Effect of Shrinkage on Primary Dendrite Arm Spacing during Binary Al-Si Alloy Solidification

Upward and downward directional solidification of hypoeutectic Al-Si alloys were numerically simulated inside a cylindrical container. Undercooling of the liquidus temperature prior to the solidification event was introduced in the numerical model. The finite-volume method was used to solve the energy, concentration, momentum, and continuity equations. Temperature and liquid concentrations inside the mushy zone were coupled with local equilibrium assumptions. An energy equation was applied to determine the liquid fraction inside the mushy zone while considering the temperature undercooling at the solidifying dendrite/liquid interface. Momentum and continuity equations were coupled by the SIMPLE algorithm. Flow velocity distribution at various times, G, R, λ ₁, and solidification time at mushy zone/liquid interface during solidification were predicted. The effect of shrinkage during solidification on these solidification parameters was quantified. Transient temperature distribution, solidification time for the mushy zone/liquid interface, and λ ₁ were validated by laboratory experiments. It was found that better agreement could be achieved when the fluid flow due to solidification shrinkage was considered. Considering shrinkage in upward solidification was found to only have a marginal effect on solidification parameters, such as G, R, and λ ₁; whereas, in the downward solidification, fluid flow due to shrinkage had a significant effect on these solidification parameters. Considering shrinkage during downward solidification resulted in a smaller R, stronger fluid flow, and increased solidification time at the mushy zone/liquid interface. Further, the flow pattern was significantly altered when solidification shrinkage was considered in the simulation. The effect of shrinkage on G and λ ₁ strongly depended on the instantaneous location of the mushy zone/liquid interface in the computational domain. The numerical results could be validated by experimental data only when both the undercooling of the liquidus temperature prior to solidification and fluid flow in the liquid caused by the effect of shrinkage during solidification were included in the model.     

Microstructure of Y3Al5O12 garnet solidified from the melt undercooled beyond the hypercooling limit

The microstructural evolution of Y₃Al₅O₁₂ garnet (YAG) in a wide undercooling range beyond the hypercooling limit (ΔT _hyp) was investigated by containerless solidification processing. The dendrite to cellular-dendrite transition at high-growth velocity was observed at the undercooling beyond ΔT _hyp. This transition may be explained by the hypothesis that it is difficult to form the well-developed secondary-dendritic arms from the hypercooled melt because of no remaining melt in the interdendritic regions. With a further increase in undercooling beyond ΔT _hyp, a cellular microstructure disappeared, and copious amounts of small particles appeared at an undercooling of approximately 1000 K, which is near the glass-transition temperature where the viscosity is approximately 10¹² Pas. It is suggested that multiple nucleation occurred in the highly viscous undercooled melt because of the high nucleation rate. The grain size of YAG, which was analyzed as a function of undercooling, gradually decreased with increasing undercooling even beyond ΔT _hyp, and no fragmentation of dendrites was observed.     

Steady-state cellular solidification of Al-Cu Reinforced with alumina fibers

The steady-state directional solidification of aluminum-4.5 wt pct copper and aluminum-1.0 wt pct copper alloys reinforced with parallel,continuous, closely spaced alumina fibers is investigated under growth conditions that produce a plane front or cells in corresponding unreinforced alloys. Specimens were designed to have a central reinforced region surrounded by unreinforced metal of the composite matrix composition. Each was produced by pressure infiltration, subsequently remelted, directionally solidified, and quenched to reveal the liquid/solid metal interface. Both unreinforced and composite sections were characterized to determine solidification front morphology and degree of microsegregation. In the unreinforced portion of the samples, the transition from plane-front to cellular solidification was observed to correspond to a coefficient of diffusion of copper in liquid aluminum of 5 − 10⁻⁹ m² − s⁻¹, in agreement with published values. Cell lengths, analyzed using a finite-difference model of microsegregation, are in agreement with the Bower-Brody-Flemings (BBF) model for cell tip undercooling. In the composite portion of the samples, the alloys solidify free of lateral microsegregation for all solidification conditions investigated, in agreement with theory. The shape of the liquid/solid metal interface near the fibers indicates a much lower fiber/liquid metal interfacial energy than fiber/solid metal interfacial energy. In the composite, plane front solidification is therefore not observed even when plane front solidification obtains in the unreinforced alloy. It is shown that geometrical constraint imposed on deep cells by the fibers causes significant increases in cell tip undercoolings, in agreement with current analyses of deep cell solidification.     

Last-stage solidification of alloys: Theoretical model of dendrite-arm and grain coalescence

Hot tearing in castings is closely related to the difficulty of bridging or coalescence of dendrite arms during the last stage of solidification. The details of the process determine the temperature at which a coherent solid forms; i.e., a solid that can sustain tensile stresses. Based on the disjoining-pressure concept used in fluid dynamics, a theoretical framework is established for the coalescence of primary-phase dendritic arms within a single grain or at grain boundaries. For pure substances, approaching planar liquid/solid interfaces coalesce to a grain boundary at an undercooling (ΔT _b ), given by

Predicted volume change behavior accompanying the solidification of binary alloys

For the volume changes accompanying solidification, distinctions are made between the volume changeβ _Mfor the whole freezing process, the volume changeβ _mfor liquid entrapped within the freezing zone, and the localized volume changeβ _Taccompanying the liquid-solid phase transformation at a given temperature. The first volume change is important in mold design, while the latter two are important factors in the formation of casting defects such as shrinkage pores, solidification cracks, and inverse segregation. Values ofβ _M, β_M, andβ _mare deduced for equilibrium conditions in the representative alloy systems Al-Cu, Bi-Sb, Fe-C and Pb-Sn. While the volume changeβ _Mmay vary only moderately with alloy composition,β _mis a strong function of composition and of the temperature of enclosure. The isothermal volume change,β _T, equal to the relative density difference between solid and liquid, varies during the freezing process and is strongly dependent upon composition. Isothermal volume changes and hence density differences as large as 20 pct are deduced for some Bi-Sb and Pb-Sn alloys.     

Microstructural characteristics of Ni-Sb eutectic alloys under substantial undercooling and containerless solidification conditions

Both Ni-36 wt pct Sb and Ni-52.8 wt pct Sb eutectic alloys were highly undercooled and rapidly solidified with the glass-fluxing method and drop-tube technique. Bulk samples of Ni-36 pct Sb and Ni-52.8 pct Sb eutectic alloys were undercooled by up to 225 K (0.16 T _E ) and 218 K (0.16 T _E ), respectively, with the glass-fluxing method. A transition from lamellar eutectic to anomalous eutectic was revealed beyond a critical undercooling ΔT ₁*, which was complete at an undercooling of ΔT ₂*. For Ni-36 pct Sb, ΔT ₁*≈60 K and ΔT ₂*≈218 K; for Ni-52.8 pct Sb, ΔT ₁*≈40 K and ΔT ₂*≈139 K. Under a drop-tube containerless solidification condition, the eutectic microstructures of these two eutectic alloys also exhibit such a “lamellar eutectic-anomalous eutectic” morphology transition. Meanwhile, a kind of spherical anomalous eutectic grain was found in a Ni-36 pct Sb eutectic alloy processed by the drop-tube technique, which was ascribed to the good spatial symmetry of the temperature field and concentration field caused by a reduced gravity condition during free fall. During the rapid solidification of a Ni-52.8 pct Sb eutectic alloy, surface nucleation dominates the nucleation event, even when the undercooling is relatively large. Theoretical calculations on the basis of the current eutectic growth and dendritic growth models reveal that γ-Ni₅Sb₂ dendritic growth displaces eutectic growth at large undercoolings in these two eutectic alloys. The tendency of independent nucleation of the two eutectic phases and their cooperative dendrite growth are responsible for the lamellar eutectic-anomalous eutectic microstructural transition.     

Containerless solidification of highly undercooled mullite melts: Crystal growth behavior and microstructure formation

A mullite (3Al₂O₃·2SiO₂) sample has been levitated and undercooled in an aero-acoustic levitator, so as to investigate the solidification behavior in a containerless condition. Crystal-growth velocities are measured as a function of melt undercoolings, which increase slowly with melt undercoolings up to 380 K and then increase quickly when undercoolings exceed 400 K. In order to elucidate the crystal growth and solidification behavior, the relationship of melt viscosities as a function of melt undercoolings is established on the basis of the fact that molten mullite melts are fragile, from which the atomic diffusivity is calculated via the Einstein-Stokes equation. The interface kinetics is analyzed when considering atomic diffusivities. The crystal-growth velocity vs melt undercooling is calculated based on the classical rate theory. Interestingly, two different microstructures are observed; one exhibits a straight, faceted rod without any branching with melt undercoolings up to 400 K, and the other is a feathery faceted dendrite when undercoolings exceed 400 K. The formation of these morphologies is discussed, taking into account the contributions of constitutional and kinetic undercoolings at different bulk undercoolings.     

Microstructures of undercooled Germanium droplets

Small liquid Ge droplets (0.3–0.5 mm diameter) have been undercooled 150–415 ± 20°C below T_m in B₂O₃ flux before solidifying to the diamond cubic phase. A correlation was found between initial undercooling and final grain size. Droplets undercooled <300°C exhibited a coarse grain structure. At greater undercoolings, the grain size became progressively finer. This correlation may be subsidiary to the dependence of grain size on interfacial undercooling. Ge droplets lightly doped with Sn solidified dendritically for undercoolings greater than 250°C. Twinned dendrites have been observed at small undercoolings (~ 10°C) in other experiments. It appears that larger interfacial undercoolings are necessary to grow the twin-free dendrites which we have observed. The correlation between grain size and the presence of dendrites suggests that the grain refinement observed in Ge samples undercooled > 300°C stems from dendritic break-up during solidification.     

Controlled undercooling of liquid iron in contact with Al2O3 substrates under varying oxygen partial pressures

The objective of this study was to determine the conditions under which alumina can act as a heterogeneous nucleant to initiate the solidification of undercooled liquid iron. The undercooling of a pure iron sessile droplet in contact with Al₂O₃ substrates was measured under controlled oxygen partial pressures by observing droplet recalescence. The experimental results indicated that the undercooling of liquid iron, in contact with an Al₂O₃ substrate, did not have a unique value, varied from 0 °C to 290 °C, and was significantly affected by the oxygen content of the gas phase and the degree of interaction between the oxide and the metal. Deep undercoolings are possible at low oxygen potentials, provided the oxygen potential is such that substantial substrate decomposition does not occur. The measured undercooling was a strong function of gas phase oxygen content and a maximum in undercooling of 290 °C was measured at PO₂=10⁻¹⁹ atm. The variation in undercooling was related to the wetting of the substrate by the liquid metal, where the deepest undercoolings occurred when the highest contact angle between the substrate and the liquid droplet was achieved.     

Solidification of undercooled molten Ni-based alloys

The effect of undercooling on grain structure is investigated in pure nickel, Ni₇₅Cu₂₅, and DD3 singlecrystal superalloy by employing the method of molten salt denucleating combined with thermal cycling. Meanwhile, a comparison of factors that may be related to structure formation is performed and the difference in the refined structure between Ni₇₅Cu₂₅ alloy and DD3 single-crystal superalloy is explained. Only one grain refinement occurs at the critical undercooling in pure nickel, whereas two take place at both low and high undercoolings in Ni₇₅Cu₂₅ and DD3 single-crystal superalloy melts. The first grain refinement at low undercoolings mainly originates from dendrite remelting driven by the chemical superheating produced in recalescence, and the second one at high undercoolings is due to the recrystallization process as a result of the high stress provided in the rapid solidification after high undercooling. Dislocation morphology evolution in as-solidified structure is also provided by the transmission electron microscopy (TEM) technique to further verify the recrystallization mechanism.     

High-Speed imaging and analysis of the solidification of undercooled nickel melts

Rapid solidification of undercooled pure nickel has been imaged at sufficiently high spatial resolution (64 ×X 64 pixels) and temporal resolution (40,500 frames/s) to observe interface shape and motion at solidification velocities exceeding 45 m/s. Imaging was of 8 g, quartz-enclosed melts at undercoolings of 70 to 300 K. Dendrite velocities within the melt were calculated from the surface velocities observed employing a simple geometric model of growth. Solidification was found to proceed invariably from a single nucleation point; growth velocity then followed an approximate power-law relationship with respect to undercooling up to some critical value ΔT*, where 150 K < ΔT* < 180 K. At higher undercoolings, velocity increased less rapidly than predicted by the power-law relationship and the interface morphology changed in appearance from angular to macroscopically smooth.     

Solidification kinetics and metastable phase formation in binary Ti-Al

Near-equiatomic alloys of Ti-Al were solidified at various bulk undercoolings using electromagnetic levitation. Detailed thermal histories were acquired during experiments using optical pyrometry with sampling rates as fast as 500 KHz. Solidification and other high-temperature transformation pathways were deduced from the thermal data and microstructural analysis. Re- calescence rise times were used to determine semiquantitative primary solidification kinetics for the different phases. Primary β solidification was observed at compositions well into the equi- librium α regime; this is presented as part of a near-equiatomic nucleation domain diagram mat shows the primary solidification phase (β, α, ordered γ, or disordered γ) that results for each combination of nucleation temperature and composition. Solidification kinetics are faster for primary β (V_max ≈ 15 to 18 m s^-1) than they are for primary α (V_max ≈ 10 to 12 m s^-1). For undercoolings less than about 150 K, the primary solidification kinetics are about an order of magnitude slower for γ than for α. However, at an undercooling of about 150 K, the solidi- fication kinetics for γ increase discontinuously. This discontinuity is associated with a change in the primary solidification phase from ordered γ (V_max ≈ 0.5 m s^-1) to disordered γ (V_max ≈ 10 m s^-1). formerly Doctoral Student, Vanderbilt formerly Doctoral Student, Vanderbilt formerly Doctoral Student, Vanderbilt     

Solidification of highly undercooled Fe-P alloys

Rapid solidification behavior of highly undercooled iron-phosphorus alloys was investigated by using a high-speed optical temperature measurement system. The experimental results on solidification rate as a function of bulk undercooling agree well with a model which includes a treatment of nonequilibrium effects during the solidification process. The model is based on an earlier analysis by Boettinger, Coriell, and Trivedi_[81] (BCT) and employs temperature-dependent values of equilibrium liquidus slope, equilibrium solute distribution coefficient, and solute interdiffusion coefficient. Values of the kinetic parameters,a ₀ andV ₀ , in the analysis which best fit the experimental results are 5 x 10_-10 m and 600 m/s, respectively. Comparison of experimental results and theory suggests that a transition from local equilibrium to nonequilibrium solidification takes place with increasing undercooling and that interface kinetic effects become predominant at higher undercooling (or growth velocity).     

Theory of eutectic growth under rapid solidification conditions

The Jackson-Hunt model of eutectic growth at small undercoolings is extended to large undercooling values which are commonly encountered under rapid solidification conditions. The parameters, λ²V and λΔT, are found to deviate from constant values at high velocities, and these deviations depend upon the nature of the metastable phase diagram below the eutectic temperature. A limiting velocity is predicted for the formation of a regular, coupled eutectic structure, and the reason for this limiting velocity is shown to be either the temperature dependent diffusion coefficient or the limit of undercooling.     

A solutal interaction mechanism for the columnar-to-equiaxed transition in alloy solidification

A multiphase/multiscale model is used to predict the columnar-to-equiaxed transition (CET) during solidification of binary alloys. The model consists of averaged energy and species conservation equations, coupled with nucleation and growth laws for dendritic structures. A new mechanism for the CET is proposed based on solutal interactions between the equiaxed grains and the advancing columnar front—as opposed to the commonly used mechanical blocking criterion. The resulting differences in the CET prediction are demonstrated for cases where a steady state can be assumed, and a revised isotherm velocity (V _T ) vs temperature gradient (G) map for the CET is presented. The model is validated by predicting the CET in previously performed unsteady, unidirectional solidification experiments involving Al-Si alloys of three different compositions. Good agreement is obtained between measured and predicted cooling curves. A parametric study is performed to investigate the dependence of the CET position on the nucleation undercooling and the density of nuclei in the equiaxed zone. Nucleation undercoolings are determined that provide the best agreement between measured and calculated CET positions. It is found that for all three alloy compositions, the nucleation undercoolings are very close to the maximum columnar dendrite tip undercoolings, indicating that the origin of the equiaxed grains may not be heterogeneous nucleation, but rather a breakdown or fragmentation of the columnar dendrites. An erratum to this article is available at .     

Solid-Liquid Interface Energy between Silicon Crystal and Silicon-Aluminum Melt

By examining the surface morphologies of undercooled Si-20 at. pct Al alloy during and after the solidification process, it is determined that the critical undercooling for silicon to grow from lateral mode to intermediary mode ΔT* and that from intermediary mode to continuous mode ΔT** are 131 and 239 K, respectively. A method that predicts the solid-liquid interface energy of binary lateral growth materials on the basis of ΔT* and ΔT** has been developed. Formulas between the physical parameters and the solid-liquid interface energy have been obtained. The interface energy between silicon crystal and Si-Al melt predicted from ΔT* is almost equal to that from ΔT**. The present results of the solid-liquid interface energy predicted according to ΔT* and ΔT** obtained in Si-20 at. pct Al alloy are in very good agreement with the reported results of the grain-boundary method and the critical undercooling method from ΔT* and ΔT** obtained in pure silicon.     

Microstructural investigation of a rapidly solidified 12Cr-Mo-V steel

Rapidly solidified martensitic stainless steel (11.59Cr-0.98Mo-0.28V (in wt pct) ribbons have been produced by the melt-spinning process. The microstructure of the ribbons showed three distinct zones: a columnar, a cellular, and a cellular-dendritic zone. The height of the columnar grain zone is independent of the process parameters such as the wheel material or the wheel velocity. Due to a high level of undercooling and a high growth velocity of the solid/liquid interface, the rapid solidification process is found to suppress the formation of δ-ferrite and enhance the formation of austenite. The austenite is transformed into martensite upon cooling. In comparison with conventional solidification, a reduction in the initial austenite grain size has been found to result in a very fine lath martensite (M) structure. Investigations of the texture within the ribbons along the growth direction show a weak fiber texture. Transmission electron microscopy (TEM) has revealed a [111]_M1 ‖ [001]_M2 and (011)_M1 ‖ (110)_M2 orientation relationship between two neighboring martensite laths. The observed orientation relationship is a result of a superposition of both the Kurdjumov-Sachs (K-S) and Nishiyama-Wasserman (N-W) orientation relations.