To explain the unusual stability of undercooled liquids against crystallization, Frank hypothesized that the local structures of undercooled liquids contain a significant degree of icosahedral short-range order, which is incompatible with long-range periodicity. We present here the first direct experimental demonstration of Frank's complete hypothesis, showing a correlation between the nucleation barrier and a growing icosahedral short-range order with decreasing temperature in a Ti39.5Zr39.5Ni21 liquid. A new experimental facility, BESL (Beamline Electrostatic Levitation), was developed to enable the synchrotron x-ray structural studies on deeply undercooled, reactive liquids.

New short-range order data are presented for equilibrium and undercooled liquids of Ti and Ni. These were obtained from in situ synchrotron x-ray diffraction measurements of electrostatically levitated droplets. While the short-range order of liquid Ni is icosahedral, consistent with Frank's hypothesis, significantly distorted icosahedral order is observed in liquid Ti. This is the first experimental observation of distorted icosahedral short-range order in any liquid, although this has been predicted by theoretical studies on atomic clusters.

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Comprehensive undercooling experiments on a large number of simple crystalline, polytetrahedral, and icosahedral quasicrystalline phase forming compositions in Ti-Zr-Ni alloys have been carried out using electrostatic levitation ͑ESL͒ techniques for containerless processing. Consistent with Frank's hypothesis, a direct correlation was found between the reduced undercooling ͓⌬T r = ͑T l − T r ͒ / T l , where T r and T l are the nucleation and liquidus temperatures, respectively͔ and the icosahedral short-range order in the solid. The reduced undercooling is less for liquids that form the icosahedral quasicrystal ͑i phase͒ than for those that form the hcp C14 Laves polytetrahedral phase. For many compositions near 21 at. % Ni, the primary nucleation of a metastable i phase instead of a stable C14 Laves phase demonstrates that the interfacial free energy between the liquid and the i phase is smaller than between the liquid and the C14 Laves phase, indicating icosahedral local order in the undercooled liquid. This is in agreement with a classical-nucleation-theory-based estimate of the interfacial free energy and the work of formation of the critical cluster from the undercooling data. Taken together with high-energy x-ray diffraction studies of the undercooled liquid, these results demonstrate that the local structure of liquids in Ti-Zr-Ni alloys is icosahedral, as postulated by Frank over a half century ago.

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