Small Undercooling Research Articles

Rapid solidification of undercooled Al-Cu-Si eutectic alloys

Under the conventional solidification condition, a liquid aluminium alloy can be hardly undercooled because of oxidation. In this work, rapid solidification of an undercooled liquid Al80.4Cu13.6Si6 ternary eutectic alloy was realized by the glass fluxing method combined with recycled superheating. The relationship between superheating and undercooling was investigated at a certain cooling rate of the alloy melt. The maximum undercooling is 147 K (0.18T E). The undercooled ternary eutectic is composed of α(Al) solid solution, (Si) semiconductor and θ(CuAl2) intermetallic compound. In the (Al+Si+θ) ternary eutectic, (Si) faceted phase grows independently, while (Al) and θ non-faceted phases grow cooperatively in the lamellar mode. When undercooling is small, only (Al) solid solution forms as the leading phase. Once undercooling exceeds 73 K, (Si) phase nucleates firstly and grows as the primary phase. The alloy microstructure consists of primary (Al) dendrite, (Al+θ) pseudobinary eutectic and (Al+Si+θ) ternary eutectic at small undercooling, while at large undercooling primary (Si) block, (Al+θ) pseudobinary eutectic and (Al+Si+θ) ternary eutectic coexist. As undercooling increases, the volume fraction of primary (Al) dendrite decreases and that of primary (Si) block increases.

Ｓｉ‐４５ｍａｓｓ％Ｎｉ合金過冷融液表面のシリコンデンドライト成長

Dendrite growth of silicon from the undercooled melt of Si–45mass%Ni alloy was investigated. The dendrite growing along the melt surface was in-situ observed. By changing the cooling rate of the samples, the undercooling was varied from 6.7 to 18.8 K, and the growth velocity of dendrites was measured for different undercooling conditions. Both rod- and wedge-type dendrites grew in a sample, and the growth velocity of the former was slightly larger than that of the latter. Phase-field simulations were carried out in order to estimate the dendrite growth velocity at small undercooling. As the simulations at the undercooling corresponding to experiments were difficult because of the limitation of computational time, the extrapolated values of simulation results were compared with experiments, and both were in good agreement.

Solidification Behavior and Microstructural Evolution of Near-Eutectic Zn-Al Alloys under Intensive Shear

The effect of intensive shear on the solidification behavior and microstructural evolution of binary Zn-Al alloys is presented at hypoeutectic, eutectic, and hypereutectic compositions. It is found that the intensive shear, applied on the eutectic melt prior to solidification at a temperature above but close the eutectic temperature, can significantly reduce the size of eutectic cells, but the solidified microstructure still remains the lamellar morphology. For applying intensive shear on the melt during solidification, the nucleation occurs at temperatures very close to the equilibrium condition and requires very small undercooling for both the primary solidification and the eutectic solidification. The intensive shear can significantly alter the microstructural morphology. In contrast to the dendritic morphology formed in the conventional solidification, the primary Al-rich phase in hypoeutectic Zn-Al alloy and the primary Zn-rich phase in hypereutectic Zn-Al alloy under intensive shear exhibit fine and spherical particles, respectively. The lamellae morphology of Zn-rich phase and Al-rich phase formed in the conventional eutectic solidification exhibit fine and spherical particles. The increase of intensity of shear promotes the independence of solid Zn-rich particles and Al-rich particles during the eutectic solidification, resulting in the uniform and separate distribution of two solid particles in the matrix. It is speculated that the high intensity of shear can result in the independent nucleation of individual eutectic phase throughout the whole melt, and the separate growth of solid phases in the subsequent solidification.

Influence of inoculation on solidification in cast iron

Inoculation of cast iron has been mainly studied for the nucleus materials and the development of new inoculants. The effect is widely recognised; nevertheless, the mechanism was not fully understood. Inoculation leads to a decrease in chill depth, depressed the formation of D type graphite to form A type graphite and increase in the eutectic cell number. The transition from A type to the D type graphite is also accelerated by Ti addition; therefore we used Ti added samples for the study of D type graphite formation. The increase in the eutectic cell number produces a decrease in the cell size, namely the radius; nevertheless, the solidification time of the castings does not change by inoculation. Therefore, the solidification rate of the cell, namely the linear solidification rate, should decrease with inoculation and the decrease produces a depression in the chill and D type graphite due to the smaller undercooling. Therefore, we have to consider the three-dimensional solidification rate for discussing the cooling curve.

In situ investigation of spinodal decomposition in hypermonotectic Al–Bi and Al–Bi–Zn alloys

Spinodal decomposition of hypermonotectic Al–6 wt.%Bi, Al–8 wt.%Bi and Al–6 wt.%Bi–8 wt.%Zn alloys has been investigated using synchrotron radiography. In the case of the 6 and 8 wt.%Bi binary alloys undercoolings of 70 and 110 K, respectively, were required to initiate the L→L1+L2 reaction, which appeared to occur very close to the monotectic reaction temperature. The nucleated L2 droplets were set in collective size-dependent motion by forces coupled to external fields (gravity and imposed temperature gradient) as well as forces arising due to internal fluctuations of the system. With experimental conditions similar to those realized during strip casting of the same materials, it was found that the size-dependant droplet velocity field combined with Stokes drag at the L1–L2 interfaces as well as attractive and repulsive diffusion-coupling between adjacent L2 droplets, yield complex meso- to microscale hydrodynamics. The hydrodynamics are the dominating mechanisms for L2 droplet coagulation, and are accordingly decisive for the final size distribution and geometrical dispersion of the soft Bi-rich component in the cast material. A different decomposition mode was observed in the Al–6 wt.%Bi–8 wt.%Zn ternary alloy, with the L2 droplets undergoing an immiscible–miscible–immiscible transition. In contrast to what was found for the binaries, L2 domains formed at relatively small undercoolings, and very little droplet motion was observed, as all L2 domains nucleated and remained on the crucible walls until they encroached on the monotectic front. At small distances from the monotectic front a Zn-rich solute boundary layer preceding the α-Al, caused the L2 domains to dissolve as Bi–Zn–Al regains complete miscibility upon reaching a critical Zn-concentration. In the shallow mush region behind the monotectic reaction, a high Zn solid solubility and a relatively fast diffusion of Zn in α-Al combine to cause a rapid diminishing Zn concentration in the mush liquid, restoring Bi-immiscibility and consequentially a secondary nucleation of L2 droplets in the mush.

Nucleation and polymorph selection in a model colloidal fluid

Understanding and controlling polymorph selection is important because the structure of a crystal is critical to its properties. We have explored polymorph selection during nucleation in the hard-core repulsive Yukawa fluid. This model has two polymorphs (bcc and fcc), the relative stability of which can be adjusted by changing the potential parameters. We used seeded molecular-dynamics simulations to follow the evolution of the metastable bcc structure in the fcc stable region. It was found that the degree of undercooling affected the development of the bcc seeds. At small undercoolings, the bcc seed became a bcc crystal, but at large undercoolings bcc seeds became fcc crystals. Homogenously nucleated simulations were also compared to colloidal experiments. The simulations yielded nuclei of similar shape to the experimentally observed nuclei and a similar minimum size of growth. The simulated nuclei had more bcc signature than the experimental nuclei, but upon further growth the bcc signature faded, indicating that the difference between simulations and experiments may be due to the experimental nuclei having more time to resolve their structure.

Simulation of Nucleation of Proeutectoid Ferrite at Austenite Grain Boundaries during Continuous Cooling

The nucleation kinetics of proeutectoid ferrite during continuous cooling in three Fe-C-Mn-Si steels, measured in-situ by three-dimensional X-ray diffraction microscope, are compared with numerical simulation that takes into account differences in the activation energy of nucleation among grain boundary faces, edges, and corners. The essential feature of ferrite nucleation in the 0.21 pct C steel, i.e., nucleation occurred just below Ae3 and ceased at a small undercooling, is reproduced taking into account the site consumption, primarily at grain corners and overlap of solute diffusion fields in the grain boundary region or the matrix and assuming a very small or almost null activation energy of nucleation. In the 0.35 and 0.45 pct C steels, small activation energy, as reported by Offerman et al., was not unequivocally obtained because ferrite nucleation occurred at considerably large undercoolings, even below the paraequilibrium Ae3 in these steels. The increasing rate of the observed particle number with decreasing temperature is considerably smaller than calculation.

Variant Selection in Grain Boundary Nucleation of Upper Bainite

The crystallography of bainitic ferrite nucleated at austenite grain boundaries was studied in an Fe-9Ni-0.15C (mass pct) alloy. The relationship between bainitic ferrite orientations (variants) and grain boundary characters, i.e., misorientation and boundary orientation, was examined by electron backscatter diffraction analysis in scanning electron microscopy and serial sectioning observation. Bainitic ferrite holds nearly the Kurdjumov–Sachs (K-S) orientation relationship with respect to the austenite grain into which it grows. At the beginning of transformation, the variants of bainitic ferrite are severely restricted by the following two rules, both advantageous in terms of interfacial energy: (1) smaller misorientation from the K-S relationship with respect to the opposite austenite grain and (2) elimination of the larger grain boundary area by the nucleation of bainitic ferrite. As the transformation proceeds, variant selection establishing plastic accommodation of transformation strain to a larger extent becomes important. Those kinds of variant selection result in formation of coarse blocks for small undercooling.

凝固中断実験による Sn-Cu 系合金の凝固過程の解析

Recently, lead-free solders have been used in electronic equipments. There are many reports on mechanical properties of lead free solders. It is important to understand the evolution of solidified structure, though, such reports are few. In order to understand the solidification process, the Sn-Cu alloys, which are one of the candidate alloys for lead-free solders, have been used in this study. Three alloys, hypo-eutectic, eutectic, and hyper-eutectic, have been prepared. The specimen was quenched during solidification. Then the solidified structures of interrupted specimens were compared to thermal histories. In the case of hypo-eutectic and hyper-eutectic alloys, it was found that the undercooling of approximately 10 degrees was necessary for nucleation of β-Sn as a primary dendrite or as a halo. On the other hand, the undercooling was not necessary for crystallization of primary Cu6Sn5. The latter indicates that the primary Cu6Sn5 is easy to nucleate and grow even it is a facet. Primary Cu6Sn5 may be a starting site of a halo, but it doesn't facilitate nucleation of β-Sn. In the case of the hypo-eutectic alloy, a small undercooling for nucleation of eutectic structure was observed. Such undercooling was not observed in eutectic and hyper-eutectic alloys. This may be interpreted by the difference in the liquid composition when the eutectic solidification starts.

Cross-Nucleation between d-Mannitol Polymorphs in Seeded Crystallization

Seeding the liquid of d-mannitol with its polymorphs (α, β, and δ) revealed several cases of cross-nucleation between polymorphs. Only seeds of the α polymorph (the structure of the intermediate thermodynamic stability and the fastest growth rate) yielded the same polymorph in new growth. Seeds of the δ polymorph yielded the α polymorph in new growth. Seeds of the β polymorph yielded the β polymorph in new growth at small undercoolings (a few degrees below its melting point); at lower temperatures, the α polymorph nucleated on β seeds and its amount in the product increased with decreasing temperature. Seeding with single crystals of the β polymorph (rods elongated along c) showed that the orientation of the seed crystal affected how much the seed polymorph could grow before cross-nucleation occurred. Cross-nucleation makes seeding ineffective for achieving polymorphic selectivity but is sometimes avoidable by choosing suitable crystallization conditions.

Formation of ζ phase in Cu-Ge peritectic alloys

Rapid growth behavior of ζ phase has been investigated in the undercooling experiments of Cu-14%Ge, Cu-15%Ge, Cu-18.5%Ge and Cu-22%Ge alloys. Alloys of the four compositions obtain the maximum undercoolings of 202 K(0.17T L), 245 K(0.20T L), 223 K(0.20T L) and 176 K(0.17T L), respectively. As the content of Ge increases, the microstructural transition of “α(Cu) dendrite + ζ peritectic phase → ζ peritectic phase → ζ dendrite + (ɛ+ζ) eutectic” takes place in the alloy at small undercooling, while the microstructural transition of “fragmented α(Cu) dendrite + ζ peritectic phase → ζ peritectic phase → ζ dendrite + ɛ phase” happens in the alloy at large undercooling. EDS analysis of the Ge content in ζ peritectic phase indicates that undercooling enlarges the solid solubility of α dendrite, which leads to a decrease in the Ge content in ζ phase as undercooling increases. In the Cu-18.5%Ge alloy composed of ζ peritectic phase, the Ge content in ζ phase increases when undercooling increases, which is due to the restraint of the Ge enrichment on the grain boundaries by high undercooling effect.

Dendritic and eutectic growth in Sb60Ag20Cu20 ternary alloy

The rapid solidification of Sb60Ag20Cu20 ternary alloy was realized by high undercooling method, and the maximum undercooling is up to 142 K (0.18T L). Within the wide undercooling range of 40–142 K, the solidified microstructures are composed of (Sb), ϑ and ɛ phases. High undercooling enlarges the solute solubility of (Sb) phase, which causes its crystal lattice to expand and its crystal lattice constants to increase. Primary (Sb) phase grows in two modes: at small undercoolings non-faceted dendrite growth is the main growth form; whereas at large undercoolings faceted dendrite growth takes the dominant place. The remarkable difference of crystal structures between (Sb) and ϑ phases leads to (ϑ + Sb) pseudobinary eutectic hard to form, whereas strips of ϑ form when the alloy melt reaches the (ϑ + Sb) pseudobinary eutectic line. The cooperative growth of ϑ and ɛ phases contributes to the formation of (ɛ + ϑ) pseudobinary eutectic easily. In addition, the crystallization route has been determined via microstructural characteristic analysis and DSC experiment.

Dendrite growth velocity in levitated undercooled nickel melts

Model predictions for the dendrite growth velocity at low undercoolings are deviating significantly from experimental data obtained in electromagnetic levitation with a capacitance proximity sensor (CPS) [K. Eckler, D.M. Herlach, Mater. Sci. Eng. A 178 (1994) 159]. In addition to that, previous data sets obtained by different techniques are not in good agreement with each other. For instance, growth velocity data for nickel melts obtained with a high-speed camera system [D.M. Matson, in: Solidification 1998, TMS, Warrendale PA, 1998, p. 233] show higher values at low undercoolings than data obtained with the CPS. Within this work new measurements of dendritic growth velocity in levitated undercooled nickel samples were performed as a function of undercooling Δ T to investigate this discrepancy. Solidification of the undercooled melt was detected at undercooling levels within the range of 30 K<Δ T<300 K. The new data reveal high accuracy and low scattering. These data are compared with two independent growth velocity data sets and discrepancies are discussed. For verification of the new CPS data dendrite growth velocity was also measured by using a high-speed camera where the morphology of the intersection of the solidification front with the sample surface was investigated. The new experimental data are analyzed within the model of dendrite growth obtained on the basis of Brener's theory [E. Brener, J. Crystal Growth 99 (1990) 165] and the model of dendrite growth with melt convection in a solidifying levitated drop, presently being developed. Special attention is paid to the effects of convection and small amounts of impurities on the growth dynamics at small undercoolings.

Dendritic solidification and fragmentation in undercooled Ni–Zr alloys

Kinetics of dendritic solidification and fragmentation of dendritic crystals in undercooled Ni–Zr samples are studied. Using the capacitance proximity sensor technique and a high-speed-camera system, the dendrite growth velocity has been measured as a function of initial undercooling in solidifying droplets processed by the electromagnetic levitation technique. Analyses of solidified droplets give evidence to a transition from coarse grained dendrites to grain refined dendrites (CG-GR) at small undercooling, a transition from grain refined dendrites to coarse grained dendrites (GR-CG) at moderate undercooling, and to a second transition from coarse grained dendrites to grain refined dendrites (CG-GR) at a higher undercooling. Predictions of a sharp-interface model are compared with the results of experiments on Ni–Zr samples.

Creation of semisolid slurries containing fine and spherical particles by grain refinement based on the Mullins–Sekerka stability criterion

A non-agitation liquid processing approach for the production of semisolid magnesium slurries containing fine and spherical particles has been proposed on the basis of the Mullins–Sekerka stability criterion for spherical growth and recent advances in grain refinement of magnesium. It is shown that semisolid magnesium slurries containing fine and spherical particles are obtainable directly from the liquid state without agitation, via effective control of nucleation and growth by grain refinement with zirconium. The solid fraction can be varied in a wide range up to more than 50%. The formation of spherical primary magnesium particles is attributed to the combined effects of both dissolved and undissolved zirconium, which give rise to a high nucleation rate and a small undercooling when the melt contains a high level of dissolved zirconium and a sufficient number of suitably sized, undissolved zirconium particles. Grain refinement offers a promising non-agitation liquid processing approach for semisolid structure formation.

Phase-Field Modeling of Dendritic Solidification in Undercooled Droplets Processed by Electromagnetic Levitation

The results on modeling dendritic solidification from undercooled melts processed by the electromagnetic levitation technique are discussed. In order to model the details of formation of dendritic patterns we use a phase-field model of dendritic growth in a pure undercooled system with convection of the liquid phase. The predictions of the phase-field model are discussed referring to our latest high accuracy measurements of dendrite growth velocities in nickel samples. Special emphasis is given to the growth of dendrites at small and moderate undercoolings. At small undercoolings, the theoretical predictions deviate systematically from experimental data for solidification of nickel dendrites. It is shown that small amounts of impurities and forced convective flow can lead to an enhancement of the velocity of dendritic solidification at small undercoolings.

Comparison of optical properties of thermally reversible light scattering films consisting in dispersions of polystyrene/naphthalene domains or polystyrene/liquid crystal (EBBA) domains in epoxy matrices

Thermally reversible light scattering (TRLS) films are materials that can be reversibly switched from opaque to transparent states by varying temperature. TRLS films containing different types of dispersed domains in an epoxy matrix: a) naphthalene/polystyrene (NP/PS), and b) liquid crystal (EBBA/PS), were synthesized by polymerization-induced phase separation. The intensity of transmitted light was measured as a function of temperature in successive heating/cooling cycles. Transparent states were observed during heating cycles at temperatures close to the melting point of NP (81 °C) or the nematic-isotropic transition of EBBA (at about 70 °C). The NP crystallization from their polystyrene solutions in the course of cooling cycles required large undercooling (about 30 °C). In the temperature range comprised between melting and crystallization, optical properties depend on the cooling rate and the thermal history of the material. The situation was quite different for TRLS films based on EBBA. In this case, the generation of a nematic phase from the polystyrene solution required a small undercooling (about 2–3 °C), leading to a relatively sharp transition between opaque and transparent states, independent of the thermal history. This constitutes a significant advantage of the use of liquid crystals compared to organic crystals in the manufacture of TRLS films.

Athermal heterogeneous nucleation of solidification

For heterogeneous nucleation of solidification, the conditions for initiation of solid grains on nucleant areas of defined size are analysed. Calculations of the work of formation show that the solid formed on a nucleant area has both metastable- and unstable-equilibrium configurations, which permit analysis of the competition between thermal nucleation (a stochastic process) and athermal nucleation, a deterministic process in which the number of nucleation events depends on the undercooling, but not on time nor on the mechanism (adsorption, wetting or nucleation) of the initial formation of a thin solid layer on the nucleant area. It is concluded that for potent nucleants, initiating grains at small undercooling, athermal nucleation dominates. Thermal nucleation in advance of athermal is negligible, but athermal nucleation can be delayed when solute restricts solid growth.

The Mechanism of Intragranular Ferrite Nucleation on Inclusion in Steel

The intragranular ferrite, which renders fabrication of fine-microstructure and improves toughness of welds in ultra-fine grain steels, is often observed to nucleation on non-metallic inclusion. The mechanism of this nucleation is related to the interfacial energy between austenite, ferrite with inclusions, the solute depletion zone around the inclusions and the strain energy due to different thermal coefficients between matrix and inclusions, et al. The interfacial energy of iron with nitrides and carbides is crucial to promote the ferrite nucleation on such as VN. On the other hand, the composition change in local austenite is probably the control reason for ferrite on MnS and Ti2O3. The thermal strain energy is calculated to be far less than the driving force for phase transformation and not effective to promote ferrite nucleation unless at very small undercoolings.

Dendritic solidification of binary alloys with free and forced convection

Dendritic solidification with forced convection and free convection driven by contraction and thermo- solutal buoyancy is simulated in two-dimensional space using a sharp-interface model. Both pure substances and alloys are considered. The model is formulated using the finite element method and works directly with primitive variables. The coupled energy- and solutal concentration-equations, along with the Navier–Stokes equations for incompressible flow, are solved using different meshes. Temperature is solved in a fixed mesh that covers the whole domain (solid + liquid) where the solid–liquid interface is explicitly tracked using marker points. The concentration and momentum equations are solved in the liquid region using an adaptive mesh of triangular elements that conforms to the interface. The velocity boundary conditions are applied directly on the interface. The model is validated using a series of problems that have analytical, experimental and numerical results. Four simulations are presented: (1) crystal growth of succinonitrile with thermal convection under two small undercoolings; (2) dendritic growth into an undercooled pure melt with a uniform forced flow; (3) equiaxial dendritic growth of a pure substance and an alloy with contraction-induced convection; and (4) directional solidification of Pb–0.2 wt% Sb alloy with convection driven by the combined action of contraction, thermal and solutal buoyancy. Some of the simulation results are compared to those reported using other methods including the phase-field method; others are new. In each case, the effects of convection on dendritic solidification are analysed. Copyright © 2005 John Wiley & Sons, Ltd.