Link between liquid structure and the nucleation barrier for icosahedral quasicrystal, polytetrahedral, and simple crystalline phases in Ti-Zr-Ni alloys: Verification of Frank's hypothesis

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 (ESL) techniques for containerless processing. Consistent with Frank's hypothesis, a direct correlation was found between the reduced undercooling [Delta T-r=(T-l-T-r)/T-l, where T-r and T-l are the nucleation and liquidus temperatures, respectively] and the icosahedral short-range order in the solid. The reduced undercooling is less for liquids that form the icosahedral quasicrystal (i phase) 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.