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Selective breakdown of phonon quasiparticles across superionic transition in CuCrSe2


Superionic crystals exhibit ionic mobilities comparable to liquids while maintaining a periodic crystalline lattice. The atomic dynamics leading to large ionic mobility have long been debated. A central question is whether phonon quasiparticles—which conduct heat in regular solids—survive in the superionic state, where a large fraction of the system exhibits liquid-like behaviour. Here we present the results of energy- and momentum-resolved scattering studies combined with first-principles calculations and show that in the superionic phase of CuCrSe2, long-wavelength acoustic phonons capable of heat conduction remain largely intact, whereas specific phonon quasiparticles dominated by the Cu ions break down as a result of anharmonicity and disorder. The weak bonding and large anharmonicity of the Cu sublattice are present already in the normal ordered state, resulting in low thermal conductivity even below the superionic transition. These results demonstrate that anharmonic phonon dynamics are at the origin of low thermal conductivity and superionicity in this class of materials.

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Fig. 1: Anomalous atomic dynamics across the superionic transition in CuCrSe2.
Fig. 2: Phonon spectra from INS and DFT simulations, showing large damping and softening of Cu in-plane modes across Tod.
Fig. 3: Momentum-resolved IXS measurements on single-crystalline CuCrSe2, compared with DFT simulations.
Fig. 4: Diffusive behaviour of Cu ions probed with quasielastic neutron scattering and ab initio molecular dynamics.

Data availability

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


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

    ADS  Article  Google Scholar 

  2. Brüesch, P. Phonons: Theory and Experiments I (Springer, Berlin, Heidelberg, 1982).

  3. Mahan, G. D. & Roth, W. L. (eds.) Superionic Conductors (Springer, Boston, 1976).

  4. Salamon, M. B. (ed.) Physics of Superionic Conductors (Springer, Berlin, Heidelberg, 1979).

  5. Chandra, S. Superionic Solids: Principles and Applications (North-Holland, 1981).

  6. Kamaya, N. et al. A lithium superionic conductor. Nat. Mater. 10, 682–686 (2011).

    ADS  Article  Google Scholar 

  7. Kato, Y. et al. High-power all-solid-state batteries using sulfide superionic conductors. Nat. Energy 1, 16030 (2016).

    ADS  Article  Google Scholar 

  8. He, X., Zhu, Y. & Mo, Y. Origin of fast ion diffusion in super-ionic conductors. Nat. Commun. 8, 15893 (2017).

    ADS  Article  Google Scholar 

  9. Liu, H. et al. Copper ion liquid-like thermoelectrics. Nat. Mater. 11, 422–425 (2012).

    ADS  Article  Google Scholar 

  10. Weldert, K. S., Zeier, W. G., Day, T. W., Panthöfer, M. & Snyder, G. J. Thermoelectric transport in Cu7SeP6 with high copper ionic mobility. J. Am. Chem. Soc. 136, 12035–12040 (2014).

    Article  Google Scholar 

  11. Damay, F. et al. Localised Ag+ vibrations at the origin of ultralow thermal conductivity in layered thermoelectric AgCrSe2. Sci. Rep. 6, 23415 (2016).

    ADS  Article  Google Scholar 

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

    Article  Google Scholar 

  13. Snyder, G. J. & Toberer, E. S. Complex thermoelectric materials. Nat. Mater. 7, 105–114 (2008).

    ADS  Article  Google Scholar 

  14. Zebarjadi, M., Esfarjani, K., Dresselhaus, M. S., Ren, Z. F. & Chen, G. Perspectives on thermoelectrics: from fundamentals to device applications. Energy Environ. Sci. 5, 5147–5162 (2012).

    Article  Google Scholar 

  15. Nolas, G. S., Sharp, J. & Goldsmid, J. Thermoelectrics: Basic Principles and New Materials Developments (Springer Verlag, Berlin Heidelberg, 2013).

  16. Keppens, V. et al. Localized vibrational modes in metallic solids. Nature 395, 876–878 (1998).

    ADS  Article  Google Scholar 

  17. Biswas, K. et al. High-performance bulk thermoelectrics with all-scale hierarchical architectures. Nature 489, 414–418 (2012).

    ADS  Article  Google Scholar 

  18. Koza, M. M. et al. Breakdown of phonon glass paradigm in La- and Ce-filled Fe4Sb12 skutterudites. Nat. Mater. 7, 805–810 (2008).

    ADS  Article  Google Scholar 

  19. Christensen, M. et al. Avoided crossing of rattler modes in thermoelectric materials. Nat. Mater. 7, 811–815 (2008).

    ADS  Article  Google Scholar 

  20. Delaire, O. et al. Giant anharmonic phonon scattering in PbTe. Nat. Mater. 10, 614–619 (2011).

    ADS  Article  Google Scholar 

  21. Ma, J. et al. Glass-like phonon scattering from a spontaneous nanostructure in AgSbTe2. Nat. Nanotech. 8, 445–451 (2013).

    ADS  Article  Google Scholar 

  22. Voneshen, D. J. et al. Suppression of thermal conductivity by rattling modes in thermoelectric sodium cobaltate. Nat. Mater. 12, 1028–1032 (2013).

    ADS  Article  Google Scholar 

  23. Lee, S. et al. Resonant bonding leads to low lattice thermal conductivity. Nat. Commun. 5, 3525 (2014).

    Article  Google Scholar 

  24. Zhao, L.-D. et al. Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals. Nature 508, 373–377 (2014).

    ADS  Article  Google Scholar 

  25. Li, C. W. et al. Orbitally driven giant phonon anharmonicity in SnSe. Nat. Phys. 11, 1063–1069 (2015).

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  27. Slack, G. A. in CRC Handbook of Thermoelectrics (ed. Rowe D. M.) Ch. 34 (CRC Press, Boca Raton, 1995).

  28. Gascoin, F. & Maignan, A. Order–disorder transition in AgCrSe2: A new route to efficient thermoelectrics. Chem. Mater. 23, 2510–2513 (2011).

    Article  Google Scholar 

  29. Danilkin, S. A. et al. Neutron scattering study of short-range correlations and ionic diffusion in copper selenide. Ionics 17, 75–80 (2011).

    Article  Google Scholar 

  30. Bhattacharya, S. et al. CuCrSe2: A high performance phonon glass and electron crystal thermoelectric material. J. Mater. Chem. A 1, 11289–11297 (2013).

    Article  Google Scholar 

  31. Gagor, A., Gnida, D. & Pietraszko, A. Order–disorder phenomena in layered CuCrSe2 crystals. Mater. Chem. Phys. 146, 283–288 (2014).

    Article  Google Scholar 

  32. Li, B. et al. Liquid-like thermal conduction in intercalated layered crystalline solids. Nat. Mater. 17, 226–230 (2018).

    ADS  Article  Google Scholar 

  33. Brüesch, P., Hibma, T. & Bührer, W. Dynamics of ions of the two-dimensional superionic conductor AgCrS2. Phys. Rev. B 27, 5052–5061 (1983).

    ADS  Article  Google Scholar 

  34. Wakamura, K., Miura, F., Kojima, A. & Kanashiro, T. Observation of anomalously increasing phonon damping constant in the β phase of the fast-ionic conductor Ag3SI. Phys. Rev. B 41, 2758–2762 (1990).

    ADS  Article  Google Scholar 

  35. Wakamura, K., Hirokawa, K. & Orita, K. Observation of characteristic phonon spectra for cage and mobile ions in the layered superionic conductor AgCrS2. J. Phys. Chem. Solids 57, 75–80 (1996).

    ADS  Article  Google Scholar 

  36. Yakshibayev, R., Zabolotsky, V. & Almukhametov, R. Structural features and ionic transport in two-dimensional M x YSe2 (M = Cu, Ag; Y = Cr, Nb) mixed conductors. Solid State Ion. 31, 1–4 (1988).

    Article  Google Scholar 

  37. Tewari, G. C., Tripathi, T. S., Yamauchi, H. & Karppinen, M. Thermoelectric properties of layered antiferromagnetic CuCrSe2. Mater. Chem. Phys. 145, 156–161 (2014).

    Article  Google Scholar 

  38. Cheng, Y. et al. CuCrSe2 ternary chromium chalcogenide: Facile fabrication, doping and thermoelectric properties. J. Am. Ceram. Soc. 98, 3975–3980 (2015).

    Article  Google Scholar 

  39. Yan, Y. et al. Sintering temperature dependence of thermoelectric performance in CuCrSe2 prepared via mechanical alloying. Scr. Mater. 127, 127–131 (2017).

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  41. Squires, G. L. Introduction to the Theory of Thermal Neutron Scattering. 3rd edn (Cambridge Univ. Press, Cambridge, 2009).

    Google Scholar 

  42. Said, A. H., Sinn, H. & Divan, R. New developments in fabrication of high-energy-resolution analyzers for inelastic X-ray spectroscopy. J. Synchrotron Radiat. 18, 492–496 (2011).

    Article  Google Scholar 

  43. Hempelmann, R. Quasielastic Neutron Scattering and Solid State Diffusion (Oxford Univ. Press, Oxford, 2001).

  44. Chudley, C. T. & Elliot, R. J. Neutron scattering from a liquid on a jump diffusion model. Proc. Phys. Soc. 77, 353–361 (1961).

    ADS  Article  Google Scholar 

  45. Bhattacharya, S. et al. High thermoelectric performance of (AgCrSe2)0.5(CuCrSe2)0.5 nano-composites having all-scale natural hierarchical architectures. J. Mater. Chem. A 2, 17122–17129 (2014).

    Article  Google Scholar 

  46. Ehlers, G., Podlesnyak, A. A., Niedziela, J. L., Iverson, E. B. & Sokol, P. E. The new cold neutron chopper spectrometer at the Spallation Neutron Source: Design and performance. Rev. Sci. Instrum. 82, 085108 (2011).

    ADS  Article  Google Scholar 

  47. Abernathy, D. L. et al. Design and operation of the wide angular-range chopper spectrometer ARCS at the Spallation Neutron Source. Rev. Sci. Instrum. 83, 015114 (2012).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  50. 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).

    ADS  Article  Google Scholar 

  51. 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  Google Scholar 

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

    ADS  Article  Google Scholar 

  53. Tewari, G. C., Karppinen, M. & Rastogi, A. K. Effects of competing magnetic interactions on the electronic transport properties of CuCrSe2. J. Solid State Chem. 198, 108–113 (2013).

    ADS  Article  Google Scholar 

  54. Togo, A. & Tanaka, I. First principles phonon calculations in materials science. Scr. Mater. 108, 1–5 (2015).

    Article  Google Scholar 

  55. Carrete, J. et al. almaBTE: A solver of the space–time dependent Boltzmann transport equation for phonons in structured materials. Comput. Phys. Commun. 220, 351–362 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  56. Tritt, T. M. (ed.) Thermal Conductivity: Theory, Properties, and Applications (Springer, Berlin, Heidelberg, 2005).

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We thank O. Hellman and M. Stone for helpful discussions. We are grateful to J. Z. Tischler for algorithms enabling deconvolution of the energy resolution from the inelastic X-ray phonon scattering data. We would also like to acknowledge technical support from D. Dunning, T. Russell and S. Elorfi at the SNS. J.L.N., J.D. and T.L.-A. were supported as part of the S3TEC EFRC, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences under award no. DE-SC0001299. D.B. and O.D. were supported by the US DOE, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under the Early Career Award no. DE-SC0016166 (principal investigator O.D.). A.F.M. was supported by the US DOE, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. The research at Oak Ridge National Laboratory’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US DOE. This research used resources of the Advanced Photon Source, a US DOE Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under contract no. DE-AC02-06CH11357. Ab initio molecular dynamics calculations were performed using resources of the National Energy Research Scientific Computing Center, a US DOE Office of Science User Facility supported by the Office of Science of the US DOE under contract no. DE-AC02-05CH11231. Density functional theory simulations for this research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the US DOE under contract no. DE-AC05-00OR22725.

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J.L.N., D.B. and O.D. performed and analysed the neutron scattering measurements with support from G.E. and D.L.A. J.L.N., D.B. and O.D. performed and analysed the X-ray measurements with support from A.S. A.F.M. synthesized the samples and performed transport measurements. T.L.-A. performed diffusivity and heat capacity measurements. D.B. and J.D. performed simulations. J.L.N., D.B. and O.D. wrote the manuscript and all authors commented on the manuscript. O.D. supervised the project.

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Correspondence to Jennifer L. Niedziela, Dipanshu Bansal or Olivier Delaire.

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Niedziela, J.L., Bansal, D., May, A.F. et al. Selective breakdown of phonon quasiparticles across superionic transition in CuCrSe2. Nature Phys 15, 73–78 (2019).

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