Model Of Eutectic Growth Research Articles

Constructing solidification microstructure selection map for AlSi10Mg alloy processed by laser powder bed fusion

The cellular structures, which consist of cells and eutectic networks at the cell boundaries, determine the mechanical properties of the Al–Si alloys fabricated by laser powder bed fusion (L-PBF). Therefore, it is scientifically interesting and technologically important to establish the relationship between cellular structures and processing parameters, which is applicable to all kinds of processing methods involving rapid directional solidification, such as L-PBF. In this work, a rapid solidification microstructure selection map (SMSM) of the Al–10Si system in temperature gradient (G)–solidification velocity (V) space is constructed by a synergistic calculation with dendritic and eutectic growth models compatible to the L-PBF process. Considering that the divorced eutectic reaction should occur as the width of the liquid film entrapped in the α-Al cell boundaries becomes smaller than the Al–Si eutectic spacing, the G–V domain suitable for acquiring the cellular structures decorated with divorced eutectic Si networks is determined on the SMSM. The microstructure evolution trends predicted by the SMSM are well consistent with those in the L-PBFed AlSi10Mg melt pools with different processing parameters. The length scales of actual microstructures observed by the experiments from this work and the literature are quantitatively compared to those estimated by the SMSM, and the experimental results are basically in accord with the SMSM. It is demonstrated that divorced eutectic Si networks prefer to form at the bottom of the melt pool, where G is large (> 5 × 106 K/m) and V is small (3 × 10−4–6 × 10−3 m/s) in the SMSM. The outcomes of this work may provide fundamental guidance for tailoring the microstructures of the L-PBFed Al–Si alloys for achieving optimal mechanical properties.

Off-Eutectic Growth Model for Solidifying Alloy from an Undercooled State

Classical eutectic growth models are based on the use of eutectic composition. These models neglect the effect of primary phase formation, and their direct use in the rapid solidification process of off-eutectic (hypoeutectic and hypereutectic) alloys is absent. Combining the effect of the primary phase in the eutectic transformation and an off-eutectic composition, the solidification growth model is derived in the present work. The effect of the model and material parameters on solidification kinetics is discussed in comparison with experimental data. Computational results on the off-eutectic growth model show that the model agrees well with experimental data on the solidification kinetics of Ni–B and Ti–Si alloys.

Simulation on in-situ crystal growth of lead-free solder Sn-57Bi alloy

Lead-free solder Sn-57Bi alloy is a good candidate material for electronic packaging. However, it is difficult to observe in-situ crystal growth process of Sn-57Bi alloy at high temperature and pressure environment. In this paper, based on the Monte Carlo method with the effect of volumetric and interfacial free energy taken into consideration quantitatively, a probability model for eutectic growth is established to simulate the in-situ crystal growth of Sn-57Bi alloy. The in-situ crystal growth of Sn-57Bi alloy at different undercoolings is studied. The simulation result shows the coupled growth of two phases in eutectic alloys, along with that lamellar spacing decreases and growth velocity increases with the increase of undercooling, agreeing with the reported experimental works on the eutectic growth. This work presents a good method to study the in-situ crystal growth process of alloys.

Rapid eutectic growth: from rod growth to diffusionless solidification.

Numerous experimental data on the rapid solidification of eutectic systems exhibit the formation of metastable solid phases with the initial (nominal) chemical composition. This fact is explained by the suppression of eutectic decomposition due to diffusionless (chemically partitionless) solidification beginning at a high but finite growth velocity of crystals. In the present work, a model is suggested for the diffusionless growth to analyse the atomic diffusion in the rod eutectic couples growing into supercooled liquid. A simplified calculating method for the equation related to the Bessel function in the solution of the growth of rod eutectics is obtained. This method can also be used in the calculation of other rod eutectic growth models. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

Rod eutectic growth in bulk undercooled melts

This article proposes an analytical model to understand the rod growth of eutectic in the bulk undercooled melt. Based on the previous derivations of the lamellar eutectic growth models, relaxing the assumptions of small Péclet numbers, the model is derived by considering melt kinetic and thermal undercoolings. The intent of this model is to predict the transitions in eutectic pattern for conditions of the low and high growth velocities. In addition to investigation of the transition between lamellar and rod eutectic patterns, mathematical simplifications of solving Bessel function are presented as well, which is the most important priority to model calculation.

A Transition from Fine to Coarse Lamellar Eutectics in the Undercooled Ni-29.8 At. Pct Si Eutectic Alloy: Experiments and Modeling

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.

Rapid solidification mechanism of liquid quinary Ni-Zr-Ti-Al-Cu alloy investigated by high-speed cinematography

<sec> The ability to undercool and solidification mechanism of liquid quinary Ni<sub>40</sub>Zr<sub>28.5</sub>Ti<sub>16.5</sub>Al<sub>10</sub>Cu<sub>5</sub> alloy are investigated by electromagnetic levitation (EML) and drop tube (DT) technique. Under the EML condition, the maximum undercooling of levitated alloy can reach up to 290 K (0.21<i>T</i><sub>L</sub>). Under the DT condition, the alloy achieves higher undercooling than EML, and solidifies finally into metallic glass. At lower undercooling, the solidification structure of the alloy is composed of primary Ni<sub>3</sub>Ti phase, secondary Ni<sub>10</sub>Zr<sub>7</sub> phase and eutectic (Ni<sub>10</sub>Zr<sub>7</sub>+Ni<sub>21</sub>Zr<sub>8</sub>) phase. With the rise of undercooling, the solidification structure displays the following evolution events: phase morphology refinement, primary phase inhibition, phase number reduction, and amorphous phase formation.</sec><sec> By using the high-speed cinematography technique, three nucleation modes are distinctly observed on the levitated alloy melt surface at the beginning of solidification, that is, single-point nucleation, multi-point nucleation and annular nucleation. The levitation state corresponding to single-point mode nucleation is relatively stable, and the alloy undercooling is also relatively low. The annular nucleation only occursin the case with high rotation speed, and the undercooling is greater than 208 K. The discrepancy between nucleation modes is due to the He gas flow for forced cooling. </sec><sec> The theoretical calculations indicate that the alloy droplets achieve high undercoolingand large cooling rate under the DT condition. The experimental results show that when the droplet diameter decreases to 498 μm, the amorphous phase begins to appear in the alloy particles. It is noteworthy that the amorphous phase is preferentially formed inside the droplet, but not on the outer surface. The morphology of solidification structure reveals that different regions of the droplet have various local undercoolings, which result in the distribution characteristics of amorphous phase. The volume fraction of amorphous phase increases linearly with the decrease of particle diameter. When the droplet diameter decreases to 275 μm, the alloy droplets are completely frozen into glassy particles.</sec><sec> The average eutecticspacing values are also measured at different alloy undercoolings. Compared with the classical binary eutectic growth model, the experimental eutectic growth law exhibits a large deviation in index. This indicates that the eutectic growth in multicomponent alloys displays more complex kinetic characteristics.</sec>

Comments on “A New Analytical Approach to Predict Spacing Selection in Lamellar and Rod Eutectic Systems”*

A mistake in the eutectic growth model published by Adrian V. Catalina et al. (Adrian V. Catalina, Subhayu Sen, and Doru M. Stefanescu: Metall. Mater. Trans. A, 2003, vol. 34A, pp. 383–94) was identified. First, we have re-derived the model following Catalina’s assumption. Furthermore, the two Fourier coefficients were directly obtained following the classical eutectic model (JH model). Finally, the validity of our derivation is closed-loop verified based on the combination of the above two derivations.

Modeling of eutectic growth kinetics with thermodynamic couplings

An original model of directional eutectic growth for lamellar eutectics is presented. This model is based on the analysis of thermodynamic equilibrium at the solidification front. Contrary to previous ones, this model does not use linearization hypothesis on the alloy phase diagram and takes into account variations of densities between phases. Moreover, curvature effects are considered on thermodynamic equilibrium at the solidification front. Its numerical implementation is made possible through a coupling with thermodynamic software based on the CALPHAD approach. This new numerical model is applied to the Al-Al2Cu eutectic structure and compared to the Jackson-Hunt theory. Large differences between results of the present model and this theory are observed at high growth rate. In particular, curvature effects on phases concentrations can no more be modeled using a linear approximation, as in the Gibbs-Thomson relation. A good agreement of the numerical model with reported experimental studies is observed for a large range of growth velocities.

Modeling of Eutectic Formation in Al-Si Alloy Using A Phase-Field Method

AbstractWe have utilized a phase-field model to investigate the evolution of eutectic silicon in Al-Si alloy. The interfacial fluctuations are included into a phase-field model of two-phase solidification, as stochastic noise terms and their dominant role in eutectic silicon formation is discussed. We have observed that silicon spherical particles nucleate on the foundation of primary aluminum phase and their nucleation continues on concentric rings, through the Al matrix. The nucleation of silicon particles is attributed to the inclusion of fluctuations into the phase-field equations. The simulation results have shown needle-like, fish-bone like and flakes of silicon phase by adjusting the noise coefficients to larger values. Moreover, the role of primary Al phase on nucleation of silicon particles in Al-Si alloy is elaborated. We have found that the addition of fluctuations plays the role of modifiers in our simulations and is essential for phase-field modeling of eutectic growth in Al-Si system. The simulated finger-like Al phases and spherical Si particles are very similar to those of experimental eutectic growth in modified Al-Si alloy.

A model for eutectic growth in multicomponent alloys

A model for eutectic growth of multicomponent alloys is proposed. Among several other modifications brought to the classic theory of eutectic growth, the model introduces the phase fraction change as the main mechanism for maintaining an isothermal solid/liquid interface during solidification of eutectic alloys. A comparison between the theoretical results and experimental measurements for the Fe-C based alloys showed a good agreement for alloys of composition not too far removed from the eutectic point. The analysis also showed that an earlier proposed criterion for spacing selection of binary irregular eutectics, based on volume fraction of the faceted phase, can be applied to multicomponent alloys as well. The investigation performed on the effect of Si on the growth kinetics of Fe-C-Si eutectic alloys showed that the growth coefficient μ decreases with the increase of Si content.

Microstructural evolution of laser surface remelting remolten Ni-28 wt%Sn alloy under liquid nitrogen cooling

The substrate of as-cast Ni-28 wt% Sn hypoeutectic alloy immersed in liquid nitrogen is rapidly remolten and solidified by laser surface remelting with a scanning velocity of 10 mm/s and the laser power of 1950 W. The microstructure of the substrate and its effect on the microstructure of the molten pool are investigated by scanning electron microscope carefully. It is found that the substrate of the Ni-28 wt%Sn ingot is composed of coarse primary α-Ni dendrites and the interdendritic (α-Ni+Ni3Sn) eutectic. The growth orientations of α-Ni dendrites and the interdendritic eutectic are distributed nearly randomly in the as-cast substrate. There are three kinds of microstructure characterstic zones from the top to the bottom of melted pool. The growth directions of α-Ni dendrites with the primary dendritic spacings ranging from 4.19 to 6.91 μm are approximately parallel to the laser scanning direction at the top of the molten pool due to the fact that the temperature gradient at the interface between the molten pool and substrate tends to be parallel to the laser scanning direction. In the middle of the molten pool, the epitaxial α-Ni columnar dendrites are found to be inclined to grow in the direction vertical to the bottom of the molten pool due to the fact that the temperature gradients in most zones of the molten pool are perpendicular to the bottom of the molten pool. The formation of new primary dendrites by the growth of the tertiary arm results in the decrease of primary dendritic spacing in comparison with that at the bottom of the molten pool. There are a small quantity of residual α-Ni primary phase and a large amount of (α-Ni+Ni3Sn) eutectic at the bottom of the molten pool. The microstructure of laser remolten zone is greatly influenced by the substrate microstructure, and the growth direction of the α-Ni dendrite in the molten pool is also affected remarkably by both the heat flux and the preferred crystal orientations for dendritic growth. Compared with the mixed lamella, rod and divorced (α-Ni+Ni3Sn) eutectic microstructures in the substrate, the eutectic structure in the molten pool is completely composed of the refined lamellar eutectic, which grows epitaxially in the direction perpendicular to the interface between the molten pool and the substrate at the bottom of molten pool. The eutectic lamellar spacing increases from the top (0.23 μm± 0.01 μm) to the bottom (0.42 μm± 0.02 μm) of the molten pool due to the interface growth velocity decreasing from the top to the bottom. The Kurz-Giovanola-Trivedi model for rapid dendritic growth and the Trivedi-Magnin-Kurz model for eutectic growth are used to estimate the growth undercooling of the microstructure in the molten pool respectively. It is found that the growth undercooling of dendrites and the eutectic in the molten pool should be between 50.4 K and 112.5 K, which is much larger than the critical undercooling for anomalous eutectic growth found in the high undercooled solidification in the previous researches. This phenomenon means that the critical undercooling for anomalous eutectic growth reported in the previous literature may be not the sufficient condition for generating the anomalous eutectic.

Kinetics of triple-junctions in eutectic solidification: a sharp interface model

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.

Modeling of free eutectic growth and competitive solidification in undercooled near-eutectic alloys based on in situ measurements

Free eutectic growth and its competition with single-phase growth in solidification of undercooled near-eutectic alloys are not yet fully understood. In this paper, the historical development of eutectic growth models was reviewed. The LZ model of free eutectic growth was evaluated using recent data of eutectic growth velocities in an undercooled Ni81.3Sn18.7 eutectic composition. An excellent agreement was achieved between the LZ model and the data. Crystal growth velocities in off-eutectic Ni83Sn17 and Ni80Sn20 compositions were measured using a high-speed camera technique. The present data of the off-eutectic compositions and the recent data of the eutectic composition were modeled using the LZ model and the LKT/BCT model of free dendritic growth. The modeling revealed that the competition between the free eutectic growth and the single-phase growth is controlled by the highest interface temperature criterion. A coupled zone of the α-Ni-Ni3Sn eutectic was calculated using this criterion. The coupled zone agrees well with studies of solidified structures of undercooled samples.

An Al2O3/Y3Al5O12 eutectic nanocomposite rapidly solidified by a new method: Liquid–metal quenching

A liquid–metal quenching method is designed for studying the rapid solidification behavior of oxide eutectic composites. The lamellar spacing of an Al2O3/Y3Al5O12 eutectic nanocomposite processed using this method is only 50 nm, which is an order of magnitude smaller than that reported previously. Results from the microstructural characterization of the resulting materials are described. Using the classical eutectic growth model, the relative solidification rate in this method is calculated to be 1.88 × 10−2 m s−1.

Peculiarities of Phase Transitions and Structure Formation in a Ternary Al-Cu-Ni Alloy with Four-Phase Peritectic Reaction

The structure formation in peritectic Al-4.5at.%Cu-11at.%Ni ternary alloy with four-phase peritectic reaction was investigated using the quantitative phase-field model of eutectic growth. This model, extended to an arbitrary number of phases, guarantees the stability requirements on individual interfaces. The thermal noise terms disturb the stability and produce the heterogeneous nucleation of secondary phases in accordance to the energetic and concentration conditions. In our recent work it was shown that in differential thermal analysis (DTA) experiments specific microstructure parts in Al-4.5at.%Cu-11at.%Ni alloy with a four-phase peritectic reaction were observed, which cannot be explained by Scheil calculation or simple phase-field modeling. In this work, it was found by numerical experiments that, due to the formation of anisotropic quasi-primary Al3Ni2 crystals and the suppression of the nucleation of (Al) phase, the eutectic-like coupled growth of Al3Ni2 and Al3Ni phases can be observed. In addition, at further cooling the anisotropic shape of quasi-secondary Al3Ni crystals promotes the nucleation of the (Al) phase. The simulated final structure is comparable to the experimental one which is characterized by large Al3Ni2 crystals enveloped by the Al3Ni phase.

Domain Wall Dynamics in Ginzburg–Landau-Type Equations with Conservative Quantities

In the Ginzburg-Landau equation, there are domain walls connecting two metastable states. The dynamics of domain walls has been intensively studied, but there remain still unsolved but crucial problems even for a single domain. We study the domain wall dynamics in three different Ginzburg-Landau-type equations satisfying conservation laws. In a modified $\phi^4$ model satisfying the law of energy conservation and the Lorentz invariance, the motion of a domain wall is accelerated and the velocity approaches its maximum. In a one-dimensional model of eutectic growth, the order parameter is conserved and a domain wall connecting a metastable uniform state and a spatially periodic pattern appears. We try to find a selection rule for the wavelength of a spatially periodic pattern. In a model equation for martensitic transformation, a domain wall connecting a uniform metastable state and a zigzag structure appears which propagates at a high velocity.

Microstructure and mechanical properties of Al2O3/Y3Al5O12/ZrO2 hypereutectic directionally solidified ceramic prepared by laser floating zone

Al2O3/Y3Al5O12/ZrO2 directionally solidified ceramic has been considered as a promising candidate for ultrahigh temperature structural materials due to its excellent performance even close to its melting point. In this work, laser floating zone (LFZ) solidification experiments were performed on Al2O3/Y3Al5O12/ZrO2 hypereutectic with the solidification rates between 2 μm/s and 30 μm/s. The full eutectic lamellar microstructure is obtained with hypereutectic composition. The solid/liquid interface morphology is investigated. The microstructure characteristic is discussed based on the solid/liquid interface. The variation of lamellar spacing with different compositions and solidification rates was reported and discussed by considering an irregular eutectic growth model. The maximum hardness and fracture toughness are 19.06 GPa and 3.8 MPa m1/2, respectively. The toughening mechanism of ZrO2 is discussed based on the scenario of the crack propagation pattern.

On the solution of solute diffusion during eutectic growth

An exact solution of solute diffusion for the stoichiometric-compound/stoichiometric-compound eutectic is derived for a planar interface. Compared with the previous work, the solution is consistent with the kinetics of triple-junction, i.e. the eutectic composition is necessarily found at the triple-junction. Adopting an averaged conservation law at the interface, a general solution is proposed for any kind of eutectics and phase diagrams. Simulation results in the Ni5Si2–Ni3Si eutectic growth show that the general solution is a good approximation. The current work makes it possible to incorporate the kinetics of triple-junction into the eutectic growth model.

Fibrous eutectic growth in succinonitrile–neopentylglycol–(D)camphor–aminomethylpropanediol alloys for thin and bulk sample geometry

The eutectic spacing (λ) was investigated in three alloys of succinonitrile–neopentylglycol–(D)camphor–aminomethylpropanediol (SCN–NPG–DC–AMPD) system over a wide range of temperature gradients (G) and growth velocities (V), both in thin ⩽5μm (two-dimensional (2-D)) samples and in bulk (three-dimensional (3-D)) samples. The compositions were selected such that fraction of rod-forming phase (f) was equal to 11.5vol.% for the invariant SCN–12.2wt.% NPG alloy, 23.3vol.% for the univariant SCN–24.2wt.% DC–0.5wt.% NPG alloy and 29.8vol.% for the bivariant SCN–33.0wt.% DC–6.0wt.% NPG–3.0wt.% AMPD alloy. For high G/V conditions significant deviations from growth at minimum undercooling were found with spacing selection closer to the pinch-off limit. The experimental results show that confining the 3-D eutectics to 2-D growth conditions invariably leads to larger values of the mean rod spacing, but to smaller values of the mean rod diameter. The 2-D/3-D ratio of the square of mean rod diameters η=d2DR/d3DR2 was found to be independent of the phase fraction of the rod-forming phase f and equal to η=0.80±0.02. The 2-D/3-D ratio of square of rod spacing k=λ2DR/λ3DR2 was found to dependent on f following k=(2f)-1 or else k=η38πf-1. These findings are discussed in terms of the Jackson–Hunt model of eutectic growth and simple geometrical considerations.