Microstructural evolution and mechanical properties of Sn-Bi-Cu ternary eutectic alloy produced by directional solidification

Sn-36Bi-22Cu (wt.%) ternary eutectic alloy was prepared using vacuum melting furnace and casting furnace. The samples were directionally solidified upwards solidification rate varying from 8.3 to 166 μm/s and at a constant temperature gradient (4.2 K/mm) in a Bridgman-type directional solidification furnace. The composition analysis of the phases and the intermetallics (Cu3Sn and Cu6Sn5) were determined from EDX and XRD analysis respectively. The variation of the lamellar spacing (Bi-rich phase) and the Cu3Sn phase spacing with the solidification rate were investigated. The dependence of microhardness, ultimate compressive strength and compressive yield strength on solidification rate were determined. The spacing and microhardness were measured from both longitudinal and transverse sections of the samples. The dependence of microhardness on the lamellar spacing and the Cu3Sn phase spacing were also determined. The relationships between phase spacings, solidification rate and mechanical properties were determined from linear regression analysis.


Introduction
Solidification plays a vital role since it forms the basis for influencing the microstructure and hence improving the quality of cast products.For this improving the casting production and solidification methods have a significant effect on the mechanical properties of the materials and enhancing the quality of cast metals [1][2][3][4] .Directional solidification 5 is one of the most important solidification methods used for material processing.The mechanical properties of the alloys can be improved by obtaining finer microstructure result from higher solidification rates and higher cooling rates under several directional solidification conditions [6][7][8][9][10][11][12][13] .The directionally solidified alloy exhibited higher strength than the non-directionally solidified alloy under the same cooling rate 14,15 .Liu et al. 16 reported that the tensile strength of the in situ composite from the directionally solidified alloy is significantly higher than that from the as-cast alloy.
Soldering technology is an essential part of electronic devices since it plays a key role not only as an electrical connection but also as a mechanical bond 17,18 .Currently, solder joints with higher reliability is demanding because the trend in electronic package is to make products smaller and faster.For global environment conservation, many researches on replacing the conventional Pb-Sn eutectic solder with a lead-free solder have been carried out.Among various leadfree solders, Sn-Bi alloy is one of the promising candidates 19 .Furthermore, the ternary Sn-Bi-Cu ternary alloys may also be considered as promising lead-free solders 19 .Recently, Ag, Bi or In-containing Sn-Cu alloys have received some attention, and in several prominent reliability test programs Sn-Cu-Ag and Sn-Cu-In alloys demonstrated superior performance, at least in its mechanical strength 20,21 .Tai et al. 22 showed that creep resistance of Sn-3.5Ag was improved significantly for Cu particle-reinforced composite solder joints at 25 o C, 65 o C and 105 o C. The tensile strength increased with increasing Bi content in the Sn-Cu eutectic solder alloy, which was attributed to the presence of Bi and its role in refining microstructure and solid solution strengthening 23 .Zhang et al. 24 reported that Sn-Bi-Cu alloys were found to have greater wettability than the Sn-Ag-Cu alloy, and it was confirmed that the addition of Bi increases the wettability.The effect of Cu 3 Sn and Cu 6 Sn 5 intermetallics (IMC's) on the mechanical properties were investigated from many researchers 25,26 .Cheng et al. 25 reported that, Cu 3 Sn single crystal consist of high ultimate strengths depending on the material directions and strain rate.Hu et al. 26 reported that,

Alloy preparation, directional solidification and metallographic processes
Weighed quantities of Sn, Bi and Cu metals in a graphite crucible determined from stoichiometric calculations were placed in a vacuum melting furnace, and the metals were completely melted.After allowing time for the melt to become homogeneous, the molten alloy was poured into graphite crucibles in a casting furnace.The molten alloy solidified from bottom to top in the casting furnace.The directional solidification of the produced alloy was performed in a Bridgman-type directional solidification furnace whose schematic diagram is given in Figure 1.For the directional solidification, the sample was placed into the sample holder.The sample was placed into the furnace.After the furnace reached the desired temperature and thermal stabilization, the sample was withdrawn from the hot region to the cold region of the furnace with the help of different speeded synchronous motors.The alloy was directionally solidified under different solidification rates (8.3-166 µm/s) at a constant temperature gradient (4.2 K/mm).When the sample solidified 12-13 cm, it was quenched in water.Details of the furnaces equipment, alloy preparation, and directional solidification are given in previous work 32 .
For the metallographic processes, the longitudinal and the transverse sections of the samples were cold mounted with epoxy-resin.The samples were then ground with 320-4000 grit SiC paper and polished with 3-0.25 µm diamond pastes.The alloys were then etched with 95 ml H 2 O, 2.5 ml HNO 3 , 1.5 ml HCI, 1 ml HF.The micrographs of the samples were taken with the Olympus BX-51 model optical microscope by using different objectives.The lamellar spacing, λ (Bi-rich were measured with the Adobe Photoshop CS3 program taking into account the magnification factor.In eutectic and intermetallic phase spacing measurements, linear intersection method is used.In both measurements, at least 30-50 values were measured for each specimen at least on ten different regions for each specimen for statistical reliability.The details of eutectic and particle spacing measurements were described elsewhere 32 .

Measurement of microhardness
Microhardness measurements were performed with a Future Tech FM-700 model digital microhardness test device.This device has the ability of applying 1-1000 g load.In this work 10 g load was applied to the sample for 10 seconds.The measurements were taken from the solid parts nearest to the solid-liquid interface.Average of 30 measurements were taken from longitudinal and transverse sections of the directionally solidified samples, and the average values were taken for the microhardness value.When the indenter of the test device applied to the sample for certain times, the trace in the shape of square occurs.The diagonal size of the trace (d) is read from the test device.By dividing the applied force by the trace area the Vickers microhardness is determined as follows (1)   where P is the applied load (kg), d is the diagonal length of trace, θ is the angle between the opposite surfaces of the diagonal trace.θ

Measurement of compressive strengths
The dependence of ultimate compressive strength and compressive yield strength on the solidification rate were determined.In this work, round rod samples have a length of 6-8 mm and a diameter of 4 mm were used.Compressive strength measurements of the samples were made at room temperature at a deformation rate of 1 mm/min.Compressive tests were performed to the directionally solidified round rod samples with different solidification rates.

Determination of the chemical components of the phases
According to the binary phase diagrams among Bi, Sn and Cu, solid solubility of Sn in solid Bi and Bi in solid Sn are about 0.1 wt.% Sn and 21 wt.%Bi, respectively at the eutectic temperature, 139°C 33 .Also, the solubility of solid Sn in Cu and solid Cu in Sn are about 1 wt.% and 0.006 wt.%, respectively at the eutectic temperature, 232°C 33 .Previous work 34 indicated that the calculated solubilities of Bi in solid Cu or Cu in solid Bi at the eutectic point are both approximately 10 -9 with the assumption that the interchange energy in the rhombohedral structure is similar to that in the fcc structure.This small amount cannot be detected with modern spectroscopy, and the material is normally treated as a pure material 34 .
Energy dispersive X-ray (EDX) analysis was performed to determine the composition of phases in the Sn-Bi-Cu eutectic alloy.EDX analysis was performed at 20 keV using the X-ray lines.According to the EDX analysis results shown in Figure 2, four different solid phases (black, dark gray, white lamellar and dark lamellar) grew at the Sn-Bi-Cu eutectic alloy.The compositions of the black phase (Cu 3 Sn intermetallic) and dark gray phase (Cu 6 Sn 5 intermetallic) were Cu-wt.%40.70 Sn and Sn-wt.%35.75 Cu, respectively.Also, the white lamellar phase (Bi-rich eutectic) and dark lamellar phase (Sn-rich eutectic) were Bi-3.38 wt.% Sn and Bi-24.16wt.% Sn, respectively.Figure 2 shows examples of representative SEM images of ternary eutectic microstructures obtained for the directionally solidified Sn-36Bi-22Cu alloys, with the eutectic mixtures being characterized by complex arrangements of Bi-rich and Sn-rich phases and the corresponding intermetallic compounds, Cu 3 Sn and Cu 6 Sn 5 , respectively.For the Cu 3 Sn IMC, its growth is governed by the reaction between Cu and Sn atoms.Clevenger et al. 35 reported the onset of Cu 3 Sn formation from the reaction between Cu 6 Sn 5 and Cu.The Cu 3 Sn phase can be formed by conventional casting 36,37 , directional solidification 8,23,26 and rapid solidification methods [38][39][40] .Due to the solidification temperature differences, initially the Cu-rich Cu 3 Sn and Cu 6 Sn 5 IMC phases solidified, followed by Sn-rich and Bi-rich phases at a lower temperature.Ternary cooperative growth has not been observed for this reason.In addition, the presence of these phases was confirmed by EDX (Fig. 2) and XRD analysis (Fig. 3).According to Fig. 2, Cu 3 Sn particles with a thickness about 4 µm were surrounded by Cu 6 Sn 5 phase and these two phases are coherent with each other very well.During the eutectic reaction, the Cu 3 Sn IMC phase grows as rods embedded in a continuous Bi-rich matrix.
X-ray diffraction (XRD) measurements were performed with a diffractometer (Rigaku Ultima IV) using Cu-Kα radiation (k=1.5405A°) at an accelerating voltage of 40 kV.The diffracted beam was scanned in steps by 0.01º across a 2θ range of 10-100º.XRD results of as-cast alloy are shown in Figure 3.As indicated, the presence of Cu 3 Sn and Cu 6 Sn 5 is confirmed due to the high number of peaks corresponding to these phases.Bi was not observed present in the Cu 3 Sn and Cu 6 Sn 5 IMC phases, and Bi did not form IMCs in the interfacial reactions.The Cu 3 Sn and Cu 6 Sn 5 intermetallics have rod-like morphologies, being characterized as faceted phases.Cu 3 Sn IMC is a more stable phase than Cu 6 Sn 5 IMC.The Cu 3 Sn intermetallic particles may grow in a rod-like form without branches, as shown in Figure 4. Kim et al. 41 reported similar morphologies for the Cu 6 Sn 5 and Ag 3 Sn particles in Sn-Ag-Cu alloys.

2 Effect of solidification rate on microstructure
The optic micrographs of the longitudinal and transverse sections of directionally solidified Sn-Bi-Cu eutectic alloy at different solidification parameters are shown in Figure 4.The microstructure is formed by dispersed rod-like particles of Cu 3 Sn within Sn-rich and Bi-rich phases.Cu 3 Sn IMC appears for each solidification rate.Cooling condition has a significant effect on the IMC thickness.For a constant temperature gradient (4.2 K/mm), it is found that the complex regular Bi-Sn lamellar spacings and Cu 3 Sn intermetallic phase spacings are mainly controlled by the solidification rate (V), and both of them decrease with increased solidification rate.Spacings between primary intermetallic particles (Cu 3 Sn) were measured.These particles are part of the complex regular eutectic microstructure.At the highest growth rate (166 µm/s), the average spacing between the particles is reduced to 22 µm.Consequently, the microstructure underwent are finement with an increase in the solidification rate (Table 1).
Higher solidification rate yields a thinner IMC, which is consistent with other researchers' results 42,43 .Because of its mechanical properties, Cu 3 Sn is also more suitable than Cu 6 Sn 5 and Sn as a joint material for microbumps 44,45 .
Rod-like Cu 3 Sn particles prevailed along the Bi-rich eutectic matrix, as can be seen in Fig. 4.These hard and brittle Cu 3 Sn particles are normally alternated with the Bi-rich phase permitting the eutectic mixture to be characterized.According to Figure 4, The primary Cu 3 Sn intermetallic phases with a thickness about 4 µm were surrounded by Cu 6 Sn 5 intermetallic phases for lowest solidification rate (8.3 µm/s) and these two  46 , Le et al. 47 and Rao et al. 48.The variation of lamellar spacing (λ) and Cu 3 Sn intermetallic phase spacing (λ I ) with solidification rate are given in Table 1 and Figure 5, and the relationships between these parameters are given in Table 2.At a constant temperature gradient (4.2 K/mm), the λ and λ I decreased with increasing solidification rate.The average eutectic spacing values measured on the longitudinal (λ L ) and transverse (λ T ) sections of the samples are given in Table 1.With increasing the solidification rate from 8.3 to 166 µm/s, λ L (lamellar) decreased from 2.72 to for Bi-2.0Zn-0.2Al(wt.%) eutectic alloy, by Yan et al. 50for Nb-22Ti-16Si-3Cr-3Al-2Hf (at.%) alloy, respectively.Since ternary cooperative growth has not been observed in this study, the exponent value of 0.5 predicted by the Jackson-Hunt eutectic theory 51 for binary eutectics was not obtained.However, as can be seen from Table 2, an exponent value of 0.52 was obtained for the dependence of the Cu 3 Sn phase spacings related to solidification rate.

Effect of solidification rate on microhardness
The dependence of microhardness on the solidification rate and phase spacing is given in Table 1 and Figures 6  and 7, and the relationships between these parameters are given in Table 3.At a constant temperature gradient (4.2 K/mm), the microhardness values increased with increasing solidification rate.The average microhardness values measured on the longitudinal and transverse sections of the samples are given in Table 1.With increasing the solidification rate from 8.3 to 166 µm/s, the HV L increased from 192.7 to 290.8 MPa and HV T increased from 193.2 to 296.7 MPa.Also, the HV IL (Cu 3 Sn phase) increased from 3054.8 to 3436.4 MPa and HV IT (Cu 3 Sn phase) increased from 2663.4 to 3144.1 MPa.The measured microhardness values for the Cu 3 Sn phase are in good agreement with the values of 3364.8, 3266.7-2795.9(0.98-4.9 N load), 3364.8 and lower than the 4231.1-4184.9MPa (1.96-4.9N load) obtained by Lee et al. 52 , Liu et al. 53 , Frear et al. 54 and Ghosh 55 , respectively.
The exponent value (0.13-0.14) of the V (for lamellar structure) is in good agreement with the value of 0.14, 0.11, 0.15, values obtained by Zhang et al. 7 for Ni-25at.%Sialloy, by Hu et al. 56 for Sn-1.0 wt.% Cu, by Fan et al. 57 for Ti-46Al-0.5W-0.5Sialloy (at.%), respectively.Decrease in lamellar spacing due to the increasing solidification rate, increased the microhardness.As can be seen from Table 1 and Figure 7, microhardness increased with decreasing lamellar spacing.With decreasing the λ L from 2.72 to 1. 41  The increment of the solidification rate not only decrease the Cu 3 Sn IMC spacings but also refines the Cu 3 Sn IMC phases.The finer microstructure causes an increment on the mechanical properties.The microhardness values of the Cu 3 Sn phases are approximately 10-15 times greater than the complex Bi-Sn eutectic phase.However, the change in complex lamellar spacing is more effective on microhardness.As shown in Table 3, the exponent value (0.53) of the Bi-Sn complex lamellar phase is quite larger than the exponent value (0.09) of the Cu 3 Sn IMC phase.This is due to the fact that the dependency of the Bi-Sn complex lamellar spacing on the solidification rate is quite large relative to the Cu 3 Sn IMC phase spacing.The exponent value (0.53) of the lamellar phase is good agreement with the 0.50 value obtained by Spinelli et al. 30 for Sn-Cu solder alloys

Effect of solidification rate on compressive strength
Compressive strength-strain curves for Sn-36Bi-22Cu alloy are shown in Figure 8.The variation of ultimate compressive strength (σ c ) and compressive yield strength (σ y ) determined form strength-strain curves with solidification rate are given in Figure 9 and Table 1, and the relationships between these parameters are given in Table 3.At a constant temperature gradient (4.2 K/mm), the compressive strength values increased with increasing solidification rate.With increasing the solidification rate from 8.3 to 166 µm/s, the σ c increased from 102.1 to 139.3 MPa and the σ y increased from 71.5 to 118.9 MPa.The exponent value (0.09) of the V for the σ c is in good agreement with the 0.08, 0.08, 0.11 values of σ t obtained by Hu et al. 23 for Sn-0.7Cu-0.7Bi(wt.%) alloy, by Hosch and Napolitano 58 for Al-12wt.%Sialloy, by Çadırlı et al. 59 for Sn-40.5Pb-2.6Sb(wt.%) ternary eutectic alloy respectively.The exponent value (0.16) of the V for the σ c is in good agreement with the 0.16 value of the σ t obtained by Hu et al. 23 for Sn-0.7Cu-0.7Bi(wt.%) alloy.
Nevertheless, the exponent value (0.09) of the V for the ultimate compressive strength is higher than the 0.04 value of ultimate tensile strength and the exponent value (0.16) of the V for the compressive yield strength is slightly higher than the 0.12 value of the tensile yield strength, σ, obtained by Hu et al. 23 for Sn-0.7Cu-1.3Bi(wt.%) alloy.Differences exist in the exponent values because of the possible differences in purity, different alloy compositions, solidification conditions and the surface preparation of the test pieces.Also, solidification rate effects the elongation of the alloy.Hu et al. 26 determined that, with increasing solidification rate from 5 to 100 µm/s, the elongation increased from % 28.2 to % 41.5 for Sn-0.7Cu-0.7Bi(wt.%) alloy.Sakuyama et al. 36 found that, the elongation of the Bi-41.8Sn-0.5Cu is higher than the Bi-41.8Sn-0.5Ag,Bi-41.8Sn-0.5Znand Bi-42Sn alloys.This situations improve the importance of the material for technological applications.
According to the literature 60 , it is well established that the two IMCs are the ε-phase (Cu 3 Sn) and η-phase (Cu 6 Sn 5 ).The presence of those intermetallic phases may increase HV and σ, but the ductility properties slightly decrease with further increased solidification rate, that may contribute to a reason.The main reason is that the high growth velocity during directional solidification may result in a radial temperature gradient, which leads to some Cu 3 Sn fibers do not grow along with the crystal growth direction.Consequently, the increment in the solidification rate caused finer microstructure.This finer microstructure has improved the some mechanical properties (HV, σ c ) of the Sn-Bi-Cu ternary eutectic alloy.The crucial role in this solidification process was played by Cu 3 Sn and Cu 6 Sn 5 IMCs in the Sn-matrix of Sn-Bi-Cu ternary system.These IMC phases build a long-range internal stress, resulting in a strengthening effect.

Conclusions
Sn-36Bi-22Cu (wt.%) ternary eutectic alloy was directionally solidified upwards at a constant temperature gradient (4.2 K/mm) under different solidification rates (8.3-166µm/s) in a Bridgman-type directional solidification furnace.The results are summarized as follows: 1.The lamellar spacing and the Cu 3 Sn phase spacing decreased with increasing solidification rate.With increasing the solidification rate from 8.3 to 166 µm/s, average λ decreased from 2.81 to 1.46 µm, average λ I decreased from 103.1 to 22.0 µm for the lamellar spacing and Cu 3 Sn phase spacing, respectively.The relationships between the eutectic spacings and solidification rate were obtained by binary regression analysis as (λ L =4.7V -0.25 ,λ IL =273V -0.52 ) 2. The microhardness increased with increasing solidification rate.Average HV increased from 192.9 to 293.7 MPa, and HV I increased from 2859.1 to 3290.3 MPa with increasing the solidification rate from 8.3 to 166 µm/s.The establishment of the relationship between HV and V can be given as (HV=367.3V 0.13 ,HV=3520.5V 0.04 ) 3. The compressive strength values increased with increasing solidification rate.The σ c increased from 102.1 to 139.3 MPa and the σ y increased from 71.5 to 118.9 MPa with increasing the solidification rate from 8.3 to 166 µm/s.The relationships between σ and V can be given as (σ c =153V 0.09 ,σ y =165V 0.16 ).

Figure 4 .
Figure 4. Optical images of the directionally solidified Sn-36Bi-22Cu eutectic alloy at a constant temperature gradient (G=4.2K/ mm) (a-e) longitudinal section (V=8.3-166.0µm/s), (f-j) transverse section (V=8.3-166.0µm/s) λ: the value of the lamellar spacing λ I : the value of the Cu 3 Sn intermetallic phase spacing HV: the microhardness value of the lamellar structure HV I :the microhardness value of the Cu 3 Sn intermetallic phase σ y : the value of the compressive yield strength σ c : the value of the ultimate compressive strength.

Figure 6 .
Figure 6.Variation of microhardness versus solidification rate

Figure 8 .Figure 9 .
Figure 8.Typical strength-strain curves of Sn-36Bi-22Cu eutectic alloy for different V at a constant G Şahin et al. 2 Materials Research increased amount of Cu 6 Sn 5 fibers caused an increment in both ultimate tensile strength and yield tensile strength.The mechanical properties (microhardness, shear stress, young and bulk modulus) and the wettability of the SnCu solder were improved with Bi addition 27 .There are numerous works on low solute content (Cu) Sn-based alloys µm, HV L increased from 192.7 to 290.8 MPa.With decreasing the λ IL from 98.3 to 18.6 µm, HV IL increased from 3054.8 to 3436.4 MPa.Similarly, With decreasing the λ T from 2.89 to 1.50 µm, HV T increased from 193.2 to 296.7 MPa.With decreasing the λ IT from 108.0 to 25.4 µm, HV IT increased from 2663.4 to 3144.1 MPa.