The fact that first graders grow crystals for science projects might lead you to think that physicists know how these snazzy shapes form and unform. Alas, there is still a big blank spot in physics textbooks where the theory of crystal melting should be. “The reason a crystalline structure melts is very subtle,” says Georg Maret of the University of Konstanz in Germany, who received this year’s Gentner-Kastler Prize from the German Physical Society and the French Physics Society for melting away some of that ignorance.
The difficulty is that crystals stabilize themselves. When an atom gets pulled out of place, its neighbors tug it back. Even if the atom jiggles wildly enough to break free, where can it go? Other atoms block its escape routes. For a crystal to turn to liquid, it seems that a type of swarm intelligence causes atoms to move all at once and in sync.
To figure it out, physicists have tried their hand at the special case of two-dimensional crystals. No such thing really exists in nature, although oil films floating on water come close. In the 1970s theorists realized that flat crystals are inherently less stable than 3-D ones. Because each atom has fewer neighbors, the forces holding it in place are weaker. And when one does wriggle free, only a couple of other atoms have to get out of its way rather than a long row of them, as in 3-D. For these and other reasons of geometry, physicists have reasoned that 2-D crystals should melt in two distinct stages, passing through a hexatic phase, in which hexagonal groups of atoms flow freely, as in a fluid, yet remain oriented in the same direction, as in a crystal.
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It has taken experimental physicists 30 years to test this theory. Maret’s team, borrowing from the experimental techniques of first graders, built a kind of Tinkertoy model of a crystal, representing atoms by micron-size balls made of a mix of plastic and iron oxide and suspended in a fluid. Though larger than atoms, the balls were still small enough to behave much like them. They jiggled randomly and, when placed in a magnetic field, exerted magnetic forces on one another. Dialing up the field was like lowering the temperature: it caused the balls to snap together into a crystalline grid. “Maret’s work is the cleanest, simplest system where you can really study how you go from solid to hexatic, hexatic to liquid,” says theorist David R. Nelson of Harvard University, who helped to develop the theory Maret has now confirmed.
The same principles of collective behavior should help physicists crack the harder nut of 3-D crystals. Like growing crystals, growing theories of crystals takes patience.