"We needed the Cray," says Martyna, "because the CPU time would have been prohibitively large on a normal machine, given the complexity of the calculation." The code the researchers developed hums along at 400 million calculations a second on a single C90 processor. Their results from a series of calculations modeling different concentrations of metal-ammonia solutions provide the first microscopic pictures of the change from an insulating to metallic state.
"We were able to map out what the electronic states look like," explains Klein. At low concentrations, the calculations confirmed an earlier postulation by Nobel-laureate Nevill Mott that the free electrons come together in peanut-shaped pairs called bipolarons.
At higher concentrations, the bipolaron-peanuts tend to cluster in an amoeba-like extended structure.
At still higher concentrations, when the solution turns metallic, electrons pervade the system. The two components -- the free electrons and the ammonia molecules -- are each separate, self-contained phases, coexisting with each other. "We've shown that in the metallic state," explains Klein, "the ammonia and electrons can be regarded like an oil-water mixture. If you sit in one of the phases, you can diffuse forever without having to contact the other." The researchers call this a "bicontinuous state," and their calculations give the first glimpse of it in metal-ammonia solutions.
The calculations are consistent with many experimental observations of both electrical and optical conductivity but go beyond the experiments in providing quantitative details of the electron states in the transition region. "The microscopic details we've obtained," says Klein, "are difficult, if not impossible, to determine experimentally." In future work, Klein and his colleagues will apply the computing technique developed for metal-ammonia solutions to other more complex systems, such as metal-amine and metal-ethylamine solutions, which exhibit their own distinctive electrical properties.
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