You may remember the demonstration experiment in some introductory physics class, when the instructor was furiously shaking the end of a rope that was hung across the lecture room, and waves were propagating from one corner of the room to the other. On a microscopic level, very similar processes carry heat in solids. In an emerging area of materials research the name of the game is to suppress these processes, so that that more of the heat is made to ride with an electrical current. How can we make new materials that are disordered and dirty with respect to the lattice vibrations that carry heat only, but look nice and clean for the electrons that do all the useful work? The work of Keppens et al. on page xxx of this issue shows us one way to do it.

There are two main thermoelectric phenomena: the Seebeck effect, in which a temperature difference along a conductor produces a voltage, and the Peltier effect, where a current causes a temperature difference. We have known of these effects for more than 100 years. The fundamental laws of the irreversible thermodynamics, discovered by Lars Onsager in the late 1920's, provide a mathematically simple, yet physically deep relationship between the corresponding materials paramaters: S=P/T, where T is the absolute temperature, and the Seebeck coefficient S and the Peltier coefficient P are defined as the ratio of the voltage to the temperature difference and the heat flow to the electric current, respectively.

Thermoelectricity is used in all kinds of devices: in thermometers, in compact nuclear energy sources on satellites, for corrosion protection of pipelines, to transfer heat away from computer chips, and as a cooling element in portable refrigerators, night vision scopes and infrared sensors. Because of the lack of chemicals and moving parts these devices tend to be reliable and simple. But their usefulness is so much limited by poor efficiency, that the widespread application of the thermoelectricity was called "a breakthrough that never came" [2]. Steady progress in the theory of the electrical and heat transport processes, together with the discovery of new materials, created a renewed interest in this field [2-6].

For good efficiency a large thermoelectric effect, by itself, is not enough. Undoped semiconductors, for example, have large S, but the low electrical conductivity s makes them unable to carry current and supply much power. Similarly, a material of large P can pump the heat out of a refrigerator, but a thermal conductivity k in the same material will let too much heat back in. The real usefullness of a compound is best measured [3] by the "coefficient of merit" Z=sS²/k. Notice that s and S are entirely due to the motion of electrons, but the heat is conducted by both the electrons and the lattice vibrations.

The efficiency of the devices depends [2,3] on the dimensionless product ZT. There is no strict theoretical upper limit here, and a ZT of about 3 would make a Peltier refrigerator competitive with the traditional, compressor based systems. For pure elements ZT<<1, and the compounds in use today have a ZT of about one. Can we improve the coefficient of merit by clever design? The key is to minimize the lattice contribution to the thermal conductivity. Lattice vibrations can not be eliminated, but they can be localized by introducing lattice defects, up to the limit set by amorphous materials[7]. But in a truly amorphous material the conductivity and the thermoelectric effect is too small! As far as the electrons are concerned, high mobility and near perfect crystal structure is preferred.

A class of compounds called skutterudites may be able to provide these contradictory properties. Skutterudites, such as CoAs₃ and IrSb₃, have a crystal structure with unusually large empty cavities. A "filled skutterudite" is obtained when lanthanide atoms are introduced to some of these gaps. But the cavity is larger than the atom, and the lanthanide is not confined to a well defined position. According to Glen Slack [3,4], as it "rattles" in its cage it may destroy the large-scale coherence of the lattice vibrations that carry heat, localizing the vibrations instead. Yet because the conduction electrons do not overlap much with the lanthanide, electrical transport processes are barely disturbed.

The work of Keppens et al., have now proved the existence of such localized rattling in several experiments. Specific heat measurements , ultrasonic spectroscopy and inelastic neutron scattering confirm the existence of a low energy resonance that can only be ascribed to the rattling of the lanthanide atom in its cage. The full story, however, proves to be more complex than expected. Instead of seeing just one resonance, the authors find two, the second being broader and at higher energy. Furthermore, the old description of this system in terms of Einstein oscillators - a relatively simple mathematical model - is not satisfactory. Quantum mechanical tunneling between atomic configurations, already seen in the physics of amorphous materials, seems to play an important part here as well.

A complete interpretation of these experiments will certainly tax existing theories of lattice vibrations. The results of Keppens et al. have no direct implications for the design of better thermoelectric devices, but as our understanding of the basic physics of filled skutterudites deepens, the hunt for higher coefficient of merit should intensify. Many laboratories tooled for materials research on high T_c superconductors are ready to expand into the re-emerging field of thermoelectric compounds. So perhaps in the not-too-distant future we can have an air conditioned car without making the worrisome hole in the ozone layer[8] even larger.

References:

1. V. Keppens et al. Nature, 395, xxx-xxx (1998)

2. G.D. Mahan, in "Solid State Physics" vol. 51, Ed. H. Ehrenreich and F. Spaepen (Academic Press, 1998)

3. G.A. Slack, in CRC Handbook of Thermoelectrics, Ed. D.M. Rowe (Chemical Rubber, Boca Raton, 1995)

4. G.A. Slack and V.G. Tsoukala, J. Appl. Phys., 76, 1665-1671 (1994)

5. G.S. Nolas, J.L. Cohn and G.A. Slack, Phys. Rev. B 58, 164-170 (1998)

6. B.C. Sales et al. Phys. Rev. B 56, 15081-15089 (1997)

7. D. G. Cahill, S. K. Watson, and R. O. Pohl, Phys. Rev. B 46, 6131-6140 (1992)

8. http://toms.gsfc.nasa.gov