A beautifully faceted diamond may be forever, but there are many types of facets in crystals that, until now, seemed to be never.
In most chunks of crystalline material, facets correspond to a few, highly favored planes within the lattice of atoms. Theorists have long postulated, however, that crystals with more mobile atoms or molecules could develop other, less readily formed facets, too. Those surfaces would lie at shallow angles relative to the main crystal planes.
In the 1980s, scientists searched for such facets in lead, gold, and solid helium. They came up empty-handed, however, observing no more than a half-dozen different facet types, none shallowly oriented.
In the March 13 Physical Review Letters, a French research team reports the discovery of the long-sought facets. The finding verifies a fundamental prediction dating to the 1950s about the shapes that samples of crystalline substances can assume, the scientists say.
Russian physicist Lev Landau had predicted then that a crystal at 0 kelvin could manifest an almost endless number of facets of different orientations. Researchers in the 1970s and 1980s extended the theory to include the possibility of such a zoo of facets appearing under the right conditions at higher temperatures.
Such facet production would subdivide the crystal surface into an array of different-size plates, in which the successively smaller ones are often set at increasingly shallow angles. The unlimited facet proliferation that was expected can be depicted by a graph that traces, ideally, an infinite number of steps. Scientists call such a graph the devil’s staircase. Theorists suggest that this pattern describes many other areas of mathematics and physics.
In the new experiments, each single crystal displayed up to 60 different orientations of facets. “This is the first time we are able to observe such rich faceting,” says team member Paul Sotta of the Université Paris-Sud in Orsay.
Michael Wortis of Simon Fraser University in Burnaby, British Columbia, says that “the key development is finding a system that gets you into a regime where you can see this phenomenon.”
The French team used a liquid crystal made of molecules of the soaplike hexaethyleneglycol mono n-dodecyl ether in water. At room temperature, the researchers exposed a blob of the transparent gel, about 1 millimeter in diameter, to high humidity, creating a uniform lattice with unit cubes about 10 nanometers on an edge. Under these conditions, the molecules were mobile enough to permit exotic facets to form, while strong forces in the lattice stabilized the surfaces. Progressions of increasingly shallow facets formed, converging from several directions on a central facet at the blob’s peak.
“It’s very spectacular,” comments Philippe Nozieres of the Laue Langevin Institute in Grenoble, France. It’s the most striking experimental demonstration so far of the extremely general devil’s staircase pattern, he says.