Directional Solidification of Sn-Cu 6 Sn 5 In Situ Composites

(e Sn-Cu system presents an important interest from academic and technological point of view because it is part of the family of alloys proposed as lead-free solder alloys for electronic components and also due to themechanisms involved during the growth of the different phases. Sn-Cu system has two intermetallic phases, i.e., ε-Cu3Sn and η-Cu6Sn5, and η can be used as the negative (anode) electrode in Li-ion batteries, alone or as part of (Co,Ni)xCu6−xSn5-type composites. Obtaining this η phase from liquid with the appropriate chemical composition is a very difficult task because it has a formation temperature lower than liquidus for such a composition. In this way, the η phase appears as a consequence of a solid-solid transformation from the ε phase However, it is possible to find the η phase as the primary or secondary phase after a eutectic reaction for lower concentrations of Cu. On the other side, the Cu6Sn5 phase shows a hexagonal to monoclinic solid-solid transformation around 187°C, which could affect the mechanical system stability when it is used as solder. In this work, directional solidification at different growth velocities of hypereutectic Sn-Cu samples was performed. (e resultant microstructure varies with the growth velocity, but it is formed for a fibber-like primary phase Cu6Sn5 which is projected towards the liquid phase. Behind this region, these fibbers are rounded by a two-phase Sn-Cu6Sn5 structure. In this way, three zones could to be defined in the sample during the directional growth: (i) an entirely solid two-phase region, formed by η rounded by β(Sn) + η eutectic-like structure, (ii) a two-phase solid (η) + liquid, and (iii) the remnant liquid in front of the interface.


Introduction
In the electronics industry, the soldering is one of the most important joining processes applied to connect electronic devices and substrates.Due to harmful effects of lead on environment and human health, a set of strict legislation (the so-called WEEE and RoHS directives) on banning the use of lead-free solders (LFS) were developed [1][2][3][4][5] to replace classical eutectic and near-eutectic Sn-Pb solder alloys.In the last two decades, binary and ternary solders such as Sn-Ag, Sn-Cu, Sn-Zn, Sn-Bi, Sn-Au, Sn-In, Sn-Ag-Cu, Sn-Bi-In, Sn-In-Zn, and Sn-Ag-Bi have been investigated and designed [6,7].ere are several candidates of LFS Sn-based alloys such as Sn-Ag-Cu alloys (SAC alloys), containing Zn, Bi, and In, which have considerably attracted attention especially for automotive, industrial, and electronic applications.As a part of the process of developing new LFS alloys, thermodynamic calculations have been extensively used [8][9][10][11] and a number of thermodynamic databases have been developed specifically for this purpose [9,[11][12][13][14][15].However, it is well known that a purely thermodynamic approach does not provide direct information on general material properties, such as thermophysical and mechanical properties that are the key to the application of new solder alloys.e knowledge of reliable data related to material properties is essential for the interpretation of alloy solidification and numerical modeling methods for the casting and soldering process.ere are several initiatives to obtain a complete alloys properties database [6,[16][17][18][19][20].
For these reasons, there exist considerable experimental works focusing on the characterization of SAC alloys [7,[21][22][23].e surface and wetting properties of solders are key properties for design of both the new solders and soldering process [23][24][25].e Sn-Cu system is characterized by the presence of two intermetallic compounds [26].In the range of temperature and composition of interest, the interfacial reaction results in formation of Cu 3 Sn (ε) and Cu 6 Sn 5 (η) layers, as already have been observed at the interface of different Snbased solders in contact with the Cu substrate [23,27,28].Cu 6 Sn 5 has two structural forms.Below 187 °C (460 K), the stable form is known as η′, presenting an ordered long-period superlattice (LPS).During the cooling, the time is usually not sufficient to produce the full transformation η ⟶ η′, and the high temperature form remains as the metastable phase [29][30][31].Reactive wetting results in the formation of intermetallic phases at the interface of a liquid solder/substrate system which results of interest for the joining process [32][33][34].
To obtain the η (Cu 6 Sn 5 ) phase from the melting process is necessary follow the solidification path from several concentrations of Sn-Cu alloys.According to the equilibrium phase diagram for Sn-Cu [26], the Cu 6 Sn 5 phase may appear as primary or secondary depending on the chemical composition of the alloy.For concentrations greater than 7.44 wt.% Cu, the Cu 3 Sn phase is the primary phase and then Cu 6 Sn 5 could appear through a solid-solid transformation during the cooling [35].Taking this in mind, there exist a series of previous works which study the directional solidification of Sn-Cu alloys, both for eutectic compositions as for hypo and hypereutectic alloys [36][37][38].
Accordingly, the aim of this work is to obtain samples with the appropriate composition that contain η as the primary phase, to be directionally grown under different conditions evaluating the relative stability of that phase and the behavior of the microstructure during the growth.

Experimental
e alloys used in this study were obtained, starting from 99.99% purity of Sn and Cu elements, melted in a SiC crucible coated internally by ceramic protective coating, and heated in an electric resistance furnace under constant argon gas flow.Once a homogeneous liquid was obtained, the samples were cast in quartz tubes of similar size, where they would subsequently directionally grow.
Directional growth was performed with a Bridgman-like apparatus, as has been previously reported [39][40][41].e device consists of two chambers located in a cylindrical symmetry.Upper chamber consists of an alumina core with a heating coil with an electronic temperature control.e lower section is refrigerated by water circulation.is disposition allows us to obtain a fixed thermal gradient in the place where the samples were located to be directionally grown.e pulling system of the samples was based in a stepper motor and a gear box, which permitted a translation velocity in the 0-10 μm/s range.e actual displacement velocity was measured with a linear variable differential transformer (LVDT) and a signal conditioning interface.After acquisition, the data were sent to a personal computer, which drives the motor.is scheme provides a very precise motion, resulting with a precision of ±0.1 μm/s.e specimens were located in a quartz tube of 10 mm of internal diameter, with a selected length of 105 mm. e quartz tube was sealed in the bottom with a conical geometry and filled with a partial vacuum of Ar after removing the atmospheric air in several opportunities, to avoid oxide formation during the growth and loses of Cu by reaction with oxygen.During the growth, the thermal gradient in front of the interface was taken in a reference sample by using a double-thermocouple type K using similar pull velocity and furnace temperatures that will be used in the different experiences, resulting in G L � 2.5 ± 0.5 K/mm.e samples were directionally grown at 0.5, 1.0, 2.0, and 5.0 μm/s and quenched after the solid phase taken approximately 40 mm long.
e preparation of the surface for optical microstructural observation and analysis requires particular attention because this alloy can show plastic deformation during the mechanical polishing giving place to twinning formation and the reprecipitation of small grains on the surface.To avoid these effects, an extremely slow and continuously refrigerated mechanical polishing was made.e microstructure was observed both in longitudinal (respect to the growth direction) and crosssectional views.e surface was set up by mechanical polishing using alumina grinding papers, up to 0000 grit, and water lubricated.Final mechanical polishing was achieved using micropolish with 2 up to 0.5 μm of Al 2 O 3 in water solution.Finally, the samples were electropolished with 2butoxyethanol (80 ml) + glycerine (10 ml) + HClO 4 (10 ml), at 20-30 VCC. e electropolishing process produces an epitaxial oxide epitaxial oxide that let us visualize the structure under polarized light.A chemical etching of HCl (2 ml) + HNO 3 (5 ml) + methanol (93 ml) was used to improve the image contrast under bright light conditions [19,42].

Results and Discussion
Directional growths of samples were carried out at different pulling velocities in the range 0.5 to 5 μm/s under a constant thermal gradient G L � 2.5 K/mm.Obtained microstructures can be seen in Figures 1-4.
As can be seen, the crystal growth is not a simple process.e primary solid phase is a Cu 6 Sn 5 intermetallic phase, which appears like projected towards the liquid, because it has a higher liquidus temperature than the rest of the solid.
e solidification ends when the liquid reaches the eutectic temperature, at a long distance away.If the different thermal conductivities between different solid phases and the liquid phase were not taken into account, at first order, the distance beyond the top of the interface depends on the thermal gradient and growth rate.In this way, at the moment of quenching, the sample is formed by three zones which can be identified by an entirely quenched liquid, a primary phase plus liquid, and an all solid zone.
Particularly, Figure 1 shows longitudinal cut of a sample grown at V � 0.5 μm/s.Figure 1 is divided in two micrographs.In Figure 1(a), it can be seen the zone of top wide faceted the η P phase and the quenched liquid, whilst in Figure 1(b), it is possible to observe that primary η P is surrounded by a two-phase β + η S .Also the primary η P phase seems to be coarsened by the effect of permanence at high temperature during a longer time.
Note the definition of η P as the primary η (Cu 6 Sn 5 ) phase in terms of the solidification path to differentiate it with 2 Advances in Materials Science and Engineering respect to η S which appears in the two-phase zone as a consequence of the eutectic reaction of the remaining liquid: Both η P as η S have the same composition and structure, but significant difference in size and distribution can be observed in the different micrographs.
Figures 2(a)-2(c) show longitudinal views of samples grown at V � 1.0, 2.0, and 5.0 μm/s at the same thermal gradient of G L � 2.5 K/mm.In these micrographs, the zone corresponding to the interface between solid and solid-+ liquid can be seen.From Figures 2(a)-2(c), the solid is clearly formed by the fibbers of the η phase, surrounded by a two-phase (β + η S ) interfibber zone.
In Figure 3, transverse sections of the growth in the solid zone can be seen.
e structure appears similar to the previous figure, showing fibbers of η P surrounded by an eutectic-like structure (β + η S ).It is clear that η, both as primary and secondary, could transform in the solid state to η′ during the cooling of the alloy.Even though micrographs do not appear as evidence of transformation, it is not possible to confirm if this transformation occurs during the growth in some point of the sample.Also from the observation of Figures 1-3, it is evident that a spacing λ η P and λ η S could be defined as a function of the solidification growth parameters.

Phase Fraction Estimation.
To interpret the solidification path and the behavior during the growth, it could be useful to use the equilibrium phase diagram of Figure 5.It can be seen that, in the lower Cu content range, this is an eutectic system, with an eutectic composition of C E � 0.87 wt.% Cu and an eutectic temperature T E � 226.8 °C (499.95K). e phases involved into the reaction are β (Sn) and η (Cu 6 Sn 5 ).It can be seen also that both β as η has a limited solubility of the other components (Cu or Sn in each case).Also, η is present in all the range shown, that is from a very dilute alloy up to approximately C ε � 61.63 wt.% Cu (corresponding to Cu 3 Sn composition).
As can be seen from this diagram, different regions could be identified, characterized by the primary phase to nucleate:  Advances in Materials Science and Engineering (i) A dilute alloy or proeutectic zone, for concentrations lesser than 0.87 wt.% Cu.In this case, the primary phase would be β (Sn), and solidification ends with a eutectic reaction like equation ( 1).(ii) Hypereutectic alloy, with chemical concentrations greater than 0 87 wt.% Cu but lesser than 7.44 wt.% Cu.In this case, the primary phase is η. e solidification ends with the isothermal eutectic reaction ( 1).(iii) Hypereutectic with the chemical composition greater than 7.44 wt.% Cu. e primary phase is the ε (Cu 3 Sn) and could transform partially to the η phase, and the final phase fraction depends on the nominal composition of the alloy.In this case, the reaction is formerly a hypoperitectic one: e situation is condensed in Table 1 and Figure 6, where the phase fraction was calculated at T ⪝ T E .For this reason, the nominal composition of Sn-7 wt.% Cu was chosen to develop the directional solidification for this work.In this case, and again following equilibrium conditions, the total expected phase fraction of η is small, being close to 20% as a primary phase, f η P , plus an additional 2% after the eutectic reaction of remnant liquid, f η S , as can be seen in Figure 7.
e solidification path and the present phases for a given During the rst stage of cooling, the phase fraction of the primary η P in the range between T L (C 0 ) and T E could be calculated using where C 0 is the nominal composition of the alloy, C η corresponds to the composition of the η phase, which can be determined from the atomic composition of η Cu 6 Sn 5 , which results in C η 39.1 wt.% Cu.C L (T) must be taken from the liquidus line T L (C) of the phase diagram.Once the system reaches T E , the nal reaction (1) implies the isothermal formation of β and η S phases simultaneously.e total η phase fraction is represented in this graph corresponding to the combination of both species (η P + η S ).In the grown samples, it is possible to observe both values, due to the limited solid di usion at low temperatures.

η P and η S Spacing.
As mentioned above, the limited di usion of β and η phases results in a wide coupled eutectic zone.In this way, the Jackson-Hunt eutectic theory could be used as a starting point to interpret the obtained microstructures [43,44].In principle, this theory is useful for regular nonfaceted/nonfaceted eutectics, which is not this case.However, it can be useful interpret to the behavior of faceted/nonfaceted eutectics, provided some constants of the model could to be adapted.Under the supposition of a minimum undercooling, the relation between the average undercooling in front of the isothermal interface (ΔT), the advance interface velocity (V), and the spacing of the bbers is where K 1 and K 2 are constants that depend on the system alloy, fundamentally the range of composition between β and η, (ΔC 0 ), the slopes of the liquidus curve, (m β,η L ), the rate of phase fraction (f β,η ), and Gibbs-omson coe cient (Γ β,η L ) related to each phase [44].e condition of minimum undercooling supposes that which means that Particularly, equation (6) gives a relationship between the spacing and interface velocity: which in principle could be used in the prediction of the fibber primary phase spacing, as for the eutectic interfibber growth.Following [35], some physical parameters of the Sn-Cu system including K 1 and K 2 can be extracted from the fitted experimental data.In this work, the spacing of the primary fiber λ η P decreases with the pulling velocity, except the growth corresponding to the smallest velocity, which shows a different tendency.e data can be fitted by the following expression:  In this expression, the constant takes into account the effective thermal gradient in front of the interface.Note that the exponent is close to the predicted one under this formalism.In a similar way, the measured spacing for the secondary or interfibber eutectic can be fitted by the following expression: ese two relations are shown together in Figure 8.In this case, as the local growth conditions differ from the conditions found in the front of the growth, both constant and exponent are different.

Solidification Model.
Taking into account the experimental observations previously made including the numerical descriptions of the phase fraction found, it is possible to imagine that the solidification proceeds like it is the schematized in Figure 9. e top of the growth corresponds to η P fibbers close to the equilibrium condition at the liquidus temperature.In the range in between liquidus and eutectic (solidus) temperatures, this primary phase should persist but is surrounded by the liquid of variable composition from approximately C 0 to C E , according that solidus temperature is the eutectic T E .
It is not possible to establish the tip temperature of the growth, to speculate how long from equilibrium is the growth being driven.However, it is not necessarily a big undercooling to let the growth take place, because it is an intermetallic phase.At a first approximation, it can be assumed that the thermal conductivities between involved species solid and liquid are similar; in this case, a simple relation could be postulated to calculate the extension of this zone: where Δx is the length extension of the primary phase into the liquid and ΔT 0 is the solidification range of the alloy at the chemical C 0 composition, which is as follows: and G L is the externally applied thermal gradient.In this case, the length is which corresponds to almost the total length of the samples.Into this zone, the liquid grows with eutectic composition in front of the deeper interface.For this reason, the interfibber solid has the appearance of a eutectic free-growth.However, it is necessary to take into account that the effective thermal gradient in this zone is smaller than G L externally imposed because of the liquid in thermal contact with the primary phase.

Figure 8 :
Figure 8: Fiber spacing λ η P and λ η S as a function of pulling velocity.

Figure 9 :
Figure 9: Schematic drawing of the solidification process.

Table 1 :
Solidi cation path of Sn-Cu alloys with di erent compositions.