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 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.

Multiple pathways of crystal nucleation in an extremely supersaturated aqueous potassium dihydrogen phosphate (KDP) solution droplet

“…In our study, nucleation occurs by continuous evaporation at a fixed temperature. Therefore, we here applied a different analysis method that has been widely used in supercooling experiments of metallic liquids (7)(8)(9)(10). This alternative analysis uses precise knowledge of the volume and concentration of the solution droplet, which are measured from magnified droplet images during supersaturation.…”

“…1 still provides an insight for the origin of the interfacial free energy in a geometrical point of view. That is, the local structural similarity between crystal and liquid determines the interfacial free energy and thus crystallization behaviors, which have been demonstrated in metal and alloy liquids (7)(8)(9)(10)(11)(12). The in situ structural studies from Raman and X-ray scattering, and statistical analysis of the nucleation events indicates the existence of two types of liquids depending on the degree of supersaturation, which we hereafter refer as low-(LCS) and high-concentration solutions (HCS).…”

“…That is, the greater difference in local structural orderings between crystal and liquid phases results in higher interfacial free energy, which consequently leads to a higher nucleation barrier and thus deeper supercooling. This concept has been verified in various metallic systems for elements (7) and many alloys (8)(9)(10)(11)(12). However, many experimental and theoretical investigations have raised questions that CNT may not be adequate to describe the initial nucleation processes in biomaterials (13)(14)(15)(16)(17) and minerals (18)(19)(20)(21)(22)(23)(24)(25)(26).…”

Formation of Metastable Crystals from Supercooled, Supersaturated, and Supercompressed Liquids: Role of Crystal-Liquid Interfacial Free Energy

“…The prediction by Frank and Spaepen, i.e., the correlation of ISRO and interfacial free energy, were directly vindicated by the aid of new technical development over a last decade. That is a combination of levitations and scattering techniques [4,7,8,[21][22][23] providing containerless environment that suppresses heterogeneous nucleation sites, makes easy deep supercooling, and gives more accurate diffraction signal.…”

“…Using the combined techniques, the interfacial free energy and SROs of supercooled liquids have been reported with elemental metals (Ti [22][23][24], Fe [25][26][27], Ni [23,27,28], Zr [28,29]) and many alloys [7,8,21,[29][30][31][32][33]. Particularly, a combination of electrostatic levitation (ESL) and X-ray synchrotron scattering revealed for the first time the relationship between SRO and nucleation barriers with Ti-Zr-Ni alloy liquids [17].…”