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.

  • Article
  • Published:

A two-dimensional type I superionic conductor


Superionic conductors possess liquid-like ionic diffusivity in the solid state, finding wide applicability from electrolytes in energy storage to materials for thermoelectric energy conversion. Type I superionic conductors (for example, AgI, Ag2Se and so on) are defined by a first-order transition to the superionic state and have so far been found exclusively in three-dimensional crystal structures. Here, we reveal a two-dimensional type I superionic conductor, α-KAg3Se2, by scattering techniques and complementary simulations. Quasi-elastic neutron scattering and ab initio molecular dynamics simulations confirm that the superionic Ag+ ions are confined to subnanometre sheets, with the simulated local structure validated by experimental X-ray powder pair-distribution-function analysis. Finally, we demonstrate that the phase transition temperature can be controlled by chemical substitution of the alkali metal ions that compose the immobile charge-balancing layers. Our work thus extends the known classes of superionic conductors and will facilitate the design of new materials with tailored ionic conductivities and phase transitions.

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

Access options

Buy this article

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

Fig. 1: QENS of KAg3Se2.
Fig. 2: Molecular dynamics simulations and structural comparison.
Fig. 3: Local structure analysis.
Fig. 4: Effects of cation substitution.

Similar content being viewed by others

Data availability

Data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.


  1. Boyce, J. B. & Huberman, B. A. Superionic conductors: transitions, structures, dynamics. Phys. Rep. 51, 189–265 (1979).

    Article  CAS  Google Scholar 

  2. Faraday, M. V. I. I. Experimental researches in electricity. Philos. Trans. R. Soc. 128, 83–123 (1838).

    Article  Google Scholar 

  3. Hull, S. Superionics: crystal structures and conduction processes. Rep. Prog. Phys. 67, 1233–1314 (2004).

    Article  CAS  Google Scholar 

  4. Goodenough, J. B. Review lecture - fast ionic conduction in solid. Proc. R. Soc. A 393, 215–234 (1984).

    CAS  Google Scholar 

  5. Bruce, P. G. Solid State Electrochemistry (Cambridge Univ. Press, 1997).

  6. Voneshen, D., Walker, H., Refson, K. & Goff, J. Hopping time scales and the phonon-liquid electron-crystal picture in thermoelectric copper selenide. Phys. Rev. Lett. 118, 145901 (2017).

    Article  CAS  Google Scholar 

  7. Ding, J. et al. Anharmonic lattice dynamics and superionic transition in AgCrSe2. Proc. Natl Acad. Sci. USA 117, 3930–3937 (2020).

    Article  CAS  Google Scholar 

  8. Bailey, T. P. & Uher, C. Potential for superionic conductors in thermoelectric applications. Curr. Opin. Green. Sustain. Chem. 4, 58–63 (2017).

    Article  Google Scholar 

  9. Keen, D. A. Disordering phenomena in superionic conductors. J. Condens. Matter Phys. 14, R819 (2002).

    Article  CAS  Google Scholar 

  10. Funke, K. AgI-type solid electrolytes. Prog. Solid. State Chem. 11, 345–402 (1976).

    Article  Google Scholar 

  11. Derrington, C. & O’Keeffe, M. Anion conductivity and disorder in lead fluoride. Nat. Phys. Sci. 246, 44–46 (1973).

    Article  CAS  Google Scholar 

  12. Boukamp, B. & Wiegers, G. Ionic and electronic processes in AgCrSe2. Solid State Ion. 9, 1193–1196 (1983).

    Article  Google Scholar 

  13. Yao, Y.-F. Y. & Kummer, J. Ion exchange properties of and rates of ionic diffusion in beta-alumina. J. Inorg. Nucl. Chem. 29, 2453–2466, IN1, 2467–2475 (1967).

    Article  CAS  Google Scholar 

  14. Engelsman, F., Wiegers, G., Jellinek, F. & Van Laar, B. Crystal structures and magnetic structures of some metal (I) chromium (III) sulfides and selenides. J. Solid State Chem. 6, 574–582 (1973).

    Article  CAS  Google Scholar 

  15. Newsam, J. & Cheetham, A. Stoichiometric silver beta alumina studied at 25, 300 and 500 degrees C by powder neutron diffraction. J. Phys. Condens. Matter 2, 2335 (1990).

    Article  CAS  Google Scholar 

  16. Tubandt, C. & Lorenz, E. Molekularzustand und elektrisches leitvermögen kristallisierter salze. Z. Phys. Chem. 87, 513–542 (1914).

    Article  CAS  Google Scholar 

  17. Miyatani, S.-y Ionic conductivity in silver chalcogenides. J. Phys. Soc. Jpn 50, 3415–3418 (1981).

    Article  CAS  Google Scholar 

  18. Majumdar, A. & Roy, R. Experimental study of the polymorphism of AgI. J. Phys. Chem. 63, 1858–1860 (1959).

    Article  CAS  Google Scholar 

  19. Banus, M. D. Pressure dependence of the alpha-beta transition temperature in silver selenide. Science 147, 732–733 (1965).

    Article  CAS  Google Scholar 

  20. Hu, T., Wittenberg, J. & Lindenberg, A. Room-temperature stabilization of nanoscale superionic Ag2Se. Nanotechnology 25, 415705 (2014).

    Article  CAS  Google Scholar 

  21. Makiura, R. et al. Size-controlled stabilization of the superionic phase to room temperature in polymer-coated AgI nanoparticles. Nat. Mater. 8, 476–480 (2009).

    Article  CAS  Google Scholar 

  22. Rettie, A. J. E. et al. Ag2Se to KAg3Se2: suppressing order–disorder transitions via reduced dimensionality. J. Am. Chem. Soc. 140, 9193–9202 (2018).

    Article  CAS  Google Scholar 

  23. Mamontov, E. Fast oxygen diffusion in bismuth oxide probed by quasielastic neutron scattering. Solid State Ion. 296, 158–162 (2016).

    Article  CAS  Google Scholar 

  24. Bée, M. Localized and long-range diffusion in condensed matter: state of the art of QENS studies and future prospects. Chem. Phys. 292, 121–141 (2003).

    Article  Google Scholar 

  25. Hamilton, M., Barnes, A., Howells, W. & Fischer, H. Ag+ dynamics in the superionic and liquid phases of Ag2Se and Ag2Te by coherent quasi-elastic neutron scattering. J. Phys. Condens. Matter 13, 2425 (2001).

    Article  CAS  Google Scholar 

  26. Chudley, C. & Elliott, R. Neutron scattering from a liquid on a jump diffusion model. Proc. Phys. Soc. 77, 353 (1961).

    Article  Google Scholar 

  27. Embs, J. P., Juranyi, F. & Hempelmann, R. Introduction to quasielastic neutron scattering. Z. Phys. Chem. 224, 5–32 (2010).

    Article  CAS  Google Scholar 

  28. Hempelmann, R. Quasielastic Neutron Scattering and Solid State Diffusion (Clarendon Press, 2000).

  29. Wind, J., Mole, R. A., Yu, D. & Ling, C. D. Liquid-like ionic diffusion in solid bismuth oxide revealed by coherent quasielastic neutron scattering. Chem. Mater. 29, 7408–7415 (2017).

    Article  CAS  Google Scholar 

  30. Niedziela, J. L. et al. Selective breakdown of phonon quasiparticles across superionic transition in CuCrSe2. Nat. Phys. 15, 73–78 (2019).

    Article  CAS  Google Scholar 

  31. Bensch, W. & Dürichen, P. Crystal structure of potassium diselenotriargentate, KAg3Se2. Z. Kristallogr. N. Cryst. Struct. 212, 97–98 (1997).

    Article  CAS  Google Scholar 

  32. Kvist, A. & Josefson, A.-M. The electrical conductivity of solid and molten silver iodide. Z. Naturforsch. A 23, 625–626 (1968).

    Article  CAS  Google Scholar 

  33. Allen, R. L. & Moore, W. J. Diffusion of silver in silver sulfide. J. Phys. Chem. 63, 223–226 (1959).

    Article  CAS  Google Scholar 

  34. Okazaki, H. Deviation from the Einstein relation in average crystals self-diffusion of Ag+ ions in α-Ag2S and α-Ag2Se. J. Phys. Soc. Jpn 23, 355–360 (1967).

    Article  CAS  Google Scholar 

  35. Rom, I. & Sitte, W. Composition dependent ionic and electronic conductivities and chemical diffusion coefficient of silver selenide at 160 C. Solid State Ion. 101, 381–386 (1997).

    Google Scholar 

  36. Barnes, A., Lague, S., Salmon, P. & Fischer, H. A determination of the structure of liquid Ag2Se using neutron diffraction and isotopic substitution. J. Phys. Condens. Matter 9, 6159–6173 (1997).

    Article  CAS  Google Scholar 

  37. Lee, S. & Xu, H. Using complementary methods of synchrotron radiation powder diffraction and pair distribution function to refine crystal structures with high quality parameters—a review. Minerals 10, 124 (2020).

    Article  CAS  Google Scholar 

  38. Sharp, K. W. & Koehler, W. H. Synthesis and characterization of sodium polyselenides in liquid ammonia solution. Inorg. Chem. 16, 2258–2265 (1977).

    Article  CAS  Google Scholar 

  39. Mamontov, E. & Herwig, K. W. A time-of-flight backscattering spectrometer at the Spallation Neutron Source, BASIS. Rev. Sci. Instrum. 82, 085109 (2011).

    Article  CAS  Google Scholar 

  40. Arnold, O. et al. Mantid – data analysis and visualization package for neutron scattering and μSR experiments. Nucl. Instrum. Methods Phys. Res. A 764, 156–166 (2014).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  42. 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 

  43. Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558 (1993).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  45. Perdew, J. P. & Zunger, A. Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 23, 5048 (1981).

    Article  CAS  Google Scholar 

  46. He, X., Zhu, Y., Epstein, A. & Mo, Y. Statistical variances of diffusional properties from ab initio molecular dynamics simulations. npj Comput. Mater. 4, 18 (2018).

    Article  Google Scholar 

  47. Toby, B. H. & Von Dreele, R. B. GSAS-II: the genesis of a modern open-source all purpose crystallography software package. J. Appl. Crystallogr. 46, 544–549 (2013).

    Article  CAS  Google Scholar 

  48. Juhás, P., Davis, T., Farrow, C. L. & Billinge, S. J. L. PDFgetX3: a rapid and highly automatable program for processing powder diffraction data into total scattering pair distribution functions. J. Appl. Crystallogr. 46, 560–566 (2013).

    Article  Google Scholar 

  49. Farrow, C. L. et al. PDFfit2 and PDFgui: computer programs for studying nanostructure in crystals. J. Phys. Condens. Matter 19, 335219 (2007).

    Article  CAS  Google Scholar 

Download references


We are indebted to W. Xu for assistance in the acquisition and analysis of X-ray total scattering data and to E. Mamontov for valuable discussions concerning the QENS data analysis. M.J.J. acknowledges HORIBA-Motor Industry Research Association (MIRA), University College London (UCL) and the Engineering and Physical Sciences Research Council (EPSRC) (EP/R513143/1) for a Collaborative Awards in Science and Engineering (CASE) studentship. This work was performed primarily at the Materials Science Division at Argonne National Laboratory, supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division. We gratefully acknowledge the computing resources provided on Bebop, the high-performance computing clusters operated by the Laboratory Computing Resource Center at Argonne National Laboratory. First-principles modelling at Duke University (J.D., O.D.) was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under award no. DE-SC0019299. Work at Oak Ridge National Laboratory’s Spallation Neutron Source is supported by the US Department of Energy, Office of Basic Energy Sciences. The Oak Ridge National Laboratory is managed by UT–Battelle for the US Department of Energy under contract no. DEAC05-00OR22725. This work made use of the Integrated Molecular Structure Education and Research Center (IMSERC) facility at Northwestern University, which has received support from the Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF ECCS-2025633) and Northwestern University. A.J.E.R. and M.J.J. gratefully acknowledge the Faraday Institution Lithium-Sulfur Technology Accelerator (LiSTAR) programme (FIRG014, EP/S003053/1) for funding.

Author information

Authors and Affiliations



A.J.E.R., S.R. and M.G.K. conceived the study. A.J.E.R., X.Z. and D.Y.C. synthesized and characterized all materials. A.J.E.R., R.O. and N.C.O. acquired and analysed the neutron scattering data. J.D. and O.D. performed the AIMD simulations. M.J.J. and C.D.M. conducted the PDF analysis and structural modelling. The manuscript was mainly written and revised by A.J.E.R., S.R. and M.G.K. All authors approved the final version of the manuscript.

Corresponding authors

Correspondence to Alexander J. E. Rettie, Stephan Rosenkranz or Mercouri G. Kanatzidis.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Materials thanks Stefan Adams, Tom Nilges and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Supplementary information

Supplementary Information

Supplementary Figs. 1–18 and Discussion.

Supplementary Video 1

Animation of molecular dynamics simulations of α-KAg3Se2 at 800 K.

Source data

Source Data Fig. 1

Source data for graphs in Fig. 1.

Source Data Fig. 2

Source data for graphs in Fig. 2.

Source Data Fig. 3

Source data for graphs in Fig. 3.

Source Data Fig. 4

Source data for graphs in Fig. 4.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rettie, A.J.E., Ding, J., Zhou, X. et al. A two-dimensional type I superionic conductor. Nat. Mater. 20, 1683–1688 (2021).

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