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.
Subscribe to Journal
Get full journal access for 1 year
only $17.42 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Goldsmid, H. J. Introduction to Thermoelectricity (Springer, 2010).
Snyder, G. J. & Toberer, E. S. Complex thermoelectric materials. Nature Mater. 7, 105–114 (2008).
Wood, C. Materials for thermoelectric energy conversion. Rep. Prog. Phys. 51, 459–539 (1988).
Chen, G., Dresselhaus, M. S., Dresselhaus, G., Fleurial, J-P. & Caillat, T. Recent developments in thermoelectric materials. Int. Mater. Rev. 48, 45–66 (2003).
Heremans, J. P. et al. Enhancement of thermoelectric efficiency in PbTe by distortion of the electronic density of states. Science 321, 554–557 (2008).
Nolas, G. S., Sharp, J. & Goldsmid, H. J. Thermoelectrics, Basic Principles and New Materials Developments (Springer, 2001).
Akhmedova, G. A. & Abdinov, D. Sh. Effect of thallium doping on the thermal conductivity of PbTe single crystals. Inorg. Mater. 8, 854–858 (2009).
Nolas, G. S. & Goldsmid, H. J. in Thermal Conductivity. Theory, Properties, and Applications (ed. Tritt, T. M.) 108 (Plenum, 2004).
Christensen, M. et al. Avoided crossing of rattler modes in thermoelectric materials. Nature Mater. 7, 811–815 (2008).
Koza, M. M. et al. Breakdown of phonon glass paradigm in La- and Ce-filled Fe4Sb12 skutterudites. Nature Mater. 7, 805–810 (2008).
Nolas, G. S., Yang, J. & Goldsmid, H. J. in Thermal Conductivity, Theory, Properties, and Applications (ed. Tritt, T. M.) (Kluwer, 2004).
Schweika, W., Hermann, R. P., Prager, M., Perßon, J. & Keppens, V. Dumbbell rattling in thermoelectric zinc antimony. Phys. Rev. Lett. 99, 125501 (2007).
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).
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).
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).
An, J., Subedi, A. & Singh, D. J. Ab initio phonon dispersions for PbTe. Solid State Commun. 148, 417–419 (2008).
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).
Bate, R. T., Carter, D. L. & Wrobel, J. S. Paraelectric behavior of PbTe. Phys. Rev. Lett. 25, 159–162 (1970).
Jantsch, W. Dynamical Properties of IV–VI Compounds 1–50 (Springer Tracts in Modern Physics, Vol. 99, Springer, 1983).
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).
Cochran, W. Crystal stability and the theory of ferroelectricity. Adv. Phys. 9, 387–423 (1960).
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).
Shirane, G., Axe, J. D., Harada, J. & Remeika, J. P. Soft ferroelectric modes in lead titanate. Phys. Rev. B 2, 155–159 (1970).
Ziman, J. M. Electrons and Phonons, The Theory of Transport Phenomena in Solids (Oxford, 1960).
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).
Hlinka, J. et al. Origin of the ‘waterfall’ effect in phonon dispersion of relaxor perovskites. Phys. Rev. Lett. 91, 107602 (2003).
Burkhard, H., Bauer, G. & Lopez-Otero, A. Submillimeter spectroscopy of TO-phonon mode softening in PbTe. J. Opt. Soc. Am. 67, 943–946 (1977).
Bozin, E. S. et al. Entropically stabilized local dipole formation in lead chalcogenides. Science 330, 1660–1663 (2010).
Morelli, D. T. & Slack, G. A. in High Thermal Conductivity Materials (eds Shindé, S. L. & Goela, J. S.) (Springer, 2006).
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.
The authors declare no competing financial interests.
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
Materials Today (2021)
Journal of Materials Chemistry C (2021)
Nature Communications (2021)
Drastic Modification of Lattice Thermal Conductivity in Thermoelectrics Induced by Electron–Hole Pairs
ACS Applied Materials & Interfaces (2021)
Effect of Refractory Tantalum Metal Filling on the Microstructure and Thermoelectric Properties of Co4Sb12 Skutterudites
ACS Omega (2021)