Microstructural Characteristics of Ni-Sb Eutectic Alloys under Substantial Undercooling and Containerless Solidification Conditions

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1 Microstructural Characteristics of Ni-Sb Eutectic Alloys under Substantial Undercooling and Containerless Solidification Conditions X.J. HAN and B. WEI 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 T 1 *, which was complete at an undercooling of T 2 *. For Ni-36 pct Sb, T 1 * 60 K and T 2 * 218 K; for Ni-52.8 pct Sb, T 1 * 40 K and T 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 -Ni 5 Sb 2 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. I. INTRODUCTION for containerless solidification in a reduced-gravity environment, but also has an advantage of combining high under- IN recent years, rapid eutectic solidification has aroused extensive research interest in the field of materials scitube technique can obtain larger undercoolings than the cooling with rapid cooling. [6] It is expected that the drop ence [1,2,3] in two respects. First, this phase-transformation process involves complicated microstructural evolution and glass-fluxing method. Therefore, these two methods have phase selection under nonequilibrium conditions and, thus, been frequently used to investigate the rapid eutectic offers an important research subject for fundamental study. solidification. [7 12] Second, it is a practical processing to produce in-situ composresearchers, a relatively complete system of eutectic growth Due to the laborious investigations of many pioneering ite materials, which can find many applications in industry. Up to now, the traditional rapid quenching method and theories has been established. For over three decades, the high-undercooling technique have been well developed to classic Jackson Hunt (JH) theory [13] has been proven to realize rapid solidification of alloy melts. Compared with the be the most successful eutectic model. Recently, Trivedi, rapid quenching method, the high-undercooling technique is Magnin, and Kurz (TMK) have extended the validity of the more advantageous in that it can realize bulk rapid solidificaout a new physical model [14,15] for regular lamellar eutectic JH theory to the case of a high Peclet number and worked tion of liquid metals at a slow cooling rate and, thus, provides a possible way for intensive research on rapid-solidification growth. In principle, the TMK model can describe the rapid kinetics. [3,4,5] Among various approaches to obtain high growth of highly undercooled eutectic alloy melts, provided undercoolings, the glass-fluxing method and drop-tube techever, a kind of anomalous eutectic frequently forms from that lamellar eutectic growth morphology is insured. How- nique have become two popular ones. By removing the heterogeneous particles from liquid metals through the physinvalidate the applicability of the TMK model. Therefore, undercooled melts in various alloy systems, [1 3,16] which ical adsorption of the molten glass and its chemical reaction with the heterogeneity, the glass-fluxing method makes alloy great attention has been paid to this lamellar eutectic melts achieve large undercoolings. Meanwhile, during the anomalous eutectic microstructural transition in the experi- undercooling experiment, the measurement of temperature mental work. and in-situ observation of rapid solidification is quite conveinterest, in that it contains two types of eutectic transforma- The Ni-Sb binary eutectic system is of great research nient. Drop-tube processing not only provides a technique tions, i.e., L (Ni) -Ni 5 Sb 2 and L -Ni 5 Sb 2 -NiSb. The former involves one solid solution and one X.J. HAN, Ph.D. Student, and B. WEI, Professor, Director, Laboratory intermetallic compound, whereas the latter involves two of Materials Science in Space and Director, Department of Applied Physics, intermetallic compounds. Obviously, this is quite meaningful are with the Department of Applied Physics, Northwestern Polytechnical to the investigation of the microstructural evolution of eutec- University, Xian , Shaanxi, People s Republic of China. Contact e- mail: lmss@nwpu.edu.cn tic alloys. However, so far, there have been few investiga- Manuscript submitted June 19, tions of the Ni-Sb eutectic system. METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 33A, APRIL

2 The objective of this article is to make Ni-36 wt pct Sb and Ni-52.8 wt pct Sb eutectic alloys obtain large undercoolings with the glass-fluxing method and drop-tube containerless processing technique and to reveal their microstructural characteristics under these two different solidification conditions. Theoretical calculations are also performed in terms of the current eutectic and dendritic growth models, to further understand the microstructural evolution and the rapid eutectic growth kinetics of these two eutectic alloys. Special attention has been paid to the lamellar eutectic anomalous eutectic morphology transition of these two eutectic alloys, which is explained by a competitive growth principle. II. EXPERIMENTAL METHODS After experiments, the specimens were processed according to the standard metallographic procedure. The etchant used was the solution of 1 g FeCl 3 10 ml HCl 50 ml H 2 O. An XJG-05 optical microscope and a JXA- 840 scanning electron microscope (SEM) were used to ana- lyze the microstructural characteristics. The solute concen- tration was detected with energy-dispersive spectroscope (EDS) installed on SEM. A. Undercooling Experiment The undercooling experiment was performed by the glassfluxing method with an apparatus which has been described in more detail elsewhere. [17] The boron silicate glass, with a composition of 70 pct Na 2 SiO pct Na 2 BO pct B 2 O 3 was used as a fluxing agent after having been fully dehydrated at 1173 K. All samples were in-situ prepared from pct pure Ni and pct pure Sb during the experiment, and each sample had a mass of 0.75 g. When beginning with an experiment, the sample, together with a suitable amount of glass, was contained in an 8-mm i.d. 10-mm o.d. 150 mm fused silica tube. In order to detect the starting point of solidification more accurately, two NiCr-NiSi thermal couples, which were assembled in a differential thermal analysis arrangement, were used to record the heating and cooling curves. After the sample has been superheated to 100 to 150 K above the liquidus temperature for 2 to 4 minutes, the electric resistance furnace was removed so that the sample was cooled to room temperature. In order to obtain undercoolings as large as possible, the process of superheating-cooling was repeated two to five times. Fig. 1 The upper left part of the Ni-Sb binary alloy phase diagram and the calculated eutectic coupled zones. pressure into the tube, and the alloy melt was separated into droplets of different sizes. Finally, the solidified particles were collected in the collection chamber. C. Microstructural Analysis III. RESULTS AND DISCUSSIONS A. Microstructures of Undercooled Bulk Samples B. Drop-Tube Experiment 1. Microstructural transition of Ni-36 pct Sb The containerless rapid solidification experiment was eutectic alloy accomplished in a drop tube. The drop tube is mainly com- Figure 1 illustrates the upper-left part of the Ni-Sb binary posed of a 3 m stainless steel tube, a vacuum chamber, a alloy phase diagram, [18] in which the shadowed regions are collection chamber, a set of vacuum pumps, a gas-supplying the calculated eutectic coupled zones. Obviously, under equilibrium system, and a temperature-sensing system consisting of a solidification conditions, the Ni-36 pct Sb eutectic NQO9/18C1V250 single-color infrared pyrometer and a alloy experiences the eutectic transformation L (Ni) three-pen recorder. (fcc) -Ni 5 Sb 2 (hcp) at 1377 K. According to the lever The master alloys were in-situ prepared from pct rule, a volume fraction of 21.7 pct is predicted for (Ni) pure Ni and pct pure Sb by induction heating. Each immediately after the eutectic transformation. Although fur- sample had a mass of 0.75 g and was contained in a 13-mm ther cooling leads to a peritectoid transformation at 973 K i.d. 15-mm o.d. 160 mm fused silica tube, which had and a eutectoid transformation occurs to the -Ni 5 Sb 2 phase an orifice of about 0.4 mm in diameter at its bottom. When at 798 K, the microstructure of the Ni-36 pct Sb eutectic alloy beginning with an experiment the tube was fixed in the is mainly characterized by eutectic solidification structures, induction coil installed in the vacuum chamber on top of since solid-state transformations only result in structural and the drop tube. Then, the drop tube was evacuated to a pressure compositional variations. less than Pa and backfilled with a gas mixture In the present work, bulk samples of a Ni-36 pct Sb of highly purified Ar and He to about 100 kpa. The sample eutectic alloy were undercooled by up to a maximum of 225 was melted by induction heating and superheated to about K (0.16 T E ), which is close to the undercooling level of K above its liquidus temperature, which was measured T L for homogeneous nucleation predicted by the classical by the temperature-sensing system. Finally, the alloy melt nucleation theory. A large undercooling represents a metastable was ejected out of the orifice by blowing a gas flow of high state far from thermodynamic equilibrium condition VOLUME 33A, APRIL 2002 METALLURGICAL AND MATERIALS TRANSACTIONS A

3 Fig. 3 The volume fraction of anomalous eutectic vs undercooling. volume fraction of anomalous eutectic and undercooling is presented in Figure 3. Obviously, when the undercooling exceeds a critical undercooling of about T 2 * 218 K, the sample is completely solidified as anomalous eutectic (Figure 2(c)). During experiments, it was observed that the formation of lamellar eutectic often induces weak recalescence, whereas the anomalous eutectic is always accompanied by a striking recalescence event. This, together with the fact that lamellar eutectic grows from anomalous eutectic epitaxially in a sample of intermediate undercooling range, lends support to the assumption that in the intermediate undercooling range, anomalous eutectic forms during rapid solidification and lamellar eutectic is the product of slow solidification after recalescence. [3] However, the cooling curves of those samples that show only anomalous eutectic also exhibit a thermal plateau after recalescence, although they only last for a very short period of time. This suggests that the growth of anomalous eutectic also involves two stages: the rapid growth during recalescence and the subsequent slow growth after recalescence. 2. Microstructural transition of a Ni-52.8 pct Sb eutectic alloy From Figure 1, it can be seen that the eutectic transformation L -Ni 5 Sb 2 (hcp) -NiSb (hcp) occurs in the Ni pct Sb alloy at 1355 K. According to the lever rule, Ni 5 Sb 2 occupies a volume fraction of 75.4 pct at the eutectic temperature. During the subsequent cooling process, - Fig. 2 (a) through (c) Solidification microstructures of the Ni-36 pct Sb eutectic alloy at different undercoolings. Therefore, the microstructural characteristics may be quite different from those of equilibrium conditions. Ni 5 Sb 2 experiences a eutectoid transformation at 833 K. As illustrated in Figure 2, the Ni-36 pct Sb eutectic alloy The maximum undercooling attained in the present work exhibits a lamellar eutectic anomalous eutectic microstruc- is 218 K(0.16 T E ). Similar to the Ni-36 pct Sb eutectic alloy, tural transition with the increase of undercooling, where the the microstructure of the Ni-52.8 pct Sb eutectic alloy also white phase is the intermetallic compound phase -Ni 5 Sb 2 transforms from lamellar eutectic to anomalous eutectic as and the gray phase is (Ni) solid solution. At a small undercooling, the undercooling increases. only regular lamellar eutectic forms (Figure 2(a)). Figure 4 illustrates this morphology transition of the Nithe As the undercooling increases, anomalous eutectic appears, 52.8 pct Sb eutectic alloy, where the white phase is and the microstructure is a mixture of lamellar eutectic plus NiSb intermetallic compound and the black one is -Ni 5 Sb 2 anomalous eutectic. The critical undercooling for this morphology intermetallic compound. Two undercooling thresholds have transition is about T 1 * 60 K. Figure 2(b) is the been observed. Below the lower undercooling limit of about solidification microstructure of a sample undercooled by T 1 * 40 K, lamellar eutectic is the unique growth mor- 152 K. It is noteworthy that the lamellar eutectic grows phology (Figure 4(a)). Above the upper limit of approximately from anomalous eutectic in an epitaxial way, which is an T 2 * 139 K, only anomalous eutectic can grow indication that the anomalous eutectic forms prior to lamellar (Figure 4(c)). The further increase of undercooling results eutectic. The greater the undercooling, the larger the volume in the refinement of anomalous eutectic, which is apparent fraction of anomalous eutectic. The relationship between the from a comparison of Figures 4(c) and (d). METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 33A, APRIL

4 Fig. 5 The measured and calculated lamellar spacings as a function of undercooling. and grow inward. Meanwhile, similar to the case of the Ni- 36 pct Sb eutectic alloy, the lamellar eutectic grows epitaxially from anomalous eutectic. The dependence of the volume fraction of anomalous eutectic on the undercooling is also presented in Figure 3. The lamellar spacing of the Ni-52.8 pct Sb eutectic alloy was measured and is presented in Figure 5, which illustrates the dependence of lamellar spacing on undercooling. It was observed that in those samples whose undercoolings were smaller than 40 K, the lamellar spacing decreased exponentially with the enhancement of undercooling. However, with the further increase of undercooling, the tendency was reversed, and increased gradually to a constant value of about 1.1 m. This is because the anomalous eutectic forms during recalescence once the undercooling is beyond 40 K and, thus, decreases the remnant undercooling after recalescence. When the volume fraction of anomalous eutectic exceeds a certain value, the remnant undercooling will be negligibly low. As a result, the lamellar spacing will be independent of the undercooling. The measured lamellar spacing is compared with that calculated by the JH and TMK models. It was found that the calculated lamellar spacing was smaller than the measured one, but both were of the same order in magnitude and had a similar decreasing tendency. This is understandable, since the measured lamellar spacing will be much bigger than the initial one, due to its coarsening process. Fig. 4 (a) through (d ) Solidification microstructures of Ni-52.8 pct Sb eutectic alloy at different undercoolings. In the intermediate undercooling range, both kinds of eutectic coexist (Figure 4(b)). Interestingly, many of the anomalous eutectic grains nucleate on the sample surface B. Microstructures of Drop-Tube Samples 1. Containerless solidification of the Ni-36 pct Sb eutectic alloy Droplets of 100 to 1100 m in diameter were obtained by the containerless solidification of a Ni-36 pct Sb eutectic alloy in a drop tube. Figure 6 illustrates the microstructural variation of the Ni-36 pct Sb eutectic alloy with droplet diameter. Apparently, the microstructural transition from lamellar eutectic to anomalous eutectic also occurs in the Ni-36 pct Sb eutectic alloy in the case of containerless solidification. The microstructure consisting of only lamellar eutectic was found in large droplets with a diameter above 720 m, as presented in Figure 6(a). Most droplets whose diameters 1224 VOLUME 33A, APRIL 2002 METALLURGICAL AND MATERIALS TRANSACTIONS A

5 Fig. 7 The estimated undercooling of Ni-36 pct Sb eutectic alloy vs droplet diameter. reduced-gravity condition, together with the small Rayleigh number (R a ) of the droplets, leads to the fact that the Stokes motion and buoyancy-driven convection in droplets are suppressed efficiently. As a result, the temperature transport field and concentration transport field exhibit good spatial symmetry. Thus, once the anomalous eutectic forms during rapid recalescence, the solid/liquid interface will advance outward spherically. Meanwhile, the magnitude of undercooling ahead of the solid/liquid interface will decrease because of latent heat release. Then, the growth of anomalous eutectic stops and the lamellar eutectic grows radiantly from the periphery of the anomalous eutectic. The high cooling rate, the containerless state, and the small possibility to form heterogeneities favor high undercooling in small droplets. However, it is quite difficult to determine the magnitude of undercooling experimentally in a short drop tube. Fortunately, the microstructure could be used to obtain the relevant information indirectly. For those droplets where anomalous eutectic exists, assuming an adiabatic recalescence process, the undercooling can be approximated with the following expression: T f r H m /C Pl. [1] Fig. 6 (a) through (c) Solidification microstructures of different size dropwhere f r is the volume fraction of anomalous eutectic, H m lets of Ni-36 pct Sb eutectic alloy in the drop tube experiment. is the latent heat of fusion (19,307 J/mol), and C PL is the specific heat of the liquid alloy (37.9 J/mol/K). After the determination of f r, the dependence of T on D can be are less than 720 m show a mixed microstructure of lamelestimated, as shown by the open circles in Figure 7. lar eutectic and anomalous eutectic (Figure 6(b)). The en- For droplets consisting of only lamellar eutectic, the largement of anomalous eutectic is presented in Figure 6(c). Compared with Figure 2(b), the peculiarity of the microstrucspacings with those of bulk samples prepared by the glass- undercoolings could be inferred from comparison of lamellar ture in Figure 6(b) is that the anomalous eutectic grain shows a spherical form and the lamellar eutectic radiates out from fluxing method. However, this will overestimate the magni- its periphery. This kind of spherical anomalous eutectic grain tude of undercooling, since the cooling rate of the sample has also been found in many other eutectic systems, such in the drop-tube experiment is much higher than that of the as Ag-Cu, [19] Co-Sb, [10] and Ag-Cu-Ge [20] in drop-tube conmicrostructure of droplets will be much finer than that of sample in the undercooling experiment. As a result, the final tainerless processing experiments. This phenomenon should be ascribed to the advantages of the drop tube. In a 3 m bulk samples, even at the same undercooling level. There- drop tube filled with a 1 atm gas mixture of argon and fore, the lamellar spacing of a droplet should be compared helium the residual gravity is estimated to be about 10 2 with that of bulk samples measured at the place where the 10 3 g 0 (g m 2 /s) during the free fall of droplets. The solidification initiates first. Taking this into account, the METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 33A, APRIL

6 Fig. 9 The interphase spacing of anomalous eutectic for Ni-52.8 pct Sb eutectic alloy vs droplet diameter. Fig. 8 (a) and (b) Solidification microstructures of Ni-52.8 pct Sb eutectic alloy in drop tube. undercoolings of droplets could be estimated semiquantitatively, as illustrated by the solid circles in Figure 7. Obviously, with the increase of droplet diameter, the corresponding undercooling decreases. The data fitting shows that T is related to droplet diameter by an exponential law: T e D/310.1 [2] According to the estimated dependence of undercooling on droplet diameter, a maximum undercooling of 312 K has Fig. 10 Calculated results of Ni-36 pct Sb eutectic alloy based on JH, TMK, and LKT/BCT models. diameter is less than 800 m. The microstructure is particular been obtained in the drop-tube experiment. in that the anomalous eutectic forms a network. This is caused by the fact that many -Ni 5 Sb 2 phases nucleate on 2. Containerless solidification of the Ni-52.8 pct Sb the droplet surface and grow inward. As shown in Figure eutectic alloy 9, the interphase spacings of NiSb phase in anomalous eutec- In the case of containerless solidification, the microstruc- tic are determined to be a linear function of droplet diameter: ture of only lamellar eutectic is not found in droplets of 200 to 1200 m in diameter. Over 90 pct of the droplets are a D ( m) [3] almost thoroughly occupied by anomalous eutectic, and the 3. Rapid eutectic growth rest are characterized by a mixed microstructure of lamellar So as to cast further light on the eutectic growth and the eutectic plus anomalous eutectic. Figure 8 illustrates these morphology transformation of these two eutectic alloys, both two kinds of microstructures. the classical JH eutectic growth model and the TMK rapid Figure 8(a) is the solidification microstructure of a droplet eutectic growth theory have been applied to calculate the whose diameter is about 1000 m. It can be easily seen that regular lamellar eutectic growth velocities at different underthe lamellar eutectic grows from -NiSb phase surrounding coolings. The calculated results are demonstrated in Figures -Ni 5 Sb 2 phase, which exists in a dendrite manner. Despite 10 and 11. The physical parameters used for these calculathe low fraction of lamellar eutectic, the tendency for the tions are listed in Table I. volume fraction of lamellar eutectic to decrease with the The JH model predicts that reduction of droplet size is still found to be reasonable. Therefore, the lamellar anomalous microstructural transition 2 V K 2 /K 1 [4] still occurs in the Ni-52.8 pct Sb alloy, although it is not so obvious as in the Ni-36 pct Sb alloy when processed T 2K 2 [5] in a drop tube. where K 1 and K 2 are constants determined by thermal physical Figure 8(b) is the typical microstructure of a droplet whose parameters of the considered eutectic alloy system VOLUME 33A, APRIL 2002 METALLURGICAL AND MATERIALS TRANSACTIONS A

7 Fig. 11 Calculated results of Ni-52.8 pct Sb eutectic alloy based on JH, TMK, and LKT/BCT models. T ma L 1 P [7] P ( P/ ) where a L is the capilarity constant of the alloy melt. Q L is a function of infinite series P and m is the liquidus slope. Under the assumption of k k, the TMK model yields a maximum undercooling limit of 354 K for the Ni-36 pct Sb eutectic alloy, which corresponds to a eutectic growth velocity of 2.51 m/s. With respect to the Ni-52.8 pct Sb eutectic alloy, the calculated maximum undercooling limit is 282 K and the corresponding growth velocity is 2.41 m/s. Meanwhile, the dendritic growth velocities of (Ni), - Ni 5 Sb 2, and -NiSb phase in these two undercooled eutectic alloy melts have also been calculated in the light of the Lipton-Kurz-Trivedi (LKT) [21] and Boettinger-Coriell- Trivedi (BCT) [22] dendritic growth theory. The LKT/BCT dendrite growth model consists of two principal equations. The first equation is concerned with the relationship between the bulk undercooling and the partial undercooling: Table I. Physical Parameters Used for Calculations T T c T r T k T t [8] Eutectic composition, C e 36 wt pct Sb 52.8 wt pct Sb Eutectic temperature, T e, K where T c is the solute undercooling, T t is the thermal Volume fraction of undercooling, T r is the curvature undercooling, and T k is phase, f the kinetic undercooling. The last one, which depicts the Length of eutectic line, C o, deviation from local equilibrium at the solid/liquid interface, wt pct is expressed as T k V/ VR g T 2 1/ H m V 0, V being the Equilibrium liquidus slope growth velocity, the kinetic growth coefficient, R g the gas of m, K/wt pct constant, T 1 the liquidus temperature, H m the heat fusion, Equilibrium liquidus slope and V 0 the speed of sound (V s 2000 m/s, in the case of of phase, m, K/wt pct Capilarity constant of collision-limited growth) or the atomic diffusive speed (V d phase, L D L /a 0 20 m/s, in the case of short-range-diffusion-,m K Capilarity constant of limited growth), with D L being the diffusion coefficient and phase, L,m K a 0 the characteristic diffusion length. Prefactor of diffusion coefficient, The second equation relates the dendrite-tip radius to the D o,m 2 /s marginally stable wavelength of perturbations at the solid/ Activation energy for solute liquid interface: diffusion, Q, J/mol Equilibrium partition coef- / * R H P C t t 2m [9] ficient of phase, k l C 0 (1 k) P c Equilibrium partition coefficient of phase, k PL 1 (1 k)i v (P c ) c Length scale for solute trap- ping, a o, m Here, is the Gibbs Thomson coefficient; * is the stability constant, equal to 1/4 2 ; C PL is the specific heat; P t and P c are the thermal and solutal Peclet numbers, respectively; t and c are the thermal and solutal stability functions respectively; m 1 m 1 (1 (k e k(1 ln (k/k e )))/(1 k e )) Evidently, if the solute-diffusion coefficient is assumed to maintain a constant value at the eutectic temperature, i.e., D L D 0 exp ( Q/R g T E ), the JH model gives a parabolic relation and no growth velocity limit is expected. However, once a temperature-dependent diffusion coefficient (D L D 0 ) exp ( Q/R g T ) is introduced, the JH model predicts a maximum eutectic growth velocity of 2.44 m/s at an under- cooling of 402 K for the Ni-36 pct Sb eutectic alloy. For the Ni-52.8 pct Sb eutectic alloy, the growth velocity attains its maximum of 1.85 m/s when the undercooling reaches 410 K. The TMK model describes the inter-relationship of the eutectic growth velocity (V ), the lamellar spacing ( ), and the undercooling ( T ) by the following two equations, after taking into account the nonequilibrium interface kinetics: 2 V a L /Q L [6] and m 1 is the effective and equilibrium liquidus slopes; C 0 is the alloy composition; I v (P c ) is the solutal Ivantsov function; k (k e V/V d )/(1 V/V d ) is the effective solute- distribution coefficient; and k e is the equilibrium partition coefficient. The results are also presented in Figures 10 and 11. Obviously, in both cases, if the undercooling is beyond a critical undercooling T*, the growth velocity of -Ni 5 Sb 2 dendrite will surpass that of lamellar eutectic. For the Ni-36 pct Sb eutectic alloy, T* 55 K, and, for the Ni-52.8 pct Sb eutectic alloy, T* 50 K. According to the competitive growth principle, it can be inferred that -Ni 5 Sb 2 dendrite growth in these two eutectic alloys displaces regular lamellar eutectic growth when T T*, at least at the initial stage of solidification. This, together with the relaxation of irreciprocal nucleation of the two eutectic phases, [3] which favors METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 33A, APRIL

8 6. The lamellar eutectic anomalous eutectic structural transition results from the combined influences of indepen- dent nucleation and cooperative dendrite growth of the two eutectic phases. Theoretical calculations in combina- tion with the competitive growth principle indicate that -Ni 5 Sb 2 phase is the leading phase during the formation of an anomalous eutectic microstructure in these two eutectic alloys. cooperative lamellar eutectic growth, has brought about the lamellar eutectic anomalous eutectic microstructural transition. Obviously, the theoretical predictions of the critical undercooling for lamellar eutectic anomalous eutectic morphology transition agree with the experimental results quantitatively. According to the competitive growth principle and the TMK eutectic growth and LKT/BCT dendrite growth theories, the coupled zones of these two eutectic alloys were also calculated and have been superimposed on the phase diagram, as illustrated in Figure 1. The coupled zone of the Ni-36 pct Sb eutectic alloy leans toward the Ni side and covers a composition range of to pct Sb, whereas that of the Ni-52.8 pct Sb eutectic alloy leans slightly toward the NiSb side and covers a narrower composition range, i.e., to pct Sb. In the coupled zone, the lamellar eutectic is insured. Once the eutectic alloy melt is under- cooled out of the coupled zone, anomalous eutectic appears. ACKNOWLEDGMENTS This work is financially supported by the National Natural Science Foundation of China under Grant Nos , , and and the Huo Yingdong Education Foundation under Grant No X.J. Han is indebted to Dr. N. Wang, Dr. X.Y. Lu, and Mr. W.J. Xie for helpful discussions. The authors are also grateful to Mr. Y.C. Wang for efficient assistance during experiments. IV. CONCLUSIONS REFERENCES 1. Bulk samples of Ni-36 pct Sb and Ni-52.8 pct Sb eutectic 1. R. Goetzinger, M. Barth, and D.M. 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TMS-AIME, 1966, vol. 236, pp. tion of highly undercooled eutectic alloys The special environment of the drop tube can bring about 14. R. Trivedi, P. Magnin, and W. Kurz: Acta Metall., 1987, vol. 35, pp novel microstructures. In the case of the Ni-36 pct Sb 15. W. Kurz and R. Trivedi: Metall. Trans. A, 1991, vol. 22A, pp eutectic alloy, anomalous eutectic shows spherical form 16. B. Wei, G.C. Yang, and Y.H. Zhou: Acta Metall. Mater., 1991, vol. and lamellar eutectic radiates out from its periphery. Such 39, pp a phenomenon is ascribed to the good spatial symmetry 17. C. Dong and B. Wei: J. Mater. Sci. Lett., 1996, vol. 15, pp of the temperature field and concentration field, caused 18. T. Lyman: Metals Handbook, vol. 8, Metallography Structures and Phase Diagrams, 8th ed., ASM, Metals Park, Ohio, 1973, p by a reduced-gravity condition and small Rayleigh num- 19. N. Wang, C.D. Cao, and B. Wei: Adv. Space Res., 1990, vol. 24 (10), ber in the droplets. pp For the Ni-52.8 pct Sb eutectic alloy, in both the glass- 20. N. Wang and B. Wei: J. Alloys Compounds, 2000, vol. 302, pp fluxing experiment and drop-tube containerless solidifi- 21. J. Lipton, W. Kurz, and R. Trivedi: Acta Metall., 1987, vol. 35, pp cation conditions, surface nucleation dominates the nucle- 22. W.J. Boettinger, S.R. Coriell, and R. Trivedi: Proc. 4th Conf. on Rapid ation event, even when the undercooling is relatively Solidification Processing: Principles and Technologies, R. Mehrabian large. and P.A. Parrish, eds., Claitors, Baton Rouge, LA, 1987, p VOLUME 33A, APRIL 2002 METALLURGICAL AND MATERIALS TRANSACTIONS A