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.

  • Article
  • Published:

Giant anharmonic phonon scattering in PbTe

Nature Materials volume 10, pages 614–619 (2011)Cite this article

Subjects

Abstract

Understanding the microscopic processes affecting the bulk thermal conductivity is crucial to develop more efficient thermoelectric materials. PbTe is currently one of the leading thermoelectric materials, largely thanks to its low thermal conductivity. However, the origin of this low thermal conductivity in a simple rocksalt structure has so far been elusive. Using a combination of inelastic neutron scattering measurements and first-principles computations of the phonons, we identify a strong anharmonic coupling between the ferroelectric transverse optic mode and the longitudinal acoustic modes in PbTe. This interaction extends over a large portion of reciprocal space, and directly affects the heat-carrying longitudinal acoustic phonons. The longitudinal acoustic–transverse optic anharmonic coupling is likely to play a central role in explaining the low thermal conductivity of PbTe. The present results provide a microscopic picture of why many good thermoelectric materials are found near a lattice instability of the ferroelectric type.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Figure 1: Anomalous features of phonon dispersions observed with INS.
Figure 2: Constant- E intensity cuts along [00L] in the (113) zone, showing the avoided-crossing behaviour of the LA and TO branches.
Figure 3: LA-mode phonon dispersion (ELA) and linewidth (ΓLA, corrected for instrument resolution), showing an anomaly at the phonon wave vector q~0.2 along [00L] .
Figure 4: Profile of the TO mode in energy at the zone centre, measured with HB3 and CNCS, showing the broad double-peak structure and its change with temperature.

Similar content being viewed by others

References

  1. Goldsmid, H. J. Introduction to Thermoelectricity (Springer, 2010).

    Book  Google Scholar 

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

    Article  CAS  Google Scholar 

  3. Wood, C. Materials for thermoelectric energy conversion. Rep. Prog. Phys. 51, 459–539 (1988).

    Article  CAS  Google Scholar 

  4. Chen, G., Dresselhaus, M. S., Dresselhaus, G., Fleurial, J-P. & Caillat, T. Recent developments in thermoelectric materials. Int. Mater. Rev. 48, 45–66 (2003).

    Article  CAS  Google Scholar 

  5. Heremans, J. P. et al. Enhancement of thermoelectric efficiency in PbTe by distortion of the electronic density of states. Science 321, 554–557 (2008).

    Article  CAS  Google Scholar 

  6. Nolas, G. S., Sharp, J. & Goldsmid, H. J. Thermoelectrics, Basic Principles and New Materials Developments (Springer, 2001).

    Google Scholar 

  7. Akhmedova, G. A. & Abdinov, D. Sh. Effect of thallium doping on the thermal conductivity of PbTe single crystals. Inorg. Mater. 8, 854–858 (2009).

    Article  Google Scholar 

  8. Nolas, G. S. & Goldsmid, H. J. in Thermal Conductivity. Theory, Properties, and Applications (ed. Tritt, T. M.) 108 (Plenum, 2004).

    Google Scholar 

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

    Article  CAS  Google Scholar 

  10. Koza, M. 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. Nolas, G. S., Yang, J. & Goldsmid, H. J. in Thermal Conductivity, Theory, Properties, and Applications (ed. Tritt, T. M.) (Kluwer, 2004).

    Google Scholar 

  12. Schweika, W., Hermann, R. P., Prager, M., Perßon, J. & Keppens, V. Dumbbell rattling in thermoelectric zinc antimony. Phys. Rev. Lett. 99, 125501 (2007).

    Article  CAS  Google Scholar 

  13. Cochran, W., Cowley, R. A., Dolling, G. & Elcombe, M. M. The crystals dynamics of lead telluride. Proc. R. Soc. Lond. A 293, 433–451 (1966).

    Article  CAS  Google Scholar 

  14. Alperin, H. A., Pickart, S. J., Rhyne, J. J. & Minkiewicz, V. J. Softening of the transverse-optic mode in PbTe. Phys. Lett. A 40, 295–296 (1972).

    Article  CAS  Google Scholar 

  15. Daughton, W. J., Tompson, C. W. & Gürmen, E. G. Lattice instability and phonon lifetimes in Pb1−xSnxTe alloys. J. Phys. C 11, 1573–1581 (1978).

    Article  CAS  Google Scholar 

  16. An, J., Subedi, A. & Singh, D. J. Ab initio phonon dispersions for PbTe. Solid State Commun. 148, 417–419 (2008).

    Article  CAS  Google Scholar 

  17. Zhang, Y., Ke, X., Chen, C., Yang, J. & Kent, P. R. C. Thermodynamic properties of PbTe, PbSe, and PbS: First-principles study. Phys. Rev. B 80, 024304 (2009).

    Article  Google Scholar 

  18. Bate, R. T., Carter, D. L. & Wrobel, J. S. Paraelectric behavior of PbTe. Phys. Rev. Lett. 25, 159–162 (1970).

    Article  CAS  Google Scholar 

  19. Jantsch, W. Dynamical Properties of IV–VI Compounds 1–50 (Springer Tracts in Modern Physics, Vol. 99, Springer, 1983).

    Book  Google Scholar 

  20. Waghmare, U. V., Spaldin, N. A., Kandpal, H. C. & Seshadri, R. First-principles indicators of metallicity and cation off-centricity in the IV–VI rocksalt chalcogenides of divalent Ge, Sn, and Pb. Phys. Rev. B 67, 125111 (2003).

    Article  Google Scholar 

  21. Cochran, W. Crystal stability and the theory of ferroelectricity. Adv. Phys. 9, 387–423 (1960).

    Article  CAS  Google Scholar 

  22. Rabe, K. M. & Joannopoulos, J. D. Ab initio relativistic pseudopotential study of the zero-temperature structural properties of SnTe and PbTe. Phys. Rev. B 32, 2302–2314 (1985).

    Article  CAS  Google Scholar 

  23. Shirane, G., Axe, J. D., Harada, J. & Remeika, J. P. Soft ferroelectric modes in lead titanate. Phys. Rev. B 2, 155–159 (1970).

    Article  Google Scholar 

  24. Ziman, J. M. Electrons and Phonons, The Theory of Transport Phenomena in Solids (Oxford, 1960).

    Google Scholar 

  25. Gehring, P. M., Park, S-E. & Shirane, G. Soft phonon anomalies in the relaxor ferroelectric Pb(Zn1/3Nb2/3)0.92Ti0.08O3 . Phys. Rev. Lett. 84, 5216–5219 (2000).

    Article  CAS  Google Scholar 

  26. Hlinka, J. et al. Origin of the ‘waterfall’ effect in phonon dispersion of relaxor perovskites. Phys. Rev. Lett. 91, 107602 (2003).

    Article  CAS  Google Scholar 

  27. Burkhard, H., Bauer, G. & Lopez-Otero, A. Submillimeter spectroscopy of TO-phonon mode softening in PbTe. J. Opt. Soc. Am. 67, 943–946 (1977).

    Article  CAS  Google Scholar 

  28. Bozin, E. S. et al. Entropically stabilized local dipole formation in lead chalcogenides. Science 330, 1660–1663 (2010).

    Article  CAS  Google Scholar 

  29. Morelli, D. T. & Slack, G. A. in High Thermal Conductivity Materials (eds Shindé, S. L. & Goela, J. S.) (Springer, 2006).

    Google Scholar 

Download references

Acknowledgements

We thank M. E. Hagen, J. L. Robertson and S. E. Nagler for discussions. The neutron scattering and theory work was supported by the US Department of Energy (DOE), Office of Basic Energy Sciences, as part of the S3TEC Energy Frontier Research Center, DOE DE-SC0001299. The Research at Oak Ridge National Laboratory’s Spallation Neutron Source and High Flux Isotope Reactor was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, US DOE. B.C.S., A.F.M. and M.A.M. acknowledge support from the US DOE, Basic Energy Sciences, Materials Sciences and Engineering Division.

Author information

Authors and Affiliations

  1. Neutron Scattering Science Division, Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, Tennessee 37831, USA

    O. Delaire, J. Ma, K. Marty, A. Podlesnyak, G. Ehlers & M. D. Lumsden

  2. Materials Science and Technology Division, Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, Tennessee 37831, USA

    A. F. May, M. A. McGuire, M-H. Du, D. J. Singh & B. C. Sales

Authors
  1. O. Delaire
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. Marty
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. F. May
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. A. McGuire
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. M-H. Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. D. J. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. A. Podlesnyak
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. G. Ehlers
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. M. D. Lumsden
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. B. C. Sales
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

O.D., J.M., K.M., A.P., G.E. and M.D.L. made the neutron scattering measurements. O.D. and J.M. analysed the neutron scattering data. A.F.M., M.A.M. and B.C.S. synthesized and characterized the samples. M-H.D. and D.J.S. carried out the DFT calculations. O.D. carried out the neutron scattering intensity and mode coupling calculations. O.D wrote the manuscript and all authors commented on and edited the manuscript.

Corresponding author

Correspondence to O. Delaire.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 685 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Delaire, O., Ma, J., Marty, K. et al. Giant anharmonic phonon scattering in PbTe. Nature Mater 10, 614–619 (2011). https://doi.org/10.1038/nmat3035

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat3035

This article is cited by

Search

Advanced 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