Link between liquid structure and the nucleation barrier for icosahedral quasicrystal, polytetrahedral, and simple crystalline phases inTi−Zr−Nialloys: Verification of Frank’s hypothesis

Abstract

Comprehensive undercooling experiments on a large number of simple crystalline, polytetrahedral, and icosahedral quasicrystalline phase forming compositions in $\mathrm{Ti}\text{\ensuremath{-}}\mathrm{Zr}\text{\ensuremath{-}}\mathrm{Ni}$ 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 [$\ensuremath{\Delta}{T}_{r}=({T}_{l}\ensuremath{-}{T}_{r})∕{T}_{l}$, 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 $21\phantom{\rule{0.3em}{0ex}}\mathrm{at.}\phantom{\rule{0.2em}{0ex}}%$ 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 $\mathrm{Ti}\text{\ensuremath{-}}\mathrm{Zr}\text{\ensuremath{-}}\mathrm{Ni}$ alloys is icosahedral, as postulated by Frank over a half century ago.