It's textbook physics: A perfect crystal ought to conduct heat well. Now, however, scientists have created an exotic new material that breaks that rule. Their theoretical explanation of how the crystal works could help researchers find better thermoelectric materials to generate electricity directly from heat. Such materials might someday power gizmos in your car from heat in the exhaust, and thermoelectric devices are already used to cool electronics and some digital cameras.
The new crystal—a cagelike array of silicon and barium atoms called a clathrate—stops heat in its tracks by converting vibrations that travel through the material to convey heat into vibrations that don't move, the researchers say. Others had seen evidence that similar crystals performed the same trick, but the new paper shows in detail how it comes about, says Mogens Christensen, a materials scientist at Aarhus University in Denmark who studied a clathrate containing barium, gallium, and germanium. "It's perfectly consistent with what we got, but it lays on top of that the theoretical analysis," he says. "It's really beautiful that the theory fits their data so well."
A crystal consists of a repeating 3D pattern of atoms, which behave like balls jointed by stiff springs. Quantum waves of electrons flow freely through the crystal lattice, forming electric currents. Quantized waves of motion of the atoms themselves, known as phonons, also flow through the crystal to carry heat. If a crystal’s pattern contains no defects, both types of waves glide along unimpeded. That’s why most metals readily conduct both heat and electricity. In contrast, glasses—disordered jumbles of atoms—are electrical and thermal insulators.
However, physicists have long known that certain thermoelectric materials conduct electricity well but heat poorly. Such materials are typically crystals "doped" randomly with impurity atoms. In the mid-1990s, theorists reasoned that the ideal thermoelectric material would act like a glass for phonons but a crystal for electrons, and clathrates, which consist of soccer ball–like polyhedrons of heavy atoms with lighter guest atoms inside them, seemed to epitomize the concept. Rattling independently, the caged atoms would create disorder and deflect heat-carrying phonons, even as the crystal conducted electricity—or so the thinking went.
But that's not how the clathrates work, report Marc de Boissieu, a condensed matter physicist at the Grenoble Institute of Technology in France, and colleagues. To show it, they painstakingly synthesized a clathrate, Ba8Si46, which has a perfectly orderly crystal structure, with barium atoms inside cages of silicon atoms. The more easily formed clathrates that scientists had studied earlier, such as the barium-gallium-germanium compound, are less orderly because the cages consist of a random mixture of atoms. The researchers then used exquisitely sensitive x-ray measurements to probe the phonons in their tiny new crystal.
Phonons come in two types. Acoustic phonons act like sound waves, zipping through a crystal at a fixed speed regardless of their wavelength. They carry heat. In contrast, optical phonons generally have higher energies, move more slowly, and carry little heat. The two types of vibrations are very different: The simplest acoustic phonon consists of all the atoms sloshing back and forth in concert. The simplest optical phonon consists of neighboring atoms oscillating in opposite directions. De Boissieu, Stéphane Pailhès of the University of Lyon in France, and colleagues measured the energy of each type of phonon as its wavelength varied.
As wavelength decreases, the energy of the acoustic phonons climbs toward the relatively unchanging energy of the optical phonons. If individual barium atoms were deflecting acoustic phonons, then as the two energies draw close, the lifetime of the acoustic phonons should fall and their energy should become more uncertain. But that's not what happens, as the researchers report in a paper in press at Physical Review Letters. Instead, as the energies grow equal, the heat-carrying acoustic phonons morph into the stationary optical phonons in which all the barium atoms oscillate in concert and the silicon atoms stand still. Detailed modeling confirms the orderly shift of motion to the barium atoms. So disorder does not kill the clathrates’ thermal conductivity, nixing the notion that it is a glass for phonons.
Previous theory and measurements had pointed to such phonon conversion in other clathrates. But by combining measurements with a perfect crystal and the theoretical calculations, the new study drives home the message, says Aarhus's Christensen. He says that in 2008, his team could not perform similar theoretical analysis of their barium-gallium-germanium compound because it contained the random mixture of gallium and germanium atoms. That disorder made the compound too difficult to model—even if it wasn't key to how it worked.
But the result may not be the final word, says Michael Koza, a physicist at the Institut Laue-Langevin in Grenoble who has seen similar effects in cagelike materials called skutterudites. Other theoretical work suggests that models that get the behavior of phonons right may still get a material's thermal conductivity wrong, he says. So there may still be some pieces missing from the puzzle of the clathrates and skutterudites. "How relevant is this [new result] to thermal conductivity?" Koza says. "There’s still a lot of work to do."