Skip to main content

Thank you for visiting nature.com. 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.

  • Letter
  • Published:

Suppression of thermal conductivity by rattling modes in thermoelectric sodium cobaltate

Subjects

Abstract

The need for both high electrical conductivity and low thermal conductivity creates a design conflict for thermoelectric systems, leading to the consideration of materials with complicated crystal structures1. Rattling of ions in cages results in low thermal conductivity2,3,4,5, but understanding the mechanism through studies of the phonon dispersion using momentum-resolved spectroscopy is made difficult by the complexity of the unit cells6. We have performed inelastic X-ray and neutron scattering experiments that are in remarkable agreement with our first-principles density-functional calculations of the phonon dispersion for thermoelectric Na0.8CoO2, which has a large-period superstructure7. We have directly observed an Einstein-like rattling mode at low energy, involving large anharmonic displacements of the sodium ions inside multi-vacancy clusters. These rattling modes suppress the thermal conductivity by a factor of six compared with vacancy-free NaCoO2. Our results will guide the design of the next generation of materials for applications in solid-state refrigerators and power recovery.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

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

Figure 1: Einstein-like rattling modes in sodium cobaltate.
Figure 2: Phonon dispersion of sodium cobaltate.
Figure 3: Influence of rattlers on the rest of the dispersion.
Figure 4: Thermal properties of sodium cobaltate.

Similar content being viewed by others

References

  1. Snyder, G. S. & Toberer, E. S. Complex thermoelectric materials. Nature Mater. 7, 105–114 (2008).

    Article  CAS  Google Scholar 

  2. Slack, G. A. in CRC Handbook of Thermoelectrics (ed. Rowe, D. M.) 407–440 (CRC, 1995).

    Google Scholar 

  3. Slack, G. A. & Tsoukala, V. G. Some properties of semiconducting IrSb3 . J. Appl. Phys. 76, 1665–1671 (1994).

    Article  CAS  Google Scholar 

  4. Nolas, G. S. et al. Semiconducting Ge clathrates: Promising candidates for thermoelectric applications. Appl. Phys. Lett. 73, 178–180 (1998).

    Article  CAS  Google Scholar 

  5. Nolas, G. S. et al. Effect of partial void filling on the lattice thermal conductivity of skutterudites. Phys. Rev. B 58, 164–170 (1998).

    Article  CAS  Google Scholar 

  6. Toberer, E. S., Baranowski, L. L. & Dames, C. Advances in thermal conductivity. Annu. Rev. Mater. Res. 42, 179–209 (2012).

    Article  CAS  Google Scholar 

  7. Roger, M. et al. Patterning of sodium ions and the control of electrons in sodium cobaltate. Nature 445, 631–634 (2007).

    Article  CAS  Google Scholar 

  8. Feldman, J. L. et al. Lattice dynamics and reduced thermal conductivity of filled skutterudites. Phys. Rev. B 61, R9209–R9212 (2000).

    Article  CAS  Google Scholar 

  9. Dong, J. et al. Theoretical study of the lattice thermal conductivity in Ge framework semiconductors. Phys. Rev. Lett. 86, 2361–2364 (2001).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  12. Terasaki, I., Sasago, Y. & Uchnikora, K. Large thermoelectric power in NaCo2O4 single crystals. Phys. Rev. B 56, R12685–R12687 (1997).

    Article  CAS  Google Scholar 

  13. Wang, Y., Rogado, N. S., Cava, R. J. & Ong, N. P. Spin entropy as the likely source of enhanced thermopower in NaxCo2O4 . Nature 423, 425–428 (2003).

    Article  CAS  Google Scholar 

  14. Foo, M. L. et al. Charge ordering, commensurability, and metallicity in the phase diagram of the layered NaxCoO2 . Phys. Rev. Lett. 92, 247001 (2004).

    Article  Google Scholar 

  15. Lee, M. et al. Large enhancement of the thermopower in NaxCoO2 at high Na doping. Nature Mater. 5, 537–540 (2006).

    Article  CAS  Google Scholar 

  16. Xiang, H. J. & Singh, D. J. Suppression of thermopower of NaxCoO2 by an external magnetic field: Boltzmann transport combined with spin-polarized density functional theory. Phys. Rev. B 76, 195111 (2007).

    Article  Google Scholar 

  17. Li, Z., Yang, J., Hou, J. G. & Zhu, Q. First-principles lattice dynamics of NaCoO2 . Phys. Rev. B 70, 144518 (2004).

    Article  Google Scholar 

  18. Jha, P. K. et al. Phonon properties of the intrinsic insulating phase of the cobalt oxide superconductor NaCoO2 . Physica B 366, 153–161 (2005).

    Article  CAS  Google Scholar 

  19. Iliev, M. N. et al. Raman phonons and ageing-related surface disorder in NaxCoO2 . Physica C 402, 239–242 (2004).

    Article  CAS  Google Scholar 

  20. Lemmens, P. et al. Effect of Na content and hydration on the excitation spectrum of the cobaltite NaxCoO2·yH2O. J. Phys. Condens. Matter 16, S857–S865 (2004).

    Article  CAS  Google Scholar 

  21. Shi, Y. G. et al. Raman spectroscopy study of NaxCoO2 and superconducting NaxCoO2·yH2O. Phys. Rev. B 70, 052502 (2004).

    Article  Google Scholar 

  22. Wang, N. L. et al. Infrared probe of the electronic structure and charge dynamics of Na0.7CoO2 . Phys. Rev. Lett. 93, 237007 (2004).

    Article  CAS  Google Scholar 

  23. Rueff, J-P. et al. Phonon softening in NaxCoO2·yH2O: Implications for the Fermi surface topology and the superconducting state. Phys. Rev. B 74, R020504 (2006).

    Article  Google Scholar 

  24. Morris, D. J. P. et al. Crystal-to-stripe reordering of sodium ions in NaxCoO2 (x≥0.75). Phys. Rev. B 79, R100103 (2009).

    Article  Google Scholar 

  25. Clark, S. J. et al. First principles methods using CASTEP. Z. Kristallogr. 220, 567–570 (2005).

    CAS  Google Scholar 

  26. Hinuma, Y., Meng, Y. S. & Ceder, G. Temperature-concentration phase diagram of P2-NaxCoO2 from first-principles calculations. Phys. Rev. B 77, 224111 (2008).

    Article  Google Scholar 

  27. Perdew, J. P. et al. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  CAS  Google Scholar 

  28. Vanderbilt, D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B 41, 7892–7895 (1990).

    Article  CAS  Google Scholar 

  29. Frank, W. et al. Ab initio force-constant method for phonon dispersions in alkali metals. Phys. Rev. Lett. 74, 1791–1794 (1995).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank the EPSRC for support through grants EP/J011150/1 and EP/J012912/1, and for use of the UK national supercomputing facility HECToR under grant EP/F036809/1. Other calculations used STFC’s e-Science facility. We wish to acknowledge the assistance of R. Hanson in developing the crystal structure and normal mode visualizations, which were created using the Jmol software (http://www.jmol.org/).

Author information

Authors and Affiliations

Authors

Contributions

Initial planning was by J.P.G., K.R., M.R., A.T.B., A.B. and M.H. The IXS experiment was performed by D.J.V., J.P.G., E.B., L.G. and M.K., and INS measurements were performed by D.J.V., J.P.G., A.P. and M.E. Single crystals were grown by S.U. The thermal conductivity was measured by D.G.P. and the structural characterization was by D.J.V., D.G.P., E.C. and M.J.G. Theoretical modelling was by K.R. and D.J.V. The manuscript was drafted by J.P.G, D.J.V. and K.R. and all authors participated in the writing and review of the final draft.

Corresponding author

Correspondence to J. P. Goff.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 891 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Voneshen, D., Refson, K., Borissenko, E. et al. Suppression of thermal conductivity by rattling modes in thermoelectric sodium cobaltate. Nature Mater 12, 1028–1032 (2013). https://doi.org/10.1038/nmat3739

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat3739

This article is cited by

Search

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