangements similar to those observed in coincidence-site lattice configurations present at grain boundaries. Regardless of the insulating nature of the bulk MgO, the bandgap of which is measured to be 7.4 eV, the MgO 1D ordered structure is a wide-bandgap semiconductor with a bandgap of 3.2 eV owing to this special atomic arrangement. The discovery of 1D ordered structures suggests that the structural categories of solids could be more abundant, with physical properties distinct from their regular counterparts.

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Fig. 1: Schematic diagrams showing the atomic structure of a 1D ordered structure.
Fig. 2: ABF STEM images showing the MgO 1D ordered structure formed in the triple-junction regions of the MgO grains.
Fig. 3: DFT calculations and STEM-EELS revealing the atomic and electronic structural characteristics of the MgO 1D ordered structure.
Fig. 4: HAADF STEM images showing the 1D ordered structure formed in the Nd2O3 thin film.

Data availability

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


  1. Hook, J. R. & Hall, H. E. Solid State Physics 2nd edn (John Wiley & Sons, Chichester, 2010).

  2. Shechtman, D., Blech, I., Gratias, D. & Cahn, J. W. Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53, 1951–1953 (1984).

    Article  CAS  Google Scholar 

  3. Levine, D. & Steinhardt, R. Quasicrystals: a new class of ordered structures. Phys. Rev. Lett. 53, 2477–2480 (1984).

    Article  CAS  Google Scholar 

  4. Zollen, R. The Physics of Amorphous Solids (Wiley, New York, 1983).

  5. Yacamán, M. J. & Torres, M. Crystal-quasicrystal Transitions (North-Holland, Amsterdam, 1993).

  6. Waseda, Y. The Structure of Non-crystalline Materials: Liquids and Amorphous Solids (McGraw-Hill, New York, 1980).

  7. Sutton, A. P. & Balluffi, R. W. Interfaces in Crystalline Materials (Clarendon Press, Oxford, 1995).

  8. Wolf, D. & Yip, S. Material Interfaces (Chapman & Hall, London, 1992).

  9. Sutton, A. P. & Vitek, V. On the structure of tilt grain boundaries in cubic metals I. Symmetrical tilt boundaries. Phil. Trans. R. Soc. A 309, 1–36 (1983).

    Article  CAS  Google Scholar 

  10. Gleiter, H. On the structure of grain boundaries in metals. Mater. Sci. Eng. 52, 91–131 (1982).

    Article  CAS  Google Scholar 

  11. Grimmer, H., Bollmann, W. & Warrington, D. H. Coincidence-site lattices and complete pattern-shift lattices in cubic-crystals. Acta Crystallogr. A 30, 197–207 (1974).

    Article  Google Scholar 

  12. Wang, Z. C. et al. Atom-resolved imaging of ordered defect superstructures at individual grain boundaries. Nature 479, 380–383 (2011).

    Article  CAS  Google Scholar 

  13. Buban, J. P. et al. Grain boundary strengthening in alumina by rare earth impurities. Science 311, 212–215 (2006).

    Article  CAS  Google Scholar 

  14. Inoue, K., Saito, M., Chen, C. L., Kotani, M. & Ikuhara, Y. Mathematical analysis and STEM observations of arrangement of structural units in <001> symmetrical tilt grain boundaries. Microscopy 65, 479–487 (2016).

    Article  CAS  Google Scholar 

  15. Inoue, K., Saito, M., Wang, Z. C., Kotani, M. & Ikuhara, Y. On the periodicity of <001> symmetrical tilt grain boundaries. Mater. Trans. 65, 281–287 (2015).

    Article  Google Scholar 

  16. Bean, J. J. et al. Atomic structure and electronic properties of MgO grain boundaries in tunneling magnetoresistive devices. Sci. Rep. 7, 45594 (2017).

    Article  CAS  Google Scholar 

  17. Mo, S. D. & Ching, W. Y. Electronic and optical properties of ɵ-Al2O3 and comparison to ɑ-Al2O3. Phys. Rev. B 57, 15219–15228 (1998).

    Article  CAS  Google Scholar 

  18. Cui, H. J. et al. The geometric and electronic transitions in body-centered-tetragonal C8: a first principles study. Carbon 120, 89–94 (2017).

    Article  CAS  Google Scholar 

  19. Mckenna, K. P. & Shluger, A. L. Electron-trapping polycrystalline materials with negative electron affinity. Nat. Mater. 7, 859–862 (2008).

    Article  CAS  Google Scholar 

  20. Pennycook, S. J. & Boatner, L. A. Chemically sensitive structure-imaging with a scanning transmission electron microcrope. Nature 336, 565–567 (1988).

    Article  CAS  Google Scholar 

  21. 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).

    Article  CAS  Google Scholar 

  22. Kirkland, E. J. Advanced Computing in Electron Microscopy (Plenum, New York, 1998).

  23. 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).

    Article  CAS  Google Scholar 

  24. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  26. Perdew, J. P. et al. Atoms, molecules, solids, and surfaces – Application of the generalized gradient approximation for exchange and correlation. Phys. Rev. B 46, 6671–6687 (1992).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  28. Feynman, R. Force in molecules. Phys. Rev. 56, 340–343 (1939).

    Article  CAS  Google Scholar 

  29. Blöchl, P. E., Jepson, O. & Andersen, O. K. Improved tetrahedron method for Brillouin-zone integrations. Phys. Rev. B 49, 16223–16233 (1994).

    Article  Google Scholar 

  30. Heyd, J., Scuseria, G. E. & Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207–8215 (2003).

    Article  CAS  Google Scholar 

  31. Heyd, J. & Scuseria, G. E. Efficient hybrid density functional calculations in solids: Assessment of the Heyd–Scuseria–Ernzerhof screened Coulomb hybrid functional. J. Chem. Phys. 121, 1187–1192 (2004).

    Article  CAS  Google Scholar 

  32. Garza, A. J. & Scuseria, G. E. Predicting band gaps with hybrid density functional. J. Phys. Chem. Lett. 7, 4165–4170 (2016).

    Article  CAS  Google Scholar 

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A part of this study was supported by Grant-in-Aid for Specially Promoted Research (Grant No. JP17H06094) from the Japan Society for the Promotion of Science (JSPS) and the ‘Nanotechnology Platform’ (Project No. 12024046) of MEXT. C.C. is grateful for support from the Key Research Program of Frontier Sciences, CAS (No. QYZDY-SSW-JSC027), the National Natural Sciences Foundation of China (No. 51771200), and the ‘Thousand Youth Talents Plan’ of China. D.Y. acknowledges support from the National Natural Science Foundation of China (No. 11332013). The computation in this work was partly done using the facilities of the Supercomputer Center, the Institute for Solid State Physics, the University of Tokyo. We thank M. Kotani of Tohoku University for useful discussions and H. Ohno and S. Ikeda of Tohoku University for providing the present MgO samples. We thank S. Kobayashi of Japan Fine Ceramics Center and J. Wei of University of Tokyo for assisting with the EELS analysis.

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D.Y. performed the calculations. C.C. and M.S. conducted the experiments. C.C. and D.Y. wrote the paper. K.I. supported the calculation and discussed the results. C.C. and Y.I. directed the entire study. All authors read and commented on the paper.

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Correspondence to Chunlin Chen or Yuichi Ikuhara.

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Yin, D., Chen, C., Saito, M. et al. Ceramic phases with one-dimensional long-range order. Nature Mater 18, 19–23 (2019).

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