The eutectic Ag-Cu alloys exhibiting fine Ag-Cu lamellar eutectic structure formed upon rapid solidification have great potentials being used in various engineering fields, such as advanced lead frames in large-scale integrated circuits [1], high-field magnet design electronic devices [2] and contacts and interconnect layers in semiconductor industry [3]. However, the desired fine primary lamellar eutectic structure (PLES) is often subject to destabilization and replaced by a coarse granular morphology called as anomalous eutectic structure (AES) when undercooling (ΔT) exceeds a certain value [[4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]]. The forming mechanism of AES upon rapid solidification of the undercooled Ag-39.9 at.% Cu eutectic alloy has been a controversial issue and aroused intensive investigations since it was first observed in the 1960′s.

Based on the observation of the as-solidified microstructures, previous models interpreting the formation of the AES in the undercooled Ag-39.9 at.% Cu eutectic alloy include repeated nucleation of Cu-rich phase ahead of the growing matrix of Ag-rich phase [4] and uncoupled dendritic growth of Ag-rich and Cu-rich phases [5]. Considering that the recalescence rate abruptly increases when ΔT is larger than 76 K, Walder and Ryder [6,7] speculated that the growth of lamellar eutectic structure might be replaced by the growth of a metastable γ’ phase during recalescence, and the remelting of the metastable γ’ phase during post-recalescence period leads to the formation of the AES. With the assistances of electron backscatter diffraction and high-speed camera techniques, a few authors [[8], [9], [10], [11], [12]] proposed that the remelting of the PLES is responsible for the formation of AES in the undercooled Ag-39.9 at.% Cu eutectic alloy. Recently, based on a quantitative analysis of the spatial distribution of AES in the Ag-39.9 at.% Cu eutectic alloy undercooled to a range of 10 K-60 K, Mullis and Coplet [13] challenged the remelting model and proposed that the formation of AES should be ascribed to a kinetic shift in the eutectic point during rapid solidification. More recently, Liu et al. [14] proposed that the formation of AES in the undercooled Ag-39.9 at.% Cu eutectic alloy was caused by remelting of the PLES by examining the microstructure of the sample which was solidified in a “thin-gauge” and subsequently reheated to a temperature between the nucleation temperature and the eutectic plateau temperature.

It should be noted that the above models all consider that the formation of AES within the undercooling range of eutectic coupled growth of Ag-39.9 at.% Cu eutectic alloy is attributed to a single mechanism. Unlike other typical binary eutectic systems (such as Ni-18.7 at.% Sn eutectic alloys, etc.), within the undercooling range of eutectic coupled growth, the AES in these systems distributes relatively uniformly in the as-solidified sample and its amount gradually increases with increasing ΔT [15,16]. While for the Ag-Cu eutectic alloy, the reported experimental results show that the distribution and amount of AES undergoes an abrupt change when the undercooling exceeds a critical value of 70-76 K [[6], [7], [8], [9],11]. Below this critical undercooling, the as-solidified microstructure exhibits eutectic cells where the regular lamellar eutectic structure appears in the cell center and the AES forms in the cell boundaries [9,11]. While above this critical undercooling, the as-solidified microstructure consists of a large amount of AES in the eutectic dendrite stems and arms and only a small amount of lamellar eutectic structure forms in the periphery region of the AES [[6], [7], [8]]. These two types of AES may be originated from different forming mechanisms because of their significantly different microstructural characteristics. The purpose of the present work aims to clarify the forming mechanisms of these two types of AES formed upon rapid solidification of the undercooled Ag-39.9 at.% Cu eutectic alloy within the undercooling range of eutectic coupled growth.

The master alloy ingot with a composition of Ag-39.9 at.% Cu (the composition of the eutectic triple point of the Ag-Cu phase diagram) was prepared by melting high purity Cu (99.9999 wt.%) and Ag (99.99 wt.%) pellets in a vacuum induction furnace. The detailed methods used for the undercooling experiments and the copper mold casting experiments are available elsewhere [15]. Thermal histories of the samples during the solidification process were monitored by a Marathon Series MM2ML infrared pyrometer with an absolute accuracy of ±2 K and a response time of 2 ms. Annealing experiments were carried out using a Nabertherm RS80/500/16 vacuum tube furnace with an absolute accuracy of ±5 K. The furnace cavity was kept under vacuum during the annealing process to prevent oxidation of the sample. The as-prepared samples were observed in an Axio Scope A1 ZEISS optical microscope (OM) and an FEI Helios G4 CX scanning electron microscope (SEM).

Fig. 1 shows the recalescence rates of the undercooled samples. The recalescence rate represents the average temperature rise rate during the recalescence process. Its value reflects the crystal growth velocity, because the recalescence during solidification is caused by the rapid release of crystallization latent heat. A larger recalescence rate corresponds to a faster crystal growth velocity [6,10]. As shown in Fig. 1, there are two abrupt increases in the recalescence rate with increasing ΔT. The first one occurs at ΔT = 72 K, and the second one takes place at ΔT = 102 K. That is to say, the crystal growth velocities undergo two sudden increases. This suggests that there are three different crystal growth modes upon the solidification of the undercooled Ag-39.9 at.% Cu eutectic alloy when ΔT<110 K (the maximum undercooling achieved in the current work).

The products of coupled eutectic growth of the undercooled Ag-39.9 at.% Cu eutectic alloy consist of two solid solution phases, i.e. α-Ag and β-Cu. Along with the transition behaviors of the recalescence rates, three types of microstructures are observed in the undercooled samples. The first type is observed within the range of ΔT<72 K, where the microstructure exhibits eutectic cells with regular lamellar eutectic structure appearing in the cell center and a small amount of AES at the cell boundaries; see Fig. 2(a) and (b). This is consistent with previous reports [9,11]. The regular lamellar eutectic structure with a cellular profile is the product of eutectic-cellular growth (ECG) [9,10]. Due to the large difference (about 81.5 at.% Cu) in equilibrium solute concentrations of the two solid solution phases of the Ag-39.9 at.% Cu eutectic alloy and the large thermal diffusion coefficient of the alloy melt, a cellular eutectic structure forms by restraining the branching of the eutectic cells in the lateral side [9,10]. The second type forms within the undercooling range of 72-94 K; see Fig. 2(c) and (d), the microstructure nearly fully consists of the AES. The third one appears in the undercooling range of 102-110 K, the α-Ag dendrites appear in the as-solidified structure, while the regular eutectic lamellar structures locate in the inter-dendritic regions (see Fig. S1 in the Supplementary Material). The formation of α-Ag dendrites in the undercooled Ag-39.9 at.% Cu eutectic alloy may be due to the shift of coupled zone of the Ag-Cu system towards the β-Cu phase, which causes the α-Ag phase to primarily solidify. In this case, when the alloy melt is undercooled to a certain level, the α-Ag phase will be expected to solidify as primary dendrites.

Compared to the natural cooling samples, when the alloy melts undercooled below 94 K are quenched and solidified in the copper mold, the as-solidified microstructures exhibit a fully regular lamellar morphology; see Fig. 3(a) and (b). This strongly suggests that the AES upon natural cooling is caused by the destabilization of PLES. In addition, the typical morphology of eutectic-dendrite microstructure of the as-quenched sample (Fig. 3(b)) suggests that the PLES forms via the eutectic-dendritic growth (EDG) [8,10,[17], [18], [19], [20]]. Accordingly, the AES observed in Fig. 2(c) and (d) is the product of destabilization of the PLES which is formed by EDG. Thus, in the range of ΔT<94 K, the solidification of the undercooled Ag-39.9 at.% Cu eutectic alloy undergoes the ECG→EDG transition at a critical undercooling (ΔT_c) of 72 K, which is in agreement with the previous reports [[8], [9], [10]]. Owing to the smaller tip radius of EDG compared to that of ECG, which facilitates the dissipation of latent heat, EDG usually proceeds much faster than ECG [9,10]. This is consistent with the result presented in Fig. 1 where an abrupt increase of the recalescence rate is observed when ΔT exceeds ΔT_c ( = 72 K).

Figs. 4(a)-(c) and 5 (a)-(c) show the morphological transition of the undercooled samples with ΔT = 68 K (Fig. 4(a)-(c)) and ΔT = 72 K (Fig. 5(a)-(c)) solidified in the copper mold and then heat treated at 1003 K (50 K below the equilibrium eutectic temperature) for various time, respectively. As shown in Fig. 4a-c, the destabilization of the PLES solidified by ECG exhibits an apparent “termination migration” characteristic [21,22]. Namely, the destabilization of PLES begins in the lamellar terminations (cell boundaries) and then gradually develops to the inner region of the lamellae (cell center). While for the PLES formed by EDG, its destabilization shows a full disintegration characteristic, i.e. the PLES fully disintegrates throughout the eutectic-dendritic arms; see Fig. 5(a)-(c). The annealed microstructures shown in Figs. 4(c) and 5 (c) are identical to the microstructures formed under the condition of natural undercooling (Fig. 2(a)-(d)), which suggests that the microstructural developments upon the heat treatment are identical to the destabilizing process of PLES during the post-recalescence period, too.

An interesting question arises that why an abrupt transition of the microstructure characteristic and the destabilization behavior of the PLES occur when the undercooling exceeds ΔT_c? In the following, we analyze the underlying mechanisms of the destabilizations of PLES. It is known that a perfect infinite lamella with flat surface is intrinsically stable, because the perturbation on such a surface is always smoothed down [23]. Thus, the destabilization of the PLES of undercooled eutectic alloys needs to be initiated by a solute gradient along the lamellar thickness direction (G_c) [15,16] or lamellar structural defects, such as lamellar termination [21,22]. For the former, the solute gradient in the lamella will lead to the formation of highly curved regions in the trough of perturbed lamellar surface [15,16]. For the latter, the curvatures of lamellar structural defects are always higher than their adjacent regions [21,22]. Both the two effects would lead to the migration of atoms from the highly curved regions to the adjacent regions with lower curvatures.

In our recent work [16], an analytical model considering the effects of solute gradient and capillary force was derived to explain the transition of PLES→AES caused by the unstable perturbation of interface. By calculating the time required for break-up of the PLES (Δτ) and comparing it with the measured post-recalescence duration (Δt_pr), this model was successfully applied to explain the destabilization of PLES in an undercooled Ni-18.7 at.% Sn eutectic alloy. In the following, this model was adopted to analyze the undercooled Ag-Cu eutectic system. In the Ag-Cu eutectic system, the β-Cu phase in PLES has a significantly steeper solidus slope than that of the α-Ag phase, the melting of the supersaturated β-Cu phase is expected to be easier than that of the α-Ag phase as observed in the undercooled Ni-18.7 at.% Sn eutectic alloy [15]. Thus, in the following, Δτ for the α-Ag lamellae was calculated to compare with the measured Δt_pr. The calculating procedure was provided in the Supplementary Material.

The calculated results are presented in Fig. 6a-d. As shown in Fig. 6a-d, dramatic changes of velocity (V), |G_c^α| (the gradient of solute concentration on the α-Ag side of the interface), lamellar spacing (λ) and Δτ appear at ΔT_c where the transition from ECG to EDG occurs. The calculations of V and λ are in principle consistent with the experimental results where an abrupt increase of the recalescence rate (Fig. 1) and an abrupt decrease of lamellar spacing (Figs. 4(a) and 5 (a)) are observed when ΔT exceeds ΔT_c = 72 K. Fig. 6(d) shows the comparison of the calculated Δτ with the measured Δt_pr. It is seen that, when ΔT>31 K, the calculated Δτ^EDG (the break-up time for the PLES formed by EDG) is smaller than Δt_pr. This means that the destabilization of PLES formed by EDG will occur during the post-recalescence period when ΔT>31 K, and vice versa. While the calculated Δτ^ECG (the break-up time of the PLES formed by ECG) is always larger than Δt_pr within the undercooling range of eutectic coupled growth, which suggests that the destabilization of the PLES formed by ECG will never be initiated by the unstable perturbation of interface during the post-recalescence period.

The above calculations clearly indicate that the destabilization of PLES in the range of ΔT<72 K should not be initiated by solute supersaturation. In this work, we proposed that the mechanism of “termination migration” where lamellar structural defects play an important role may be responsible for the destabilization of the PLES formed by ECG during post-recalescence period. The “termination migration” is one of the most common mechanisms for destabilization of lamellar structures, especially for the case that the composition of the lamellae is close to its equilibrium value [21,22]. This mechanism is often used to explain the destabilization of the lamellar structure in solid-state [21,22]. In this work, we believe that it is also suitable for the destabilization of PLES formed by ECG occurring along the α-Ag/liquid interface. According to the calculations presented above, the diffusion of the supersaturated atoms of the α-Ag lamellae into liquid exerts slight effects on the destabilization of PLES formed by slow ECG. In other words, the destabilization of PLES in this case is mainly driven by interfacial energy, and its transformation kinetics is controlled by the atomic diffusion along the α-Ag/liquid interface. This is consistent with the mechanism of “termination migration” described in Ref. [21,22]. Since the diffusion coefficient along the solid/liquid interface is generally by 3-4 orders of magnitude higher than that along the solid/solid interface [24], the destabilizing process of the PLES can rapidly occur during the post-recalescence period. As shown in Fig. 4a-c, the destabilizing process of the PLES formed by ECG during annealing process exhibits a typical characteristic of “termination migration” as illuminated in Refs. [21,22]. The microstructures formed under the condition of natural undercooling (Fig. 2(a) and (b)) are identical to the annealed microstructure (Fig. 4(c)), indicating that the microstructural developments upon the heat treatment are identical to the destabilizing process of PLES during the post-recalescence period, too. Therefore, it is believed that the destabilization of PLES formed by slow ECG during the post-recalescence period is caused by the mechanism of “termination migration”.

The mechanism of “termination migration” is briefly described here. The capillary forces due to the curvature difference between the termination tip and the adjacent flat interface can induce the atom migration from the termination tip to the flat interface. This will cause the recession of termination tip and the build-up of material on the flat interface adjacent to the termination tip [22]. Such a mass transportation process will lead to the formation of ridges along the length of the lamella as schematically shown in the Fig. 7(b). These ridges often evolve into rod-like structures via further mass transportation [22]; see Fig. 7(c). The finite radius of the curvature of the rod-like structures is unstable and will decompose into granules through interfacial diffusion due to the Rayleigh instability [25]. As a consequence, the region adjacent to the termination of lamellae will eventually transform into granules; see Fig. 7(d). The process depicted in Fig. 7(a)-(d) will be repeated and develop from the cell boundaries to the inner regions of the cells, leading to the destabilization process as observed in the Fig. 4(a)-(c).

Different from the destabilization of PLES formed by ECG which is caused by the mechanism of “termination migration”, the disintegration of the PLES formed by EDG is significantly more severe throughout the whole microstructure (see Fig. 5(a)-(c)). This is consistent with the calculations shown in Fig. 6 that the G_c inside the lamella provides a driving force to initiate the destabilization of the PLES formed by EDG. As described in details in Ref. [16], G_c inside the lamella results in the formation of high curvature regions in the trough of perturbed lamella, and then the surface tension drives atoms to migrate from the trough to the crest, causing the break-up of the eutectic lamella. The as-formed highly curved regions distribute at intervals in the lamellae, and the spacings between the intervals are equivalent to the fastest growing wavelength of perturbation [16]. This means that the mass transportations of each interval in the lamella are approximately equal. Thus, the particle size and the distribution of particles would be relatively uniform. This is in agreement with the experimental observations; see Figs. 2(d) and 5 (c). Compared to the mechanism of “termination migration” dominated destabilization which proceeds gradually from the cell boundaries to the inner region of cells, the interface perturbation induced destabilization is expected to proceed much faster. Thus, the morphological transition of PLES→AES for the case of EDG is able to nearly simultaneously develop throughout the whole microstructure as shown in Fig. 5(a)-(c). Therefore, the abrupt transition of the microstructure characteristic in the natural cooling samples when the undercooling exceeds ΔT_c is due to the destabilizing mechanism of the PLES changing from the “termination migration” to the “unstable perturbation of interface”.

In this work, the mechanisms responsible for destabilization of eutectic lamellar structures upon rapid solidification of the undercooled Ag-39.9 at.% Cu eutectic alloy were investigated. The results show that the coupled eutectic growth of the alloy undergoes a transition from slow ECG to rapid EDG when ΔT exceeds 72 K. The PLES formed by ECG and EDG subject to two different destabilization mechanisms during the post-recalescence periods. For the PLES formed by ECG, the destabilization of the PLES is caused by the mechanism of “termination migration”, while for the PLES formed by EDG, the destabilization of the PLES is ascribed to the mechanism of unstable interface perturbation induced lamella destabilization.

The authors are grateful of the National Natural Science Foundation of China (Nos. 51771153, 51371147, 51790481 and 51431008), the Innovation Guidance Support Project for Taicang Top Research Institutes (No. TC2018DYDS20), and the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (CX201825). The authors would also like to thank the Analytical & Testing Center of Northwestern Polytechnical University for providing essential experimental apparatuses.

Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.jmst.2020.05.019.