Solidification Velocity Research Articles

On the primary spacing and microsegregation of cellular dendrites in laser deposited Ni–Nb alloys

In this study, an alloy phase-field model is used to simulate solidification microstructures at different locations within a solidified molten pool. The temperature gradient G and the solidification velocity V are obtained from a macroscopic heat transfer finite element simulation and provided as input to the phase-field model. The effects of laser beam speed and the location within the melt pool on the primary arm spacing and on the extent of Nb partitioning at the cell tips are investigated. Simulated steady-state primary spacings are compared with power law and geometrical models. Cell tip compositions are compared to a dendrite growth model. The extent of non-equilibrium interface partitioning of the phase-field model is investigated. Although the phase-field model has an anti-trapping solute flux term meant to maintain local interface equilibrium, we have found that during simulations it was insufficient at maintaining equilibrium. This is due to the fact that the additive manufacturing solidification conditions fall well outside the allowed limits of this flux term.

On the Nonequilibrium Interface Kinetics of Rapid Coupled Eutectic Growth

Nonequilibrium interface kinetics (NEIK) is expected to play an important role in coupled growth of eutectic alloys, when solidification velocity is high and intermetallic compound or topologically complex phases form in the crystallized product. In order to quantitatively evaluate the effect of NEIK on the rapid coupled eutectic growth, in this work, two nonequilibrium interface kinetic effects, i.e., atom attachment and solute trapping at the solid–liquid interface, were incorporated into the analyses of the coupled eutectic growth under the rapid solidification condition. First, a coupled growth model incorporating the preceding two nonequilibrium kinetic effects was derived. On this basis, an expression of kinetic undercooling (∆T k), which is used to characterize the NEIK, was defined. The calculations based on the as-derived couple growth model show good agreement with the reported experimental results achieved in rapidly solidified eutectic Al-Sm alloys consisting of a solid solution phase (α-Al) and an intermetallic compound phase (Al11Sm3). In terms of the definition of ∆T k defined in this work, the role of NEIK in the coupled growth of the Al-Sm eutectic system was analyzed. The results show that with increasing the coupled growth velocity, ∆T k increases continuously, and its ratio to the total undercooling reaches 0.32 at the maximum growth velocity for coupled eutectic growth. Parametric analyses on two key alloy parameters that influence ∆T k, i.e., interface kinetic parameter (μ i ) and solute distribution coefficient (k e ), indicate that both μ i and k e influence the NEIK significantly and the decrease of either these two parameters enhances the NEIK effect.

Interaction of Multiple Particles with a Solidification Front: From Compacted Particle Layer to Particle Trapping.

The interaction of solidification fronts with objects such as particles, droplets, cells, or bubbles is a phenomenon with many natural and technological occurrences. For an object facing the front, it may yield various fates, from trapping to rejection, with large implications regarding the solidification pattern. However, whereas most situations involve multiple particles interacting with each other and the front, attention has focused almost exclusively on the interaction of a single, isolated object with the front. Here we address experimentally the interaction of multiple particles with a solidification front by performing solidification experiments of a monodisperse particle suspension in a Hele-Shaw cell with precise control of growth conditions and real-time visualization. We evidence the growth of a particle layer ahead of the front at a close-packing volume fraction, and we document its steady-state value at various solidification velocities. We then extend single-particle models to the situation of multiple particles by taking into account the additional force induced on an entering particle by viscous friction in the compacted particle layer. By a force balance model this provides an indirect measure of the repelling mean thermomolecular pressure over a particle entering the front. The presence of multiple particles is found to increase it following a reduction of the thickness of the thin liquid film that separates particles and front. We anticipate the findings reported here to provide a relevant basis to understand many complex solidification situations in geophysics, engineering, biology, or food engineering, where multiple objects interact with the front and control the resulting solidification patterns.

Columnar and Equiaxed Solidification of Al-7 wt.% Si Alloys in Reduced Gravity in the Framework of the CETSOL Project

During casting, often a dendritic microstructure is formed, resulting in a columnar or an equiaxed grain structure, or leading to a transition from columnar to equiaxed growth (CET). The detailed knowledge of the critical parameters for the CET is important because the microstructure affects materials properties. To provide unique data for testing of fundamental theories of grain and microstructure formation, solidification experiments in microgravity environment were performed within the European Space Agency Microgravity Application Promotion (ESA MAP) project Columnar-to-Equiaxed Transition in SOLidification Processing (CETSOL). Reduced gravity allows for purely diffusive solidification conditions, i.e., suppressing melt flow and sedimentation and floatation effects. On-board the International Space Station, Al-7 wt.% Si alloys with and without grain refiners were solidified in different temperature gradients and with different cooling conditions. Detailed analysis of the microstructure and the grain structure showed purely columnar growth for nonrefined alloys. The CET was detected only for refined alloys, either as a sharp CET in the case of a sudden increase in the solidification velocity or as a progressive CET in the case of a continuous decrease of the temperature gradient. The present experimental data were used for numerical modeling of the CET with three different approaches: (1) a front tracking model using an equiaxed growth model, (2) a three-dimensional (3D) cellular automaton–finite element model, and (3) a 3D dendrite needle network method. Each model allows for predicting the columnar dendrite tip undercooling and the growth rate with respect to time. Furthermore, the positions of CET and the spatial extent of the CET, being sharp or progressive, are in reasonably good quantitative agreement with experimental measurements.

A new model for the solidification of metal matrix nanocomposites: Wet cluster engulfment of nanoparticles by the solidification front

In this article, a new mechanism so-called wet cluster engulfment and the related formula were proposed to predict the critical solidification velocity for nanoparticles engulfment by a solidification front. According to the mechanism, the most important issue in the engulfing of the nanoparticles is the aggregation of nanoparticles, i.e. the formation of wet clusters in front of solidifying phase. In fact, local clustering of nanoparticles created highly viscous zones in the vicinity of the solidification front so that the nanoparticles and the liquid-filled spaces between them move as a unified mass. Thus, the van der Waals and drag forces between a nanoparticles cluster and the solidification front were calculated analytically. The new formulae were derived for the critical solidification velocity and critical diameter of the clusters as a function of the melt viscosity, the nanoparticle size, the cluster size, and the nanoparticle volume concentration inside the cluster. The theoretical results showed that the new model predicted more accurate values for the critical velocity than the earlier models. The proposed model can explain the formation of nanoparticle-rich zones and zones with a low concentration of nanoparticles in the microstructure of the nanocomposites produced via casting.

Numerical simulation of heat transfer and melting of Fe-based powders in SLM processing

Modelling of selective laser melting (SLM) of Fe and stainless steel powders has been performed to analyze unsteady heat transfer in a porous medium under conditions of rapid phase transformations. The pulsed laser heat source develops high temperature gradients that lead to large solidification velocities, which can be used in acquisition of complex microstructures in SLM manufacturing. First, the effective thermal conductivity as a function of the local porosity which is a dynamically varying parameter in SLM was evaluated numerically. It showed a high role of heat transfer through the gas phase in powders with low thermal conductivity, i.e. in stainless steel. At the porosity 65% and above, the mechanism of heat transfer drastically changed and a linear dependence of thermal conductivity on porosity frequently used in literature becomes incorrect. Second, the obtained dependence was accounted for modelling of thermal fields and powder consolidation in the powder bed. The results of simulation agree well with the obtained experimental data and show the importance of correct dynamical evaluation of the thermophysical properties in SLM processes.

Rapid solidification growth mode transitions in Al-Si alloys by dynamic transmission electron microscopy

In situ dynamic transmission electron microscope (DTEM) imaging of Al-Si thin-film alloys was performed to investigate rapid solidification behavior. Solidification of alloys with compositions from 1 to 15 atomic percent Si was imaged during pulsed laser melting and subsequent solidification. Solely α-Al solidification was observed in Al-1Si and Al-3Si alloys, and solely kinetically modified eutectic growth was observed in Al-6Si and Al-9Si alloys. A transition in the solidification mode in eutectic and hypereutectic alloys (Al-12Si and Al-15Si) from nucleated α-Al dendrites at lower solidification velocities to planar eutectic growth at higher solidification velocities was observed, departing from trends previously seen in laser-track melting experiments. Comparisons of the growth modes and corresponding velocities are compared with previous solidification models, and implications regarding the models are discussed.

Fractional Crystallization Model of Multicomponent Aluminum Alloys: A Case Study of Aircraft Recycling

A one-dimensional numerical solidification model has been developed to predict the recovery and refining efficiency of fractional crystallization applied to a blend of aircraft Al scraps with variations of Fe and Si. The model incorporates the effective partition coefficient depending on the degree of melt stirring. Moreover, the kinetic factors that affect the formation of primary Al FCC during fractional crystallization such as solidification velocity, thermal gradient, cooling rate, and solute back-diffusion are taken into account. The simulation results suggest that the optimum solidification velocities that are able to yield the highest refining can be ranged between 1.0 × 10−6 and 1.0 × 10−5 m/s with medium to high stirring levels. The maximum recovery of refined Al has been estimated to be 31 wt pct of the initial scrap when the process is carried out at 1 × 10−6 m/s and the initial concentrations of Fe and Si are 1 and 2 pct, respectively.

Accelerated onset of cellular breakdown at increased solidification speed after laser melting of indium in silicon

We report on the incidence of cellular breakdown in silicon wafers implanted with indium and pulsed laser melted at varying laser fluence. We predict from heat flow calculations that as laser fluence is decreased, (a) the melt depth decreases, (b) the solidification velocity increases, and (c) the solidification front should be more stable with respect to cellular breakdown (based on the binary alloy solidification theory), which should result in observed incidence of cellular breakdown at a relatively shallower depth below the surface. However, secondary ion mass spectrometry (SIMS) data show that cellular breakdown at lower fluence is observed deeper, indicating that the interface became unstable earlier in its solidification. The SIMS data show significant In evaporation, with greater evaporation occurring as fluence increases. Calculations show that surface evaporation can reduce the bulk liquid concentration during solidification, reducing the degree of instability. The longer melt durations after irradiation at higher fluence give more time for evaporation, which may result in a relatively larger delay in the onset of breakdown compared to lower fluence by suppressing the bulk liquid concentration and suppressing the growth of unstable perturbation. Under certain conditions, this effect could dominate over the role of reducing the interface speed, which would tend to accelerate amplification of a perturbation, which leads to breakdown. Calculations qualitatively support this interpretation.

Solidification interface transformation and solute redistribution of FeCrAl stainless steel

The solid–liquid interface structures and the Al segregation in the solidifying front were investigated by directional solidification and electron probe microanalysis. The results show that the interface structure would vary greatly with solidification velocity, the morphology of which changed from planar at 1 µ m/s, dendrite at 25 µ m/s, cellular–dendrite at 50 µ m/s, to hexagon cell at 100 and 150 µ m/s and finally high-velocity cell at 200 µ m/s. The stability of the planar interface was mainly influenced by Al segregation. The narrow solidification temperature range benefited the transformation of dendrite to cell-dendrite. Regarding Fe, Cr as solvents and Al as solute, the secondary dendrite arm spacing when solidification velocity is 25 µ m/s could be predicted by the formula which was widely adopted in binary alloy system, and the predicted values fit well with the experimental results. The Al partition coefficient was found to be 0.96, and it indicated that there existed slight Al segregation when solidification velocity is 1 µ m/s, which was the main stabilizing factor of the planar interface. Al segregation is not obvious at velocities above 25 µ m/s and the interface transformed to various structures when solidification velocities were higher than 25 µ m/s.

Evolution of Columnar-Dendritic Microstructure during Upward Directional Solidification of Eutectic and Off-Eutectic Pb-Sn Alloys

Upward directional solidification experiments were carried out on various Pb-Sn alloys using water cooled copper chills. Different combinations of growth rate V and composition Co were used to investigate their effect on microstructure evolution during solidification. The effect of solidification velocity and composition on the structure formation is analyzed. It is observed that the hypoeutectic Pb-Sn alloys exhibit columnar dendritic structure with α phase rich region. In case of hypereutectic alloys the columnar dendritic structure is with β phase rich region. In both the cases dendritic structure was found to surround by the eutectic structure, a typical result of non equilibrium cooling. The eutectic composition exhibits complete eutectic structure aligned in the direction of solidification.

Fragmentation-driven grain refinement in directional solidification of AlCu10wt-% alloy at low pulling speeds

The formation of the grain structure in Al-10 wt%Cu alloy during directional solidification was investigated experimentally. The alloy composition was chosen because of its special feature that both the initial melt composition and the solidifying primary Al dendrites have almost identical densities. Therefore, gravity-related effects such as buoyancy or sedimentation acting on nucleated or fragmented solid particles in the melt are expected to be minor. In 3D bulk samples at low solidification velocities, unexpected equiaxed grain growth was found instead of columnar growth. This behavior was investigated in accompanying solidification experiments with thin samples using in-situ X-ray diagnostics. It is demonstrated that fragments detach from the dendrite tip region and move slightly ahead of the solid-liquid interface as they grow. As a result, a dendritic microstructure consisting of elongated equiaxed grains is developed. Accordingly, fragmentation was identified as responsible for grain refinement in the given parameter range.

Effect of alloying elements on pore characteristics of lotus-type porous Cu-X alloys (X = Ni, Co, Mn, Si, Sn, P)

The effect of alloying elements on the formation of long cylindrical pores was investigated for lotus-type porous Cu. The lotus-type porous Cu was fabricated using the centrifugal casting technique under hydrogen atmosphere with the addition of Ni, Co, Mn, Si, Sn, or P. The porosity and average pore diameter were significantly affected by the addition of alloying elements. The porosity was independent of the addition of Ni or Co but decreased with increasing Mn, Si, Sn, or P content. The average pore diameter exhibited minimum at 0.05at.% Ni content and 0.02at.% Co, Mn, or Si. It then increased as the content of alloying elements was increased up to 0.1at.%. The average pore diameter sharply increased with increasing Sn or P content up to 0.1at.%. It is suggested that the addition of alloying elements is an effective way to control the porosity and average pore diameter in lotus-type porous Cu without additional change of processing parameters such as the hydrogen gas pressure and solidification velocity.

A parametric multi-scale, multiphysics numerical investigation in a casting process for Al-Si alloy and a macroscopic approach for prediction of ECT and CET events

Understanding of columnar-to-equiaxed transition (CET) and equiaxed-to-columnar transition (ECT) is difficult not only due to the involvement of multiple factors like advection of equiaxed grains, fragmentation of dendrites, etc. but also due to its complex relationship with temperature gradient (G), solidification velocity (R), and cooling rate (Ṫ) at the solidification front over a broad range of solidification conditions. Parametric multi-scale, multiphysics grain structure simulations were performed to develop the relationship between process-parameters and grain structure for the casting process over a wide range of process parameters. The effect of interfacial heat transfer coefficient, superheat, and nucleation site density on the grain structure is studied using a coupled finite-volume-method-cellular-automaton (FVM-CA) multi-scale, multiphysics solidification model. A numerical averaging strategy at the solidification front is proposed for monitoring the occurrence of CET and ECT. We attempt to study the grain structure evolution obtained from the multi-scale model with the transient macroscopic average thermal parameters. Unlike the previous attempts here we evolve criteria independently from the macro-model that obeys the phase diagram. It was found that the temperature field has the imbibed signatures for the occurrence of CET and ECT.

Laser recrystallization and inscription of compositional microstructures in crystalline SiGe-core fibres.

Glass fibres with silicon cores have emerged as a versatile platform for all-optical processing, sensing and microscale optoelectronic devices. Using SiGe in the core extends the accessible wavelength range and potential optical functionality because the bandgap and optical properties can be tuned by changing the composition. However, silicon and germanium segregate unevenly during non-equilibrium solidification, presenting new fabrication challenges, and requiring detailed studies of the alloy crystallization dynamics in the fibre geometry. We report the fabrication of SiGe-core optical fibres, and the use of CO2 laser irradiation to heat the glass cladding and recrystallize the core, improving optical transmission. We observe the ramifications of the classic models of solidification at the microscale, and demonstrate suppression of constitutional undercooling at high solidification velocities. Tailoring the recrystallization conditions allows formation of long single crystals with uniform composition, as well as fabrication of compositional microstructures, such as gratings, within the fibre core.

Particle engulfment dynamics under oscillating crystal growth conditions

To better understand the physical mechanisms behind particle engulfment dynamics under fluctuating solidification velocities, transient simulations are performed for a SiC particle in a silicon solidification system with oscillating growth rates using a rigorous finite-element model developed previously. Simulations reveal complicated behaviors that require a re-examination of the classical notion of a steady-state, critical growth velocity, vc, for particle engulfment. Under sinusoidal growth variations at a frequency representative of turbulent fluctuations in a large-scale melt, stable pushing states featuring nonlinear particle-growth front oscillations can arise, even when the maximum growth velocity slightly exceeds vc. However, higher-amplitude growth oscillations at the same frequency are shown to result in particle engulfment. Significantly, engulfment under such dynamic conditions can occur at average solidification rates far below the steady-state critical velocity, a behavior consistent with many experimental observations.

Solidification velocity of undercooled Fe–Co alloys

The goal of this work was to investigate intra-alloy relationships, as they pertain to rapid solidification, which can be applied to computational materials modeling. Those relationships can be utilized to improve the accuracy of predictive modeling by leveraging previous experimental results. With that in mind, Fe–Co samples were prepared with 30–50 at.% cobalt and they were processed via electrostatic levitation (ESL) or electromagnetic levitation (EML). The samples were levitated, melted, and allowed to cool and solidify in a vacuum for ESL testing and under He gas for EML testing. If sufficient undercooling was achieved, the sample solidified via double recalescence. In that event, the metastable δ–phase would grow into the undercooled liquid, and then the stable γ–phase would grow into a combination of the metastable phase and remaining undercooled liquid, or mushy zone. The velocities of the solid phases growing into undercooled liquid were analyzed with current dendrite growth theories. The purpose of the growth velocity analyses was two-fold: 1) Assess the validity of current dendrite theory as it applies to the Fe–Co system. 2) Evaluate the kinetic growth coefficient, μ, assuming a constant kinetic rate parameter, Vo. The results of the analyses indicate that it is reasonable to assume that the kinetic rate parameter, Vo, is constant for a given phase within an alloy system if ΔHf/Tm2 does not vary significantly within the system, or within the composition range of interest. The average growth velocities of the stable phase into the mushy zone, V¯γδ, for the Fe–30, 40, and 50 at.% Co compositions are 1.6, 2.4, and 4.9 m/s, respectively, which scale with the thermal driving forces of the transformations, ΔTγδ, which are 10 K, 24 K, and 40 K, respectively.

Relation of microstructure, microhardness and underlying thermodynamics in molten pools of laser melting deposition processed TiC/Inconel 625 composites

Laser melting deposition (LMD) was applied to deposit nano-TiC particles reinforced Inconel 625 composite parts. The mechanisms of microstructure evolution and microhardness distinction in the different zones of the individual molten pool which was produced in LMD-processed composites were investigated. The layer-wise microstructural features of the manufactured parts were generally observed with clear outline curves of the molten pool as a result of the layer-by-layer deposition manner of the LMD shaping process. It could be observed that the microstructures in the upper part of the molten pool were mainly cellular structures, whereas which in the bottom and edge region were predominantly columnar dendrites. The increasing ratio of the temperature gradient to the solidification velocity (G/R), which resulted in a gradual change from columnar dendrite growth to cellular grain growth in the solidification regime, accounted for this phenomenon. The different sizes of cellular grains and dendrite spacing were ascribed to the varied cooling rates of diverse regions in the molten pool as well as the heat affecting nearby the overlapping zone. The factors contributing to microhardness variety could be summed up in three aspects, which were sizes of grains, TiC reinforcing particles and solid solution strengthening.

Determination of crystal growth rates during rapid solidification of polycrystalline aluminum by nano-scale spatio-temporal resolution in situ transmission electron microscopy

In situ investigations of rapid solidification in polycrystalline Al thin films were conducted using nano-scale spatio-temporal resolution dynamic transmission electron microscopy. Differences in crystal growth rates and asymmetries in melt pool development were observed as the heat extraction geometry was varied by controlling the proximity of the laser-pulse irradiation and the associated induced melt pools to the edge of the transmission electron microscopy support grid, which acts as a large heat sink. Experimental parameters have been established to maximize the reproducibility of the material response to the laser-pulse-related heating and to ensure that observations of the dynamical behavior of the metal are free from artifacts, leading to accurate interpretations and quantifiable measurements with improved precision. Interface migration rate measurements revealed solidification velocities that increased consistently from ∼1.3 m s−1 to ∼2.5 m s−1 during the rapid solidification process of the Al thin films. Under the influence of an additional large heat sink, increased crystal growth rates as high as 3.3 m s−1 have been measured. The in situ experiments also provided evidence for development of a partially melted, two-phase region prior to the onset of rapid solidification facilitated crystal growth. Using the experimental observations and associated measurements as benchmarks, finite-element modeling based calculations of the melt pool evolution after pulsed laser irradiation have been performed to obtain estimates of the temperature evolution in the thin films.

A new microsegregation model for rapid solidification multicomponent alloys and its application to single-crystal nickel-base superalloys of laser rapid directional solidification

The microsegregation in single-crystal nickel-base superalloys, which may result in many undesired precipitated phases, can be effectively reduced by rapid solidification. A new microsegregation model for rapid solidification multicomponent alloys was developed in this paper to predict the microsegregation in the single-crystal superalloys of laser rapid directional solidification and study the influence of processing parameters on the microsegregation behavior. To verify the predicted accuracy of the present model, the concentration profiles and microsegregation ranges under different processing conditions were examined and compared with those calculated by different models. Compared with previous models, this multicomponent model not only has definite physical meaning but also takes nonequilibrium solidification and dendritic tip undercooling into account. Therefore, it is suitable for a wide range of solidification conditions and can obtain better predicted results for complex multicomponent alloys. Moreover, although the microsegregation behavior depends primarily on the solidification velocity, a high temperature gradient also contributes to reducing the microsegregation. Consequently, the microsegregation can be effectively controlled by using a set of processing parameters that can obtain high temperature gradient and solidification velocity. Such a model contributes to the control of the microsegregation while determining relevant processing windows for the preparation of superalloy components using a controlled single-crystal laser processing.