Modeling structure parameters of irregular eutectic growth: Modification of Magnin-Kurz theory

A new approach to irregular eutectic growth (faceted/nonfaceted crystallization) in Fe-C and Al-Si alloys has been presented in this article. The results of unidirectional crystallization of the irregular eutectic in the Fe-C, Al-Si, and Al-Fe systems were used for the experimental verification of the resulting model. For the oriented graphite, α(Al)-Si and α(Al)-Al₃Fe eutectics, a decrease of the interlamellar spacing λ and in protrusion δ_β of the nonfaceted phase (austenite, α(Al)) by the leading faceted phase (graphite, silicon, and Al₃Fe), the increase of growth rate v was observed. The Magnin-Kurz theory of irregular eutectic growth has been modified in order to better understand the physical mechanisms driving the crystallization process. A comparison of the measured and calculated average λ values has revealed good agreement for the (γ)Fe-graphite, α(Al)-Si, and α(Al)-Al₃Fe eutectics. The developed model also considered the influence of the material constants of the examined alloys on the interlamellar spacing and protrusion of the leading phase—graphite, silicon, and Al₃Fe. It has been found that material constants such as the wetting angle, diffusion coefficient, and Gibbs-Thomson coefficient are of great importance in this eutectic growth.     

Growth of interdendritic eutectic in directionally solidified Al-Si alloys

Interdendritic eutectic microstructures in Al-Si (6 to 12.6 wt pct Si) alloys have been investigated as a function of growth velocity and temperature gradient. The interface morphology, as well as the behavior of the eutectic spacing and undercooling, suggest that the resultant microstructure is governed by two different growth processes. That is, at low growth rates, steady-state columnar eutectic growth is found and obeys the relationship, λ²V = constant, where λ is the eutectic spacing andV is the growth rate. At higher growth rates, the nucleation of equiaxed eutectic grains occurs in the interdendritic liquid. The experimental findings are interpreted in the light of recently developed models for the columnar to equiaxed transition and for irregular eutectic growth.     

Microstructure and mechanical properties of unidirectionally solidified Al-Si-Ni ternary eutectic

Al-10.98 pct Si-4.9 pct Ni ternary eutectic alloy was unidirectionally solidified at growth rates from 1.39μm/sec to 6.95μm/sec. Binary Al-Ni and Al-Si eutectics prepared from the same purity metals were also solidified under similar conditions to characterize the growth conditions under the conditions of present study. NiAl₃ phase appeared as fibers in the binary Al-Ni eutectic and silicon appeared as irregular plates in the binary Al-Si eutectic. However, in the ternary Al-Si-Ni eutectic alloy both NiAl₃ and silicon phases appeared as irregular plates dispersed in α-Al phase, without any regular repctitive arrangement. The size and spacing of NiAl₃ and Si platelets in cone shaped colonies decreased with an increase in the growth rate of the ternary eutectic. Examination of specimen quenched during unidirectional solidification indicated that the ternary eutectic grows with a non-planar interface with both Si and NiAl₃ phases protruding into the liquid. It is concluded that it will be difficult to grow regular ternary eutectic structures even if only one phase has a high entropy of melting. The tensile strength and modulus of unidirectionally solidified Al-Si-Ni eutectic was lower than the chill cast alloys of the same composition, and decreased with a decrease in growth rate. Tensile modulus and strength of ternary Al-Si-Ni eutectic alloys was greater than binary Al-Si eutectic alloy under similar growth conditions, both in the chill cast and in unidirectionally solidified conditions.     

Microstructure and mechanical properties of unidirectionally solidified Al-Si-Ni ternary eutectic

Al-10.98 pct Si-4.9 pct Ni ternary eutectic alloy was unidirectionally solidified at growth rates from 1.39μm/sec to 6.95μm/sec. Binary Al-Ni and Al-Si eutectics prepared from the same purity metals were also solidified under similar conditions to characterize the growth conditions under the conditions of present study. NiAl₃ phase appeared as fibers in the binary Al-Ni eutectic and silicon appeared as irregular plates in the binary Al-Si eutectic. However, in the ternary Al-Si-Ni eutectic alloy both NiAl₃ and silicon phases appeared as irregular plates dispersed in α-Al phase, without any regular repctitive arrangement. The size and spacing of NiAl₃ and Si platelets in cone shaped colonies decreased with an increase in the growth rate of the ternary eutectic. Examination of specimen quenched during unidirectional solidification indicated that the ternary eutectic grows with a non-planar interface with both Si and NiAl₃ phases protruding into the liquid. It is concluded that it will be difficult to grow regular ternary eutectic structures even if only one phase has a high entropy of melting. The tensile strength and modulus of unidirectionally solidified Al-Si-Ni eutectic was lower than the chill cast alloys of the same composition, and decreased with a decrease in growth rate. Tensile modulus and strength of ternary Al-Si-Ni eutectic alloys was greater than binary Al-Si eutectic alloy under similar growth conditions, both in the chill cast and in unidirectionally solidified conditions.     

Overstability of lamellar eutectic growth below the minimum-undercooling spacing

We investigate the stability of lamellar eutectic growth by thin-sample directional solidification experiments and two-dimensional phase-field simulations. We find that lamellar patterns can be morphologically stable for spacings smaller than the minimum undercooling spacing λ _m . Key to this finding is the direct experimental measurement of the relationship between the front undercooling and spacing, which identifies λ _m independently of the Jackson and Hunt (JH) theory and of uncertainties of alloy parameters. This finding conflicts with the common belief that patterns with λ<λ _m should be unstable, which is based on the Jackson-Hunt-Cahn assumption that lamellae grow normal to the envelope of the front. Our simulation results reveal that lamellae also move parallel to this envelope to reduce spacing gradients, thereby weakly violating this assumption but strongly overstabilizing patterns for a range of spacing below λ _m that increases with G/V (temperature gradient to growth rate ratio). This range is much larger than predicted by previous stability analyses and can be significant for standard experimental conditions. An analytical expression is obtained phenomenologically, which predicts well the variation of the smallest stable spacing with G/V. We also present results that shed light on the history-dependent selection and long-time evolution of the experimentally observed range of spacings.     

Growth of interdendritic eutectic in directionally solidified Al-Si alloys

Interdendritic eutectic microstructures in Al-Si (6 to 12.6 wt pct Si) alloys have been investigated as a function of growth velocity and temperature gradient. The interface morphology, as well as the behavior of the eutectic spacing and undercooling, suggest that the resultant microstructure is governed by two different growth processes. That is, at low growth rates, steady-state columnar eutectic growth is found and obeys the relationship, λ²V = constant, where λ is the eutectic spacing andV is the growth rate. At higher growth rates, the nucleation of equiaxed eutectic grains occurs in the interdendritic liquid. The experimental findings are interpreted in the light of recently developed models for the columnar to equiaxed transition and for irregular eutectic growth.     

The Effect of Fluid Flow on the Eutectic Lamellar Spacing

The effect of fluid flow on the lamellar spacing of unidirectionally solidified Al-CuAl₂ eutectic alloy has been investigated experimentally. It was found that the practical condition for the modification of lamellar spacing can conveniently be given byPe > 1(Pe = Uλ/2D, whereU: flow rate, λ : lamellar spacing,D : solute diffusion coefficient in the melt), when the value ofU at the characteristic distance λ/8 ahead of the solid-liquid interface is used. The theoretical prediction of the relation between λ andv, given by Quenisset and Naslain, λ²v = A/(1 − BG_uλ²/D) where G_u is the flow velocity gradient at the solid-liquid interface and v is the solidification rate, was confirmed to be valid. The numerical constantsA andB are determined to be 8.46 x 10^-17 m³ per second and 1.56 × 10^-2, respectively. Associate Professor, on leave from the Department of Metallic Materials and Technology, Dalian Institute of Technology, Dalian, China.     

X-Ray Videomicroscopy Studies of Eutectic Al-Si Solidification in Al-Si-Cu

Al-Si eutectic growth has been studied in-situ for the first time using X-ray video microscopy during directional solidification (DS) in unmodified and Sr-modified Al-Si-Cu alloys. In the unmodified alloys, Si is found to grow predominantly with needle-like tip morphologies, leading a highly irregular progressing eutectic interface with subsequent nucleation and growth of Al from the Si surfaces. In the Sr-modified alloys, the eutectic reaction is strongly suppressed, occurring with low nucleation frequency at undercoolings in the range 10 K to 18 K. In order to transport Cu rejected at the eutectic front back into the melt, the modified eutectic colonies attain meso-scale interface perturbations that eventually evolve into equiaxed composite-structure cells. The eutectic front also attains short-range microscale interface perturbations consistent with the characteristics of a fibrous Si growth. Evidence was found in support of Si nucleation occurring on potent particles suspended in the melt. Yet, both with Sr-modified and unmodified alloys, Si precipitation alone was not sufficient to facilitate the eutectic reaction, which apparently required additional undercooling for Al to form at the Si-particle interfaces.     

Phase Selection and Microstructure Evolution in Nonequilibrium Solidification of Fe40Ni40B20 Alloy

Phase selection and microstructure evolution in nonequilibrium solidification of ternary eutectic Fe₄₀Ni₄₀B₂₀ alloy have been studied. It is shown that γ-(Fe, Ni) and (Fe, Ni)₃B prevail in all the as-solidified samples. No metastable phase has been found in the deeply undercooled samples. This is explained as resulting from the size effect of undercooled solidification. At small and medium undercoolings, the dendrite γ-(Fe, Ni) appears as the leading phase. This is ascribed to the existence of the skewed coupled growth zone in FeNiB alloy. With increasing undercooling, the amount of dendrites first increases and then decreases, accompanied by a transition from regular eutectic to anomalous eutectic. The formation mechanisms of the anomalous eutectics are discussed. Two kinds of microstructure refinement are found with increasing undercooling in a natural or water cooling condition. However, for melts with the same undercooling, the as-solidified microstructure refines first, and then coarsens with an increasing cooling rate. The experimental results show that the nanostructure eutectic cell has been obtained in the case of Ga-In alloy bath cooling with an initial melt undercooling of approximately 50 K (50 °C).     

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.     

Modeling of irregular eutectic microstructures in solidification of Al-Si alloys

A modified cellular automaton (MCA) model was developed and applied to simulate the evolution of solidification microstructures of both eutectic and hypoeutectic Al-Si alloys. The present MCA model considers the equilibrium and metastable equilibrium solidification processes in a multiphase system. It accounts for the aspects including the nucleation of a new phase, the growth of primary α dendrites and two eutectic solid phases from a single liquid phase, as well as the coupling between the phase transformation and solute redistribution in liquid. The effects of alloy composition and eutectic undercooling on eutectic morphology and eutectic nucleation mode were investigated. The simulated results were compared with those obtained experimentally.     

Ordering and the strength of an aligned Ag3Mg-AgMg eutectic

A fine lamellar structure with interlamellar spacings from 1 to 7μ has been produced by directional solidification of an Ag₃Mg-AgMg eutectic alloy. The tensile properties were measured as a function of test temperature, interlamellar spacing,λ, and degree of order in the Ag₃Mg phase. The dependence of flow stress onλ ^-1/2 increased sharply with ordering of Ag₃Mg and this strengthening persisted at elevated temperatures. Work hardening rate and ductility of the eutectic at low temperatures also were affected, leading to the conclusion that ordering changes the compatibility of slip across interphase boundaries.     

Directional solidification of white cast iron

Several studies of the ledeburite eutectic (Fe-Fe₃C), in pure Fe-C alloys have shown that it has a lamellar morphology under plane front growth conditions. The structure of ledeburite in white cast irons, Fe-C-Si, consists of a rod morphology. It is generally not possible to produce plane front growth of Fe-C-Si eutectic alloys in the Fe-Fe₃C form, because at the slow growth rates required for plane front growth, the Fe₃C phase is replaced by graphite. By using small additions of Te, the growth of graphite was suppressed, and the plane front growth of the ledeburite eutectic in Fe-C-Si alloys was carried out with Si levels up to 1 wt pct. It was found that the growth morphology became a faceted rod morphology at 1 wt pct Si, but in contrast to the usual rod morphology of white cast irons, the rod phase was Fe₃C rather than iron. It was shown that the usual rod morphology only forms at the sides of the two-phase cellular or dendritic growth fronts in Fe-C-Si alloys. Possible reasons for the inability of plane front directional solidification to produce the usual rod morphology in Fe-C-Si alloys are discussed. Also, data are presented on the spacing of the lamellar eutectic in pure Fe-C ledeburite, which indicates that this system does not follow the usual λ² V = constant relation of regular eutectics. Formerly Graduate Student, Department of Materials Science and Engineering, Iowa State University.     

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.     

Effect of cooling rate on the solidification behavior of Al-7 Pct Si-SiCp metal-matrix composites

The solidification behavior of two composites based on Al-Si alloy has been investigated as a function of cooling rate. Thermal analysis techniques have been used to establish the relationship between solidification history and the microstructure developed. The results of thermal analysis show that the characteristic parameters are influenced by the cooling rate. A marked difference in these parameters is observed between the reinforced and the unreinforced materials at all cooling rates studied. The cooling rates used in the present study range from 0.3 to 20 K/s. Increasing the cooling rate is shown to affect the undercooling parameters both in the liquidus and eutectic solidification region. The eutectic growth temperature of the composites is observed to be higher than that of the base alloy at all cooling rates. The depression in eutectic temperature ΔT is found to decrease by 27 K for the unreinforced alloy (A356) and by 17 K for the composites (A356 + 10, 20 vol pct SiC) at a higher cooling rate of ≃16 K/s. The presence of SiC reinforcement is observed to suppress the Mg₂Si precipitate formation and decrease the amount of heat liberated during both primary and eutectic phase formation. Dendrite arm spacing (DAS) is correlated to the cooling rate by a relationship of the form DAS =AT ^-n, wheren is found to be of the order of 0.33.     

Heterogeneous nucleation of solidification of Si by solid AI in hypoeutectic Al-Si alloy

Melt-spun Al-3 wt pct Si with and without ternary additions of Na and Sr has been heat-treated above the Al-Si eutectic temperature in a differential scanning calorimeter to form a microstructure of Al-Si eutectic liquid droplets embedded in the α-Al matrix. During subsequent cooling in the calorimeter, the heterogeneous nucleation temperature for solidification of Si in contact with the surrounding Al matrix depends sensitively on the alloy purity, with a nucleation undercooling which increases with increasing alloy purity from 9 to 63 K below the Al-Si eutectic temperature. These results are consistent with Southin’s hypothesis that low levels of trace P impurities are effective in catalyzing Si nucleation in contact with the surrounding Al matrix. With a low Al purity alloy, 0.1 wt pct Na addition increases the Si nucleation undercooling from 9 to 50 K, 0.15 wt pct Sr addition does not affect the Si nucleation temperature, and 0.3 wt pct Sr addition decreases the Si nucleation undercooling from 9 to 3 to 4 K. The solidified microstructure of the liquid Al-Si eutectic droplets embedded in the Al matrix depends on the Si nucleation undercooling. With low Si nucleation undercooling, each Al-Si eutectic liquid droplet solidifies to form one faceted Si particle; however, with high Si nucleation undercooling, each Al-Si eutectic droplet solidifies to form a large number of nonfaceted Si particles embedded in Al. Formerly with the Oxford Centre for Advanced Materials and Composites, Department of Materials, Oxford University     

Solidification of binary and Sr-modified AlSi eutectic alloys: Theoretical analysis of solute fields

This paper analyses experimental data in available literature concerning the eutectic spacing λ and growth undercooling ΔT in the AlSi binary eutectic and in the strontium-modified eutectic. The expression for ΔT obtained in Jackson and Hunt's model is used, before application of the minimum undercooling growth criterion. It is shown that, for the binary eutectic, the results can be interpreted quantitatively by means of this equation. On the other hand, it is shown that the results for the modified ally cannot be interpreted on this basis and that a contribution of the kinetic undercooling for growth of Si has to be taken into account. A high level of kinetic undercooling is found (ranging from 5 to 15 K depending on the solidification rate). This analysis also predicts a significant silicon-enrichment of the interfacial liquid, especially in the modified eutectic (up to 2 wt %).     

Interparticle spacings and undercoolings in Al-Si eutectic microstructures

Modified methods for the measurement of interparticle spacing and undercooling of the Al-Si eutectic have been applied in an attempt to test the applicability to this system of the accepted equation for diffusion-controlled normal eutectic growth. Good agreement with some published measurements has been obtained. For the unmodified and chill-modified eutectic microstructures it seems probable that the basic equation is applicable but that the extremum condition is not. For the impurity modified eutectic there is no agreement with the theoretical prediction, although the possibility is advanced of adding an undercooling term based on twin boundary energy.     

Fatigue crack propagation in two classes of directionally solidified eutectic alloys

Fatigue crack propagation rates were measured in two classes of directionally solidified eutectic alloys under isothermal, stress-controlled cycling at temperatures of 298 to 1311 K. Alloy 73C, a cobalt-base material reinforced by fibers of Cr₇C₃, and γ/γ′ + δ, a nickel-base alloy reinforced by lamellae (platelets) of Ni₃Cb, were grown at solidification rates of 1 and 25 cm/h to achieve significant differences in interfiber and interlamellar spacing (λ). No influence of the spacing of the reinforcing phase on crack growth rates were found for either alloy. In addition, chromium level and perfection of the microstructure had a minimal effect on propagation rates for γ/γ′ + δ. The independence of the fatigue crack growth rates on λ may be associated with the ratio of the cyclic plastic zone diameter at the crack tip to λ. In all instances, this ratio was estimated to be greater than one for the test conditions employed. At the lower temperatures, crack propagation rates in γ/γ′ + δ were up to two orders of magnitude lower than those in Alloy 73C due to crack deflection at interlamellar interfaces and grain boundaries which lowered the effective stress intensity range for opening mode cracking. Formerly of Pratt & Whitney Aircraft