George S Nolas & Glen A Slack. American Scientist. Volume 89, Issue 2. Mar/Apr 2001.
One of us works for a company that makes refrigerators-small ones. Actually, tiny ones: The largest is about the size of a postage stamp. These devices use no messy liquids or gases, have no moving parts and can reduce the temperature by as much as 150 degrees Celsius. Modern miracles? Not exactly These coolers operate on a principle discovered the same year that Abraham Lincoln attained his first political office. That was when an ex-watchmaker named Jean Charles Althanse Peltier found that electrons moving through a solid can carry heat from one side of the material to the other. Soon afterward another 19th-century physicist, Heinrich Lenz, demonstrated Peltier’s effect dramatically by freezing a drop of water with nothing more than the electrons flowing through some bismuth and antimony.
Early in the 20th century, the German scientist Edmund Altenkirch investigated the physical properties that made it possible to pump heat with electricity and, conversely, to generate electricity with heat. His work alerted many engineers to the potential value of specialized “thermoelectric” substances. The modern era of research and development started in earnest in 1946, when Abram Ioffe began theoretical and experimental studies in the Soviet Union to improve the efficiencies of various thermoelectric semiconductors. Considerable research then began in the U.S. Indeed, it might be fair to say that the much of the pioneering work in semiconductor physics during the 1950s and 1960s was motivated not by the invention of the transistor but by the quest to construct solid-state refrigerators for use in the home.
Despite the fact that thermoelectric devices remain too inefficient to replace one’s Frigidaire, they do have some key advantages that make them perfect for certain niche applications. With no moving parts, they are silent, reliable and require no maintenance. Thermoelectric materials that produce electricity from heat find excellent use, for example, in space exploration. The Cassini probe, which is en route to Saturn, and the quarter-century-old Voyagers, now operating at the fringes of the solar system, contain radioisotope thermoelectric generators in which a mass of plutonium-238 (serving as a heat source) is coupled to a thermo-electric material, a combination that allows these and other spacecraft to produce electricity without relying on solar panels.
Suitable applications also arise here on earth. Thermoelectric generators powered by fossil fuels are, for example, built for battlefield use. And thermoelectric refrigerators, also called Peltier devices, provide pinpoint cooling for heat-sensitive electronic components such as infrared detectors, low-noise amplifiers and computer chips. These compact cooling units are also used to stabilize the operating temperature of laser diodes. Similar thermoelectric components can also be found today in portable beverage chillers that are powered by an automobile battery.
So thermoelectric devices are indeed widespread-but not nearly as widespread as they would be if they could be made to work more efficiently. We, along with many other scientists, are laboring to do just that. And we believe that a breakthrough may be close at hand. The most promising candidates in our view are clathrates, solids with cagelike atomic arrangements. To understand why we are so enthusiastic about these materials requires first a little background knowledge about how thermoelectrics work.
Thermoelectrics 101
In a thermoelectric device, it is the flow of electric current that pumps heat from one place to another. The ratio of heat flow to current for a particular material is known as the Peltier coefficient. Its value is intimately related to another intrinsic property called the Seebeck coefficient, named for Thomas Seebeck, who in 1822 discovered that some materials develop small voltages across them when one side is made hotter than the other.
Having large Peltier and Seebeck coefficients is not, however, the only requirement for a useful thermoelectric. The material must also be a good electrical conductor and an equally good thermal insulator. A thermoelectric cooler with poor electrical conductivity, for example, would warm through resistance heating when power was applied, just as the wire in a toaster does. And if the material did not act as an excellent thermal insulator, the heat transported by the flow of electric current would tend to leak backward from the hot side to the cold one.
Although combinations of metals sometimes serve as thermoelectrics, the electrical and thermal conductivities of these materials are both quite high. So the efficiencies of metallic thermoelectrics are very low. More typical devices contain semiconductors, which have Seebeck coefficients that are 100 times larger than can be obtained with metals and for which the designer can, to some extent, adjust electrical and thermal conductivity independently through the judicious choice of constituents.
These semiconductor devices pump electricity through two different thermoelectric substances. One leg of the circuit contains a surplus of mobile electrons (making it an N-type semiconductor), whereas the other (a P-type semiconductor) has a deficit. In a thermoelectric cooler, the battery essentially drives valence electrons from atoms in the P-type semiconductor into the N-type, where they join the ranks of higher-energy mobile electrons occupying the conduction band. In this process they absorb thermal energy from the junction between the two materials. This transformation is reversible: That is, the device can also pump heat out of the junction if the electric current is made to flow in the opposite direction. But resistance heating and the leakage of heat through thermal conduction are irreversible processes, which degrade efficiency
Modern thermoelectric coolers operate at efficiencies that are less than five percent of the maximum possible value (imposed by the second law of thermodynamics). The best thermoelectric power generators have efficiencies that are less than 15 percent of the theoretical ceiling. For comparison, household refrigerators operate at about 30 percent of the thermodynamic limit.
Useful as such statistics are, practitioners in the design of thermoelectrics rarely report the conversion efficiencies of their devices in these terms, preferring to quote a different number, the figure of merit or Z (equal to the Seebeck coefficient squared divided by the product of electrical resistivity and thermal conductivity). And because the temperature of operation (T) also influences the final efficiency, specialists frequently cite the dimensionless quantity ZT, which provides a convenient way to score different thermoelectrics.
The materials now being used to generate electricity from heat and to provide localized cooling have values of ZT that are, at best, close to unity. To compete with compressor-driven household refrigerators would require a three- to fourfold improvement. Although there is no theoretical limit to the value of ZT that a thermoelectric solid might achieve, in practice this important number has gone up little since the 1960s.
Fortunately, there are some novel materials under investigation that show great promise. Most of the new research has been fueled by the military as well as by the automotive and electronics industries. Advances are being made on several fronts, but it seems that a general approach one of us (Slack) proposed many years ago may finally be coming to fruition, in part through research Nolas recently spearheaded. The key idea was to engineer a solid with an atomic structure that is at once orderly and disorderly, so that it conducts electricity but not heat.
Phonon Glass, Electron Crystal
In a semiconductor, the electrons (or electron vacancies, also known as holes) propagate through a lattice of neatly arrayed atoms. Quantum mechanics explains why such arrangements allow the electric charges to travel considerable distances before hitting atoms in the crystal lattice and scattering off in other directions. Thus these materials can be made to conduct electricity extremely well. All that is needed is a supply of mobile electrons or holes.
In the same semiconductors, heat is carried mainly by the vibrational waves coursing through the atomic lattice. As with light waves, these vibrations have a dual quantum nature and can be equally well represented as discrete particles: Light waves can be viewed as packets of electromagnetic energy, called photons; heat waves in a crystal lattice can be viewed as packets of vibrational energy, called phonons. The ease with which phonons propagate through an orderly crystal lattice accounts for the high thermal conductivity of diamond, for example, which is one of the best heat carriers known. This phenomenon also explains the good thermal conductivity of most semiconductors.
As Slack pointed out more than two decades ago, if the propagation of atomic vibrations-the phonons-in a semiconductor can be impeded, the normally high value of thermal conductivity will plummet. In fact, if the phonons are made to scatter each time they encounter an atom in the lattice, the value of thermal conductivity for the bulk material will be as low as that of a glass, which conveys heat poorly precisely because its internal atomic arrangement is so disorderly. Glasses also transmit electricity very poorly, so they cannot serve in thermoelectrics. Instead materials “designers” must make sure the electrons see a well-ordered crystal lattice, which allows these charges to move freely That is, the ideal thermoelectric should be a “phonon glass” and an “electron crystal.”
Semiconductors with these properties do, in fact, exist. They are quite different from the materials now employed in commercial thermoelectric devices-bismuth telluride, lead telluride and silicon-germanium alloys, for example-which are products of an approach to designing thermoelectrics that dates back to the 1920s. This traditional strategy calls for making alloys of metals or constructing binary compounds, replacing a certain fraction of the major-constituent atoms with ones of greater atomic weight, thus creating microscopic areas of disorder within the crystal. These irregularities scatter phonons, impeding their passage and thereby reducing the thermal conductivity. Thermoelectrics designed along these lines work reasonably well, but they do not by any means scatter all of the phonons moving through the crystal lattice. Indeed, they only disrupt the high-energy phonons, whereas the low-energy ones conduct most of the heat.
Crystals containing small, heavy atoms within oversized “cages” can, at least in theory, do a better job of scattering the passing phonons. We first tested this idea together at Rensselaer Polytechnic Institute in 1994 using skutterudites, a class of “holey” crystals named for Skutterud, the Norwegian town where a mineral containing this structure was first unearthed. More recently we began investigating a yet more promising family of crystals-clathrates, a general term for solids in which one constituent forms enclosures that entrap another.
The first material of this kind ever to be examined, chlorine hydrate, was discovered in 1810. But it took more than a century for x-ray studies to show that the chlorine molecules are held inside polyhedra formed of hydrogen and oxygen atoms. That is, the chlorine molecules are imprisoned within tiny cages of ice. In 1952 Linus Pauling performed a thorough structural investigation of chlorine-bearing ice clathrate and determined that this curious substance contains two different kinds of polyhedral cages: One is a pentagonal dodecahedron (a 12-sided polyhedron with pentagonal faces); the second is a tetrakaidecahedron (a 14-sided polyhedron with 12 pentagonal and two hexagonal faces). He further found that each unit cell-the fundamental building block that is repeated over and over in the bulk material-contains two dodecahedra and six tetrakaidecahedra.
Since Pauling’s pioneering studies, crystallographers have uncovered a second kind of clathrate structure that contains 16 pentagonal dodecahedra and eight large hexakaidecahedra-polyhedra with 12 pentagonal and four hexagonal faces. These two geometries (named type-I and II, respectively) comprise the majority of different ice clathrates known to exist.
Investigations undertaken more than two decades ago showed that the thermal conductivities of ice clathrates are much lower than that of common ice. Indeed, the value can be even lower than that of water, which can be viewed as an amorphous, or glassy, form of ice. This result alone hinted that semiconducting clathrates might have similarly low values of thermal conductivity, making them ideal candidates for use in future thermoelectrics.
It is fortunate that the elements commonly used to construct semiconductors (silicon and germanium) form clathrates. As long as the voids in the crystal structure remain empty, these materials transmit heat too well to serve in thermoelectric devices. But if the openings are filled with small, heavy atoms, the thermal conductivity of the composite material can be made extremely low. In essence, the “rattling” of the heavy atoms in their spacious crystalline cages interferes with the passage of heat-carrying phonons. Yet the presence of a rigid crystal lattice surrounding the cages allows mobile electrons to move about easily, providing the needed high value for electrical conductivity.
Germanium Clathrates
In 1997 we fabricated a germanium clathrate and evaluated its thermoelectric properties. We began our investigations with germanium rather than silicon, in part because we knew that the atomic cages would be larger. We also knew that other groups were examining silicon clathrates for interesting electro-optical or superconducting properties, and so we thought that germanium might provide more fertile ground for discovery.
We synthesized a series of compounds with the general composition of Sr^sub 8^Ga^sub 16^Ge^sub 30^ in each 54-atom unit cell. The presence of strontium (Sr) induces a change in the normal crystal structure of germanium, making it into a type-I clathrate, with the relatively heavy strontium atoms sitting within the openings. We added roughly twice as much gallium (Ga) to the mix to compensate for the two negative charges each strontium atom gives off when it becomes incorporated into the lattice as a positive, divalent ion. That is, two gallium atoms are needed to “accept” the two electrons that each strontium atom “donates.” In actuality, we used slightly less than a two-to-one ratio (with a dash less gallium and an equal amount more germanium than the general formula prescribes). Varying the proportions of gallium and germanium in this way allowed us to adjust the concentration of mobile electrons in these N-type semiconductors.
At the outset, we had envisioned making a material in which the strontium atoms shifted back and forth freely from their equilibrium positions at the centers of the gallium-germanium cages. But after we and our colleagues investigated these new substances in greater detail, we realized that something more subtle might be going on. There may in fact be two separate contributions to the disorder: a dynamic rattling motion of the strontium atoms and static quantum-mechanical tunneling.
According to this notion, a strontium atom normally sits not in the middle but near one of four off-center positions within a cage. When struck by a passing phonon, the atom jostles about somewhat, and it can also make a quantum leap into another of its four allowed positions, even though it has not received enough energy to occupy the forbidden zone between them. Such an atom is said to have “tunneled” through a potential energy barrier.
Another interesting result of this work came when we examined the thermal properties of these compounds. Above 100 kelvins (-173 degrees Celsius), the thermal conductivity of Sr^sub 8^Ga^sub 16^Ge^sub 30^ proved to be lower than that of quartz glass. Indeed, the thermal conductivity comes quite close to the theoretical minimum, which arises when all the heat-carrying phonons bounce around clumsily from one atom to the next. So we have definitely achieved our aim of synthesizing a crystal that acts as a phonon glass.
Still, we are a long way from complete success: The best semiconducting clathrates we have fabricated so far give figures of merit (values of ZT) that are only about half as good as the materials now being used commercially for cooling. But there is reason to expect that performance will yet improve. One cause for optimism comes from progress that we and others have made with the other “holey” crystals, the skutterudites, which in the past few years have shown greater ZT values at high temperature than the materials now being used to generate electric power. For example, just last fall Nolas and Michael Kaeser, Roy Littleton, IV, and Terry Tritt of Clemson University synthesized an ytterbium-bearing skudderudite that boasts a figure of merit that exceeds 1 above about 600 kelvins.
Another indication that thermoelectric materials with cagelike crystal lattices stand to gain from future tinkering comes from recent attempts at pressure tuning. Jin-Feng Meng, N. V Chandra Shekar and John Badding, all then at the Pennsylvania State University, recently joined with Nolas to investigate a sample of a germanium clathrate squeezed by a diamond anvil, and we found that the thermo-electric figure of merit increased nearly three and a half times. Although building a device that is permanently kept under high pressure would be awkward (to say the least), our result shows that modest changes to the crystal structure of existing germanium clathrates-alterations that we hope to be able to induce by tweaking the chemical composition-can boost performance markedly.
We thus anticipate that further efforts along these lines will soon provide thermoelectric materials that are more efficient than any now being sold commercially. Whether the improvements will be enough to justify their use in one’s kitchen or car is impossible to predict. But even if such success is not forthcoming, just matching the efficiencies of the current crop of thermoelectrics should lower the cost of production. The reason is that many of the thermoelectric materials now being produced have directionally dependent properties. Thus they must be fabricated from oriented single crystals, and they must be carefully aligned within the thermoelectric device, steps that make them difficult to manufacture. The replacements we are promoting, however, are isotropic-their physical properties do not depend on the orientation of the crystal lattice. Thus devices can be constructed from an amalgam of small crystals that are randomly oriented, making them especially easy to mass produce. These compounds are also relatively hard, which makes them easy to work with during manufacture and provides in the end for rather rugged units.
If we are wrong, if our research into thermoelectric clathrates fails ultimately to spawn commercial products, we will be surprised and disappointed but not regretful. After all, our search for novel thermoelectrics has brought to light some intriguing physical phenomena, and the results of our investigations have added more than a few bricks to the edifice of basic science.