Order in metallic glasses and icosahedral crystals

The relationship between short-range icosahedral order in metallic glasses and long-range order in icosahedral crystals is explored. Metallic-glass structure factors are assumed to describe liquids in metastable equilibrium just above the glass transition. A density-functional mean-field theory is then used to search for nearby crystalline states with a lower free energy. We find that undercooled liquids are metastable with respect to an icosahedral crystal, similar to the recently discovered icosahedral phase of Al-Mn. Conventional bcc and fcc crystals have an even lower free energy. The icosahedral phase is favored by the short-range icosahedral order present in the liquid. There is, however, an energetic cost associated with long-wavelength fluctuations forced in by the incommensurability of the icosahedral density waves. The theory predicts a rapid falloff of intensities in reciprocal space at small wave vectors, and a specific decoration of Penrose rhombahedra with atoms in real space. Our results are obtained via an exact mapping, in the density-functional framework, of the theory of icosahedral crystals onto the theory of conventional crystals in six dimensions.