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.

Avoided crossing of rattler modes in thermoelectric materials


Engineering of materials with specific physical properties has recently focused on the effect of nano-sized ‘guest domains’ in a ‘host matrix’ that enable tuning of electrical, mechanical, photo-optical or thermal properties. A low thermal conductivity is a prerequisite for obtaining effective thermoelectric materials, and the challenge is to limit the conduction of heat by phonons, without simultaneously reducing the charge transport. This is named the ‘phonon glass–electron crystal’ concept and may be realized in host–guest systems. The guest entities are believed to have independent oscillations, so-called rattler modes, which scatter the acoustic phonons and reduce the thermal conductivity. We have investigated the phonon dispersion relation in the phonon glass–electron crystal material Ba8Ga16Ge30 using neutron triple-axis spectroscopy. The results disclose unambiguously the theoretically predicted avoided crossing of the rattler modes and the acoustic-phonon branches. The observed phonon lifetimes are longer than expected, and a new explanation for the low κL is provided.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: The clathrate type-I structure and a schematic illustration of phonons in cage structures.
Figure 2: Phonon dispersion maps measured by inelastic neutron scattering.
Figure 3: Comparison of phonon dispersion branches and constant-q scans around the region of avoided crossing.
Figure 4: Comparison of single-crystal and powder inelastic neutron scattering and Raman spectroscopy.


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

    CAS  Article  Google Scholar 

  2. Kimura, Y. & Zama, A. Thermoelectric properties of p-type half-Heusler compound HfPtSn and improvement for high-performance by Ir and Co additions. Appl. Phys. Lett. 89, 172110 (2006).

    Article  Google Scholar 

  3. Hsu, K. F. et al. Cubic AgPbmSbTe2+m: Bulk thermoelectric materials with high figure of merit. Science 303, 818–821 (2004).

    CAS  Article  Google Scholar 

  4. Poudeu, P. F. R. et al. High thermoelectric figure of merit and nanostructuring in bulk p-type Na1−xPbmSbyTem+2 . Angew. Chem. Int. Ed. 45, 3835–3839 (2006).

    CAS  Article  Google Scholar 

  5. Nolas, G. S., Cohn, J. L., Slack, G. A. & Schujman, S. B. Semiconducting Ge clathrates: Promising candidates for thermoelectric applications. Appl. Phys. Lett. 73, 3133–3144 (1998).

    Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  7. Slack, G. A. CRC Handbook of Thermoelectrics Vol. 407 (1995).

    Google Scholar 

  8. Uher, C. Skutterudites: Prospective novel thermoelectrics. Semicond. Semimet. 69, 139–253 (2001).

    CAS  Article  Google Scholar 

  9. Kovnir, K. A. & Shevelkov, A. V. Semiconducting clathrates: Synthesis, structure and properties. Russ. Chem. Rev. 73, 923–938 (2004).

    CAS  Article  Google Scholar 

  10. Dong, J., Sankey, O. F. & Myles, C. W. Theoretical study of the lattice thermal conductivity in Ge framework semiconductors. Phys. Rev. Lett. 86, 2361–2364 (2001).

    CAS  Article  Google Scholar 

  11. Takasu, Y. et al. Dynamical properties of guest ions in the type-I clathrate compounds X8Ga16Ge30 (X=Eu, Sr, Ba) investigated by Raman scattering. Phys. Rev. B 74, 174303 (2006).

    Article  Google Scholar 

  12. Hermann, R. P. et al. Neutron and nuclear inelastic scattering study of the Einstein oscillators in Ba-, Sr-, and Eu-filled germanium clathrates. Phys. Rev. B 72, 174301 (2005).

    Article  Google Scholar 

  13. Christensen, M., Juranyi, F. & Iversen, B. B. The rattler effect in thermoelectric clathrates studied by inelastic neutron scattering. Physica B 385/386, 505–507 (2006).

    Article  Google Scholar 

  14. Schober, H., Itoh, H., Klapproth, A., Chihaia, V. & Kuhs, W. F. Guest–host coupling and anharmonicity in clathrate hydrates. Eur. Phys. J. E 12, 41–49 (2003).

    CAS  Article  Google Scholar 

  15. Nolas, G. S. et al. Thermal conductivity of elemental crystalline silicon clathrate Si-136. Appl. Phys. Lett. 82, 910–912 (2003).

    CAS  Article  Google Scholar 

  16. Guloy, A. M. et al. A guest-free germanium clathrate. Nature 443, 320–323 (2006).

    CAS  Article  Google Scholar 

  17. Christensen, M., Lock, N., Overgaard, J. & Iversen, B. B. Crystal structures of thermoelectric n- and p-type Ba8Ga16Ge30 studied by single crystal, multitemperature, neutron diffraction, conventional X-ray diffraction and resonant synchrotron X-ray diffraction. J. Am. Chem. Soc. 128, 15657–15665 (2006).

    CAS  Article  Google Scholar 

  18. Bentien, A. et al. Thermal conductivity of thermoelectric clathrates. Phys.Rev.B. 69, 045107 (2004).

    Article  Google Scholar 

  19. Avila, M. A., Suekuni, K., Umeo, K., Fukuoka, H. & Takabatake, T. Glasslike versus crystalline thermal conductivity in carrier-tuned Ba8Ga16X30 clathrates (X=Ge, Sn). Phys. Rev. B 74, 125109 (2006).

    Article  Google Scholar 

  20. Baumbach, R. et al. Off-center phonon scattering sites in Eu8Ga16Ge30 and Sr8Ga16Ge30 . Phys. Rev. B 71, 024202 (2005).

    Article  Google Scholar 

  21. Laermans, C., Parshin, M. A., Parshin, D. A. & Keppens, V. Ultrasound versus thermal conductivity in Ge clathrates. Physica B 316/317, 273–275 (2002).

    Article  Google Scholar 

  22. Tse, J. S. et al. Anharmonic motions of Kr in the clathrate hydrate. Nature Mater. 4, 917–921 (2005).

    CAS  Article  Google Scholar 

  23. Yang, C. P. et al. Phonon dispersion curves in CeOs4Sb12 . J. Phys. Condens. Matter 19, 226214–226219 (2007).

    Article  Google Scholar 

  24. Lee, C. H., Hase, I., Sugawara, H., Yoshizawa, H. & Sato, H. Low-lying optical phonon modes in the filled skutterudite CeRu4Sb12 . J. Phys. Soc. Japan 75, 123602–123607 (2006).

    Article  Google Scholar 

  25. Lee, C. H. et al. Neutron scattering study of phonon dynamics on type-I clathrate Ba8Ga16Ge30 . J. Phys. 92, 012169 (2007).

    Google Scholar 

  26. Lee, C.H. et al. Phonon dynamics of type-i clathrate Sr8Ga16Ge30 studied by inelastic neutron scattering. J. Phys. Soc. Jpn. 77 (suppl. A), 260–262 (2008).

    Article  Google Scholar 

  27. Madsen, G. K. H. & Santi, G. Anharmonic lattice dynamics in type-I clathrates from first-principles calculations. Phys. Rev. B 72, 220301 (2005).

    Article  Google Scholar 

  28. Williams, R.K. et al. Experimental and theoretical evaluation of the phonon thermal conductivity of niobium at intermediate temperatures. Phys. Rev. 28, 6316–6324 (1983).

    CAS  Article  Google Scholar 

  29. Sales, B. C., Chakoumakos, B. C., Jin, R., Thompson, J. R. & Mandrus, D. Structural, magnetic, thermal, and transport properties of X8Ga16Ge30 (X=Eu, Sr, Ba) single crystals. Phys. Rev. B 63, 245113 (2001).

    Article  Google Scholar 

  30. Bridges, F. & Downward, L. Possible mechanism for glass-like thermal conductivities in crystals with off-center atoms. Phys. Rev. B 70, 140201 (2004).

    Article  Google Scholar 

Download references


This work is based on experiments carried out at the Swiss spallation neutron source SINQ, Paul Scherrer Institute, Villigen, Switzerland. N. Lock, B. L. Pedersen and T. B. S. Jensen are thanked for assistance during measurements at PSI. Support by A. Schultz and M. Miller was highly appreciated during single-crystal testing at SCD, IPNS at Argonne National Laboratory. We acknowledge the initial beamtime at BT7 supported by Y. Chen and J. Lynn at NIST Center for Neutron Research. The work was supported by the Danish Research Councils through DANSCATT. N.B.C. was supported by Swiss NSF grant 200020-105175. J.A. acknowledges support from the Swedish Research Council and the Foundation for Strategic Research.

Author information

Authors and Affiliations


Corresponding authors

Correspondence to Mogens Christensen or Bo B. Iversen.

Supplementary information

Supplementary Information

Supplementary Information (PDF 496 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Further reading


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