The Effect of Fluid Flow on Eutectic GrowthJ.H. LEE, SHAN LIU, and R. TRIVEDIThe effect of fluid flow on eutectic microstructure is systematically examined in Al-Cu alloys of com-positions varying from 19.5 to 45.0 wt pct Cu. It is shown that significantly different fluid-flow effects are present in hypo- and hypereutectic alloys, since the modes of convection are different in these two cases. In hypoeutectic alloys, the rejected solute is copper, which is heavier than aluminum,and fluid flow gives rise to radial solute segregation in cylindrical samples. In hypereutectic alloys, a lighter aluminum is rejected that causes a double diffusive convection and gives rise to macrosegregation.These composition variations are shown to produce nonuniform microstructures that vary either radially (in hypoeutectic alloys) or axially (in hypereutectic alloys) and can give rise to a single phase–to-eutectic, lamellar-to–rod eutectic, or rod-to–lamellar eutectic transition in a given sample. Composi-tion measurements are carried out to characterize solute segregation due to fluid flow. The fluid-flow effect on eutectic spacing in eutectic or near-eutectic alloys is found to be very small, whereas it increases the eutectic spacing in hypoeutectic alloys for a given local composition and it can increase or decrease the spacing in hypereutectic alloys, depending on the microstructure and solidification fraction. Theoretical models, based on diffusive growth, are modified to predict the spatio-temporal variation in eutectic microstructure caused by fluid flow.I.INTRODUCTIONT HE theoretical model of eutectic growth under diffusivegrowth conditions is now well established for lamellar growth in three dimensions.[1]In contrast, most directional solidifica-tion experiments in bulk metallic systems are carried out under conditions where significant natural convection is present during the growth process, and the effect of fluid flow on eutectic microstructures has remained controversial. For nat-ural convection in the Bridgman system, Drevet et al .[2]and Curreri et al .[3]showed that the eutectic spacing of a sample unidirectionally solidified under microgravity is not the same as that on the ground. Drevet et al .[2]ascribed this effect to the presence of a long-range solute-boundary layer in off-eutectic alloys that is altered by the presence of fluid flow in the melt. They developed a theoretical model based on the boundary-layer concept. Although this model is applicable for laminar flow in hypereutectic Al-Cu alloys in which a lighter solute is rejected, the bulk composition in the boundary-layer model changes with solid fraction so that the spacing and microstructure will be a function of solid fraction, so that a time evolution of the eutectic pattern needs to be examined.In addition, the boundary-layer model is not applicable for large-diameter samples in which convective flows can be more complex, and it is not appropriate for hypoeutectic Al-Cu alloys in which the rejected solute is heavier and fluid flow causes significant radial variations in composition.[4]All the previous studies were carried out to characterize the effect of fluid flow on eutectic spacing only, and Curreri et al .[3]concluded that the eutectic spacing can increase,decrease, or remain constant in a low-gravity environment,depending on the alloy system. A more quantitative study is,thus, required that precisely establishes how different modes of fluid flow influence not only the spacing but also the microstructure. The aim of this article is to present the results of detailed systematic experimental studies on the effect of fluid flow on the eutectic microstructure in the Al-Cu system.Since the fluid flow gives rise to composition variations in the liquid in the radial and/or axial direction, we shall first char-acterize these composition variations and then establish how it influences the eutectic spacing, primary phase–to-eutectic transition, and lamellar-to-rod or rod-to-lamellar transition.Experiments are carried out by using two concentric cylin-drical ampoules [5,6,7]in which diffusive growth is present in the inner-capillary sample for a hypoeutectic alloy and con-vective growth is present in the larger concentric (or bulk)region. Thus, the effect of convection can be quantitatively established by comparing the results in the thin and in the bulk region. The radial and axial segregation patterns induced by convection were analyzed through composition measurements,and the effects of these composition variations on microstructure evolution were quantitatively characterized. The effect of fluid flow on eutectic spacing and on morphological transitions is analyzed quantitatively, and the necessary modifications in the models required to include the fluid-flow effect are discussed.II.EXPERIMENTAL PROCEDUREAl-Cu alloys of compositions in the range of 19.5 to 45.0wt pct Cu were examined, and this composition range is shown on the phase diagram in Figure 1. The eutectic composition is Al-33.2 wt pct Cu.[8]Experiments were carried out by using an upward Bridgman solidification technique described pre-viously.[5,6]To examine the effect of convection, a thin cylin-drical tube, Յ1.0 mm inner diameter (i.d.), was inserted inside the bulk cylindrical sample of 5.5 mm i.d., as shown in Figure 2. The growth in the capillary tube was found to be diffusive for hypoeutectic alloys, whereas convection effects were present in the concentric region. In general, the fluid-flow effect can be quite complex and can give rise to laminar,oscillating, or turbulent flow.[9,10,11]We shall only considerMETALLURGICAL AND MATERIALS TRANSACTIONS AU.S. GOVERNMENT WORKVOLUME 36A, NOVEMBER 2005—3111NOT PROTECTED BY U.S. COPYRIGHTJ.H. LEE, Associate Professor, is with the Department of Metallurgy and Materials Science, Changwon National University, Kyungnam, South Korea 741-773. SHAN LIU, Division of Materials and Engineering Physics, and R. TRIVEDI, Senior Scientist, Department of Materials Science and Engi-neering, are with Ames Laboratory, Iowa State University, Ames, IA 50011.Contact e-mail: trivedi@ Manuscript submitted April 6, 2005.3112—VOLUME 36A, NOVEMBER 2005METALLURGICAL AND MATERIALS TRANSACTIONS Alaminar flow, which can be readily analyzed and obtained experimentally by controlling the width of the concentric region, which was kept at about 2.0 mm.A seed crystal was used so that the orientations in the thin and the concentric region were the same. The orientation was usually maintained in the thin tube, but small variations in orientations were often observed in the concentric region.Only those grains in a bulk sample that had the same orien-tation as the thin sample were selected for spacing mea-surements. In this manner, the measurements in the thin and bulk samples were comparable and not influenced by the orientation effect. Microstructure observations and spacingmeasurements in the bulk region were made at three different locations, shown in Figure 2, and these locations will be referred as the inner, middle, and outer (edge) regions of the concentric region. They will be specified by the radial dis-tance (r ) from the axis of the concentric samples.The temperature gradient in the liquid at the growth interface was first characterized for different solidification rates and was found to vary from 9.0 to 11.5 K/mm for a fixed furnace temperature of T F ϭ900 °C. Solidification studies were con-ducted at relatively low solidification rates (Ͻ3.0m/s), where significant fluid-flow effects are expected and where the eutectic spacing is larger. Solidification microstructures were investigated with both optical metallography and scanning electron microscopy (SEM). The composition was analyzed using electron-probe microanalysis (EPMA). To improve the composition measurements, several standards with different compositions (Al-4.0, 20.0, 32.7, and 40.0 wt pct Cu) were used. The eutectic spacing and volume fractions of two phases were obtained by using an image analyzer. About 60 to 200individual lamellar or rod spacings were measured to determine the spacing distribution.III.EXPERIMENTAL RESULTSThe microstructure evolution in different alloy compositions was first examined under different growth rates, and the results are summarized in Table I. We shall present the results to show the effect of convection on (1) the microstructure and radial segregation, (2) the axial segregation, (3) the eutectic spacing,(4) the eutectic-interface temperature, and (5) the morphological transitionsA.Microstructural and Compositional Inhomogeneities The results on the effect of fluid flow on microstructure evolution will be presented for the eutectic alloy, the hypoeu-tectic alloys (19.5 to 30.0 wt pct Cu), and the hypereutec-tic alloys (40.0 and 45.0 wt pct Cu).1.Eutectic alloyThe microstructure in a thin sample is shown in Figure 3for an alloy of eutectic composition solidified at V ϭ1.25m/s. The SEM picture of two perpendicular sections was viewed at the edge of the two sections at 45 deg from each plane. The microstructure in the thin sample is a single crystal with some faults present in the transverse section.The orientations of the lamellae in all experiments were found to be within 1 to 5 deg from the growth direction,so that the angular correction for spacing measurement was negligible.For the measurement of individual spacings, a line scan was taken by using image-analysis software. The eutectic-spacing distributions in the thin sample and in the neighboring bulk were measured and are compared in Figure 4. The spacing dis-tributions in the thin sample and in the radially different loca-tions of the bulk sample were found to be very close, although a small shift toward a smaller spacing in the bulk edge is observed where some fluid flow is present (Figures 4(a) and (b)). The average spacing in the thin sample is 8.60 m,whereas the average spacing in the middle and outer regions of the bulk sample are 8.53 and 8.39 m, respectively. Thus,the fluid-flow effect on spacing in eutectic alloys is quite small.Fig. 1—A partial phase diagram of Al-Cu, showing the range of compo-sitions used in this study. The composition range from 19.5 to 45.0 wt pctCu encompasses both the hypo- and hypereutectic alloys.Fig. 2—A schematic drawing of the thin-tube immersion technique used in this study. Experimental observations of microstructures were made at the radial position of r ϭ0 in the thin sample and at different radial positions from the center in the bulk region, as shown by small filled circles. These three locations in the bulk will be referred to as locations 1 (inner edge),2 (middle edge), and 3 (outer edge).METALLURGICAL AND MATERIALS TRANSACTIONS AVOLUME 36A, NOVEMBER 2005—3113Table I.Directional Solidification Experiments from Hypo- to Hypereutectic Alloys (G ؍9.0 to 11.5 K/mm)Interface MicrostructureWt Pct Cu V , m/s Exp.T F (°C)f s Bulk (5.5-mm i.d.)Thin (0.8-mm i.d.)19.50.5109000.45␣D␣D 0.4129000.51RE (I.E.) ϩME (O.E.)ME 0.4138750.46␣C (I.E.) ϩME (O.E.)RE 0.311*9500.48RE RE 20.00.5219000.60␣D ␣D 0.4229000.45␣D ME 21.00.5239000.65␣D ␣D 0.4249000.56␣DRE 22.00.7198500.54␣D (I.E.) ϩME (O.E.)ME 0.5178500.51␣C (I.E.) ϩME (O.E.)ME 0.4168500.69RE (I.E.) ϩME (O.E.)ME 24.00.9209000.62␣DME 0.7189000.60␣D (I.E.) ϩME (O.E.)ME 0.5159000.55RE (I.E.) ϩME (O.E.)ME 0.4289000.45RE (I.E.) ϩME (O.E.)ME 0.3259000.70RE (I.E.) ϩME (O.E.)ME 30.00.599000.51LE LE 32.02279000.65LE LE 1269000.65LE LE 0.5319000.62LE LE 33.25E1900—LE LE 2.5E2900—LE LE 1.25E3900—LE LE 40.02359000.64C C 1349000.52C C 0.532*9000.67LE LE 45.00.5369000.66LE CAbbreviations: RE: rod eutectic, LE: lamellar eutectic, ME: rod and lamellar coexistence, ␣C and ␣D: cellular and dendritic growth of the ␣phase, C:cellular growth of the phase, I.E.: inner edge region, O.E.: outer edge region in the concentric region, and T F : furnace temperature.*A 0.6-mm-i.d. thin tube was used.Fig. 3—Three-dimensional view of eutectic growth in a 0.8-mm-i.d. thin sample.Since the effect of convection on the eutectic spacing in an alloy of eutectic composition is small, we now examine all the results on the average eutectic spacing in the bulk alloy of Al-Cu of eutectic composition, as presented in the literature.[12–16]Figure 5 shows the results over the velocity range of 0.6 to 1000 m/s, and all the data with some scatter follow the relationship V 2ϭ95 m 3/s. Through detailedexperimental studies in the Al-Cu system in thin samples with oriented single crystals, Walker et al .[1]have shown that the minimum observed spacing agrees with the theoretical value (m ) corresponding to the minimum undercooling pre-dicted by the Jackson and Hunt model.[17]The average spac-ing was shown to be given by 1.10 m . Using the values of the system parameters (Table II), the theoretical value is obtained as V ave 2ϭ91.0 m 3/s, and this predicted value is shown in Figure 5. A good match is observed except at higher rates, where slightly larger spacings are observed which could be due to the orientation effects, since the orientation was not controlled in these experiments and the average spacings were measured over several eutectic subgrains.2.Hypoeutectic alloysWhen hypoeutectic alloys were directionally solidified,significant convection effects were observed in the bulk region. The effect of convection was examined under different velocity and composition conditions. We first consider the effect of velocity, and examine the result in an Al-22.0 wt pct Cu alloy solidified at V ϭ0.4 and 0.5 m/s for the same solidification fraction. Both these velocity conditions fall within the theoretically calculated coupled zone, so that a uniform eutectic microstructure is predicted by the theory based on diffusive growth. Figures 6(a) and (b) show the microstructures (longitudinal sections) in a thin sample of 0.8 mm i.d. and in the bulk region for V ϭ0.4 and 0.5 m/s,respectively. At V ϭ0.4 m/s, both the thin sample and the3114—VOLUME 36A, NOVEMBER 2005METALLURGICAL AND MATERIALS TRANSACTIONS A(a )(b)Fig. 4—A comparison of eutectic spacing (Al-33.2 wt pct Cu, V ϭ1.25 m/s): (a ) between the thin sample and the adjacent concentric region and (b )betweenthe middle and the edge of the concentric region.Fig. 5—Comparison of the present experimental results with the previous studies on the eutectic spacing in Al-Cu alloys of eutectic composition.Table II.Physical Properties of ␣/EutecticPropertyValue ReferenceDiffusion coefficient thin: 2.4 ϫ10Ϫ97(D L ), m 2/s bulk: 3.26 ϫ10Ϫ9213.2 ϫ10Ϫ922Eutectic temperature (T E ), K821.48Eutectic composition (C E ), wt pct Cu33.28␣-phase contact angle with liquid (␣), deg7023-phase contact angle with liquid (), deg5223␣-phase Gibbs–Thomson coefficient (⌫␣), K m 2.4 ϫ10Ϫ723-phase Gibbs–Thomson coefficient (⌫␣), K m 0.55 ϫ10Ϫ723Density of ␣phase at T E (d ␣), kg/m 32.74 ϫ10318Density of phase at T E (d ), kg/m 34.0 ϫ10318␣-phase solubility at T E (C S ␣), wt pct Cu5.658-phase solubility at T E (C S ), wt pct Cu52.58Liqudius slope of ␣phase at T E (m L ␣), K/wt pct5.78Liquidus slope of phase at T E (m L ), K/wt pct4.58Solute-distribution coefficient of ␣phase at T E (k ␣)0.188Solute-distribution coefficient of phase at T E (k )0.058Volume fraction of ␣phase at T E (f ␣)0.506Volume fraction of phase at T E (f )0.494bulk region show the coupled eutectic-growth interface. How-ever, magnified views of the transverse sections show that the microstructure in the thin sample is a uniform rod eutectic,except at the edge where some coalescence of rods onto a lamellar eutectic is observed (Figure 7(a). In the bulk region,even though a coupled growth is observed across the quenched interface, a significant radial segregation is present (Figure 6(c)) that influences the eutectic morphology. In the region closer to the thin sample (i.e ., the inner edge region),the morphology is rod eutectic (Figure 7(b)), whereas at the periphery (i.e ., the outer edge region), a mixed rod and lamel-lar microstructure is observed (Figure 7(c)). The fraction of lamellar eutectic is found to increase with distance toward the outer edge of the sample.When the velocity was increased to 0.5 m/s, convection effects in the bulk region altered the microstructure quite significantly, as seen in Figure 6(b). The thin sample shows a flat coupled-growth interface, while the microstructure in the neighboring bulk shows cellular ␣growth in the region close to the thin sample and a coupled eutectic growth nearthe outer edge of the bulk. The cell length decreases radi-ally toward the periphery of the bulk sample until it becomes zero where coupled eutectic growth takes over.METALLURGICAL AND MATERIALS TRANSACTIONS AVOLUME 36A, NOVEMBER 2005—3115(a)(b )(d )(c)Fig. 6—The effect of growth velocity on microstructures in samples grown in (a ) Al-22.0 wt pct Cu (V ϭ0.4 m/s) and (b ) Al-22.0 wt pct Cu (V ϭ0.5m/s).The composition variation in solid below the eutectic interface for (c ) Al-22.0 wt pct Cu (V ϭ0.4 m/s) and (d ) Al-22.0 wt pct Cu (V ϭ0.5 m/s), showing a significant segregation in the radial direction in the concentric region.In order to correlate the morphological variations in the radial direction with the composition variations caused by fluid flow, the composition in the solid just below the quenched eutectic interface was measured, and the results are shown in Figures 6(c) and (d) for the two velocities. The compositions in thin samples were found to be very close to the initial alloy compositions, indicating that steady-state growth under a diffusive condition was present at both veloc-ities. This conclusion is also supported by the uniformity of the eutectic structure in the radial direction, as shown in Figure 7(a). In contrast, the composition in the concentric region is found to increase radially outward. The composition near the thin sample is smaller than the alloy composition,whereas it is higher than the alloy composition near the outer edge of the concentric region. This variation in compositions is similar to the earlier experimental observations in single-phase growth of Al-4.0 wt pct Cu,[4,5,6]where the composition variation in the radial direction was shown to occur due to the fluid-flow effect. Figure 6(c) shows that the composition in the bulk near the thin sample is about 19.5 wt pct Cu,which is much lower than the alloy composition of 22.0 wt pct Cu, and a rod eutectic morphology is favored. The com-position at the periphery of the bulk is 23.3 wt pct, which is higher than the nominal alloy composition, and it favors the formation of a rod/lamellar eutectic coexistence. Similarly,in Figure 6(d), the composition in the bulk near the thin sample is reduced sufficiently such that the undercooling-composition point goes outside the coupled-growth region that causes the formation of a primary phase with an inter-cellular lamellar eutectic. In both cases, the nonuniform microstructures in the radial direction can be correlated with the composition variation caused by fluid flow, as will be analyzed later.The effect of alloy composition is now examined by studying more-concentrated alloys. In the Al-24.0 wt pct Cu alloy,eutectic microstructures were observed in both the thin and the bulk region for the solidification rates of 0.4 and 0.5 m/s.The microstructure for 24.0 wt pct Cu at V ϭ0.5 m/s is shown in Figure 8(a), which is different from the microstructure in the Al-22.0 wt pct Cu alloy solidified at V ϭ0.5 m/s,although it is analogous to that in the 22.0 wt pct Cu alloy at a lower velocity of V ϭ0.4 m/s (Figure 6(a)). The eutectic morphology in the thin sample of this Al-24.0 wt pct Cu alloy was mainly lamellar, although a very small fraction of rod eutectic was also observed. For the concentric region closer to the thin sample (i.e ., the inner-edge region), the eutectic was completely rodlike, whereas at the outer edge of the concentric region, lamellar and rod eutectics occupied about 80 and 20pct of the area, respectively. For the regions in between, the rodlike region shrank and the lamellar region expanded toward the edge of the bulk. When the velocity was increased to 0.7 m/s,primary ␣-phase growth was observed in the bulk sample near the thin tube (Figure 8(b)). This microstructure is analogous to that observed in 22.0 wt pct Cu (Figure 6(b)), but it forms at a higher velocity.The radial-composition variations in the solid in the con-centric region for 24.0 wt pct Cu are shown in Figures 8(c)and (d). Similar to Figures 6(c) and (d), the fluid flow causes3116—VOLUME 36A, NOVEMBER 2005METALLURGICAL AND MATERIALS TRANSACTIONS A(a)(b )(c)Fig. 7—Magnified views of eutectic microstructures in the thin sample and in the bulk region in the Al-22.0 wt pct Cu alloy (V ϭ0.4 m/s and G ϭ8.9 K/mm).(a ) A rod eutectic microstructure in the thin sample, which forms under diffusive growth conditions. (b ) The formation of a rod eutectic in the bulk sample near the inner edge of the bulk sample (r ϭ0.8 mm). (c ) A mixed rod and lamellar microstructure at the periphery of the bulk sample (r ϭ2.7 mm). The scale bar in the upper-left corner of (b) and (c) is 200-m long.the solute composition to continuously increase radially out-ward in the concentric region, which gives rise to different morphologies in the radial direction. The measured compo-sition in the thin sample is the same as in the initial alloy composition, indicating that steady-state diffusive growth has been reached. From Figures 6(d) and 8(d), we can also deter-mine the local composition at which the transition from the leading primary phase to the coupled eutectic-growth interface occurs in the bulk region. The local composition for the tran-sition in the Al-22.0 wt pct Cu alloy, at V ϭ0.5m/s, is about 19.0 wt pct Cu, while that in the Al-24.0wt pct alloy,at V ϭ0.7 m/s, is about 22.0 wt pct Cu. These results will be used later on to determine the boundary of the coupled growth under convective conditions.The radial-composition variation in the concentric region should also result in the variation in local volume fraction of the two phases. For completely coupled growth in the hypoeutectic alloys, obtained in compositions from 21.0 to 30.0 wt pct Cu, an independent check was, thus, made bymeasuring the local volume fraction of the phase. The results are summarized in Figure 9 and are compared with the theoretical calculations (the solid line) based on the com-positions of the solid phases from the phase diagram and the densities of the ␣and phase.[18]The experimentally measured f value as a function of local composition agrees well with the computed result. These results clearly show that the local morphology and local volume fractions are related to the local composition at the interface, rather than to the initial alloy composition.3.Hypereutectic alloyExperimental studies were carried out in two hypereu-tectic alloys: Al-40.0 wt pct Cu and Al-45.0 wt pct Cu (Table I),where the convection effects were found to be significantly different from those in hypoeutectic alloys due to the rejection of a lighter Al. The rejection of a lighter solute into the bulk liquid increases the composition of Al with fraction solidi-fied until it reaches the eutectic composition. The changeMETALLURGICAL AND MATERIALS TRANSACTIONS AVOLUME 36A, NOVEMBER 2005—3117(a)(b)(c )(d)Fig. 8—Magnified views of the eutectic microstructures in thin and bulk samples: (a ) Al-24.0 wt pct Cu (V ϭ0.5 m/s and G ϭ8.9 K/mm), (b ) Al-24.0wt pct Cu (V ϭ0.7 m/s). The composition variations in the bulk for (a) and (b) are shown in (c ) and (d).Fig. 9—Change in the -phase volume percentage in the eutectic phase with the measured local composition. The solid line is calculated from the phase diagram using the densities of the ␣and phases.in bulk composition gives rise to a variation in microstructure with fraction solidified (f s ). In this experiment, an even thin-ner sample, 0.6 mm i.d., was used, and fluid-flow effects were still found to be significant.Microstructure observations were carried out on several transverse sections taken at different f s values, and the mainfeatures are shown in Figure 10 for different f s values in an Al-40.0 wt pct Cu alloy solidified at V ϭ0.5 m/s. Initially,leading primary phase is observed in both the thin and the bulk samples for 0 Ͻf s Յ0.24. Figure 10(a) corresponds to a solidification fraction f s ϭ0.22, where faceted cells of primary phase are present in the entire bulk sample, while the phase is close to disappearing in the thin sample. The eutectic microstructure between the primary phase is lamellar. With increasing f s value, the phase disappears and coupled eutectic growth occurs in the thin sample, while cells of the primary phase are still present in the bulk region,as seen in Figure 10(b) for f s ϭ0.36. When f s Ͼ0.40, cou-pled eutectic growth was observed in both the thin and the bulk sample. The cell-to-eutectic transition was found to occur at about f s ϭ0.24 in the thin sample and at about f s ϭ0.40 in the concentric region. In addition, the intercellular eutectic is lamellar, which transforms to a rod eutectic when the cells disappear, as shown in Figure 10(c) for the thin sample at f s ϭ0.28. This rod eutectic subsequently trans-forms to a lamellar eutectic as f s is increased, as shown in Figure 10(d) for f s ϭ0.64. The dynamics of the lamellar-to-rod transition and that back to lamellar is discussed in separate articles.[19,20]The dependence of microstructure on solid fraction unam-biguously shows the presence of macrosegregation induced by convection. In the bulk region, -phase cells grow uniformly over the entire cross section, i.e ., there was no observable3118—VOLUME 36A, NOVEMBER 2005METALLURGICAL AND MATERIALS TRANSACTIONS A(a)(b )(c )(d)Fig. 10—Microstructure evolution in the Al-40.0 wt pct Cu alloy solidified at V ϭ0.5 m/s: (a ) f s ϭ0.22 and (b ) f s ϭ0.36. Eutectic microstructures in thin samples showing (c ) rod eutectic formation at f s ϭ0.28 and (d ) lamellar eutectic formation at f s ϭ0.64.Fig. 11—Longitudinal and radial segregations with solidification fractions at V ϭ0.5 m/s in the hypereutectic alloy of Al-40.0 wt pct Cu.microstructure variation in the radial directions in the bulk region (Figures 10(a) and (b)). This is in strong contrast to the hypoeutectic alloys, in which radially different microstruc-tures developed (Figures 6(b) and 8(b)). A significant differ-ence in composition was also observed in the thin and the concentric regions, which were quantitatively measured and are shown in Figure 11. In concentric regions, compositions in the middle and the edge regions are the same, indicating that strong convection exists in the concentric region that causes uniform solute distribution in the radial direction. Also,the copper content decreases (or the aluminum content increases) with increasing fraction solidified, so that the far-field composition moves toward the eutectic composition. In contrast, the thin sample shows both axial and radial segre-gation when the solid fraction is less than 0.44. The copper composition near the edge of the sample is much lower than in the center region. For f s Ͼ0.44, no appreciable compositiondifference between the center and the edge is observed inMETALLURGICAL AND MATERIALS TRANSACTIONS AVOLUME 36A, NOVEMBER 2005—3119Fig. 12—Comparison of macrosegregation between an Al-22.0 wt pct Cu alloy and an Al-40.0 wt pct Cu alloy. For the hypereutectic alloy, the measurement was made in the center of a 0.6-mm-i.d. sample (Fig. 11,inverse triangle), where laminar convection was present in the melt. For the hypoeutectic alloy, the measurements were made in a 0.8-mm-i.d. thin sample where diffusive growth was present, and the growth in this samplereached a steady state when about 15 pct of the sample was solidified.Fig. 13—Solute profiles in the solid and the quenched liquid for the Al-24.0 wt pct Cu alloy directionally solidified at V ϭ0.5 m/s and G ϭ10.0K/mm. The filled circle is for a 0.8-mm-i.d. thin sample, and the open circle is for the middle of the concentric region.the thin sample. As the composition approaches the eutectic composition with increasing solidification fraction, the radial composition becomes uniform in both the thin and the large samples.B.Axial-Composition ProfilesThe variations in composition of copper in solid with frac-tion solidified in hypo- and hypereutectic alloys are compared in Figure 12, in which the axial segregation is shown for thin samples of both hyper- and hypoeutectic alloys. In hyper-eutectic alloys, the composition in the center is used and it decreases with the fraction solidified, whereas in hypoeutec-tic alloys. The composition variation showed an initial sharp increase during the transient growth, which then became con-stant after the solid fraction of about 0.12. The observation of a constant composition of eutectic in the hypoeutectic alloy,which was equal to the initial alloy composition, also shows that steady-state growth was established in thin samples.To examine the effect of fluid flow on mass transport in hypoeutectic alloys, axial-composition profiles in the thin sam-ple and in the bulk were measured in both solid and quenched liquid around the growth interface. A typical result for Al-24.0wt pct Cu, directionally solidified at V ϭ0.5m/s, is shown in Figure 13. The composition profile in the bulk region was taken at the middle point, i.e ., r ϭ1.67 mm from the center.Two important observations are made. (1) The composition in the liquid at the interface is the same, but the composition in the solid is lower in the convective regime, indicating that the composition in the solid rises slowly in presence of con-vection. (2) Both the composition profiles decay exponentially in the liquid with different decay constants that can be related to the diffusion coefficient. The diffusion coefficient in the thin sample is obtained as 2.4 ϫ10Ϫ9m 2/s, whereas the effec-tive diffusion coefficient in the bulk region is 3.2 ϫ10Ϫ9m 2/s.The increase in the effective diffusion coefficient in the bulk region comes from the additional mass transfer due to fluid flow. Recently, Lee et al .[7]have obtained similar results, and they have shown that the effective diffusion coefficient is always larger in hypoeutectic Al-Cu alloys and increases as the diameter of the sample used in the experiment is increased.The enhanced diffusion coefficient (3.2 ϫ10Ϫ9m 2/s), obtained in the concentric region of about 2.0 mm in width, is the same as that obtained by Sharp and Hellawell [21]and Jordan and Hunt [22]in 2.0 mm i.d. tubes, and we shall use this diffusion-coefficient value to analyze the results in the bulk region.C.Eutectic SpacingWe shall first consider the spacing variation in hypoeutectic alloys. Eutectic spacings were measured on the transverse section for alloys of compositions in the range 21.5to 30.0wt pct Cu. Since the eutectic spacing in the bulk sample varies significantly along the radial direction where rod and/or lamel-lar microstructures are observed, it is necessary to specify the location, local composition, and local morphology where the spacing was measured.In order to establish the effect of convection, spacing dis-tributions in the thin and bulk regions were determined in the same experiment in which the growth rate and thermal gra-dient are identical. Furthermore, the spacing in the bulk sam-ple was measured at the location where the local composition was the same as in the thin sample. Typical results for two growth conditions with different eutectic morphologies are shown in Figures 14(a) and (b). Figure 14(a) shows the spac-ing distribution for the lamellar growth with the measured local composition of 24.0 wt pct Cu, and Figure 14(b) is for the rod-eutectic growth with a local composition of 22.0 wt pct Cu. The spacings in the thin sample and the bulk follow a normal distribution, but the average spacing in the bulk is larger than that in the thin sample by a factor of 1.17 for both the rod and lamellar morphologies. Thus, convection always increases the rod or lamellar spacing in hypoeutectic alloys for the same condition of composition, velocity, and thermal gradient.In the hypereutectic alloy, the composition changes in the axial direction so that the eutectic morphology and eutectic。
