Phase selection and microstructure formation in undercooled Co–61.8 at.% Si melts under various containerless processing conditions

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Acta Materialia 61 (2013) 4861–4873 www.elsevier.com/locate/actamat

Phase selection and microstructure formation in undercooled Co–61.8 at.% Si melts under various containerless processing conditions Y.K. Zhang a,b, J. Gao a,⇑, M. Kolbe b, S. Klein b, C. Yang a, H. Yasuda c, D.M. Herlach b, Ch.-A. Gandin d a

Key Laboratory of Electromagnetic Processing of Materials (Ministry of Education), Northeastern University, Shenyang 110004, People’s Republic of China b Institut fu¨r Materialphysik im Weltraum, Deutsches Zentrum fu¨r Luft- und Raumfahrt (DLR), 51170 Ko¨ln, Germany c Department of Adaptive Systems, Osaka University, Osaka 565-0781, Japan d MINES Paris Tech, CEMEF UMR CNRS 7635, BP207, 06904 Sophia Antipolis, France Received 19 April 2013; accepted 21 April 2013 Available online 3 June 2013

Abstract The hypoeutectic composition Co–61.8 at.% Si was undercooled and solidified using electromagnetic levitation, electromagnetic levitation under a static magnetic field, electrostatic levitation and glass-fluxing. The samples generally showed two thermal events, either separated or continuous depending on undercooling. In situ monitoring of the two thermal events with a high-speed camera revealed a sudden decrease of dendritic growth velocities of primary phases at a critical undercooling of 88 K. Scanning electron microscopy studies of the solidified samples showed that the CoSi compound and the CoSi2 compound nucleate as the primary phase for low and high undercoolings, respectively. The microstructure of the samples depends not only on undercooling, but also on the onset temperature or delay time of the second thermal event. Melt convection has no effect on the primary phase selection in undercooled melts, but it has a significant effect on the delay time and therefore on microstructure formation of the samples for high undercoolings. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: CoSi–CoSi2 eutectic; Undercooling; Nucleation; Microstructure; Convection

1. Introduction Eutectic alloys have important applications in industry because of their relatively low melting points, zero solidification temperature intervals and good fluidity in the liquid state. Solid solution–solid solution and solid solution–compound eutectic alloys have been intensively studied to understand their solidification behavior and microstructure formation under various processing conditions [1–4]. In recent years, there has been increasing interest in compound–compound eutectic alloys. Technically, several compound–compound eutectic alloys show a potential for high-temperature or surface engineering applications [5– ⇑ Corresponding author. Tel.: +86 24 83681915; fax: +86 24 83681758.

E-mail address: [email protected] (J. Gao).

10]. Fundamentally, the compound–compound eutectic alloys exhibit a unique solidification behavior and freeze into novel microstructure patterns [11–20]. However, the current knowledge of the compound–compound eutectic alloys is poor when compared with that of other eutectic alloys. The CoSi–CoSi2 eutectic at composition Co38.2Si61.8 was chosen as a model system of the compound–compound eutectic and investigated by two groups [17,20]. A novel microstructure consisting of dispersed CoSi dendrites in the matrix of CoSi2 grains was commonly observed for highly undercooled melt droplets of different sizes. However, the phase formation sequence during solidification is in dispute due to the lack of an accurate knowledge of nucleation and growth kinetics of the two compound phases. Several effects of melt convection on solidification

1359-6454/$36.00 Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.04.061

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microstructure were observed for low and high undercoolings [20], but the underlying mechanisms are not fully understood. In the present work, phase selection and microstructure formation in undercooled melts of the Co38.2Si61.8 composition were investigated using three containerless processing techniques: electromagnetic levitation (EML), electromagnetic levitation under a static magnetic field (EML + SMF), and electrostatic levitation (ESL). These techniques provide different levels of melt convection in addition to easy access to high undercoolings. In samples processed by EML, melt convection is driven by a radio frequency magnetic field and is turbulent in nature [21,22]. In samples processed by EML + SMF, the turbulent melt convection is damped by the imposition of a strong static magnetic field and becomes laminar [23,24]. In samples processed by ESL, melt convection is driven by a gradient of surface tension and is very weak [25]. A comparative study of these samples allowed us to have insight into the effects of melt convection on microstructure formation. Complementary undercooling experiments were performed using the glass-fluxing technique to measure crystal growth velocities with the aid of a high-speed camera. The measured data provided experimental proof of the physical mechanism determining the phase selection sequence in undercooled melts. 2. Experimental 2.1. Preparation of master alloys Master alloys of composition Co38.2Si61.8 were prepared by arc-melting of high purity elemental materials (99.99% or better) under a Ti-gettered argon atmosphere. The alloys for ESL experiments had a mass of 0.05 g and a diameter of 2 mm. The alloys for other experiments had a mass of 1.0 g and a diameter of 6 mm. Mass loss during arcmelting was less than 0.5%. 2.2. Experimental procedures 2.2.1. Electromagnetic levitation (EML) An alloy sample was positioned in the coil of an electromagnetic levitation facility with a sample holder. After evacuation to a pressure of 1  103 Pa, the levitation chamber was backfilled with pure argon (99.999% purity) to a pressure of 5  104 Pa. The alloy sample was levitated, melted and overheated. After keeping for 1 or 2 min, the sample was cooled by a gas stream of He–5 vol.% H2 and solidified in the levitated state. The surface temperature of the sample was measured using a single-color pyrometer at a sampling rate of 10 Hz. The measured temperature was calibrated by adjusting the emissivity of the pyrometer to make the mean temperature of a long thermal arrest observed during the melting process equal to a thermodynamically assessed invariant temperature of 1587 K of the CoSi–CoSi2 eutectic [26]. As explained in Section 4.1, the

alloy composition under study actually falls into the hypoeutectic composition. Thus, the undercooling of the samples, DT, was defined as a difference between a theoretical liquidus temperature of 1612 K [26] and the nucleation temperature of a primary solid during solidification. The same method for calibration of the measured temperature and the same definition of the undercooling of the samples were adopted for other undercooling experiments. In total 12 samples were processed by EML. Eight of them were melted and solidified for more than one cycle to attain a large undercooling. The mass losses of the samples were not more than 0.003 g. 2.2.2. Electromagnetic levitation under static magnetic fields (EML + SMF) An advanced electromagnetic levitation facility was used; the levitation chamber was placed at the center of the bore of a cryogen-free superconducting magnet [24]. The main procedures for undercooling and solidification were similar to those described in Section 2.2.1. A static magnetic field of 2 T was imposed on the samples prior to levitation and was held throughout the melting–solidification process. The surface temperature of the samples was measured using a two-color pyrometer at a sampling rate of 50 Hz. In total 16 samples were processed by EML + SMF. Three of them were melted and solidified for five to ten cycles, and others were melted and solidified for one or two cycles only. 2.2.3. Electrostatic levitation (ESL) An alloy sample was positioned on a grounded central electrode of an electrostatic levitation facility installed at DLR, Ko¨ln [27]. The ultrahigh vacuum chamber of the electrostatic levitation facility was evacuated to a pressure of 1  106 Pa. The sample was preheated by two infrared heating lasers to evaporate impurities on the sample surface. The voltage of the main electrodes was increased to charge the sample capacitively. When the sample was sufficiently charged, it was levitated in between the main electrodes and the grounded central electrode. The position of the levitated sample was maintained by a fully automated active positioning control system. The sample was melted and overheated using the infrared heating lasers for a few minutes. The surface temperature of the sample was measured using a single-color pyrometer at a sampling rate of 83 Hz. Then the heating laser was switched off. The sample was cooled by radiation to the levitation chamber and solidified spontaneously. In total four samples were processed by ESL. One of them was melted and solidified for one cycle, and others were melted and solidified for three cycles to attain a large undercooling. 2.2.4. Glass-fluxing (GF) An alloy sample was placed on the top of an alumina crucible containing soda lime glass powders. The crucible was positioned in the coil of an electromagnetic levitation facility [28]. After evacuation to a pressure of

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5.0  103 Pa, the vacuum chamber of the furnace was back-filled with high-purity argon to a pressure of 2.0  104 Pa. The sample was heated, melted and overheated inductively. By switching off the heating power, the sample was cooled and solidified spontaneously. The melting–solidification process was cycled 20–30 times to generate different undercoolings. In each cycle, the surface temperature of the sample was measured using a singlecolor pyrometer at a sampling rate of 50 Hz. Meanwhile, the recalescence process of the sample was monitored and recorded by an Ultima-APX digital high-speed camera at a frame rate of 4000 fps. The camera was focused on the top surface of the sample. The recorded images were simulated using the software POV Ray 3.7 [29] to determine crystal growth velocities in the undercooled sample. The mass loss of the sample after the last cycle was determined to be 0.004 g.

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Fig. 1. Illustration of temperature–time profiles of the samples during containerless solidification. Two dashed lines show the liquidus temperature TL and the eutectic temperature TE. Both of them are taken from a thermodynamic assessment of the Co–Si phase diagram [26]. Curves a–c show the profiles of three samples processed by EML, curve d shows the profile of a sample processed by EML + SMF, and curves e and f show the profiles of two samples processed by ESL.

2.3. Microstructure analysis The as-solidified samples were mounted in an epoxy resin, ground, and polished. The solidification microstructure of the samples was examined by scanning electron microscopy (SEM) in the back-scattering mode. Grain orientations were resolved using the electron back-scattering diffraction (EBSD) technique. Compositions of the bulk samples and phase constituents were analyzed using an energy dispersive X-ray spectrometer (EDS). The bulk composition of the samples generally showed a slight increase in Si concentration after solidification, which was relatively larger for the samples processed by ESL. However, the Si concentration of most of the samples is still lower than that of the eutectic structures formed in a sample with very low undercoolings. Therefore, the bulk composition still lies in the hypoeutectic region. 3. Results

Fig. 2. An overview of different types of thermal behavior of the samples. Symbols below the horizontal axis: S = single thermal event, SD = separated dual thermal events, CD = continuous dual thermal events and T = triple thermal events. The horizontal dashed line shows a critical undercooling of DTc = 88 K for a transition of thermal behavior from two separated thermal events to two continuous thermal events.

3.1. Thermal behavior of the samples As illustrated in Fig. 1, the present samples show three types of thermal behavior during solidification: single, dual and triple. The single-type thermal behavior refers to a single thermal event, which is characterized by a steep rise of temperature, namely recalescence (see curve c). The dualtype thermal behavior refers to two thermal events and can be classified into two sub-types. In a separated subtype, the second event sets in at a lower temperature than the first event (see curve a). There is a large interval of temperature and time between the two events. In a continuous sub-type (also termed double recalescence), the second event sets in at a higher temperature than the first event (see curves b and d). There is a delay time between the two events given by the intervening thermal plateau. This delay time has a great influence on microstructure formation of the samples for high undercoolings, as detailed in Section 3.3. The triple-type thermal behavior refers to three

sequential recalescence events, where a strong one is followed by a weak one and then by another strong one (see curves e and f). Apart from the three types of thermal behavior, the samples occasionally show an overshooting of temperature. As shown by curves d and f, the temperature of the samples rises beyond the liquidus temperature after a strong recalescence event. This phenomenon can be related to rapid solidification of locally Co-richer melt composition in addition to a difference in the emissivity between the solid and liquid samples, as is explained in Section 4.2. Fig. 2 shows an overview of the three types of thermal behavior. The dual-type thermal behavior is predominant over a wide range of DTs. A transition from the separated sub-type to the continuous sub-type takes place at a critical undercooling, DTc, of 88 K independent of the experimental techniques. The single-type thermal behavior is rare and

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Fig. 3. Illustration of high-speed video images during two separated thermal events of a glass-fluxed sample for DT = 72 K. The time following the start of recalescence is shown for each image: (a) the first event, (b) the second event.

Fig. 4. Illustration of high-speed video images during two continuous thermal events of a glass-fluxed sample for DT = 100 K. The time following the start of recalescence is shown for each image: (a) the first event, (b) the second event.

occurs in the samples processed by EML or by ESL. The corresponding DTs fall into the high DT region, where double recalescence prevails. This result differs from an earlier study [20], where the single-type thermal behavior prevails for DTs below 75 K. The triple-type thermal behavior is also rare and occurs in the samples processed by ESL only. However, the corresponding DTs are very high (166 K or above). 3.2. In situ diagnosis with high-speed camera Figs. 3 and 4 show the recorded high-speed camera images of a glass-fluxed sample. A circle at the center of each image represents a two-dimensional projection of the sample surface. The bright part of the circle corresponds to the growing solid (primary or secondary), and the dark part corresponds to the undercooled melt or the mushy zone. The interface between the two parts delineates a macroscopic thermal front, which advances from one side of the sample to the other side. The time consumed by the two events is dependent on DT of the samples. For a low DT of 72 K, the first event takes much less time than the second event (21.00 vs. 162.75 ms). For a high DT of 100 K, the first event takes a much longer time than the sec-

ond event (225.25 vs. 9.75 ms). These differences in the time consumption between the two events suggest that a slowly growing solid replaces a fast growing solid as the primary phase at the higher DT. Fig. 5 shows the measured crystal growth velocities of the primary and secondary solids as a function of DT. The growth velocities of the primary solids are decreased by one order suddenly at a critical undercooling of DTc = 88 K. This DTc agrees well with the DTc determined in Fig. 2. The growth velocities of the secondary solids for high DTs are of the same order as those of the primary solids for low DTs, and vice versa. Such an “exchange” of growth velocities between the primary solids and the secondary solids suggests that the sequence of phase formation during solidification is reversed above the DTc. 3.3. Microstructure 3.3.1. Samples processed by EML The SEM investigations showed that the samples freeze into a homogeneous microstructure for low DTs (<88 K). As shown in Fig. 6a, the microstructure consists of three microconstituents: coarse particles of the CoSi compound, halos of the CoSi2 compound and grains of rod-like CoSi–

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Fig. 5. Measured growth velocities of primary and secondary solids as a function of DT of the samples. The growth velocities of the primary solids shows a sudden decrease of one order at a critical undercooling of DTc = 88 K.

CoSi2 eutectic. The coarse CoSi particles are identified as the primary phase because each of them is enveloped by a halo of the CoSi2 compound. These particles occasionally show a dendritic morphology, indicating that they originate from dendrites of the primary CoSi compound. The volume fraction of the eutectic grains is generally high. But there is an exception. One sample with DT = 40 K has a low volume fraction of the eutectic grains in parts close to the sample surface. As shown in Fig. 6b, the local microstructure consists mainly of coarse CoSi particles and equiaxed CoSi2 grains. The samples freeze into an inhomogeneous microstructure for high DTs (>88 K). As shown in Fig. 6c and d, there are three distinct zones, which are arranged in sequence of increasing distance from the sample surface. For convenience, they are termed outer zone, middle zone and inner

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zone, respectively. The outer zone shows a single-phase layer of the CoSi2 compound and a pile-up of irregular particles or fine dendrites of the CoSi compound. The middle zone consists of rounded particles of the CoSi compound and equiaxed grains of the CoSi2 compound. The rounded CoSi particles close to the outer zone are distributed preferentially in intergranular regions, whereas those far away are distributed randomly in the matrix of the CoSi2 grains. There is a tiny amount of divorced eutectic grains in intergranular regions. The inner zone shows the same microconstituents as those of the bulk samples for low DTs. This zone should be the last freezing part of the samples. Accordingly, the outer zone is supposed to be the first freezing part, of which the single-phase layer of the CoSi2 compound should be the primary solid. The two samples showing the single-type thermal behavior also freeze into an inhomogeneous microstructure with three zones. This resemblance in the microstructure suggests that the two samples should show the dual-type thermal behavior during solidification as other samples with high DTs do. Probably their delay times between the two thermal events are too short to be resolved by the pyrometer for a low sampling rate of 10 Hz. Fig. 7 illustrates the EBSD micrographs of the samples. In the sample with DT = 68 K, clusters of CoSi particles often show identical orientations (Fig. 7a), indicating that they belong to the same dendrites of the primary CoSi compound. On the other hand, the surrounding CoSi2 halos share a common orientation with the CoSi2 matrix of eutectic grains nearby (Fig. 7b). This observation shows that the formation of eutectic grains is controlled by nucleation of the CoSi compound on the CoSi2 halos. In the sample with DT = 127 K, the CoSi2

Fig. 6. Back-scattered SEM micrographs of the samples processed by EML. The bright phase is CoSi and the dark phase is CoSi2. (a) DT = 68 K, (b) DT = 40 K, (c)-(d) DT = 127 K.

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Fig. 7. EBSD micrographs of the samples processed by EML. (a and b) DT = 68 K, (c–f) DT = 127 K. The grains of the CoSi compound are indexed with colors in (a), (c) and (e). The grains of the CoSi2 compound are indexed with colors in (b), (d) and (f). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

layer on the sample surface is divided into several segments with close orientations (Fig. 7d). Clusters of the CoSi particles nearby have identical orientations and are identified as small dendrites. These dendrites appear to grow from the inner surface of the CoSi2 layer (see Fig. 7c). This phase relation confirms that the CoSi2 compound is the primary phase. In contrast, the CoSi particles of the middle zone show a scatter of orientations. They usually share their orientation with the nearest neighbor only (see Fig. 7e). The orientations of the CoSi2 grains are diverse generally (see Fig. 7f). 3.3.2. Samples processed by EML + SMF The samples generally freeze into a homogeneous microstructure for low DTs. The resultant microstructure is similar to that shown in Fig. 6a. But one sample shows a low volume fraction of eutectic grains near the sample surface. As shown in Fig. 8a, the local microstructure is characterized by a dispersion of equiaxed dendrites of the CoSi compound in a matrix of the CoSi2 compound. It looks very similar to the microstructure shown in Fig. 6b, except for a complete dendritic morphology of the primary CoSi compound. This difference in the grain morphology verifies damping of melt convection by the static magnetic field in the light of a previous study [30].

The microstructure is dependent on the delay time during double recalescence for high DTs. In the case of a short delay time, the microstructure is inhomogeneous and consists of three zones as those observed for the samples processed by EML (see Fig. 6b). In the case of a long delay time, the inner zone vanishes from the sample center. Fig. 8b and c shows the microstructure of two samples with delay times of 3.95 s and 6.78 s, respectively. The outer zone is discerned by a characteristic layer of the primary CoSi2 compound around the sample surface (see insets of Fig. 8b and c). The middle zone is dominated by coarse dendrites or equiaxed grains of the CoSi2 compound. The intergranular regions exhibit a gathering of grains of the CoSi compound. On the other hand, flower-like precipitates of the CoSi compound are discerned in the CoSi2 grains. As shown in Fig. 8d, these precipitates have a high density in the CoSi2 grains of the outer zone, and are coarsened in neighboring parts of the middle zone. Fig. 9 shows the EBSD micrographs of two samples. As displayed in Fig. 9a, a nearly complete dendrite of the CoSi compound is preserved in a sample with DT = 4 K, though all of its neighbors are fragmented. In Fig. 9b, this dendrite appears to be surrounded by eight “grains” of the CoSi2 compound. Each “grain” of the CoSi2 compound comprises a piece of the halos and a neighboring eutectic grain.

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Fig. 8. Back-scattered SEM micrographs of the samples processed by EML + SMF. The bright phase is CoSi, and the dark phase is CoSi2. (a) DT = 30 K, (b) DT = 121 K with a delay time of 3.95 s, (c and d) DT = 199 K with a delay time of 6.77 s. Arrows in (d) show precipitates of the CoSi compound in equiaxed CoSi2 grains.

Fig. 9. EBSD micrographs of the samples processed by EML + SMF. (a and b) DT = 4 K, (c and d) DT = 199 K. The grains of the CoSi compound are indexed with colors in (a) and (c). The grains of the CoSi2 compound are indexed with colors in (b) and (d). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

These features of grain orientations are similar to those observed in the samples processed by EML, except for the complete dendrite of the CoSi compound. In the sample with DT = 199 K, the CoSi particles of the middle zone

show a reduced scatter of orientations with respect to the same species in the samples processed by EML for high DTs. But the equiaxed CoSi2 grains still show a large scatter of orientations.

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Fig. 10. Back-scattered SEM micrographs of the samples processed by ESL. The bright phase is CoSi, and the dark phase is CoSi2. (a) DT = 95 K, (b) DT = 102 K, (c) DT = 213 K, (d) DT = 304 K.

Fig. 11. EBSD micrographs of the samples processed by ESL. (a and b) DT = 95 K, (c) DT = 102 K, (d) DT = 304 K. The grains of the CoSi compound are indexed with colors in (a). The grains of the CoSi2 compound are indexed with colors in (b–d). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

3.3.3. Samples processed by ESL The microstructure of the samples is essentially homogeneous independent of DT. As shown in Fig. 10a, the sample with DT = 95 K freezes into a dendritic microstructure. Elongated dendrites of the primary CoSi compound are

embedded in the matrix of equiaxed CoSi2 grains with their trunks pointing towards the sample center. Such a microstructure suggests that the dendrites of the CoSi compound nucleate at the sample surface and grow inwards under the influence of a radial temperature gradient. Eutectic grains

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are very few and present in the sample center only. In the sample with DT = 102 K, the CoSi2 compound nucleates as the primary phase. As shown in Fig. 10b, the microstructure is dominated by equiaxed grains of the CoSi2 compound. Fine precipitates of the CoSi compound are often discerned near the peripheries of these grains. The intergranular regions constitute an interconnected network of the CoSi compound and show good wetting to the equiaxed CoSi2 grains. A similar microstructure is formed in the sample with DT = 213 K. Grains of the primary CoSi2 compound look more dendritic than equiaxed (Fig. 10c), while the grains of the CoSi compound in intergranular regions do not show any discernible changes. In the sample with the maximum DT of 304 K, the dendritic-looking grains of the CoSi2 compound are refined remarkably. In contrast, the intragranular precipitates of the CoSi compound are coarsened. Additionally, the intergranular regions seem to be slightly remelted (see Fig. 10d). Fig. 11 illustrates the EBSD micrographs of the samples. In the sample with DT = 95 K, the dendrites of the primary CoSi compound show different orientations (see Fig. 11a), indicating that they arise from different nucleation sites on the surface of the sample. These dendrites are surrounded by a few blocks of the CoSi2 compound. Each of the blocks comprises several equiaxed CoSi2 grains with close orientations (see Fig. 11b). In the sample with DT = 112 K, the equiaxed CoSi2 grains show diverse orientations (Fig. 11c). The intergranular network of the CoSi compound is divided into many segments of different orientations (not shown for saving space). In the samples with higher DTs, the CoSi2 grains show very similar orientations, indicating that they are parts of a giant dendrite (Fig. 11d). The orientations of the intergranular CoSi grains do not show any notable changes. 4. Discussion 4.1. Phase selection mechanism The present results show the formation of the CoSi2 halos around the primary CoSi dendrites for low DTs (Figs. 6a and 8a). This observation agrees with earlier studies [20,31]. Halos of one eutectic phase about another usually appear in hypoeutectic compositions [32,33]. We suppose that the present alloy composition also lies at the hypoeutectic region. This assumption is supported by our observations of the two separated thermal events for low DTs (see Fig. 2). It is also consistent with the prediction of a Si-richer eutectic composition by a recent thermodynamic assessment of the Co–Si system [26]. Thus, a liquidus temperature of 1612 K predicted by the thermodynamic assessment is referred to for defining DTs of the samples (see Fig. 1). The formation of the primary CoSi2 compound for high DTs was revealed by an in situ X-ray diffraction analysis of the early study [20]. The present results provide more proofs of this alternative solidification path. Firstly, the

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microstructure of the present samples shows the formation of the single-phase layer or and the dendrites of the CoSi2 compound (see Figs. 6b, 8b–c and 10c–d). Secondly, the in situ diagnosis of the solidification process with the high-speed camera revealed an abrupt decrease of dendritic growth velocities of the primary phases at the DTc of 88 K (see Fig. 5). However, two opposite explanations were proposed in earlier studies. Yao et al. [17] suggested with model calculations that the CoSi2 compound had a lower nucleation rate than that of the CoSi compound, but grew faster over a wide range of DTs. Li et al. [20] presumed with crystallographic considerations that the two compounds had comparable growth kinetics, but that the CoSi2 compound had a higher nucleation rate than that of the CoSi compound. In terms of the data of Fig. 5, neither of the explanations gave a reliable evaluation of the growth velocities of the two compounds. Due to the fact that a metastable phase often grows more slowly than a stable phase [34,35], we ascribe the formation of the primary CoSi2 compound to an advantage in nucleation kinetics over the CoSi compound. A quantitative analysis is presented below. Nucleation is heterogeneous even in containerlessly undercooled melts [27,36], because a barrier of nucleation, namely critical work of nucleation, can be reduced by a catalytic substrate remarkably. According to the classical theory on nucleation [37], the critical work of nucleation of a cap-like nucleus on a flat substrate, DG, can be expressed by DG ¼

16pr3S=L 3DG2V

f ðhÞ

ð1Þ

where rS/L is the interfacial energy between the solid phase and the liquid phase, DGV is a difference in volumetric free energy between the solid phase and the liquid phase and f(h) is the wetting factor of the substrate to the solid phase at a contact angle of h. The DGV is often approximated by a product of the volumetric entropy of fusion, DSV, and the nucleation undercooling of the liquid phase with respect to the TL of the solid phase. The data of DSV of the two compounds can be calculated from the measured latent heat of fusion at congruently melting compositions [38].1 The primary CoSi2 compound is metastable thermodynamically. Its TL is estimated with the temperature of the thermal plateau following the first thermal event for high DTs. The latter quantity is determined to have a mean value of 1556 ± 6 K (see curves b and d of Fig. 1). The rS/L of the two compounds is available in the literature [39,40].2 The f(h) is rarely documented and is treated as a free parameter. These parameters are summarized in Table 1. By substituting them into Eq. (1), the DGs of the two compounds are

1 Note that the measured heat of fusion in J/g is converted into a lower value in J/mol by mistake. This error is corrected in the present calculations. 2 The rS/L is derived from the Gibbs–Thompson coefficient.

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Table 1 List of parameters used for calculations of the critical work of nucleation of the CoSi compound and of the CoSi2 compound. Phases

CoSi

CoSi2

Ref.

Liquidus temperature TL (K) Heat of fusion DHf (J mol–1) Interfacial energy rS/L (J m–2) Wetting factor f(h)

1612 38,950 0.445 0.22, 0.43

1556 79,960 0.212 0.43

[26], present work [38] [39,40] Present work

Fig. 12. Calculated critical work of nucleation of the CoSi compound (blue lines) and the CoSi2 compound (red line). Two different critical undercoolings, DTc, for the preferred nucleation of the CoSi2 compound are predicted under assumptions of identical and non-identical wetting factors, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

calculated as a function of DT. The calculated results are shown in Fig. 12. Under an assumption of identical f(h)s, the DG of the CoSi2 compound becomes smaller than that of the CoSi compound above a DTc of 76 K. This advantage in DG can explain the preferred nucleation of the CoSi2 compound for high DTs qualitatively. But the calculated DTc is 12 K lower than the experimentally determined DTc. In order to bridge this gap, we tentatively assume different f(h)s for the two compounds. It is found that the experimentally determined DTc of 88 K is reproduced by assuming a double f(h) for the CoSi2 compound. Such a requirement can be satisfied by choosing h = 84.6° and 67° for the CoSi2 compound and for the CoSi compound, respectively. 4.2. Effects of melt convection on microstructure formation An early study [20] suggested three effects of melt convection on microstructure formation in the alloy composition under study: (1) promotion of fragmentation of the primary CoSi dendrites for low DTs, (2) suppression of eutectic grains for low DTs, and (3) “squeezing” of CoSi particles into intergranular regions for high DTs. Except for the first effect, the other effects are disputable in terms of the present results. First, the microstructure with a low volume fraction of the eutectic grains is not unique for the sample processed

by ESL with DT = 95 K. As shown in Figs. 6b and 8a, it is also formed locally in one sample processed by EML with DT = 40 K and in one sample processed by EML + SMF with DT = 30 K. Therefore, it is not reasonable to correlate it to a difference in the level of melt convection. After a careful examination of the temperature– time profiles of the latter two samples, we find that the nucleation temperature of the CoSi2 compound, namely the onset temperature of the second thermal event, is depressed by more than 100 K below the eutectic temperature. This depression is much more significant that that of the other samples. With this finding, we ascribe the locally reduced volume fraction of the eutectic grains to overgrowth of the primary CoSi compound. From a thermodynamic point of view, the CoSi compound can continue to grow in the mushy zone, though at lower velocities, after its rapid growth ceases at the end of the first recalescence. If the nucleation temperature of the CoSi2 compound is depressed by 100 K, the time for slow growth of the primary CoSi compound will be increased to more than 3 s (assuming a cooling rate of 30 K s–1). As a result, the melt composition surrounding the primary CoSi compound can bypass the eutectic composition and even approach the stoichiometry of the CoSi2 compound. Once the CoSi2 compound nucleates in this Si-richer melt composition, its growth will dominate the following solidification process due to a small difference in composition. When the melt composition changes back to the eutectic composition after predominant growth of the CoSi2 compound, the solidification process will end with eutectic growth. But the volume of the melt is very little by then. Thus, the fully solidified samples show a very low volume fraction of the eutectic grains. It should be pointed out that a large DT of the bulk samples can undoubtedly increase the volume fraction of the primary CoSi compound, and makes a contribution to the reduction of the volume fraction of the eutectic grains. However, this contribution should not be overestimated because the hypercooling of the samples is estimated to be of the order of 1000 K. Therefore, complete suppression of eutectic grains in the samples relies not only on the time available for the slow growth of the CoSi compound in the mushy zone, but also on the sample size. For larger sample sizes, the dendrites of the primary CoSi compound cannot grow through the bulk volume of the samples processed by EML or by ESL during a time of few seconds. As a result, the eutectic grains are suppressed in local parts of the two samples only. In contrast, the volume of the sample processed by ESL is about seven times smaller, and its DT is more than doubled. Thus, the dendrites of the primary CoSi compound have enough time to grow into the sample center, leading to complete suppression of the eutectic grains throughout the bulk volume. The third effect of melt convection is in conflict with the present results directly. On one hand, some of the samples processed by EML show a random distribution of the CoSi particles in the matrix of CoSi2 grains (see Fig. 6d). On the other hand, the samples processed by EML + SMF show

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the “squeezed” morphology of the CoSi particles, i.e. gathering in intergranular regions (see Fig. 8b and c). As described in Section 3.2, this difference in the distribution of the CoSi particles can be related to a difference in the delay time during double recalescence. The question is what factors control the delay time. From a physical point of view, the delay time has dual meanings: (1) the time available for ripening and slow growth of the primary CoSi2 compound; (2) an incubation time for nucleation of the secondary CoSi compound in the mushy zone. The first meaning is valid also for solidification of undercooled single-phase alloys, and is usually termed plateau time. The plateau time decreases with increasing DT in consideration of a thermal balance between the remaining melt and the freezing primary solid. However, the delay times of the present samples do not show such dependence on DT. For example, the samples processed by EML + SMF exhibit a delay time of 3.765 s at DT = 122 K, but a delay time of 0.94 s at DT = 222 K. This contrast suggests that the delay times of the samples are not determined by DT, but by nucleation of the secondary CoSi compound. Matson et al. [41] found that the delay times during double recalescence of undercooled hypoeutectic Fe–Cr–Ni alloys are dependent on melt convection via experimental techniques. Thus, the delay times of the present samples are also examined with respect to the experimental techniques. It is found that the delay times do not exceed 2 s for the samples processed by EML, but range from 0.94 to 6.77 s for the samples processed by EML + SMF, and range from 3.7 to 17.614 s for the samples processed by ESL. These data, though overlapping at the low ends, do show a dependence on the experimental techniques and therefore on the level of melt convection. By reference to Matson’s explanation [42], we suppose that the difficulty in nucleation of the secondary CoSi compound is eased at low-angle grain boundaries of the primary CoSi2 compound, which can be readily formed under action of strong melt convection. This assumption is supported by the EBSD analysis of a sample processed by EML. As shown in Fig. 7c and d, fine dendrites of the secondary CoSi compound often stem from the boundaries between primary CoSi2 grains having close orientations. In the samples processed by ESL, melt convection is weak. The nucleation of the secondary CoSi compound may suffer from a lack of the low-angle boundaries of the primary CoSi2 grains, leading to a very long delay time. In the samples processed by EML + SMF, melt convection is moderately weak. The delay times are reduced to some extent, but are generally longer than those of the samples processed by EML. However, the delay times of the samples can show a scatter even under identical conditions of DT and melt convection due to the stochastic nature of nucleation [27,43]. This scatter accounts for the overlapping of the delay times of the present samples at the low ends. It should be pointed out that the difficulty in the nucleation of the secondary CoSi compound under conditions of weak melt convection may be eased alternatively by the

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formation of a metastable novel phase in the highly undercooled melt of the mushy zone. The evidence is shown by an additional and weak recalescence event of the triple thermal behavior observed during solidification of the samples processed by ESL for very high DTs (see curves e and f of Fig. 1). The metastable phase is assumed to have a lower solid/liquid interfacial energy of the CoSi compound and thus can nucleate earlier in the mushy zone. After nucleation, it may act as a catalytic substrate for heterogeneous nucleation of the CoSi compound. However, the grains of the metastable phase cannot survive at high temperatures due to their metastable nature. Therefore, they are likely to have decomposed into the two stable compounds through the following strong recalescence. The observations of the fine precipitates of the CoSi compound near the peripheries of the primary CoSi2 grains seem to support this hypothesis. Since similar precipitates are formed in some of the samples processed by EML + SMF (see Fig. 8d), the formation of the metastable phase is assumed to be common for the samples with high DTs and weak melt convection.

Fig. 13. Schematic diagrams showing microstructure formation with different DTs and delay times. The dark phase is the CoSi compound, and the grey phase is the CoSi2 compound.

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The long delay times are also supposed to be partially responsible for the overshooting of temperature of the samples in addition to a difference in the emissivity between the solid samples and the melted samples. Due to solute rejection, the growth of the primary CoSi2 compound makes the melt composition in the mushy zone more Co-richer than the bulk composition is. Although the temperature of the bulk samples keeps constant by external cooling, the undercooling of the interdendritic melt is rapidly increased with elapsing delay time due to a steep liquidus at the hypoeutectic region of the Co–Si phase diagram (see Ref. [26]). Once the CoSi compound nucleates in the mushy zone, it will grow rapidly leading to a strong recalescence event. In this event, local temperatures of the samples tend to approach the liquidus temperature of the interdendritic Co-rich melt composition, and rise much beyond the liquidus of the bulk composition (see curves c and e of Fig. 1). Similarly, a richening of solute atoms occurs in the remaining melt through the overgrowth of the primary CoSi compound. But the liquidus is not steep at the hypereutectic region so that local temperatures during recalescence cannot exceed the liquidus of the bulk composition (see curve a of Fig. 1). As a summary, microstructure formation in hypoeutectic CoSi–CoSi2 composition depends not only on DT, but also on the thermal behavior of the samples. For high DTs, it depends strongly on the delay time during double recalescence. The major processes are schematically shown in Fig. 13. The formation and decomposition of the metastable phase in the mushy zone is not shown for simplicity. Despite such progress, the present work does not yield a complete understanding of microstructure formation in the undercooled samples. It is suggested that a numerical modeling of the solidification process with a volume averaging-based method [44,45] may shed more light on the details of the physical processes underlying microstructure formation at different DTs. 5. Conclusions Phase selection and microstructure evolution in undercooled melts of hypoeutectic Co–61.8 at.% Si alloys have been investigated using a variety of containerless processing techniques and in situ observations. The conclusions are drawn as follows: (1) The samples show a sharp transition of thermal behavior from two separated thermal events to two continuous thermal events (double recalescence) at a critical undercooling of 88 K. The former behavior corresponds to a solidification path with the CoSi compound as the primary phase, and the latter behavior corresponds to an alternative solidification path with the CoSi2 compound as the primary phase. (2) The growth velocities of the CoSi compound have been determined to be generally larger than those of the CoSi2 compound independent of their nucleation

sequences. The preferred formation of the primary CoSi2 compound above the critical undercooling of 88 K has been explained by a quantitative analysis of the critical work of nucleation of the two compounds under the assumption of non-identical wetting factors. (3) The microstructure of the samples depends on undercooling and on the thermal behavior as well. At low undercoolings, the samples generally freeze into a high volume fraction of the eutectic grains in addition to the primary CoSi dendrites and the CoSi2 halos. However, a few samples freeze into a low volume fraction of the eutectic grains either locally or globally. This difference in the microstructure has been correlated to the depressed nucleation temperatures of the secondary CoSi2 compound during solidification. At high undercoolings, the microstructure is either homogeneous or inhomogeneous depending on the delay time during double recalescence. The samples processed by ESL and by EML + SMF generally have a long delay time during double recalescence and thus freeze into a homogeneous microstructure. In contrast, the samples processed by EML show a short delay time and freeze into an inhomogeneous microstructure with three distinct zones. This difference in the microstructure has been explained by assuming eased difficulties in nucleation of the secondary CoSi compound under conditions of strong melt convection [41,42]. (4) The observations of the additional and weak thermal event as well as the fine precipitates of the CoSi compound in the primary CoSi2 grains give hints at the formation of a metastable phase from a highly undercooled Co-rich melt composition of the mushy zone. This metastable phase may play a catalytic role in the nucleation of the CoSi compound, but decomposes during the subsequent strong recalescence event. (5) A complete understanding of microstructure formation in the hypoeutectic CoSi–CoSi2 eutectic composition is still expected. It has been suggested that a numerical modeling of the solidification process with the volume averaging-based method [44,45] may shed more light onto the physical processes underlying microstructure formation at different undercoolings.

Acknowledgements The authors thank M. Li, D. Matson and T. Volkmann for stimulating discussions and thank D. Brown for reading the manuscript. The authors also thank T. Fukuda for his assistance in the EML + SMF experiments. The work is supported by the Fundamental Research Funds for the Central Universities (N090109001 and N110408003) and by the Ministry of Education, China (20060145023 and NCET05-0292). Part of the work is supported also by National Science Foundation of China

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