# Directional Solidification of Sn-Cu6Sn5 In Situ Composites

Authors: Osvaldo Fornaro
Journal: Advances in Materials Science and Engineering
 (2019)

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## Abstract

The 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 the mechanisms 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. The 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.


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## Body

## 1. 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 [1–5] 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]. There 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 [8–11] and a number of thermodynamic databases have been developed specifically for this purpose [9, 11–15]. 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. The 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. There are several initiatives to obtain a complete alloys properties database [6, 16–20].For these reasons, there exist considerable experimental works focusing on the characterization of SAC alloys [7, 21–23]. The surface and wetting properties of solders are key properties for design of both the new solders and soldering process [23–25]. The 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 Cu3Sn (ε) and Cu6Sn5 (η) layers, as already have been observed at the interface of different Sn-based solders in contact with the Cu substrate [23, 27, 28]. Cu6Sn5 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 [29–31]. 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 [32–34].To obtain theη (Cu6Sn5) 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 Cu6Sn5 phase may appear as primary or secondary depending on the chemical composition of the alloy. For concentrations greater than 7.44 wt.% Cu, the Cu3Sn phase is the primary phase and then Cu6Sn5 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 [36–38].Accordingly, the aim of this work is to obtain samples with the appropriate composition that containη 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.


## 2. Experimental

The 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 [39–41]. The 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. The lower section is refrigerated by water circulation. This disposition allows us to obtain a fixed thermal gradient in the place where the samples were located to be directionally grown. The 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. The 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. This scheme provides a very precise motion, resulting with a precision of ±0.1 μm/s. The specimens were located in a quartz tube of 10 mm of internal diameter, with a selected length of 105 mm. The 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 GL = 2.5 ± 0.5 K/mm. The 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.The 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. The microstructure was observed both in longitudinal (respect to the growth direction) and cross-sectional views. The 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 0.5μm of Al2O3 in water solution. Finally, the samples were electropolished with 2-butoxyethanol (80 ml) + glycerine (10 ml) + HClO4 (10 ml), at 20–30 VCC. The electropolishing process produces an epitaxial oxide epitaxial oxide that let us visualize the structure under polarized light. A chemical etching of HCl (2 ml) + HNO3 (5 ml) + methanol (93 ml) was used to improve the image contrast under bright light conditions [19, 42].


## 3. Results and Discussion

Directional growths of samples were carried out at different pulling velocities in the range 0.5 to 5μm/s under a constant thermal gradient GL = 2.5 K/mm. Obtained microstructures can be seen in Figures 1–4.Figure 1
Sn-0.7 wt.% Cu samples directionally solidified and grown from right to left.V = 0.5 µm/s; GL = 2.5 K/mm. Longitudinal view of (a) (ηP + Liq) + Liq. interface at the top of growth; (b) solid + (ηP + Liq) interface.
(a)
(b)Figure 2
Longitudinal view of Sn-7 wt.% Cu samples directionally grown at increasing values of pulling velocity: (a) 1.0µm/s; (b) 2.0 µm/s; (c) 5.0 µm/s (GL = 2.5 K/mm).
(a)
(b)
(c)Figure 3
Transverse sections of samples grown at (a)V = 0.5 µm/s and (b) V = 2.0 µm/s and GL = 2.5 K/mm.
(a)
(b)Figure 4
Detailed longitudinal views corresponding to the solidified zone (below solid + (ηP+Liq) interface) for different pulling velocities: (a) V = 0.5 µm/s; (b) V = 1.0 µm/s; (c) V = 2.0 µm/s; (d) V = 5.0 µm/s. In all cases, GL = 2.5 K/mm.
(a)
(b)
(c)
(d)As can be seen, the crystal growth is not a simple process. The primary solid phase is a Cu6Sn5 intermetallic phase, which appears like projected towards the liquid, because it has a higher liquidus temperature than the rest of the solid. The 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, Figure1 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 ηP phase and the quenched liquid, whilst in Figure 1(b), it is possible to observe that primary ηP is surrounded by a two-phase β + ηS. Also the primary ηP phase seems to be coarsened by the effect of permanence at high temperature during a longer time.Note the definition ofηP as the primary η (Cu6Sn5) phase in terms of the solidification path to differentiate it with respect to ηS which appears in the two-phase zone as a consequence of the eutectic reaction of the remaining liquid:(1)liquid⟶β+ηS.BothηP as ηS have the same composition and structure, but significant difference in size and distribution can be observed in the different micrographs.Figures2(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 GL = 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+ηS) interfibber zone.In Figure3, transverse sections of the growth in the solid zone can be seen. The structure appears similar to the previous figure, showing fibbers of ηP surrounded by an eutectic-like structure (β+ηS). 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 ληP and ληS could be defined as a function of the solidification growth parameters.


### 3.1. 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 Figure5. It can be seen that, in the lower Cu content range, this is an eutectic system, with an eutectic composition of CE = 0.87 wt.% Cu and an eutectic temperature TE = 226.8°C (499.95 K). The phases involved into the reaction are β (Sn) and η (Cu6Sn5). 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 Cε = 61.63 wt.% Cu (corresponding to Cu3Sn composition).Figure 5
Sn-Cu equilibrium phase diagram.As can be seen from this diagram, different regions could be identified, characterized by the primary phase to nucleate:(i)
A dilute alloy or proeutectic zone, for concentrations lesser than 0.87 wt.% Cu. In this case, the primary phase would beβ (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 isη. The solidification ends with the isothermal eutectic reaction (1).(iii)
Hypereutectic with the chemical composition greater than 7.44 wt.% Cu. The primary phase is theε (Cu3Sn) 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:(2)L+ε⟶L′+η.The situation is condensed in Table1 and Figure 6, where the phase fraction was calculated at T⪝TE. 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, fηP, plus an additional 2% after the eutectic reaction of remnant liquid, fηS, as can be seen in Figure 7. The solidification path and the present phases for a given value of temperature can be determined under equilibrium considerations by using the lever rule.Table 1
Solidification path of Sn-Cu alloys with different compositions.
Composition range (wt.% Cu)
Primary phase
Secondary phase
Final transformation
0–0.87
β (Sn)
η
L
⟶
β
+
η
0.87
β + η
0.87–7.44
η
β
L
⟶
β
+
η
7.44–39.07
ε
β
L
+
ε
⟶
L
′
+
β
L
′
⟶
β
+
η
39.07
ε
ε
⟶
η
39.07–61.63
ε
η
L
+
ε
⟶
ηFigure 6
Origin of theη phase depending on the solidification path and composition of the alloy.Figure 7
Phase fraction during solidification (calculated under equilibrium considerations).The composition of interest for this work is remarked.During the first stage of cooling, the phase fraction of the primaryηP in the range between TLC0 and TE could be calculated using(3)fηP=C0−CLTCη−CLT,where C0 is the nominal composition of the alloy, Cη corresponds to the composition of the η phase, which can be determined from the atomic composition of η = Cu6Sn5, which results in Cη = 39.1 wt.% Cu. CLT must be taken from the liquidus line TLC of the phase diagram. Once the system reaches TE, the final reaction (1) implies the isothermal formation of β and ηS phases simultaneously. The total η phase fraction is represented in this graph corresponding to the combination of both species ηP+ηS. In the grown samples, it is possible to observe both values, due to the limited solid diffusion at low temperatures.


### 3.2.ηP and ηS Spacing

As mentioned above, the limited diffusion ofβ 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 fibbers is(4)ΔT=K1Vλ+K2λ,where K1 and K2 are constants that depend on the system alloy, fundamentally the range of composition between β and η, ΔC0, the slopes of the liquidus curve, mLβ,η, the rate of phase fraction fβ,η, and Gibbs–Thomson coefficient ΓLβ,η related to each phase [44]. The condition of minimum undercooling supposes that(5)∂ΔT∂λV=0,which means that(6)λ2V=K2/K1,(7)ΔTV=4K1K2,(8)λΔT=2K2.Particularly, equation (6) gives a relationship between the spacing and interface velocity:(9)λ=K′V−1/2,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 K1 and K2 can be extracted from the fitted experimental data. In this work, the spacing of the primary fiber ληP decreases with the pulling velocity, except the growth corresponding to the smallest velocity, which shows a different tendency. The data can be fitted by the following expression:(10)ληP=478⋅V−0.56μm.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:(11)ληS=11.2⋅V−0.96μm.These two relations are shown together in Figure8. 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.Figure 8
Fiber spacingληP and ληS as a function of pulling velocity.


### 3.3. 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 Figure9. The top of the growth corresponds to ηP 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 C0 to CE, according that solidus temperature is the eutectic TE.Figure 9
Schematic drawing of the solidification process.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:(12)Δx=ΔT0GL,where Δx is the length extension of the primary phase into the liquid and ΔT0 is the solidification range of the alloy at the chemical C0 composition, which is as follows:(13)ΔT0=TLC0−TSC0=TLC0−TE,and GL is the externally applied thermal gradient. In this case, the length is(14)Δx≈70mm,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 GL externally imposed because of the liquid in thermal contact with the primary phase.


## 3.1. 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 Figure5. It can be seen that, in the lower Cu content range, this is an eutectic system, with an eutectic composition of CE = 0.87 wt.% Cu and an eutectic temperature TE = 226.8°C (499.95 K). The phases involved into the reaction are β (Sn) and η (Cu6Sn5). 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 Cε = 61.63 wt.% Cu (corresponding to Cu3Sn composition).Figure 5
Sn-Cu equilibrium phase diagram.As can be seen from this diagram, different regions could be identified, characterized by the primary phase to nucleate:(i)
A dilute alloy or proeutectic zone, for concentrations lesser than 0.87 wt.% Cu. In this case, the primary phase would beβ (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 isη. The solidification ends with the isothermal eutectic reaction (1).(iii)
Hypereutectic with the chemical composition greater than 7.44 wt.% Cu. The primary phase is theε (Cu3Sn) 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:(2)L+ε⟶L′+η.The situation is condensed in Table1 and Figure 6, where the phase fraction was calculated at T⪝TE. 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, fηP, plus an additional 2% after the eutectic reaction of remnant liquid, fηS, as can be seen in Figure 7. The solidification path and the present phases for a given value of temperature can be determined under equilibrium considerations by using the lever rule.Table 1
Solidification path of Sn-Cu alloys with different compositions.
Composition range (wt.% Cu)
Primary phase
Secondary phase
Final transformation
0–0.87
β (Sn)
η
L
⟶
β
+
η
0.87
β + η
0.87–7.44
η
β
L
⟶
β
+
η
7.44–39.07
ε
β
L
+
ε
⟶
L
′
+
β
L
′
⟶
β
+
η
39.07
ε
ε
⟶
η
39.07–61.63
ε
η
L
+
ε
⟶
ηFigure 6
Origin of theη phase depending on the solidification path and composition of the alloy.Figure 7
Phase fraction during solidification (calculated under equilibrium considerations).The composition of interest for this work is remarked.During the first stage of cooling, the phase fraction of the primaryηP in the range between TLC0 and TE could be calculated using(3)fηP=C0−CLTCη−CLT,where C0 is the nominal composition of the alloy, Cη corresponds to the composition of the η phase, which can be determined from the atomic composition of η = Cu6Sn5, which results in Cη = 39.1 wt.% Cu. CLT must be taken from the liquidus line TLC of the phase diagram. Once the system reaches TE, the final reaction (1) implies the isothermal formation of β and ηS phases simultaneously. The total η phase fraction is represented in this graph corresponding to the combination of both species ηP+ηS. In the grown samples, it is possible to observe both values, due to the limited solid diffusion at low temperatures.


## 3.2.ηP and ηS Spacing

As mentioned above, the limited diffusion ofβ 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 fibbers is(4)ΔT=K1Vλ+K2λ,where K1 and K2 are constants that depend on the system alloy, fundamentally the range of composition between β and η, ΔC0, the slopes of the liquidus curve, mLβ,η, the rate of phase fraction fβ,η, and Gibbs–Thomson coefficient ΓLβ,η related to each phase [44]. The condition of minimum undercooling supposes that(5)∂ΔT∂λV=0,which means that(6)λ2V=K2/K1,(7)ΔTV=4K1K2,(8)λΔT=2K2.Particularly, equation (6) gives a relationship between the spacing and interface velocity:(9)λ=K′V−1/2,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 K1 and K2 can be extracted from the fitted experimental data. In this work, the spacing of the primary fiber ληP decreases with the pulling velocity, except the growth corresponding to the smallest velocity, which shows a different tendency. The data can be fitted by the following expression:(10)ληP=478⋅V−0.56μm.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:(11)ληS=11.2⋅V−0.96μm.These two relations are shown together in Figure8. 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.Figure 8
Fiber spacingληP and ληS as a function of pulling velocity.


## 3.3. 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 Figure9. The top of the growth corresponds to ηP 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 C0 to CE, according that solidus temperature is the eutectic TE.Figure 9
Schematic drawing of the solidification process.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:(12)Δx=ΔT0GL,where Δx is the length extension of the primary phase into the liquid and ΔT0 is the solidification range of the alloy at the chemical C0 composition, which is as follows:(13)ΔT0=TLC0−TSC0=TLC0−TE,and GL is the externally applied thermal gradient. In this case, the length is(14)Δx≈70mm,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 GL externally imposed because of the liquid in thermal contact with the primary phase.


## 4. Conclusions

The directional solidification of Sn-7 wt.% Cu results in in situ composites ofηP (Cu6Sn5) fibbers surrounded by the two-phase eutectic β(Sn) + ηS (Cu6Sn5). Note that the composition of ηP and ηS is the same (Cu6Sn5) but have a different origin: the first (ηP) is the primary phase of the growth, whilst the second (ηS) appears during the solidification of the remaining liquid.The spacing of these phases has a logarithmic dependence with the pulling velocity, similar to a Burden–Hunt growing law, showing different exponents due to the different local solidification conditions of the both interfaces.



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*Source: 9210713-2019-03-13.xml*