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During containerless processing, the oscillating drop method can be used to measure the surface tension and viscosity of a levitated melt. Through containerless processing, reactive melts that cannot be measured through conventional methods can be accurately measured; however, the accuracy of this method is dependent on the internal flow within the drop. While laminar flow does not redistribute the momentum of the oscillations, turbulent flow does redistribute the momentum of the flow and, as a result, dominates the damping. As a result, it is important to understand the internal flow behavior and the factors that affect the flow during these experiments. Models are used for the indirect quantification and characterization of the internal flow using the experimental parameters and material properties. In some cases, such as Cu50Zr50, the flow is laminar over the full range of the experiment. In other cases, including Al75Ni25, the sample is dominated by turbulent flow at high temperatures and applied electromagnetic fields, but upon cooling, transitions to laminar flow. Additionally, cases exist in which the flow is fully turbulent over the range of interest and valid measurements using the oscillating drop method are not possible. During the design phase of the experiment, the experimental parameters should be modeled to characterize the flow behavior and ensure a clean experiment.

This paper reports on the undercooling and growth morphology of Al-4.5 wt pct Cu and Al-4.5 wt pct Cu-0.4 wt pct Sc with a focus on the effect of Sc addition. It is found that the addition of Sc reduces the undercoolings of both primary phase and eutectic. In addition, the morphology of the Al-4.5 wt pct Cu-0.4 wt pct Sc dendrites is less favored in the 〈111〉 direction at similar undercoolings as with Al-4.5 wt pct Cu. The development of solidification continuous cooling transformation diagrams that relate the solidification paths to the inherent solidification microstructures is also introduced. The solidification continuous cooling transformation diagrams are obtained based on the measurement of phase fractions of a solidified microstructure. The quantitative data are combined with well-established solidification models and phase diagrams to yield undercooling temperatures of individual phases. The thermal history and undercooling of different phases in the solidified alloy are estimated for a wide range of cooling rates (from 10−2 to 104 K/s). It is found that a minimum cooling rate of about 1 K/s is required to avoid the nucleation of the detrimental intermetallic, W-phase in hypoeutectic Al-Cu-Sc.

The thermodynamic extremal principle was applied to model of rapid solidification of non-stoichiometric intermetallic compounds and the Co-xat.%Si alloys (x = 50, 53, 55) were undercooled to test the model. It is the model with but not the model without solute drag that can be derived self-consistently in thermodynamics. Unique dual sluggish and abrupt growth stages were found in undercooled Co-53 at.%Si and Co-55 at.%Si alloys. The first (second) sluggish stage is solute-controlled (thermal-controlled). The first (second) abrupt growth stage is ascribed to the sharp occurrence of solute trapping (inverted partitioning) and disorder trapping that initiates the transition from solute-controlled (thermal-controlled) to thermal-controlled (kinetic-controlled) growth. Since the predictions by the current (previous) model with (without) solute drag predicted well (deviate drastically from) the experimental results, solute drag was suggested be significant upon rapid solidification. The current work solved such an open problem, i.e. solute drag in solidification, and is helpful for not only understanding the non-equilibrium phenomena that is of theoretical importance but also controlling the non-equilibrium microstructures that is of technological importance.

Glass formation of a liquid undercooled below its melting temperature requires the complete avoidance of crystal nucleation and subsequent crystal growth. Even though they are not part of the glass formation process, a detailed knowledge of both processes involved in crystallization is mandatory to determine the glass-forming ability of metals and metallic alloys. In the present work, methods of containerless processing of drops by electrostatic and electromagnetic levitation are applied to undercool metallic melts prior to solidification. Heterogeneous nucleation on crucible walls is completely avoided giving access to large undercoolings. A freely suspended drop offers the additional benefit of showing the rapid crystallization process of an undercooled melt in situ by proper diagnostic means. As a reference, crystal nucleation and dendrite growth in the undercooled melt of pure Zr are experimentally investigated. Equivalently, binary Zr-Cu, Zr-Ni and Zr-Pd and ternary Zr-Ni-Cu alloys are studied, whose glass-forming abilities differ. The experimental results are analyzed within classical nucleation theory and models of dendrite growth. The findings give detailed knowledge about the nucleation-undercooling statistics and the growth kinetics over a large range of undercooling.

Rapid solidification of D2 tool steel is investigated experimentally using electromagnetic levitation (EML) under terrestrial and reduced gravity conditions and impulse atomization (IA), a drop tube type of apparatus. IA produces powders 300 to 1400 μm in size. This allows the investigation of a large range of cooling rates (~100 to 10,000 K/s) with a single experiment. On the other hand, EML allows direct measurements of the thermal history, including primary and eutectic nucleation undercoolings, for samples ~6 to 7 mm in diameter. The final microstructures at room temperature consist of retained supersaturated austenite surrounded by eutectic of austenite and M7C3 carbides. Rapid solidification effectively suppresses the formation of ferrite in IA, while a small amount of ferrite is detected in EML samples. High primary phase undercoolings and high cooling rates tend to refine the microstructure, which results in a better dispersion of the eutectic carbides. Evaluation of the cell spacing in EML and IA samples shows that the scale of the final microstructure is mainly governed by coarsening. Electron backscattered diffraction (EBSD) analysis of IA samples reveals that IA powders are polycrystalline, regardless of the solidification conditions. EBSD on EML samples reveals strong differences between the microstructure of droplets solidified on the ground and in microgravity conditions. While the former ones are polycrystalline with many different grains, the EML sample solidified in microgravity shows a strong texture with few much larger grains having twinning relationships. This indicates that fluid flow has a strong influence on grain refinement in this system.

The dendrite growth velocity in Al₇₅Ni₂₅ melts has been measured in a containerless procedure as a function of undercooling using an electromagnetic levitation technique both in the Earth laboratory and in Space on board the International Space Station. The growth shows an anomalous behavior inasmuch as the growth velocity decreases with increasing undercooling, confirming previous experiments on Earth. Within the scatter of experimental data, results obtained on Earth and in Space do not show significant differences. Thus, convection effects as the origin of the anomalous growth characteristics can be excluded. However, high-speed video recording exhibits multiple nucleation events in front of the growing solid-liquid interface. This effect is identified as the origin of the anomalous dendrite growth characteristics in undercooled melts of Al-rich Al-Ni melts.

In this work, the directional solidification of NiZr–NiZr $$_2$$ eutectics under isothermal conditions is investigated through numerical and theoretical means. Multiple three-dimensional phase-field simulations, including a large-scale simulation, are performed to study the free pattern selection and the velocity–spacing relation of the evolving solidification microstructures. The computed velocities for different spacings of the stoichiometric NiZr rods in the as-well stoichiometric NiZr $$_2$$ matrix are compared with the predictions of the classical Jackson–Hunt analysis. Due to certain simplifying assumptions invoked in the original theory which are not entirely representative of the numerically realized microstructures, significant deviations are observed between the two. In view of this, an extended theory is formulated accounting for the global hexagonal arrangement of the evolving rods as well as the solidification front curvatures. Owing to that, a superior compliance is achieved between the analytical and simulated growth kinetics. The key elements of symmetry incorporation are of particular importance, especially in applications to ternary systems.

In contrast to the classical eutectic growth models, according to which the eutectic spacing decreases invariably with undercooling, an anomalous transition from fine to coarse lamellar eutectics was found in the undercooled Ni-29.8 at. pct Si eutectic alloy. In this study, the growth kinetics, recalescence processes, and grain orientations were analyzed. A sharp increase of the growth velocity at an undercooling of about 100 K was found. The recalescence front transited in sequence from a diffuse one with tips, to a diffuse one without tips and then to a sharp one. The microstructures changed from a mixture of directional rod-shaped γ-Ni31Si12 grains and fine lamellar eutectics to solely coarse lamellar eutectics. Coarse lamellar eutectics were found to be formed by rapid solidification of primary directional rod-shaped Ni31Si12 intermetallic compound and subsequent epitaxial growth of secondary Ni2Si intermetallic compound, being consistent with the predictions of eutectic–dendritic and dendritic growth models. Coarse anomalous eutectics at low undercooling were formed by fragmentation of fine lamellar eutectics and their subsequent coarsening. At high undercooling, they were formed by decoupled-eutectic growth.

In the original article the Acknowledgments are incomplete. Following is the corrected text

Electrostatic levitation is applied in order to undercool liquid glass forming NiZr significantly below its melting temperature. For NiZr large undercoolings are found to be highly reproducible with this experimental method. One single NiZr sample of high purity is undercooled 200 consecutive times which leads to a distribution function of undercooling temperatures. Within a statistical approach of classical nucleation theory, the undercooling distribution is analyzed yielding parameters, e.g., a pre-exponential factor of KV ≈ 1035 m-3 s-1, which indicates homogeneous nucleation. This result is consistent with the crystallization behavior of NiZr at high undercooling and with the corresponding microstructural analysis. Since NiZr is a representative of the very common CrB structure type, with 132 isostructural phases existing, understanding its nucleation behavior adds important knowledge to the nucleation of binary alloys in general.

We report on measurements of crystal growth dynamics in semiconducting pure Ge and pure Si melts and in Ge 100− x Si x ( x = 25, 50, 75) alloy melts as a function of undercooling. Electromagnetic levitation techniques are applied to undercool the samples in a containerless way. The growth velocity is measured by the utilization of a high-speed camera technique over an extended range of undercooling. Solidified samples are examined with respect to their microstructure by scanning electron microscopic investigations. We analyse the experimental results of crystal growth kinetics as a function of undercooling within the sharp interface theory developed by Peter Galenko. Transitions of the atomic attachment kinetics are found at large undercoolings, from faceted growth to dendrite growth. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.

Crystallization is one of the most important phase transformations of first order. In the case of metals and alloys, the liquid phase is the parent phase of materials production. The conditions of the crystallization process control the as-solidified material in its chemical and physical properties. Nucleation initiates the crystallization of a liquid. It selects the crystallographic phase, stable or meta-stable. Its detailed knowledge is therefore mandatory for the design of materials. We present techniques of containerless processing for nucleation studies of metals and alloys. Experimental results demonstrate the power of these methods not only for crystal nucleation of stable solids but in particular also for investigations of crystal nucleation of metastable solids at extreme undercooling. This concerns the physical nature of heterogeneous versus homogeneous nucleation and nucleation of phases nucleated under non-equilibrium conditions. The results are analyzed within classical nucleation theory that defines the activation energy of homogeneous nucleation in terms of the interfacial energy and the difference of Gibbs free energies of solid and liquid. The interfacial energy acts as barrier for the nucleation process. Its experimental determination is difficult in the case of metals. In the second part of this work we therefore explore the potential of colloidal suspensions as model systems for the crystallization process. The nucleation process of colloids is observed in situ by optical observation and ultra-small angle X-ray diffraction using high intensity synchrotron radiation. It allows an unambiguous discrimination of homogeneous and heterogeneous nucleation as well as the determination of the interfacial free energy of the solid-liquid interface. Our results are used to construct Turnbull plots of colloids, which are discussed in relation to Turnbull plots of metals and support the hypothesis that colloids are useful model systems to investigate crystal nucleation.

We investigate crystal-growth kinetics in the presence of strong shear flow in the liquid, using molecular-dynamics simulations of a binary-alloy model. Close to the equilibrium melting point, shear flow always suppresses the growth of the crystal-liquid interface. For lower temperatures, we find that the growth velocity of the crystal depends non-monotonically on the shear rate. Slow enough flow enhances the crystal growth, due to an increased particle mobility in the liquid. Stronger flow causes a growth regime that is nearly temperature-independent, in striking contrast to what one expects from the thermodynamic and equilibrium kinetic properties of the system, which both depend strongly on temperature. We rationalize these effects of flow on crystal growth as resulting from the nonlinear response of the fluid to strong shearing forces., Comment: to appear in Phys. Rev. Materials

Containerless processing of droplets and drops by atomization and electromagnetic levitation are applied to undercool metallic melts and alloys prior to solidification. Heterogeneous nucleation on crucible walls is completely avoided giving access to large undercoolings. Experiments are performed both under terrestrial (1 g) conditions and in reduced gravity (µg) as well. Microgravity conditions are realized by the free fall of small droplets during atomization of a spray of droplets, individual drops in a drop tube and by electromagnetic levitation of drops during parabolic flights, sounding rocket missions, and using the electro-magnetic levitator multi-user facility on board the International Space Station. The comparison of both sets of experiments in 1 g and µg leads to an estimation of the influence of forced convection on dendrite growth kinetics and microstructure evolution., We thank ESA for financial support of all institutions listed on the cover page. DMH thanks the German Research Foundation DFG for additional support within the Contract HE1601/26. P.K.G. is grateful to the German Space Center Space Management under Contract Number 50WM1541 and the Russian Science Foundation under Contract Number 16-11-10095 for financial support.

Glass-forming Ni50Zr50 intermetallic compound is containerless undercooled and solidified using electrostatic levitation. Large undercoolings up to ∆T = 300 K are achieved. The dendrite growth velocity of the congruently melting alloy is measured as a function of undercooling using a high-speed camera technique. The experimental data is analysed within a sharp interface theory. It is found that the driving force of crystallisation is controlling the growth kinetics at ∆T

A model for anisotropic growth of a dendritic crystal in a binary mixture under non-isothermal conditions is presented. A criterion for a stable growth mode is given for the dendrite tip as a function of the thermal Peclet number and the ratio between the velocities of dendrite growth and solute diffusion in the liquid bulk. Limiting cases of known criteria for anisotropic dendrite growth at low and high growth Peclet numbers are provided. The inclusion of forced convective flow extends the range of theoretical predictions, especially to low growth velocities, thus eliminating systematic discrepancies between earlier models and observed experimental data, as shown by a comparison of model predictions with measured growth velocities in Ti–55 at% Al alloys solidified under electromagnetic levitation.

The kinetics of triple-junctions (TJs) in eutectic solidification is modeled by the thermodynamic extremum principle (TEP). It consists of two parts. First, TJs as the interaction of interfaces follow the interface kinetics according to which the temperature and concentration at the TJs are determined. This interface part of TJ kinetics is closely related to the eutectic point in the kinetic phase diagram. Second, TJs have their specific kinetics according to which their morphology (e.g., the contact angles in two dimensions) is determined. Using a new solution of solute diffusion in liquid, the TJ kinetics is incorporated into the current lamellar eutectic growth model. The model is applicable to the concentrated alloy systems and can be extended to any kind of eutectics. Simulation results of the rapid solidification of a lamellar Ni5Si2–Ni2Si (γ–δ) eutectic show that both parts of TJ kinetics can play important roles in eutectic solidification and need to be considered to improve the current eutectic theory.

Nd–14.2 at%Al and Nd–20.0 at%Ag eutectic alloys were containerlessly solidified in an 8 m drop tube. The droplets were undercooled during the free fall in about 1 s under reduced gravity condition in He atmosphere. The cooling rates at the solidification temperature were computed as a function of droplet size by making use of heat balance calculations. They were ranging between 40 × 103 and 0.8 × 103 K s−1 for droplets in size range of 100–900 μm diameters. Nusselt, Reynolds, and Prandtl numbers of the droplets were calculated. Microstructures of the alloys were analyzed and eutectic spacings were determined. Microhardnesses of the droplets with different sizes were measured to reveal a dependence on the cooling rates with which the droplets are solidified.

Dendrite growth velocity V as a function of undercooling on the Al-rich side of the Al-Ni system has recently been measured by electromagnetic levitation. The results have shown an anomalous behaviour, which so far cannot be theoretically described. The present work uses two simplified qualitative models of sharp interface theory, one of them treating the forming AlNi (B2) phase as a solid-solution, one treating it as an intermetallic phase, to investigate the influence of the phase diagram on the growth velocities. The results imply that the concentration dependent growth behaviour is a superposition of at least two effects: 1) A strong decrease of the total growth velocitiy level for increasing Al concentrations. 2) An increase of growth velocities with increase of Al concentration at medium and low undercoolings. The present work is able to explain the first effect, namely the concentration dependent reduction of velocities. Results are compared to experimental data. In both models the properties of the phase diagram lead to an increase of the constitutional undercooling ΔTc when the Al content increases. This reduces the fraction left for kinetic undercooling ΔTk, which is responsible for interface migration and which determines the growth velocity. Neither of the models can reproduce the second effect.

The maximal entropy production principle was applied to model the growth kinetics of a multi-component stoichiometric compound. Compared with the solid-solution phase and the non-stoichiometric compound, the dissipation by the trans-interface diffusion makes the interface slow down by decreasing the effective interface mobility and does not result in solute trapping or disorder trapping. An application to the crystallization of a CuZr stoichiometric compound shows that the transition from the thermodynamic-controlled to the kinetic-controlled growth can be predicted.

The solid–liquid interface of metallic systems of small entropy of fusion is characterized by a rough interface and dendritic morphology. In contrast, systems of high entropy of fusion like semimetals and semiconductors show smooth interfaces and facetted interfaces. The present work demonstrates that, in an undercooled melt of a metal–metalloid alloy Ni2B of intermediate entropy of fusion, a transition from a rough to a smooth interface is induced by forced convection of the melt. Electrostatic levitation is used to container-less undercool droplets in a quiescent state with no convection while electromagnetic levitation (EML) is used to undercool droplets with forced convection. The growth velocity of the solid phase is monitored as a function of undercooling by a high-speed video camera. The data are analysed within dendrite growth theory. In the case of EML, a transition from a rough to a smooth interface is indicated during dendrite growth in the undercooled melt. This is confirmed by facetted micros...

International audience; The hypoeutectic composition Co-61.8 at.% Si was undercooled and solidified using electromagnetic levitation, electromagnetic levitation under a static magnetic field, electrostatic levitation and glass-fluxing. The samples generally showed two thermal events, either separated or continuous depending on undercooling. In situ monitoring of the two thermal events with a high-speed camera revealed a sudden decrease of dendritic growth velocities of primary phases at a critical undercooling of 88 K. Scanning electron microscopy studies of the solidified samples showed that the CoSi compound and the CoSi2 compound nucleate as the primary phase for low and high undercoolings, respectively. The microstructure of the samples depends not only on undercooling, but also on the onset temperature or delay time of the second thermal event. Melt convection has no effect on the primary phase selection in undercooled melts, but it has a significant effect on the delay time and therefore on microstructure formation of the samples for high undercoolings

The Co–Cu system is analyzed in the region of the metastable miscibility gap with separation of the undercooled melt into the Co-rich and Cu-rich liquids. Phase separation of undercooled and quenched samples of the Co50Cu50 melt are investigated experimentally using an electromagnetic levitation technique, quenching on a Pb-solder-coated copper chill substrate and splat-quenching methods. It is found that quenching of the liquid samples with cooling rate ≳ 10 6 K s - 1 leads to a freezing of splats having the microstructure of spinodally decomposed liquids. The composition of the Co-rich phase measured by transmission electron microscopy is Co71.7Cu28.3 and that of the Cu-rich phase is Co26.8Cu73.2. These compositions are inside the spinodal region and close to the calculated spinodal boundary in the phase diagram of the Co–Cu system at temperatures below T ≈ 1450 K. Experimental results are compared with predictions of computational modeling using a model of fast spinodal decomposition.

International audience; Segregation is a key phenomenon responsible for altering alloys' properties during solidi-fication. The factors that lead to solute partitioning at the scale of the solidified parts are related to movements of liquid and solid phases. However, when considering a reduced gravitational field, convection forces become less significant compared to other factors. Consequently, predicting segregation in this context requires considering other prevailing driving forces, namely solidification shrinkage that arises from the density difference be-tween the liquid and solid phases. We propose a numerical model that accounts for energy conservation via a thermodynamic database, together with fluid momentum conserva-tion and species conservation to predict segregation driven by solidification shrinkage in a multicomponent alloy. We apply it on a specific steel grade for which reduced-gravity experiments were performed via parabolic flights.

Containerless rapid solidification of hypereutectic Al–8wt%Fe is investigated experimentally using the Impulse Atomization technique (IA), as well as ElectroMagnetic Levitation (EML) under terrestrial and reduced gravity conditions. The samples were analyzed using scanning and transmission electron microscopy, X-ray and neutron diffraction, as well as electron backscattered diffraction. In both EML and IA, the samples experience some undercooling for the solidification of the primary intermetallic phase, which is likely metastable AlmFe (m = 4.0–4.4). After recalescence, the solidification path then continues with the nucleation and growth of stable Al13Fe4. While Al13Fe4 dominates in EML samples, it becomes minor in favor of AlmFe in IA droplets. The morphology differences of the primary intermetallics growing under terrestrial and microgravity conditions in EML are clear with acicular morphology for the former and a star-like morphology for the latter. The α–Al has a strong texture in microgravity EML and in IA samples while a weak one is observed on terrestrial EML. This difference is attributed to the weaker fluid flow occurring under reduced gravity conditions and in IA droplets.

The interfacial free energy is a central quantity in crystallization from the meta-stable melt. In suspensions of charged colloidal spheres, nucleation and growth kinetics can be accurately measured from optical experiments. In previous work, from this data effective non-equilibrium values for the interfacial free energy between the emerging bcc-nuclei and the adjacent melt in dependence on the chemical potential difference between melt phase and crystal phase were derived using classical nucleation theory. A strictly linear increase of the interfacial free energy was observed as a function of increased meta-stability. Here, we further analyze this data for five aqueous suspensions of charged spheres and one binary mixture. We utilize a simple extrapolation scheme and interpret our findings in view of Turnbull's empirical rule. Our first estimates for the reduced interfacial free energy, $\sigma_{0,bcc}$, between coexisting equilibrium uid and bcc-crystal phases are on the order of a few $k_BT$. Their values are not correlated to any of the electrostatic interaction parameters but rather show a systematic decrease with increasing size polydispersity and a lower value for the mixture as compared to the pure components. At the same time, $\sigma_0$ also shows an approximately linear correlation to the entropy of freezing. The equilibrium interfacial free energy of strictly monodisperse charged spheres may therefore be still greater., Comment: main paper 11 pages, 4 appendices, 13 figures, 2 tables, revised version submitted to PRE, 2nd Revision

Until recently understanding the solidification behavior of high temperature materials, including many intermetallic systems, required evaluation of a great number of individual solidification experimental results. An additional challenge was the reactivity of metallic melts at elevated temperatures. Alternative methods for in situ observation of solidification processes using the high-energy synchrotron X-ray diffraction, which came up in the last decade, are reviewed in the present work. Here, solidifying phases and transformation sequences are directly related to their X-ray diffraction pattern, which avoids any confusion caused by subsequent phase transformations especially in complex systems. By containerless processing with aerodynamic, electrostatic and electromagnetic levitation methods, adapted to the application at the synchrotron beamline, contamination of the melt with impurities is avoided, which can corrupt the results of solidification studies by conventional methods. To date, the majority of the studies is focused on metastable phase formation and the structure of undercooled melts. Current efforts on liquid–solid phase transformations under conditions close to the equilibrium, which provide a great potential for acquisition of phase diagram data of refractory and reactive alloys, are also addressed.

Cu–Co alloys of bulk compositions Cu75Co25 and Cu84Co16 were undercooled and solidified using electromagnetic levitation. Microstructure of the samples was characterized using optical microscopy, scanning electron microscopy, energy dispersive spectrometry, and micro X-ray diffraction analysis. It was found that besides a bimodal size distribution, droplets of the Co-rich L1 phase resulting from liquid phase separation have a broad composition distribution. The bimodal size distribution of the droplets is more pronounced for the Cu75Co25 sample than for the Cu84Co16 sample, whilst the composition distribution of the droplets is broader in the Cu75Co25 sample than in the Cu84Co16 sample. The droplets were found to also have different types of substructures in the two samples. The results provide novel insight into microstructural evolution of phase-separated alloys under influence of forced convection.

An undercooled melt possesses an enhanced free enthalpy that opens up the possibility to crystallize metastable crystalline solids in competition with their stable counterparts. Crystal nucleation selects the crystallographic phase whereas the growth dynamics controls microstructure evolution. We apply containerless processing techniques such as electromagnetic and electrostatic levitation to containerlesss undercool and solidify metallic melts. Owing to the complete avoidance of heterogeneous nucleation on container-walls a large undercooling range becomes accessible with the extra benefit that the freely suspended drop is direct accessible for in situ observation of crystallization far away from equilibrium. Results of investigations of maximum undercoolability on pure zirconium are presented showing the limit of maximum undercoolability set by the onset of homogeneous nucleation. Rapid dendrite growth is measured as a function of undercooling by a high-speed camera and analysed within extended theories of non-equilibrium solidification. In such both supersaturated solid solutions and disordered superlattice structure of intermetallics are formed at high growth velocities. A sharp interface theory of dendrite growth is capable to describe the non-equilibrium solidification phenomena during rapid crystallization of deeply undercooled melts. Eventually, anomalous growth behaviour of Al-rich Al–Ni alloys is presented, which may be caused by forced convection.

Rapid solidification processes of glass-fluxed Ni 81.3 Sn 18.7 eutectic alloys at various undercoolings were observed in situ using a high-speed camera. The microstructure of the samples was characterized using optical microscopy, scanning electron microscopy and electron back-scattering diffraction analysis. It was found that the recalescence front sweeps the sample surface from one side to the other, which coincides with the formation of a directional solidification microstructure. Such a finding suggests that it is feasible to measure crystal growth velocities in the undercooled liquid by tracking the loci of the recalescence front. The measured data show sudden acceleration of crystal growth kinetics at a medium undercooling, giving evidence for a transition from coupled growth to uncoupled growth. Microscopic studies revealed that the sample with an undercooling of 202 K comprises two types of anomalous eutectic, which are distinguished by the size and orientations of Ni-rich grains. The results verify a recent hypothesis that anomalous eutectic in undercooled Ni–Sn alloys has a dual origin: it results from eutectic dendrites growing at low undercoolings and from single-phase Ni-rich dendrites growing at high undercoolings.

A free dendrite growth during solidification into external forced flow is analyzed using a sharp interface model. A criterion for selection of the stable growth mode is derived for the axisymmetric dendrite growing into non-isothermal binary system under convective flow. The criterion obtained rallies analytic results for dendrite growth under forced convection in a pure system [Ph. Bouissou, P. Pelce, Phys. Rev. A 40 (1989) 6673] and dendrite growth in a stagnant binary system [M. Ben Amar, P. Pelce, Phys. Rev. A 39 (1989) 4263].

This letter presents a re-examination of a disputable fluid flow effect on α-Fe content of Nd–Fe–B ingots. Alloys of hyperperitectic Nd–Fe–Co–B composition were melted and solidified using electromagnetic levitation and resistance furnace melting under a static magnetic field of up to 6 T. With either solidification method, α-(Fe,Co) content of the samples does not show any clear dependence on the static magnetic field. It was thus suggested that damping of fluid flow cannot alter α-Fe content of Nd–Fe–B ingots significantly.

The influence of gradient magnetic field on the undercooling behavior of glass-fluxed pure Sb melts was investigated using a superconducting magnet. It was found that under a positive gradient magnetic field, the mean undercooling of pure Sb melts increased with increasing magnetic field intensity. However, under a negative gradient magnetic field, the mean undercooling showed a decreasing tendency following an initial increase with increasing magnetic field intensity. The results were discussed by considering the Lorentz force and the magnetization force imposed by the gradient magnetic field.

The kinetics of dendritic solidification in a ternary Ni98Zr1Al1 alloy is investigated experimentally in a range of melt undercoolings 40 K ⩽ Δ T ⩽ 320 K . The growth velocity is measured for samples processed by the electromagnetic levitation technique using a high-speed video camera. With Δ T ≲ 220 K the measured growth rates are the same as those of a binary Ni99Zr1 alloy. In the regime of rapid solidification, especially within the regime of thermal dendritic growth at Δ T ≳ 220 K , growth rates are decreased. Sharp-interface modeling predicts growth rates over the whole range of undercooling. Phase-field simulations give quantitative predictions for the dendritic growth velocity in the solute-controlled growth regime. Results show that the composition and temperature dependency of the thermodynamic data, e.g. liquidus slope and solute partition coefficient, are important for describing the alloys. Our findings give improved sharp-interface model predictions compared to calculations based on an approximation of the thermodynamic data derived from binary phase diagrams.

The effect of interfacial ordering kinetics on growth morphology is examined for undercooling solidification of intermetallics. The focus is on NiAl, which has been found to solidify into completely irregular seaweed-like morphologies at growth velocities of ∼2 m s−1. The transition from regular dendritic to seaweed growth in this material is simulated using a hybrid deterministic–probabilistic model of microstructure evolution, taking account of the interfacial kinetic effects. Modelling shows that seaweed formation in intermetallic forming systems can be attributed in part to transient entrapment of the chemical and orientational disorder at the solid/liquid interface. Both types of disorder trapping give rise to strongly preferential depression of the interfacial temperature, while orientational disorder trapping also reduces the definitiveness of crystal orientation at the interface. These effects counterbalance the role of crystallographic anisotropy in promoting growth into preferred directions, and hence lead to relatively easy breakdown of regular dendritic patterns in highly ordered materials.

The interaction of ceramic particles with a dendritic solidification front was investigated by comparative solidification experiments in reduced gravity and under terrestrial conditions. Inductive melting of Ni 98 Ta 2 samples containing Ta 2 O 5 particles under gravity induces strong forced convection, which hinders the engulfment of particles in the dendrite stem. Comparative experiments in reduced gravity lead to a drastic decrease of forced convection. That enables the entrapment of Ta 2 O 5 particles during rapid propagation of Ni 98 Ta 2 dendrites.

Microsegregation in the Al 4 wt pct Cu alloy was investigated experimentally in a large range of cooling rates from 0.01 to 20,000 K/s using different solidification techniques. The microstructure was modeled using two-dimensional (2-D) pseudo-front tracking (PFT) developed by Jacot and co-workers. The experimentally determined amount of nonequilibrium eutectics increases with the cooling rate in the range 0.01 to 3 K/s and then decreases in the range 20 to 20,000 K/s. The fraction of eutectic calculated from the 2-D PFT model shows not only the same tendency, but also agrees quantitatively very well with the experiments over the range of cooling rates. It can also be explained qualitatively how the observed in terms of coarsening of the secondary dendrite arms and the back diffusion in the way both depend on the local solidification time.

The kinetics of dendritic solidification in undercooled Ni–Zr samples is analyzed using new experimental results and theoretical studies based on a sharp-interface model and phase-field simulations. The predictions of a sharp-interface model and of a diffuse-interface model describing the phase transition considering both thermal and solutal diffusion are compared with the new experimental results by evaluating the dendritic tip velocity in electromagnetically levitated Ni–Zr samples.

We report growth velocity measurements of highly undercooled pure Si and Si–Ge melts (2.5 and 10.0 at.% Ge) processed by containerless electromagnetic levitation. The existence of two regimes of growth for pure Si can be confirmed: faceted growth at low undercoolings and dendritic growth at high undercoolings, separated by a transitional regime. The growth velocity-undercooling relation of pure Si can be reproduced using the Lipton-kurz-Trivedi–Boettinges-coriell-Trivedi dendrite growth model whereas the Si–Ge results show a break in the velocity-undercooling relation. The microstructure of the solidified Si–Ge samples changes from coarse elongated grains at low undercoolings to a fine grained structure at high undercoolings, which can be attributed to the change from faceted to dendritic growth.

The alloy system Ti–Fe(–O, –Si) shows a great variety of stable and metastable solid phases including structurally complex phases such as quasicrystals and approximant phases. In this work the change in phase selection during solidification as a function of composition on going from the binary Ti 72.3 Fe 27.7 over the ternary Ti 69.4 Fe 26.6 O 4.0 to the quaternary Ti 65.4 Fe 25.0 Si 5.7 O 3.9 alloy (numbers indicate at.%) is investigated. The liquid samples are processed and analyzed in situ using a combination of the electromagnetic levitation technique and energy-dispersive diffraction of synchrotron radiation. This allows us to directly determine the crystal structures of the solid phases formed during solidification.

SmxCo100−x alloy melts (x = 10.5, 12.5 and 17 at.%) are processed containerlessly by electromagnetic levitation and drop-tube technique in order to get access to the metastable state of the undercooled melt. By dint of undercooling non-equilibrium phase formation is facilitated. The solidified specimen are subsequently analyzed by electron microscopy, X-ray diffraction and thermal magnetic analyses. The results show that different types of solidification behaviors are observed depending on alloy composition and undercooling level prior to solidification. Bulk samples processed by electromagnetic levitation technique are solidified by primary formation of either Sm2Co17 or SmCo5, whereas primary phase formation of metastable SmCo7 is detected in small particles attained by drop-tube processing where cooling rates lie in the order of 103–105 K/s.

We report on progress in direct experimental investigations of non-equilibrium crystallization in undercooled melts. Containerless processing is applied for undercooling and is combined with diagnostic means. The results of such experiments are utilized to critically assess physical models for rapid solidification. Existing models of rapid growth of solid into undercooled melts are reviewed. The sharp interface model is applied to quantitatively describe rapid dendrite growth of metals and alloys. It is extended to include effects of fluid flow in liquids induced by forced convection in electromagnetically levitated drops. Morphological transitions resulting in grain refinement via instabilities of growing dendrites are analyzed and used to evaluate the effect of fluid flow on grain refinement. Theoretical predictions given by sharp-interface model are compared with results of phase-field modeling and with new data of crystal growth dynamics measured with high accuracy. Depending on the undercooling prior to solidification the effects of solute diffusion, convective flow, solute trapping and microstructure evolution are demonstrated.

Undercooling experiments on Co–Pd melts have shown that the nucleation behaviour of these melts is influenced by the onset of magnetic ordering, as the temperature of the liquid approaches the Curie temperature. These experimental findings on the maximum undercoolability of Co–Pd melts can be described, if the classical nucleation model is extended by a magnetic contribution to the Gibbs free energy difference between the liquid and solid phase.

An effective mobility for non-equilibrium solute diffusion is introduced to develop a hyperbolic phase-field model of rapid solidification in which long-range solute diffusion and short-range solute-redistribution are under local non-equilibrium conditions. At equilibrium, the model provides decoupling of bulk and interface properties. Far from equilibrium, the model predicts a transition from diffusion-limited growth to diffusionless solidification at an interface velocity that is equal to the solute diffusion speed in liquid. At this critical velocity, the solute drag effect disappears abruptly, being consistent with the previous local non-equilibrium model for the sharp interface. A comparison with other phase-field models is made and an agreement between the present model predictions and the experimental results of rapid solidification of Si-9at.%As alloy is obtained.