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Microtexture and macrotexture formation in the containerless solidification of undercooled Ni–18.7 at.% Sn eutectic melts
Acta Materialia 53 (2005) 731–741 www.actamat-journals.com
Microtexture and macrotexture formation in the containerless solidification of undercooled Ni–18.7 at.% Sn eutectic melts Mingjun Li a
a,*
, Kosuke Nagashio b, Takehiko Ishikawa a, Shinichi Yoda a, Kazuhiko Kuribayashi b
Japan Aerospace Exploration Agency, The Institute of Space and Astronautical Science, Tsukuba Space Center, ISS Science Project Office, 2-1-1 Sengen, Tsukuba, Ibaraki 305-8505, Japan b Japan Aerospace Exploration Agency, The Institute of Space and Astronautical Science, Sagamihara Campus, 3-1-1 Yoshinodai, Sagamihara, Kanagawa 229-8510, Japan Received 14 September 2004; received in revised form 12 October 2004; accepted 13 October 2004 Available online 19 November 2004
Abstract The microscopic orientations of Ni–18.7 at.% Sn eutectics solidified from undercooled states, in particular, within an individual eutectic colony and among neighboring eutectic colonies, have been measured with respect to the eutectic Ni3Sn and Ni phases; this was done using a scanning electron microscope equipped with the electron backscatter diffraction pattern (EBSP) mapping technique. The EBSPs and inverse pole figures indicate that the Ni3Sn intermetallic compound is continuous and well oriented whereas the Ni solid solution is discontinuous and randomly oriented within an anomalous eutectic grain. Further examination reveals that although Ni particulates are random from an overall view, most neighboring Ni grains have small misorientations of less than 10. The specific solidification sequence and the effect of released crystallization heat on subsequent crystallization are further considered, which enables the primary Ni phase to segment into individual grains whereas Ni3Sn does not due to higher entropy of fusion. A little rotation or floating within the constrained framework of the crystallizing Ni3Sn compound may yield small misorientation angles. The discontinuous Ni particulates and continuous Ni3Sn network are of great significance in revealing the anomalous eutectic formation. The orientation among independent eutectic colonies is random owing to the random appearance of nuclei throughout the volume of undercooled melts. The macrotextures of pole figures (PFs) of two eutectic phases are also mapped versus melt undercooling, which can be interpreted well when considering the nucleation frequency, variation of eutectic colony size, microtexture within a single eutectic colony, and the overall microstructure evolution as a function of melt undercooling. 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Containerless processing; Nucleation; Anomalous eutectic; Crystallographic orientation; Texture formation
1. Introduction Powell and Hogan [1] undercooled various silver– copper eutectic alloys in graphite and unglazed porcelain crucibles; the alloys were processed under different atmospheric and cover conditions. From microstruc*
Corresponding author. Tel.: +81 29 868 3628; fax: +81 29 868 3957. E-mail address: [email protected] (M. Li).
tural observation they found that the anomalous eutectic consisted of discontinuous copper particles in a continuous matrix of silver. Based on this microstructure, Hogan [2] proposed that the ‘‘discontinuous’’ nature of the minor phase in anomalous eutectic indicated that it was formed by repeated nucleation after being overtaken by the faster-growing phase. However, Kattamis and Flemings [3] successively polished and then examined the parallel sections, and concluded that the minor phase, although irregular, was not particulate
1359-6454/$30.00 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2004.10.029
Ag–Cu [1]
One phase is continuous and the other is discontinuous. Both phases are continuous to form a polyhedral network. Both phases are discontinuous particulates.
Ni–Sn [3], Ag–Cu [4], Co–Sb [5], Ni–Si, Co–Sn, and Ni–Sn [6] Ni–Si, Co–Sb, and Ni–Al–Ti [7]
Repeated nucleation yields discontinuous particulates that inlay into the continuous matrix. Decoupled growth or cooperative growth of eutectic phases forms the irregular continuous network. Fragmentation of primary fine lamellae results in independent grains at the semisolid state.
Alloys Continuity characteristics
and both eutectic phases in anomalous Ni–Sn eutectic region were continuously interconnected along a polyhedral network. They proposed that the anomalous eutectic structure originated from the dendritic growth of the supersaturated a-Ni phase and subsequently, these a-Ni dendrites decomposed into a-Ni and b-Ni3Sn [3]. In accordance with this continuous model, Jones [4], after examining microstructures of several silver–copper eutectics, suggested that the anomalous eutectic originated from simultaneous uncoupled growth of the two terminal eutectic phases from undercooled melts. Based on microstructures of Co–Sb eutectic alloys, Wei et al. [5] assumed that the cooperative dendritic growth of independent phases was responsible for the formation of anomalous eutectics. It is worth noting that in both the Jones [4] and Wei et al. [5] models, there is an important unanswered question: why can decoupled growth take place when the eutectic melt is undercooled to exceed a certain undercooling. Li and Kuribayashi [6] considered the growth kinetics of terminal eutectic phases within one eutectic colony, in particular, when a nonfacetted disordered solid solution competes with a facetted ordered intermetallic compound. They proposed that the disordered phase overgrows the competing ordered phase because the collision-limited growth of the disordered phase always yields a highly mobile interface, whereas the diffusion-limited growth can only result in a sluggish interface for the competing ordered intermetallic compound. Obviously, from Jones [4] to Wei et al. [5] and finally Li and Kuribayashi [6], both eutectic phases should be continuous in these models since only growth of terminal eutectic phases was considered. In addition to these uncoupled growth models, Goetzinger et al. [7] concluded that the segmentation of primary eutectic lamellae took place during the semisolid state in Ni–Si, Co–Sb, and Ni–Al–Ti alloys by using the fragmentation model and thus the discontinuous anomalous eutectic particulates should be yielded for both phases. Table 1 summarizes the continuity features of anomalous eutectics proposed by different researchers in various alloys in literature. It should be emphasized that the conclusion that both eutectic phases are continuous was based on either the optical or the secondary electron microstructure (SEM) observation, which only depicts contrast in brightness of different phases from morphological appearance. The primary limitation of these analysis techniques is that they cannot supply any detailed orientation relation among neighboring grains. The electron back-scatter diffraction pattern (EBSP) technique is a delicate approach for microanalysis from the threedimensional view and can enable a quantitative and accurate determination of crystallographic orientations within a micrometer-scale area [8,9]. Furthermore, when the EBSP technique is combined with the SEM, the relation among neighboring grains in the area of interest can
Remarks
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Table 1 The summary of continuity features of terminal eutectic phases in anomalous eutectics after surveying literature
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be determined, which will supplement more experimental evidence in clarifying the growth mechanism. In the present paper, we employed the EBSP approach to obtain the microtexture of the anomalous eutectic in the Ni–18.7 at.% Sn alloy solidified from undercooled states. For a better understanding of the texture formation, we also employed the X-ray diffraction (XRD) technique to achieve the macrotexture development of pole figures (PFs) of two eutectic phases as a function of melt undercooling, where the diffraction area covers several square millimeters and thus generating macrotexture development. The formation of the microtexture and macrotexture was discussed when the nucleation and growth kinetics are considered, either within one eutectic colony or throughout the volume of a bulk sphere. The microtexture from the EBSPs was of great significance in deepening our understanding of the solidification mechanism, in particular the crystallization sequence and the effect of subsequent thermal release on anomalous eutectic formation.
2. Experimental procedures The Ni–18.7 at.% Sn eutectic ingot was cast in an arcmelting furnace with a water-cooled copper hearth. Pure nickel pellets and tin grains were alloyed after the Tigettered processing was conducted to consume the adsorbed oxygen. The sample was melted and turned over several times to homogenize the alloy composition completely. The prepared ingot was weighed to confirm that total mass loss was less than 1.5 wt% compared with the original metal pellets and grains. The as-cast ingot was cut into bulks weighing about 1 g for processing in an electromagnetic levitator (EML). The EML chamber was evacuated to 1 · 103 Pa and then backfilled with 5 N Ar to atmospheric pressure. A two-color pyrometer with an accuracy of better than 0.5% of measured temperature was utilized to monitor the thermal history of specimens, whose sampling rate and spot size were 100 scans/s and 1 mm in diameter, respectively. The molten sphere could crystallize at a preset temperature by controlling the overheating degree and cooling intensity. The sample was weighed again after levitation to guarantee that the mass loss was less than 1.5%, indicating that the chemical composition was the same as the original integrant. Further details on bulk sphere processing by the EML have been presented elsewhere [10]. Since the interaction depth between the electron beam and the specimen surface is on nanometer scale for EBSP analysis, the interactive layer must be relatively free of scratches so that clean patterns can be obtained. The processed sample was first sectioned on a non-contact electric discharging cutting facility and then
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the sample surface was carefully polished. The scanning step was 0.5 lm at a low magnification and 0.2 lm at a high magnification. In terms of a sample for PF mapping, it is also important to avoid yielding surface deformation and internal stresses during mechanical cutting. Therefore, the solidified bulks were sectioned with two parallel planes on the electric discharging cutting setup and then were slighted ground and polished. For accuracy, X-ray beam alignment was accomplished prior to each experimental run. The diffraction 2h angles were examined for Ni3Sn and Ni phases accurately for each specimen. Standard PF mapping was completed at those planes corresponding to high diffraction intensities for Ni3Sn and Ni phases. Here it is worth noting that the solubility of Sn in solid solution Ni can reach 10.6 at.% even at equilibrium solidification near melting temperature. However, the present analysis was accomplished at ambient temperature after the samples underwent solid phase transformations, during which precipitation would take place and thus yielding severe distortion in crystal lattice. This is why the 2h peak of present Ni deviates about 1 from that of the standard pure Ni. However, for the Ni3Sn compound, no pronounced deviation can be found in the 2h peaks since there is a comparatively small solubility of Ni in Ni3Sn and a wide solubility range of the compound at room temperature according to the Ni–Sn phase diagram [11].
3. Experimental results 3.1. Microtextural EBSP mapping Fig. 1 shows the EBSPs of the Ni–Sn eutectic solidified at about DT = 50 K. For comparison, Fig. 1(a) depicts the SEM, in which the red square indicates the area of interest for EBSP analysis. From the SEM, one can see that only one anomalous eutectic grain is included, in which the white phase is the Ni3Sn compound and the black phase is the Ni solid solution. Fig. 1(b) shows the EBSP after both phases are indexed. When Ni3Sn compound and Ni solid solution are indexed separately, the patterns are shown in Fig. 1(c) and (e), respectively. The primary Ni3Sn compound skeleton exhibits only one green color. Near the edge of the grain, a small blue area and a light brown region can be found, which may be from other colonies. The [0 0 1] partial inverse pole figure (IPF) of Ni3Sn, shown in Fig. 1(d), is consistent with the EBSP map having one primary (green) diffraction direction close to the crystallographic direction of 2 1 10 and two secondary diffraction directions, all of which have a highly textured crystallographic orientation. This
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Fig. 1. The Ni–18.7 at.% Sn eutectic specimen solidified at an undercooling of about DT = 50 K: (a) the SEM image showing one anomalous eutectic colony, in which the red square indicates the area for orientation analysis; (b) the EBSP of the anomalous eutectic colony when both Ni and Ni3Sn phases are indexed; (c) the EBSP only when Ni3Sn compound is indexed with one primary green color in the colony; (d) the [0 0 1] IPF of the Ni3Sn compound with a well oriented texture; (e) the EBSP only when Ni solid solution is indexed with various colors; (f) the IPF of corresponding Ni particulates showing a random texture.
reveals that the Ni3Sn phase has only one crystallographic orientation in terms of the green Ni3Sn phase and thus has a continuous network within the anomalous eutectic grain. However, when the Ni solid solution is indexed, the particulate phase exhibits a colorful pattern, as shown in Fig. 1(e). The [0 0 1] IPF of Ni phase exhibits a random distribution; no preference in diffraction directions can be found in Fig. 1(f). Both the EBSP and the
IPF indicate that the Ni phase is discrete even within one eutectic colony. Fig. 2(a) depicts a similar SEM with an anomalous eutectic grain surrounded by regular lamellae. However, when the Ni3Sn phase is indexed by EBSP mapping, the anomalous eutectic area contains eight different subregions as numbered in Fig. 2(c). The IPF of the Ni3Sn phase, shown in Fig. 2(d), contains several diffraction
Fig. 2. The Ni–Sn eutectic specimen solidified at about T = 50 K: (a) shows the SEM of another anomalous eutectic colony with a similar morphological appearance in Fig. 1(a), in which the red square indicates the area for orientation mapping; (b) the EBSP of the area when both Ni and Ni3Sn phases are indexed; (c) the EBSP only when Ni3Sn is indexed with eight separate eutectic colonies; (d) the [0 0 1] IPF of the Ni3Sn compound with oriented textures; (e) the EBSP only when Ni is indexed with many colorful grains; (f) the IPF of Ni particulates showing a fully random texture.
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directions, with the green sub-region #8 having a similar orientation as that primarily indexed in Fig. 1(c) and (d) near to the direction of 2 1 10. Region #6 is blue, which is quite different from its surroundings. Similar to Fig. 1(d) for Ni particulates, Ni phase embedded in the Ni3Sn matrix still exhibits a colorful pattern. The IPF shows that the distribution of these particulates is completely random, which provides convincing evidence that Ni grains within anomalous eutectic regions are discrete regardless of the relation of eutectic colonies. 3.2. Macrotextural PFs development versus melt undercooling Fig. 3 shows the PFs development of the Ni3Sn and Ni phase versus melt undercooling. The PFs for Ni3Sn phase was obtained at 2h = 44.88, which corresponds to the peak of (2 0 1) with the maximum intensity. The macrotexture of the phase exhibits a random distribution from a low to a high undercooling level from an overall view. The only difference is that with the increase of melt undercooling, the diffraction intensity in a certain direction is increased, which is characterized by the number of poles at the diffraction position. In the meanwhile, the number of independent poles increases with the increase of melt undercooling. When the melt is undercooled to the highest undercooling of about 210 K, almost all diffraction patterns exhibit independent poles, distributing randomly throughout of the normal and transverse directions.
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In addition to the texture obtained at 2h = 44.88, we have also measured macrotextures of the Ni3Sn compound at 2h = 39.26 and 42.54, which reveal almost the same evolution tendency as that at 2h = 44.88 at different undercooling levels, indicating that the distribution of the Ni3Sn phase is random at all these three diffraction planes. To avoid repeating, we omit the macrotexture development obtained at 2h = 39.26 and 42.54. The PFs of Ni solid solution were obtained at 2h = 43.40, corresponding to the (1 1 1) plane with the highest intensity. The Ni phase in texture development has the same characteristics as that of Ni3Sn with regard to overall orientation; there is no preferential distribution and the texture is random. However, in terms of number of individual poles and the intensity variation versus melt undercooling, the macrotexture of Ni is completely contrary to that of Ni3Sn, consisting of several independent poles at a low undercooling of about DT = 20 K and then the number of individual poles increasing when the melt is undercooled to DT = 60 K. Further increase of melt undercooling to about 160 K results in a completely random distribution without any intensified poles at any direction in the diffraction plane, as shown in Fig. 3(c 0 ). When the melt is undercooled to the deepest undercooling of DT = 210 K, the macrotexture also is random, as mapped in Fig. 3(d 0 ). Note that in all these PFs, the relative intensity levels are maintained at the same level in order to make these PFs comparable.
Fig. 3. The macrotexture PFs of Ni3Sn compound and Ni solid solution versus melt undercooling of about: (a) DT = 20 K; (b) DT = 60 K; (c) DT = 160 K; (d) DT = 210 K. The diffraction angles for Ni3Sn and Ni phases are 2h = 44.88 and 43.40, respectively, corresponding to the (2 0 1) plane for Ni3Sn and (1 1 1) for Ni, both of which are at their highest intensity.
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4. Discussion 4.1. Microtexture formation in anomalous eutectics The present EBSP mapping indicates that only the Ni3Sn phase is continuous within one anomalous eutectic grain whereas the Ni phase is discontinuous, which differs from observations and models of Kattamis and Flemings [3], Jones [4], Wei et al. [5] and Li and Kuribayahsi [6]. This controversy should be attributed to the limitation of analysis technique, either by the optical or the SEM observation. A good example to verify this idea is that Figs. 1(a) and 2(a) have almost the same SEMs, however, EBSPs reveal that there is only one eutectic grain in Fig. 1(a) whereas eight independent eutectic colonies are contained in Fig. 2(a) in terms of Ni3Sn skeletons. In order to have a further understanding on the formation of an anomalous eutectic grain, we should first enlarge a central region within an anomalous eutectic grain, as marked in Fig. 2(a) by the green square. The SEM, EBSPs, and corresponding IFPs are depicted in Fig. 4. The Ni3Sn phase shows one diffraction direction from the EBSP and IPF, consistent with the SEM, in which the bright phase forms the matrix. For convenience, Ni particulates are numbered in Fig. 4(e). Only from the SEM, several connecting parts can be found, e.g. grain #1 and grain #2 (thereafter only the number with the mark # is used), #13 and #14, which should share the same orientation if they are really continuous within a complete one grain. However, from the EBSP, different orientations arise between #1 and #2, #13 and
#14 in color contrast, indicating that #1 and #2 are independent and discrete. This investigation once again confirms that the conclusion based on the optical or SEM observation is not reliable with respect to the continuity feature of crystals. It is this discrete feature of the Ni particulates that results in the random orientation, as depicted by IPF in Fig. 4(f). Since the Ni particulates are independent grains, it is important to know the misorientation degree among neighboring grains. Fig. 5(a) outlines misorientation degrees and Fig. 5(b) shows the number fraction versus misorientation angles. The number fraction is calculated when the number counted within the misorientation angle is divided by the total number counted within the area. If each Ni grain is formed from an independent nucleus within the interstitial space in the anomalous eutectic colony, as Hogan [2] suggested in Ag–Cu alloys, these Ni particulates should have a fully random distribution with an equal probability in misorientation angle distribution even among neighboring grains. However, among the misorientation angles of neighboring grains, nearly 50% are less than 10 and about 30% are around 60. Considering that #11 and #12, #36 and #37 are two grains with typical twins owing to stacking fault during growth for the cubic Ni phase, which should be treated as one grain, the proportion with small misorientation angle is further increased. This indicates that although these grains are discrete from an overall view, most of neighboring grains have similar orientations. One example is that five out of six misorientation angles are less than 10 between grain #1 and its neighboring grains. Actually, similar situations can be found in col-
Fig. 4. A magnified region within one anomalous eutectic colony: (a) the SEM of the area corresponds the green square in Fig. 2(a); (b) the EBSP of the area when both Ni and Ni3Sn phases are indexed; (c) the EBSP when Ni3Sn is indexed with only one color; (d) the [0 0 1] IPF of the Ni3Sn compound with only one diffraction direction; (e) the EBSP when Ni is indexed with colorful grains; (f) the IPF of Ni particulates.
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Fig. 5. Further detailed misorientation analysis within the small area: (a) the data straddling two numbers in parentheses are the misorientation angles and the number within parentheses corresponds to the Ni grain position numbered in Fig. 4(e); (b) the number fraction of neighboring Ni grains within the area of interest as a function of misorientation angle.
ony #2 and colony #3 with green particulates and colony #6 with blue particulates in Fig. 2(c) and (e), which should share similar crystallographic direction with small misorientations, i.e. at least most of neighboring Ni grains should not have a complete random misorientation. Here, it is worth noting that Li and Kuribayashi [6] only outlined the critical condition under which the decoupled growth can occur, but they did not consider the subsequent solidification behavior, i.e. solidification sequence, thermal release, and its influence on the as-solidified primary phase at the semi-solid state. Here, we consider this sequence and subsequent effects as follows: when Ni overgrows Ni3Sn compound, irregular Ni skeleton is formed owing to the limitation in chemical composition of the eutectic. Note that this irregular cylinder-like Ni skeleton in three dimensions can not form a closed chamber, which enables remaining liquids with Sn-riched composition connecting to form a continuous net when they are pushed to occupy the interstitial place, i.e. the primary Ni is immersing in remaining liquids after decoupled growth takes place. The solidification of the Ni3Sn compound begins and its crystallization heat, together with the crystallization heat from solidified Ni, is dissipated to heat the primary Ni and crystallizing Ni3Sn, which may favor the primary Ni dendrite to segment into fragments. Note that at this stage, it is difficult for the fragmented Ni particulates
to rotate, move, or float freely throughout the entire volume of the melt because of the crystallizing frame of Ni3Sn phase. Therefore, only a little rotation or displacement may be favored owing to the stirring effect of electromagnetic force. This is why most neighboring Ni fragments have small misorientation angles less than 10. Actually, we also checked the misorientation angles between two grains with a large distance, e.g. 48 between #22 and #29, 30 between #27 and #32 in Fig. 4(e). Since the breakup fragment cannot float freely within the entire bulk, the misorientation relation between two far grains is of less interest in revealing solidification mechanism. Except Ni twin with a misorientation angle of 60, the accurate angle between (1 1 1) and (0 0 1) in Ni is 54.7, which may be responsible for the second important number faction with misorientation angles around 60 after particulates have some rotation or displacement. Considering this solidification sequence, it is understandable that Ni phase exhibits a random distribution from an overall view. This brings us to the next question: why Ni can fragment into independent particulates whereas Ni3Sn cannot. This can be simply interpreted from KarmaÕs fragmentation model [12], which was developed for a single-phase dendrite with a paraboloid tip when considering the capillarity effect and supersaturation inside the trunk. Since the unconstrained growth behavior of Ni is similar to that of Ni-based dendrite after decoupled
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growth occurs in the eutectic [6], here it is assumed that all assumptions in the fragmentation model can be applied to the primary Ni in the eutectic and then we employ the fragmentation model to explain why Ni is readily to fragment whereas Ni3Sn is not. The characteristic time for breakup of dendrites, Dtb, can be expressed in a first approximation as below [12]: 3 ð20RÞ DS f T m C p ml c0 ð1 k e Þ at 1 Dtb ; ð1Þ DS f T m CC p at D where R is the radius of dendrite tip, DSf is entropy of fusion, Tm is melting temperature, C is the Gibbs– Thomson coefficient, Cp is the specific heat, at is the thermal diffusivity, ml is the slope of liquidus, c0 is the chemical composition, ke is the equilibrium partition coefficient, and D is the chemical diffusion coefficient. In terms of Ni and Ni3Sn phases at the eutectic composition, R, Tm, C, Cp, at, D, ml, ke, and c0 are irrelevant to crystalline structure and have comparable values whereas only DSf is strongly dependent on crystal structure. The entropy of fusion of Ni3Sn compound, DSf(Ni3Sn), can be approximately calculated from the entropy of fusion of Ni–18.7 at.% Sn eutectic, which is 48.04 J mol1 K1 [13]. Considering the volume fractions of Ni and Ni3Sn phases, together with the entropy of fusion of Ni, DSf (Ni) = 10.1 J mol1 K1 [14], it follows DSf (Ni3Sn) = 65.54 J mol1 K1, about six times higher than that of Ni solid solution, which is reasonable for the facetted intermetallic compound when the mixture entropy of both phases is neglected. Another assumption in calculating entropy of fusion is that there is no significant difference in DSf for pure Ni and Ni solution, stoichiometric Ni3Sn and Ni3Sn with certain solubility. Note that DSf is in pre-factor and denomina-
tor in Eq. (1), the breakup time for Ni3Sn phase should be about 10 times longer than that for Ni. The other reason is that unlike primary Ni immersing into the remaining liquid, no remaining liquid can be found to generate capillarity force after the Ni3Sn phase solidifies; there is no driving force to fragment. This is why Ni can readily fragment into pieces whereas Ni3Sn cannot, which may be owing to insufficient time and absent driving force for breakup in an anomalous eutectic grain. The dissipation of crystallization heat from Ni and Ni3Sn can lead to the fragmentation of Ni within the central part in an anomalous eutectic colony. In the meanwhile, it can increase temperature of remaining liquid ahead of growing interface to lower the interface undercooling and thus enabling regular eutectic lamellae to develop from the periphery of the anomalous eutectic grain, as observed in many eutectic systems [5,6,10,13]. After examining the central part, we should investigate the microtexture near the edge of an anomalous eutectic grain. The EBSPs, together with SEM and IPFs, are shown in Fig. 6, in which two colonies are included, as indicated in Fig. 6(c) and (d). From the indexed Ni3Sn pattern, one can see that Ni3Sn phase in each respective colony exhibits a continuous feature not only at anomalous region, but also shares the same orientation at regular lamellar region. A minor difference in Ni3Sn phase color, typically marked by #1 and #2, arises, which is originated from a small misorientation angle with about 2 between these neighboring parts. Here, it should be noted that solidification is accomplished at high temperatures whereas analysis is operated at ambient temperatures. In terms of the solid solution Ni, there is no structure transformation but only precipitation during cooling.
Fig. 6. Near the edge of the anomalous eutectic region with a hybrid microstructure of anomalous and regular lamellae: (a) depicts the SEM with a red square for the EBSP mapping; (b) shows the EBSP when both Ni and Ni3Sn phases are indexed; (c) the EBSP only when Ni3Sn compound is indexed with two individual colonies; (d) the IPF of the Ni3Sn compound with two diffraction directions; (e) the EBSP only when Ni solid solution is indexed, which are primarily blue; (f) the IPF of corresponding Ni particulates showing a biased texture to the direction of 1 1 1.
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However, the high-temperature Ni3Sn phase must transform to the low-temperature Ni3Sn counterpart with a D019 structure at 1250 K when it is cooled down [11]. Note that the growth of regular lamellae in free solidification is a non-steady state process, as Trivedi et al. [15] recently analyzed in atomized Al–Si eutectics, this may lead to a heterogeneous distribution in solute and internal stress. These non-uniformity characteristics may influence the massive phase transformation process during cooling and thus generating small-angle misorientations within one Ni3Sn network. Similar situations can be found in the same colony and the neighboring colony as marked by #3 and #4, with misorientations of about 2–5. Fragmented Ni particulates near lamellae region within the anomalous eutectic grain, as circled by the dashed line in Fig. 6(e), have small misorientation angles, from several of which Ni lamellae grow with small misorientation angles, covering from light blue to deep blue in color. When the lamellar Ni is further examined, five regions, as marked in Fig. 6(e), can be classified, where the misorientation angle within each region is less than 0.8, which falls into the tolerance of the facility. Obviously, the Ni lamellae, for instance, in region #1, have only one orientation, which should be owing to the radiated growth of lamellae originating from one fragmented Ni particulate. This investigation verifies that fragmentation does not occur during lamellar Ni growth, which differs from that within an anomalous eutectic grain. In developing the fragmentation model, one necessary condition is that primary dendrite should immerse into the remaining liquid so that breakup can occur due to a Rayleigh-like instability of the dendritic morphology. However, for alternative eutectic lamellae growing in a coupled manner, no remaining liquid can be found since the lamellae contact closely side by side. Therefore, no driving force can be generated to fragment the lamellae in terms of capillarity effect. This is why these fine Ni lamellae, as marked in Fig. 6(e), share the same orientation in each region. Based on the fragmentation model, Goetzinger et al. [7] concluded that the primary lamellae can segment into spherical elements and thus anomalous eutectics are formed from the breakup of the cylindrical phase, which should result in a random distribution for both Ni and Ni3Sn phases. However, our observation and analysis indicate that only Ni is readily to fragment whereas Ni3Sn is difficult owing to higher entropy of fusion. Furthermore, fine Ni lamellae from one Ni grain have one orientation and cannot fragment because of the absence of driving force. Obviously, their proposed model [7] is contradictory to theoretical analysis and experimental facts. After discussing the orientation relation within one eutectic grain, from center to edge, we should consider
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the inter-relation of individual eutectic colonies. Fig. 7 shows the misorientation angles of the Ni3Sn phase among independent eutectic colonies. The positions of eutectic colonies are numbered in parentheses with the mark, corresponding to those in Fig. 2(c). Obviously, the misorientation angles cover a wide range from several degrees to more than 80, indicating that these eutectic colonies are randomly distributed. Further examination of some other parts reveals a similar distribution with a random orientation of independent eutectic colonies in terms of individual Ni3Sn colonies. Since copious or massive nucleation occurs in the undercooled Ni–Sn eutectic melts [10], the random distribution of independent nuclei leads to the development of separate eutectic colonies, which, of course, should have a random distribution without any preferential orientation. 4.2. Macrotextural development as a function of melt undercooling When we have a full understanding of microtexture formation in separate eutectic colonies, we shall come to the macrotexture formation of the eutectic versus melt undercooling, which should be the sum of microtextures within the macro area of interest. As indicated by Fig. 3, the macrotexture of both Ni3Sn and Ni phases is random from an overall view within the undercooling range attainable in the present experiments, which should be owing to the random distribution of nuclei in undercooled melts, from which independent eutectic colonies can develop. In terms of the macrotexture of Ni3Sn phase versus melt undercooling, it can be interpreted when nucleation frequency is considered as a function of melt undercooling. At low undercoolings, the nucleation rate is low and the duration time near eutectic melting point after
22.6 (#7) 52.6 (#5) 36.7 (#8) 32.9 81.9 82.2 81.0 50.3 36 (#6) 6.0 28.5 76.6 81.5
(#4)18.2 26.8
(#3)
36.2 (#1)
85.8
31.4
37.3
(#2) Fig. 7. The misorientation angles of the Ni3Sn phase among neighboring continuous networks. The data straddling two numbers in parentheses are the misorientation angles and the number within parentheses corresponds to the position of Ni3Sn colonies numbered in Fig. 2(c).
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recalescence is rather long, which favors a full development of eutectic colonies and thus yielding large eutectic colonies with about hundreds micrometers in diameter, as we have reexamined elsewhere [10]. Only a few random eutectic colonies may be included within the diffraction area. With the increase of melt undercooling, the nucleation rate increases and eutectic colony size decreases to tens of micrometers. Although the distribution of nuclei is random from an overall view, the increased total number in eutectic colonies within the diffraction area will correspondingly increase the number of those colonies having a similar crystallographic orientation; i.e. with one diffraction direction, the number of eutectic colonies may increase, which should result in improved diffraction intensity at this direction. Indeed, one can find that number of poles increases when the melt is deeply undercooled from DT = 60 to 160 K and finally DT = 210 K, as shown in Fig. 3. With respect to the macrotexture evolution of Ni phase versus melt undercooling, we should consider both nucleation and solidification sequence, in particular the fragmentation of Ni in an anomalous eutectic grain. When the melt undercooling is less than about DT = 45 K, only regular Ni lamellae can grow, which share one orientation within one eutectic colony if they originate from one nucleus, as discussed in Section 4.1. Since large eutectic colonies will be formed randomly at low undercoolings, only several random poles can be observed in Fig. 3(a 0 ). When the melt undercooling is increased to about DT = 60 K, more eutectic colonies will be contained in the diffraction area and thus more diffraction poles appear, similar to that of Ni3Sn phase with improved intensity, as evidenced by the increased number of poles at a certain diffraction direction. When the melt undercooling is beyond DT = 120 K, only unique anomalous eutectic will be yielded [10]. Considering that the discrete Ni grains have random orientations even within one anomalous eutectic colony, it is no wonder that the macrotexture is fully random at about DT = 160 K. Similar random distribution can be found when the melt is solidified at the maximum undercooling of DT = 210 K. Note that at high undercoolings, the macrotexture of Ni3Sn phase differs from that of Ni phase with regard to pole numbers and intensity, this should be owing to a pronounced difference of their microtextures, i.e. Ni3Sn exhibits a continuous network whereas Ni does not.
solid solution is discontinuous and thus has a random distribution even within one anomalous eutectic colony. The random distribution of Ni particulates should be attributed to the fragmentation of primary Ni dendrite when considering solidification sequence. Because of the spatial limitation of the crystallizing Ni3Sn in configuration, it is impossible for the fragmented Ni particulates to move freely but with a small rotation or floating and thus resulting in small misorientation angles, frequently less than 10, among most neighboring Ni grains. In contrast, the Ni3Sn intermetallic compound is continuous and thus well oriented within one anomalous eutectic colony, i.e. fragmentation of the Ni3Sn compound does not take place, which may be due to higher entropy of fusion of the compound and absence of driving force to fragment compared with the Ni phase. The discontinuous Ni particulates and continuous Ni3Sn network within the anomalous eutectic colony are of great significance in improving our understanding of anomalous eutectic formation since the previous models and analysis were based on the fundamental idea that both eutectic phases were continuously interconnected along a polyhedral network. This indicates that an optical microstructure or an SEM cannot provide convincing evidence for the continuity feature of a phase. In the meantime, the present examination by EBSPs excludes the mechanism that anomalous eutectic is formed via the fragmentation of primary fine eutectic lamellae, which should result in a random distribution for both Ni and Ni3Sn within one anomalous eutectic colony. Fine Ni lamellae at the edge of an anomalous eutectic grain share one orientation if they originate from one Ni particulate. Fragmentation cannot occur because of the absence of driving force when the alternative Ni and Ni3Sn lamellae grow in a coupled manner with a planar front. The random relation among independent eutectic colonies should be induced by the random appearance of nuclei throughout the volume of undercooled melts, which leads to a random distribution in macrotextures of two eutectic phases versus melt undercooling from an overall view. Further subtle difference in pole numbers and diffraction intensity in macrotextures can be well interpreted when considering the nucleation frequency, variation of eutectic colony size, microtexture within a single eutectic colony, and microstructure evolution as a function of melt undercooling.
5. Conclusions The microtextures of Ni3Sn and Ni terminal eutectic phases, in particular, in anomalous eutectic grains, were revealed when the Ni–18.7 at.% Sn eutectic melts were containerlessly solidified from undercooled states. The EBSPs and IPFs of eutectic phases indicate that the Ni
Acknowledgements Partial experimental work was completed when one of the authors (M. Li) held the Foreign Research Fellowship from the Japan Aerospace Exploration Agency
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(formerly the Institute of Space and Astronautical Science, which was renamed after it was merged with the National Space Development Agency of Japan and National Aerospace Laboratory of Japan). Sincere thanks are also due to Dr. K. Kitazono and Dr. S. Ozawa for their technical assistance in pole figure measurement. We acknowledge Dr. Y. Arai and Dr. J. Yu for their interest in the present work. References [1] Powell GL, Hogan LM. J Inst Met 1965;93:505. [2] Hogan LM. J Aust Inst Met 1964;9:228. [3] Kattamis TZ, Flemings MC. Metall Trans 1970;1:1449.
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[4] Jones BL. Metall Trans 1971;2:2950. [5] Wei B, Herlach DM, Feuerbacher B, Sommer F. Acta Metall Mater 1993;41:1801. [6] Li M, Kuribayashi K. Metall Mater Trans A 2003;34:2999. [7] Goetzinger R, Barth M, Herlach DM. Acta Mater 1998;46: 1647. [8] Dingley DJ, Randle V. J Mater Sci 1992;27:4545. [9] Humphreys FJ. J Mater Sci 2001;36:3833. [10] Li M, Nagashio K, Kuribayashi K. Acta Mater 2002;50:3239. [11] Nash P, Nash A. In: Massalski TB, editor. Binary alloy phase diagrams, 2nd ed., vol. 2. ASM International Materials Park (OH): The Materials Information Society; 1996. p. 2863. [12] Karma A. Int J Non-Equilib Pr 1998;11:201. [13] Wei B, Yang G, Zhou Y. Acta Metall Mater 1991;39:1249. [14] Lide DR, editor. CRC handbook of chemistry and physics. 78th ed. Boca Raton: CRC Press; 1997. p. 6–120. [15] Trivedi R, Jin F, Anderson IE. Acta Mater 2003;51:289.
Microtexture and macrotexture formation in the containerless solidification of undercooled Ni–18.7 at.% Sn eutectic melts Mingjun Li a
a,*
, Kosuke Nagashio b, Takehiko Ishikawa a, Shinichi Yoda a, Kazuhiko Kuribayashi b
Japan Aerospace Exploration Agency, The Institute of Space and Astronautical Science, Tsukuba Space Center, ISS Science Project Office, 2-1-1 Sengen, Tsukuba, Ibaraki 305-8505, Japan b Japan Aerospace Exploration Agency, The Institute of Space and Astronautical Science, Sagamihara Campus, 3-1-1 Yoshinodai, Sagamihara, Kanagawa 229-8510, Japan Received 14 September 2004; received in revised form 12 October 2004; accepted 13 October 2004 Available online 19 November 2004
Abstract The microscopic orientations of Ni–18.7 at.% Sn eutectics solidified from undercooled states, in particular, within an individual eutectic colony and among neighboring eutectic colonies, have been measured with respect to the eutectic Ni3Sn and Ni phases; this was done using a scanning electron microscope equipped with the electron backscatter diffraction pattern (EBSP) mapping technique. The EBSPs and inverse pole figures indicate that the Ni3Sn intermetallic compound is continuous and well oriented whereas the Ni solid solution is discontinuous and randomly oriented within an anomalous eutectic grain. Further examination reveals that although Ni particulates are random from an overall view, most neighboring Ni grains have small misorientations of less than 10. The specific solidification sequence and the effect of released crystallization heat on subsequent crystallization are further considered, which enables the primary Ni phase to segment into individual grains whereas Ni3Sn does not due to higher entropy of fusion. A little rotation or floating within the constrained framework of the crystallizing Ni3Sn compound may yield small misorientation angles. The discontinuous Ni particulates and continuous Ni3Sn network are of great significance in revealing the anomalous eutectic formation. The orientation among independent eutectic colonies is random owing to the random appearance of nuclei throughout the volume of undercooled melts. The macrotextures of pole figures (PFs) of two eutectic phases are also mapped versus melt undercooling, which can be interpreted well when considering the nucleation frequency, variation of eutectic colony size, microtexture within a single eutectic colony, and the overall microstructure evolution as a function of melt undercooling. 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Containerless processing; Nucleation; Anomalous eutectic; Crystallographic orientation; Texture formation
1. Introduction Powell and Hogan [1] undercooled various silver– copper eutectic alloys in graphite and unglazed porcelain crucibles; the alloys were processed under different atmospheric and cover conditions. From microstruc*
Corresponding author. Tel.: +81 29 868 3628; fax: +81 29 868 3957. E-mail address: [email protected] (M. Li).
tural observation they found that the anomalous eutectic consisted of discontinuous copper particles in a continuous matrix of silver. Based on this microstructure, Hogan [2] proposed that the ‘‘discontinuous’’ nature of the minor phase in anomalous eutectic indicated that it was formed by repeated nucleation after being overtaken by the faster-growing phase. However, Kattamis and Flemings [3] successively polished and then examined the parallel sections, and concluded that the minor phase, although irregular, was not particulate
1359-6454/$30.00 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2004.10.029
Ag–Cu [1]
One phase is continuous and the other is discontinuous. Both phases are continuous to form a polyhedral network. Both phases are discontinuous particulates.
Ni–Sn [3], Ag–Cu [4], Co–Sb [5], Ni–Si, Co–Sn, and Ni–Sn [6] Ni–Si, Co–Sb, and Ni–Al–Ti [7]
Repeated nucleation yields discontinuous particulates that inlay into the continuous matrix. Decoupled growth or cooperative growth of eutectic phases forms the irregular continuous network. Fragmentation of primary fine lamellae results in independent grains at the semisolid state.
Alloys Continuity characteristics
and both eutectic phases in anomalous Ni–Sn eutectic region were continuously interconnected along a polyhedral network. They proposed that the anomalous eutectic structure originated from the dendritic growth of the supersaturated a-Ni phase and subsequently, these a-Ni dendrites decomposed into a-Ni and b-Ni3Sn [3]. In accordance with this continuous model, Jones [4], after examining microstructures of several silver–copper eutectics, suggested that the anomalous eutectic originated from simultaneous uncoupled growth of the two terminal eutectic phases from undercooled melts. Based on microstructures of Co–Sb eutectic alloys, Wei et al. [5] assumed that the cooperative dendritic growth of independent phases was responsible for the formation of anomalous eutectics. It is worth noting that in both the Jones [4] and Wei et al. [5] models, there is an important unanswered question: why can decoupled growth take place when the eutectic melt is undercooled to exceed a certain undercooling. Li and Kuribayashi [6] considered the growth kinetics of terminal eutectic phases within one eutectic colony, in particular, when a nonfacetted disordered solid solution competes with a facetted ordered intermetallic compound. They proposed that the disordered phase overgrows the competing ordered phase because the collision-limited growth of the disordered phase always yields a highly mobile interface, whereas the diffusion-limited growth can only result in a sluggish interface for the competing ordered intermetallic compound. Obviously, from Jones [4] to Wei et al. [5] and finally Li and Kuribayashi [6], both eutectic phases should be continuous in these models since only growth of terminal eutectic phases was considered. In addition to these uncoupled growth models, Goetzinger et al. [7] concluded that the segmentation of primary eutectic lamellae took place during the semisolid state in Ni–Si, Co–Sb, and Ni–Al–Ti alloys by using the fragmentation model and thus the discontinuous anomalous eutectic particulates should be yielded for both phases. Table 1 summarizes the continuity features of anomalous eutectics proposed by different researchers in various alloys in literature. It should be emphasized that the conclusion that both eutectic phases are continuous was based on either the optical or the secondary electron microstructure (SEM) observation, which only depicts contrast in brightness of different phases from morphological appearance. The primary limitation of these analysis techniques is that they cannot supply any detailed orientation relation among neighboring grains. The electron back-scatter diffraction pattern (EBSP) technique is a delicate approach for microanalysis from the threedimensional view and can enable a quantitative and accurate determination of crystallographic orientations within a micrometer-scale area [8,9]. Furthermore, when the EBSP technique is combined with the SEM, the relation among neighboring grains in the area of interest can
Remarks
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Table 1 The summary of continuity features of terminal eutectic phases in anomalous eutectics after surveying literature
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be determined, which will supplement more experimental evidence in clarifying the growth mechanism. In the present paper, we employed the EBSP approach to obtain the microtexture of the anomalous eutectic in the Ni–18.7 at.% Sn alloy solidified from undercooled states. For a better understanding of the texture formation, we also employed the X-ray diffraction (XRD) technique to achieve the macrotexture development of pole figures (PFs) of two eutectic phases as a function of melt undercooling, where the diffraction area covers several square millimeters and thus generating macrotexture development. The formation of the microtexture and macrotexture was discussed when the nucleation and growth kinetics are considered, either within one eutectic colony or throughout the volume of a bulk sphere. The microtexture from the EBSPs was of great significance in deepening our understanding of the solidification mechanism, in particular the crystallization sequence and the effect of subsequent thermal release on anomalous eutectic formation.
2. Experimental procedures The Ni–18.7 at.% Sn eutectic ingot was cast in an arcmelting furnace with a water-cooled copper hearth. Pure nickel pellets and tin grains were alloyed after the Tigettered processing was conducted to consume the adsorbed oxygen. The sample was melted and turned over several times to homogenize the alloy composition completely. The prepared ingot was weighed to confirm that total mass loss was less than 1.5 wt% compared with the original metal pellets and grains. The as-cast ingot was cut into bulks weighing about 1 g for processing in an electromagnetic levitator (EML). The EML chamber was evacuated to 1 · 103 Pa and then backfilled with 5 N Ar to atmospheric pressure. A two-color pyrometer with an accuracy of better than 0.5% of measured temperature was utilized to monitor the thermal history of specimens, whose sampling rate and spot size were 100 scans/s and 1 mm in diameter, respectively. The molten sphere could crystallize at a preset temperature by controlling the overheating degree and cooling intensity. The sample was weighed again after levitation to guarantee that the mass loss was less than 1.5%, indicating that the chemical composition was the same as the original integrant. Further details on bulk sphere processing by the EML have been presented elsewhere [10]. Since the interaction depth between the electron beam and the specimen surface is on nanometer scale for EBSP analysis, the interactive layer must be relatively free of scratches so that clean patterns can be obtained. The processed sample was first sectioned on a non-contact electric discharging cutting facility and then
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the sample surface was carefully polished. The scanning step was 0.5 lm at a low magnification and 0.2 lm at a high magnification. In terms of a sample for PF mapping, it is also important to avoid yielding surface deformation and internal stresses during mechanical cutting. Therefore, the solidified bulks were sectioned with two parallel planes on the electric discharging cutting setup and then were slighted ground and polished. For accuracy, X-ray beam alignment was accomplished prior to each experimental run. The diffraction 2h angles were examined for Ni3Sn and Ni phases accurately for each specimen. Standard PF mapping was completed at those planes corresponding to high diffraction intensities for Ni3Sn and Ni phases. Here it is worth noting that the solubility of Sn in solid solution Ni can reach 10.6 at.% even at equilibrium solidification near melting temperature. However, the present analysis was accomplished at ambient temperature after the samples underwent solid phase transformations, during which precipitation would take place and thus yielding severe distortion in crystal lattice. This is why the 2h peak of present Ni deviates about 1 from that of the standard pure Ni. However, for the Ni3Sn compound, no pronounced deviation can be found in the 2h peaks since there is a comparatively small solubility of Ni in Ni3Sn and a wide solubility range of the compound at room temperature according to the Ni–Sn phase diagram [11].
3. Experimental results 3.1. Microtextural EBSP mapping Fig. 1 shows the EBSPs of the Ni–Sn eutectic solidified at about DT = 50 K. For comparison, Fig. 1(a) depicts the SEM, in which the red square indicates the area of interest for EBSP analysis. From the SEM, one can see that only one anomalous eutectic grain is included, in which the white phase is the Ni3Sn compound and the black phase is the Ni solid solution. Fig. 1(b) shows the EBSP after both phases are indexed. When Ni3Sn compound and Ni solid solution are indexed separately, the patterns are shown in Fig. 1(c) and (e), respectively. The primary Ni3Sn compound skeleton exhibits only one green color. Near the edge of the grain, a small blue area and a light brown region can be found, which may be from other colonies. The [0 0 1] partial inverse pole figure (IPF) of Ni3Sn, shown in Fig. 1(d), is consistent with the EBSP map having one primary (green) diffraction direction close to the crystallographic direction of 2 1 10 and two secondary diffraction directions, all of which have a highly textured crystallographic orientation. This
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Fig. 1. The Ni–18.7 at.% Sn eutectic specimen solidified at an undercooling of about DT = 50 K: (a) the SEM image showing one anomalous eutectic colony, in which the red square indicates the area for orientation analysis; (b) the EBSP of the anomalous eutectic colony when both Ni and Ni3Sn phases are indexed; (c) the EBSP only when Ni3Sn compound is indexed with one primary green color in the colony; (d) the [0 0 1] IPF of the Ni3Sn compound with a well oriented texture; (e) the EBSP only when Ni solid solution is indexed with various colors; (f) the IPF of corresponding Ni particulates showing a random texture.
reveals that the Ni3Sn phase has only one crystallographic orientation in terms of the green Ni3Sn phase and thus has a continuous network within the anomalous eutectic grain. However, when the Ni solid solution is indexed, the particulate phase exhibits a colorful pattern, as shown in Fig. 1(e). The [0 0 1] IPF of Ni phase exhibits a random distribution; no preference in diffraction directions can be found in Fig. 1(f). Both the EBSP and the
IPF indicate that the Ni phase is discrete even within one eutectic colony. Fig. 2(a) depicts a similar SEM with an anomalous eutectic grain surrounded by regular lamellae. However, when the Ni3Sn phase is indexed by EBSP mapping, the anomalous eutectic area contains eight different subregions as numbered in Fig. 2(c). The IPF of the Ni3Sn phase, shown in Fig. 2(d), contains several diffraction
Fig. 2. The Ni–Sn eutectic specimen solidified at about T = 50 K: (a) shows the SEM of another anomalous eutectic colony with a similar morphological appearance in Fig. 1(a), in which the red square indicates the area for orientation mapping; (b) the EBSP of the area when both Ni and Ni3Sn phases are indexed; (c) the EBSP only when Ni3Sn is indexed with eight separate eutectic colonies; (d) the [0 0 1] IPF of the Ni3Sn compound with oriented textures; (e) the EBSP only when Ni is indexed with many colorful grains; (f) the IPF of Ni particulates showing a fully random texture.
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directions, with the green sub-region #8 having a similar orientation as that primarily indexed in Fig. 1(c) and (d) near to the direction of 2 1 10. Region #6 is blue, which is quite different from its surroundings. Similar to Fig. 1(d) for Ni particulates, Ni phase embedded in the Ni3Sn matrix still exhibits a colorful pattern. The IPF shows that the distribution of these particulates is completely random, which provides convincing evidence that Ni grains within anomalous eutectic regions are discrete regardless of the relation of eutectic colonies. 3.2. Macrotextural PFs development versus melt undercooling Fig. 3 shows the PFs development of the Ni3Sn and Ni phase versus melt undercooling. The PFs for Ni3Sn phase was obtained at 2h = 44.88, which corresponds to the peak of (2 0 1) with the maximum intensity. The macrotexture of the phase exhibits a random distribution from a low to a high undercooling level from an overall view. The only difference is that with the increase of melt undercooling, the diffraction intensity in a certain direction is increased, which is characterized by the number of poles at the diffraction position. In the meanwhile, the number of independent poles increases with the increase of melt undercooling. When the melt is undercooled to the highest undercooling of about 210 K, almost all diffraction patterns exhibit independent poles, distributing randomly throughout of the normal and transverse directions.
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In addition to the texture obtained at 2h = 44.88, we have also measured macrotextures of the Ni3Sn compound at 2h = 39.26 and 42.54, which reveal almost the same evolution tendency as that at 2h = 44.88 at different undercooling levels, indicating that the distribution of the Ni3Sn phase is random at all these three diffraction planes. To avoid repeating, we omit the macrotexture development obtained at 2h = 39.26 and 42.54. The PFs of Ni solid solution were obtained at 2h = 43.40, corresponding to the (1 1 1) plane with the highest intensity. The Ni phase in texture development has the same characteristics as that of Ni3Sn with regard to overall orientation; there is no preferential distribution and the texture is random. However, in terms of number of individual poles and the intensity variation versus melt undercooling, the macrotexture of Ni is completely contrary to that of Ni3Sn, consisting of several independent poles at a low undercooling of about DT = 20 K and then the number of individual poles increasing when the melt is undercooled to DT = 60 K. Further increase of melt undercooling to about 160 K results in a completely random distribution without any intensified poles at any direction in the diffraction plane, as shown in Fig. 3(c 0 ). When the melt is undercooled to the deepest undercooling of DT = 210 K, the macrotexture also is random, as mapped in Fig. 3(d 0 ). Note that in all these PFs, the relative intensity levels are maintained at the same level in order to make these PFs comparable.
Fig. 3. The macrotexture PFs of Ni3Sn compound and Ni solid solution versus melt undercooling of about: (a) DT = 20 K; (b) DT = 60 K; (c) DT = 160 K; (d) DT = 210 K. The diffraction angles for Ni3Sn and Ni phases are 2h = 44.88 and 43.40, respectively, corresponding to the (2 0 1) plane for Ni3Sn and (1 1 1) for Ni, both of which are at their highest intensity.
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4. Discussion 4.1. Microtexture formation in anomalous eutectics The present EBSP mapping indicates that only the Ni3Sn phase is continuous within one anomalous eutectic grain whereas the Ni phase is discontinuous, which differs from observations and models of Kattamis and Flemings [3], Jones [4], Wei et al. [5] and Li and Kuribayahsi [6]. This controversy should be attributed to the limitation of analysis technique, either by the optical or the SEM observation. A good example to verify this idea is that Figs. 1(a) and 2(a) have almost the same SEMs, however, EBSPs reveal that there is only one eutectic grain in Fig. 1(a) whereas eight independent eutectic colonies are contained in Fig. 2(a) in terms of Ni3Sn skeletons. In order to have a further understanding on the formation of an anomalous eutectic grain, we should first enlarge a central region within an anomalous eutectic grain, as marked in Fig. 2(a) by the green square. The SEM, EBSPs, and corresponding IFPs are depicted in Fig. 4. The Ni3Sn phase shows one diffraction direction from the EBSP and IPF, consistent with the SEM, in which the bright phase forms the matrix. For convenience, Ni particulates are numbered in Fig. 4(e). Only from the SEM, several connecting parts can be found, e.g. grain #1 and grain #2 (thereafter only the number with the mark # is used), #13 and #14, which should share the same orientation if they are really continuous within a complete one grain. However, from the EBSP, different orientations arise between #1 and #2, #13 and
#14 in color contrast, indicating that #1 and #2 are independent and discrete. This investigation once again confirms that the conclusion based on the optical or SEM observation is not reliable with respect to the continuity feature of crystals. It is this discrete feature of the Ni particulates that results in the random orientation, as depicted by IPF in Fig. 4(f). Since the Ni particulates are independent grains, it is important to know the misorientation degree among neighboring grains. Fig. 5(a) outlines misorientation degrees and Fig. 5(b) shows the number fraction versus misorientation angles. The number fraction is calculated when the number counted within the misorientation angle is divided by the total number counted within the area. If each Ni grain is formed from an independent nucleus within the interstitial space in the anomalous eutectic colony, as Hogan [2] suggested in Ag–Cu alloys, these Ni particulates should have a fully random distribution with an equal probability in misorientation angle distribution even among neighboring grains. However, among the misorientation angles of neighboring grains, nearly 50% are less than 10 and about 30% are around 60. Considering that #11 and #12, #36 and #37 are two grains with typical twins owing to stacking fault during growth for the cubic Ni phase, which should be treated as one grain, the proportion with small misorientation angle is further increased. This indicates that although these grains are discrete from an overall view, most of neighboring grains have similar orientations. One example is that five out of six misorientation angles are less than 10 between grain #1 and its neighboring grains. Actually, similar situations can be found in col-
Fig. 4. A magnified region within one anomalous eutectic colony: (a) the SEM of the area corresponds the green square in Fig. 2(a); (b) the EBSP of the area when both Ni and Ni3Sn phases are indexed; (c) the EBSP when Ni3Sn is indexed with only one color; (d) the [0 0 1] IPF of the Ni3Sn compound with only one diffraction direction; (e) the EBSP when Ni is indexed with colorful grains; (f) the IPF of Ni particulates.
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Fig. 5. Further detailed misorientation analysis within the small area: (a) the data straddling two numbers in parentheses are the misorientation angles and the number within parentheses corresponds to the Ni grain position numbered in Fig. 4(e); (b) the number fraction of neighboring Ni grains within the area of interest as a function of misorientation angle.
ony #2 and colony #3 with green particulates and colony #6 with blue particulates in Fig. 2(c) and (e), which should share similar crystallographic direction with small misorientations, i.e. at least most of neighboring Ni grains should not have a complete random misorientation. Here, it is worth noting that Li and Kuribayashi [6] only outlined the critical condition under which the decoupled growth can occur, but they did not consider the subsequent solidification behavior, i.e. solidification sequence, thermal release, and its influence on the as-solidified primary phase at the semi-solid state. Here, we consider this sequence and subsequent effects as follows: when Ni overgrows Ni3Sn compound, irregular Ni skeleton is formed owing to the limitation in chemical composition of the eutectic. Note that this irregular cylinder-like Ni skeleton in three dimensions can not form a closed chamber, which enables remaining liquids with Sn-riched composition connecting to form a continuous net when they are pushed to occupy the interstitial place, i.e. the primary Ni is immersing in remaining liquids after decoupled growth takes place. The solidification of the Ni3Sn compound begins and its crystallization heat, together with the crystallization heat from solidified Ni, is dissipated to heat the primary Ni and crystallizing Ni3Sn, which may favor the primary Ni dendrite to segment into fragments. Note that at this stage, it is difficult for the fragmented Ni particulates
to rotate, move, or float freely throughout the entire volume of the melt because of the crystallizing frame of Ni3Sn phase. Therefore, only a little rotation or displacement may be favored owing to the stirring effect of electromagnetic force. This is why most neighboring Ni fragments have small misorientation angles less than 10. Actually, we also checked the misorientation angles between two grains with a large distance, e.g. 48 between #22 and #29, 30 between #27 and #32 in Fig. 4(e). Since the breakup fragment cannot float freely within the entire bulk, the misorientation relation between two far grains is of less interest in revealing solidification mechanism. Except Ni twin with a misorientation angle of 60, the accurate angle between (1 1 1) and (0 0 1) in Ni is 54.7, which may be responsible for the second important number faction with misorientation angles around 60 after particulates have some rotation or displacement. Considering this solidification sequence, it is understandable that Ni phase exhibits a random distribution from an overall view. This brings us to the next question: why Ni can fragment into independent particulates whereas Ni3Sn cannot. This can be simply interpreted from KarmaÕs fragmentation model [12], which was developed for a single-phase dendrite with a paraboloid tip when considering the capillarity effect and supersaturation inside the trunk. Since the unconstrained growth behavior of Ni is similar to that of Ni-based dendrite after decoupled
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growth occurs in the eutectic [6], here it is assumed that all assumptions in the fragmentation model can be applied to the primary Ni in the eutectic and then we employ the fragmentation model to explain why Ni is readily to fragment whereas Ni3Sn is not. The characteristic time for breakup of dendrites, Dtb, can be expressed in a first approximation as below [12]: 3 ð20RÞ DS f T m C p ml c0 ð1 k e Þ at 1 Dtb ; ð1Þ DS f T m CC p at D where R is the radius of dendrite tip, DSf is entropy of fusion, Tm is melting temperature, C is the Gibbs– Thomson coefficient, Cp is the specific heat, at is the thermal diffusivity, ml is the slope of liquidus, c0 is the chemical composition, ke is the equilibrium partition coefficient, and D is the chemical diffusion coefficient. In terms of Ni and Ni3Sn phases at the eutectic composition, R, Tm, C, Cp, at, D, ml, ke, and c0 are irrelevant to crystalline structure and have comparable values whereas only DSf is strongly dependent on crystal structure. The entropy of fusion of Ni3Sn compound, DSf(Ni3Sn), can be approximately calculated from the entropy of fusion of Ni–18.7 at.% Sn eutectic, which is 48.04 J mol1 K1 [13]. Considering the volume fractions of Ni and Ni3Sn phases, together with the entropy of fusion of Ni, DSf (Ni) = 10.1 J mol1 K1 [14], it follows DSf (Ni3Sn) = 65.54 J mol1 K1, about six times higher than that of Ni solid solution, which is reasonable for the facetted intermetallic compound when the mixture entropy of both phases is neglected. Another assumption in calculating entropy of fusion is that there is no significant difference in DSf for pure Ni and Ni solution, stoichiometric Ni3Sn and Ni3Sn with certain solubility. Note that DSf is in pre-factor and denomina-
tor in Eq. (1), the breakup time for Ni3Sn phase should be about 10 times longer than that for Ni. The other reason is that unlike primary Ni immersing into the remaining liquid, no remaining liquid can be found to generate capillarity force after the Ni3Sn phase solidifies; there is no driving force to fragment. This is why Ni can readily fragment into pieces whereas Ni3Sn cannot, which may be owing to insufficient time and absent driving force for breakup in an anomalous eutectic grain. The dissipation of crystallization heat from Ni and Ni3Sn can lead to the fragmentation of Ni within the central part in an anomalous eutectic colony. In the meanwhile, it can increase temperature of remaining liquid ahead of growing interface to lower the interface undercooling and thus enabling regular eutectic lamellae to develop from the periphery of the anomalous eutectic grain, as observed in many eutectic systems [5,6,10,13]. After examining the central part, we should investigate the microtexture near the edge of an anomalous eutectic grain. The EBSPs, together with SEM and IPFs, are shown in Fig. 6, in which two colonies are included, as indicated in Fig. 6(c) and (d). From the indexed Ni3Sn pattern, one can see that Ni3Sn phase in each respective colony exhibits a continuous feature not only at anomalous region, but also shares the same orientation at regular lamellar region. A minor difference in Ni3Sn phase color, typically marked by #1 and #2, arises, which is originated from a small misorientation angle with about 2 between these neighboring parts. Here, it should be noted that solidification is accomplished at high temperatures whereas analysis is operated at ambient temperatures. In terms of the solid solution Ni, there is no structure transformation but only precipitation during cooling.
Fig. 6. Near the edge of the anomalous eutectic region with a hybrid microstructure of anomalous and regular lamellae: (a) depicts the SEM with a red square for the EBSP mapping; (b) shows the EBSP when both Ni and Ni3Sn phases are indexed; (c) the EBSP only when Ni3Sn compound is indexed with two individual colonies; (d) the IPF of the Ni3Sn compound with two diffraction directions; (e) the EBSP only when Ni solid solution is indexed, which are primarily blue; (f) the IPF of corresponding Ni particulates showing a biased texture to the direction of 1 1 1.
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However, the high-temperature Ni3Sn phase must transform to the low-temperature Ni3Sn counterpart with a D019 structure at 1250 K when it is cooled down [11]. Note that the growth of regular lamellae in free solidification is a non-steady state process, as Trivedi et al. [15] recently analyzed in atomized Al–Si eutectics, this may lead to a heterogeneous distribution in solute and internal stress. These non-uniformity characteristics may influence the massive phase transformation process during cooling and thus generating small-angle misorientations within one Ni3Sn network. Similar situations can be found in the same colony and the neighboring colony as marked by #3 and #4, with misorientations of about 2–5. Fragmented Ni particulates near lamellae region within the anomalous eutectic grain, as circled by the dashed line in Fig. 6(e), have small misorientation angles, from several of which Ni lamellae grow with small misorientation angles, covering from light blue to deep blue in color. When the lamellar Ni is further examined, five regions, as marked in Fig. 6(e), can be classified, where the misorientation angle within each region is less than 0.8, which falls into the tolerance of the facility. Obviously, the Ni lamellae, for instance, in region #1, have only one orientation, which should be owing to the radiated growth of lamellae originating from one fragmented Ni particulate. This investigation verifies that fragmentation does not occur during lamellar Ni growth, which differs from that within an anomalous eutectic grain. In developing the fragmentation model, one necessary condition is that primary dendrite should immerse into the remaining liquid so that breakup can occur due to a Rayleigh-like instability of the dendritic morphology. However, for alternative eutectic lamellae growing in a coupled manner, no remaining liquid can be found since the lamellae contact closely side by side. Therefore, no driving force can be generated to fragment the lamellae in terms of capillarity effect. This is why these fine Ni lamellae, as marked in Fig. 6(e), share the same orientation in each region. Based on the fragmentation model, Goetzinger et al. [7] concluded that the primary lamellae can segment into spherical elements and thus anomalous eutectics are formed from the breakup of the cylindrical phase, which should result in a random distribution for both Ni and Ni3Sn phases. However, our observation and analysis indicate that only Ni is readily to fragment whereas Ni3Sn is difficult owing to higher entropy of fusion. Furthermore, fine Ni lamellae from one Ni grain have one orientation and cannot fragment because of the absence of driving force. Obviously, their proposed model [7] is contradictory to theoretical analysis and experimental facts. After discussing the orientation relation within one eutectic grain, from center to edge, we should consider
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the inter-relation of individual eutectic colonies. Fig. 7 shows the misorientation angles of the Ni3Sn phase among independent eutectic colonies. The positions of eutectic colonies are numbered in parentheses with the mark, corresponding to those in Fig. 2(c). Obviously, the misorientation angles cover a wide range from several degrees to more than 80, indicating that these eutectic colonies are randomly distributed. Further examination of some other parts reveals a similar distribution with a random orientation of independent eutectic colonies in terms of individual Ni3Sn colonies. Since copious or massive nucleation occurs in the undercooled Ni–Sn eutectic melts [10], the random distribution of independent nuclei leads to the development of separate eutectic colonies, which, of course, should have a random distribution without any preferential orientation. 4.2. Macrotextural development as a function of melt undercooling When we have a full understanding of microtexture formation in separate eutectic colonies, we shall come to the macrotexture formation of the eutectic versus melt undercooling, which should be the sum of microtextures within the macro area of interest. As indicated by Fig. 3, the macrotexture of both Ni3Sn and Ni phases is random from an overall view within the undercooling range attainable in the present experiments, which should be owing to the random distribution of nuclei in undercooled melts, from which independent eutectic colonies can develop. In terms of the macrotexture of Ni3Sn phase versus melt undercooling, it can be interpreted when nucleation frequency is considered as a function of melt undercooling. At low undercoolings, the nucleation rate is low and the duration time near eutectic melting point after
22.6 (#7) 52.6 (#5) 36.7 (#8) 32.9 81.9 82.2 81.0 50.3 36 (#6) 6.0 28.5 76.6 81.5
(#4)18.2 26.8
(#3)
36.2 (#1)
85.8
31.4
37.3
(#2) Fig. 7. The misorientation angles of the Ni3Sn phase among neighboring continuous networks. The data straddling two numbers in parentheses are the misorientation angles and the number within parentheses corresponds to the position of Ni3Sn colonies numbered in Fig. 2(c).
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recalescence is rather long, which favors a full development of eutectic colonies and thus yielding large eutectic colonies with about hundreds micrometers in diameter, as we have reexamined elsewhere [10]. Only a few random eutectic colonies may be included within the diffraction area. With the increase of melt undercooling, the nucleation rate increases and eutectic colony size decreases to tens of micrometers. Although the distribution of nuclei is random from an overall view, the increased total number in eutectic colonies within the diffraction area will correspondingly increase the number of those colonies having a similar crystallographic orientation; i.e. with one diffraction direction, the number of eutectic colonies may increase, which should result in improved diffraction intensity at this direction. Indeed, one can find that number of poles increases when the melt is deeply undercooled from DT = 60 to 160 K and finally DT = 210 K, as shown in Fig. 3. With respect to the macrotexture evolution of Ni phase versus melt undercooling, we should consider both nucleation and solidification sequence, in particular the fragmentation of Ni in an anomalous eutectic grain. When the melt undercooling is less than about DT = 45 K, only regular Ni lamellae can grow, which share one orientation within one eutectic colony if they originate from one nucleus, as discussed in Section 4.1. Since large eutectic colonies will be formed randomly at low undercoolings, only several random poles can be observed in Fig. 3(a 0 ). When the melt undercooling is increased to about DT = 60 K, more eutectic colonies will be contained in the diffraction area and thus more diffraction poles appear, similar to that of Ni3Sn phase with improved intensity, as evidenced by the increased number of poles at a certain diffraction direction. When the melt undercooling is beyond DT = 120 K, only unique anomalous eutectic will be yielded [10]. Considering that the discrete Ni grains have random orientations even within one anomalous eutectic colony, it is no wonder that the macrotexture is fully random at about DT = 160 K. Similar random distribution can be found when the melt is solidified at the maximum undercooling of DT = 210 K. Note that at high undercoolings, the macrotexture of Ni3Sn phase differs from that of Ni phase with regard to pole numbers and intensity, this should be owing to a pronounced difference of their microtextures, i.e. Ni3Sn exhibits a continuous network whereas Ni does not.
solid solution is discontinuous and thus has a random distribution even within one anomalous eutectic colony. The random distribution of Ni particulates should be attributed to the fragmentation of primary Ni dendrite when considering solidification sequence. Because of the spatial limitation of the crystallizing Ni3Sn in configuration, it is impossible for the fragmented Ni particulates to move freely but with a small rotation or floating and thus resulting in small misorientation angles, frequently less than 10, among most neighboring Ni grains. In contrast, the Ni3Sn intermetallic compound is continuous and thus well oriented within one anomalous eutectic colony, i.e. fragmentation of the Ni3Sn compound does not take place, which may be due to higher entropy of fusion of the compound and absence of driving force to fragment compared with the Ni phase. The discontinuous Ni particulates and continuous Ni3Sn network within the anomalous eutectic colony are of great significance in improving our understanding of anomalous eutectic formation since the previous models and analysis were based on the fundamental idea that both eutectic phases were continuously interconnected along a polyhedral network. This indicates that an optical microstructure or an SEM cannot provide convincing evidence for the continuity feature of a phase. In the meantime, the present examination by EBSPs excludes the mechanism that anomalous eutectic is formed via the fragmentation of primary fine eutectic lamellae, which should result in a random distribution for both Ni and Ni3Sn within one anomalous eutectic colony. Fine Ni lamellae at the edge of an anomalous eutectic grain share one orientation if they originate from one Ni particulate. Fragmentation cannot occur because of the absence of driving force when the alternative Ni and Ni3Sn lamellae grow in a coupled manner with a planar front. The random relation among independent eutectic colonies should be induced by the random appearance of nuclei throughout the volume of undercooled melts, which leads to a random distribution in macrotextures of two eutectic phases versus melt undercooling from an overall view. Further subtle difference in pole numbers and diffraction intensity in macrotextures can be well interpreted when considering the nucleation frequency, variation of eutectic colony size, microtexture within a single eutectic colony, and microstructure evolution as a function of melt undercooling.
5. Conclusions The microtextures of Ni3Sn and Ni terminal eutectic phases, in particular, in anomalous eutectic grains, were revealed when the Ni–18.7 at.% Sn eutectic melts were containerlessly solidified from undercooled states. The EBSPs and IPFs of eutectic phases indicate that the Ni
Acknowledgements Partial experimental work was completed when one of the authors (M. Li) held the Foreign Research Fellowship from the Japan Aerospace Exploration Agency
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(formerly the Institute of Space and Astronautical Science, which was renamed after it was merged with the National Space Development Agency of Japan and National Aerospace Laboratory of Japan). Sincere thanks are also due to Dr. K. Kitazono and Dr. S. Ozawa for their technical assistance in pole figure measurement. We acknowledge Dr. Y. Arai and Dr. J. Yu for their interest in the present work. References [1] Powell GL, Hogan LM. J Inst Met 1965;93:505. [2] Hogan LM. J Aust Inst Met 1964;9:228. [3] Kattamis TZ, Flemings MC. Metall Trans 1970;1:1449.
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