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.

Previously, the formation of the thermodynamically stable icosahedral Ti±Zr± Ni i-(Ti±Zr±Ni) phase has been observed in rapidly quenched alloys, or by a lowtemperature solid-state transformation from crystal phases that form at higher temperatures. Here we report the nucleation and growth of the icosahedral (i) phase directly from the liquid in as-cast Ti 33 Zr 46 Ni 21 and Ti 37 Zr 42 Ni 21 alloys. DiOE raction patterns obtained by transmission electron microscopy and X-ray diOE raction con®rm the phase identity. DiOE erential scanning calorimetry measurements show an endothermic transformation from the i-phase to a phase mixture of a C14 Laves phase and a solid-solution phase, demonstrating that this i-phase is also stable. The short time that the liquid remains in the Lavesphase-forming ®eld and the higher nucleation rate for the i-phase, owing to strong similarities in the local structures of the i-phase and liquid, allow i-phase nucleation and growth directly from the liquid. } 1. Introduction Most Ti-based icosahedral (i) quasicrystal s are produced only by rapid quenching from the melt. They are metastable and disordered (Kelton 1995, Kim and Kelton 1995, complicating structural studies. In contrast, the icosahedral Ti±Zr±Ni (i-(Ti±Zr±Ni)) produced by annealing at approximatel y 600°C (over 200°C below the solidus temperature) are stable and better ordered ). There the i-phase forms by a solid-state transformation of a phase mixture of a hexagonal Laves phase (C14) and a bcc solid solution phase b-(Ti±Zr), the primary solidi®cation products from the liquid. The increased order and the discovery of a 1/1 crystal approximant to i-(Ti±Zr±Ni), which forms by a solid-state transformatio n of the C14 and b-(Ti±Zr) phase mixture at a slightly higher temperature , has allowed the construction of a realistic structural model for Ti±Zr-based quasicrystals . A knowledge of the structure is important for basic as well as practical reasons, since the high storage capacity for hydrogen of i-(Ti±Zr±Ni) has attracted interest for possible applications .The structural order of the quasicrystal s formed by annealing is better than for rapidly quenched samples. However, the small driving free-energy for i-phase formation (since the C14 phase is also a polytetrahedra l phase with a similar Gibbs free energy) and the required long-range diOE usion with slow kinetics due to the low temperature limit the degree of chemical order that can be achieved. Recently electro-static levitation undercooling experiments and annealing studies were made to determine the Ti±Zr±Ni phase diagram and to investigate possible structural