Abstract

1. 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 metals¹1 Stefanescu DM. Science and Engineering of Casting Solidification, Kluwer Academic/Plenum Publishers, New York, 2002.

2 Campbell J. Effects of vibration during solidification. International Metals Reviews. 1981;26(1):71-108.

3 Verma A, Tewari SP, Prakash J. Vibratory stress, solidification and microstructure of weldments under vibratory welding condition - A review. International Journal of Engineering Science and Technology. 2011;3(6):5215-5220.^-44 Yao L, Hao H, Ji SH, Fang CF, Zhang XG. Effects of ultrasonic vibration on solidification structure and properties of Mg-8Li-3Al alloy. Transactions of Nonferrous Metals Society of China. 2011;21(6):1241-1246.. Directional solidification⁵5 Gündüz M, Çadırlı E. Directional solidification of aluminium-copper alloys. Materials Science and Engineering: A. 2002;327(2):167-185. 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 conditions⁶6 Verissimo NC, Brito C, Santos WLR, Cheung N, Spinelli JE, Garcia A. Interconnection of Zn content, macrosegregation, dendritic growth, nature of intermetallics and hardness in directionally solidified Mg-Zn alloys. Journal of Alloys and Compounds. 2016;662:1-10.

7 Zhang B, Li X, Wang T, Liu Z. Microstructures and mechanical properties of directionally solidified Ni-25%Si full lamellar in situ composites. Materials Science and Engineering: A. 2016;674:242-249.

8 Silva BL, Garcia A, Spinelli JE. Complex eutectic growth and Bi precipitation in ternary Sn-Bi-Cu and Sn-Bi-Ag alloys. Journal of Alloys and Compounds. 2017;691:600-605.

9 Luo S, Yang G, Liu S, Wang J, Li J, Jie W. Microstructure evolution and mechanical properties of directionally solidified Mg-xGd (x=0.8, 1.5, and 2.5) alloys. Materials Science and Engineering: A. 2016;662:241-250.

10 Reyes RV, Bello TS, Kakitani R, Costa TA, Garcia A, Cheung N, et al. Tensile properties and related microstructural aspects of hypereutectic Al-Si alloys directionally solidified under different melt superheats and transient heat flow conditions. Materials Science and Engineering: A. 2017;685:235-243.

11 Fan J, Liu J, Tian S, Wu S, Wang S, Gao H, et al. Effect of solidification parameters on microstructural characteristics and mechanical properties of directionally solidified binary TiAl alloy. Journal of Alloys and Compounds. 2015;650:8-14.

12 Bertelli F, Freitas ES, Cheung N, Arenas MA, Conde A, Damborenea J, et al. Microstructure, tensile properties and wear resistance correlations on directionally solidified Al-Sn-(Cu; Si) alloys. Journal of Alloys and Compounds. 2017;695:3621-3631.^-1313 Zhai W, Wang B, Hu L, Wei B. Ternary eutectic growth during directional solidification of Ag-Cu-Sb alloy. Philosophical Magazine Letters. 2015;95(4):187-193.. The directionally solidified alloy exhibited higher strength than the non-directionally solidified alloy under the same cooling rate¹⁴14 Liu S, Yang G, Jie W. Microstructure, Microsegregation, and Mechanical Properties of Directional Solidified Mg-3.0Nd-1.5Gd Alloy. Acta Metallurgica Sinica (English Letters). 2014;27(6):1134-1143.^,1515 Wang JH, Yang GY, Liu SJ, Jie WQ. Microstructure and room temperature mechanical properties of directionally solidified Mg-2.35Gd magnesium alloy. Transactions of Nonferrous Metals Society of China. 2016;26(5):1294-1300.. Liu et al.¹⁶16 Liu K, Jiang Z, Zhao J, Zou J, Chen Z, Lu D. Effect of directional solidification rate on the microstructure and properties of deformation-processed Cu-7Cr-0.1Ag in situ composites. Journal of Alloys and Compounds. 2014;612:221-226. 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 bond¹⁷17 Kang SK, Sarkhel AK. Lead (Pb)-free solders for electronic packaging. Journal of Electronic Materials. 1994;23(8):701-707.^,1818 Liu KC, Duh JG. Microstructural evolution in Sn/Pb solder and Pd/Ag thick film conductor metallization. IEEE Transactions on Components, Hybrids, and Manufacturing Technology. 1991;14(4):703-707.. 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 lead-free solders, Sn-Bi alloy is one of the promising candidates¹⁹19 Lee JI, Chen SW, Chang HY, Chen CM. Reactive wetting between molten Sn-Bi and Ni substrate. Journal of Electronic Materials. 2003;32(3):117-122.. Furthermore, the ternary Sn-Bi-Cu ternary alloys may also be considered as promising lead-free solders¹⁹19 Lee JI, Chen SW, Chang HY, Chen CM. Reactive wetting between molten Sn-Bi and Ni substrate. Journal of Electronic Materials. 2003;32(3):117-122.. 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 strength²⁰20 El-Daly AA, Hammad AE. Development of high strength Sn-0.7Cu solders with the addition of small amount of Ag and In. Journal of Alloys and Compounds. 2011;509(34):8554-8560.^,2121 El-Daly AA, Hammad AE. Enhancement of creep resistance and thermal behavior of eutectic Sn-Cu lead-free solder alloy by Ag and In-additions. Materials & Design. 2012;40:292-298.. Tai et al.²²22 Tai F, Guo F, Han MT, Xia ZD, Lei YP, Shi YW. Creep and thermomechanical fatigue properties of in situ Cu6Sn5 reinforced lead-free composite solder. Materials Science and Engineering: A. 2010;527(15):3335-3342. showed that creep resistance of Sn-3.5Ag was improved significantly for Cu particle-reinforced composite solder joints at 25 ^oC, 65 ^oC and 105 ^oC. 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 strengthening²³23 Hu X, Li Y, Liu Y, Min Z. Developments of high strength Bi-containing Sn0.7Cu lead-free solder alloys prepared by directional solidification. Journal of Alloys and Compounds. 2015;625:241-250.. Zhang et al.²⁴24 Zhang X, Matsuura H, Tsukihashi F, Yuan Z. Wettability of Sn-Zn, Sn-Ag-Cu and Sn-Bi-Cu alloys on copper subsrates. Materials Transactions. 2012;53(5):926-931. 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 Cu₃Sn and Cu₆Sn₅ intermetallics (IMC's) on the mechanical properties were investigated from many researchers²⁵25 Cheng HC, Yu CF, Chen WH. Strain- and strain-rate-dependent mechanical properties and behaviors of Cu3Sn compound using molecular dynamics simulation. Journal of Materials Science. 2012;47(7):3103-3114.^,2626 Hu X, Li K, Min Z. Microstructure evolution and mechanical properties of Sn0.7Cu0.7Bi lead-free solders produced by directional solidification. Journal of Alloys and Compounds. 2013;566:239-245.. Cheng et al.²⁵25 Cheng HC, Yu CF, Chen WH. Strain- and strain-rate-dependent mechanical properties and behaviors of Cu3Sn compound using molecular dynamics simulation. Journal of Materials Science. 2012;47(7):3103-3114. reported that, Cu₃Sn single crystal consist of high ultimate strengths depending on the material directions and strain rate. Hu et al.²⁶26 Hu X, Li K, Min Z. Microstructure evolution and mechanical properties of Sn0.7Cu0.7Bi lead-free solders produced by directional solidification. Journal of Alloys and Compounds. 2013;566:239-245. reported that, increased amount of Cu₆Sn₅ 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 addition²⁷27 Mohammed S, El-Maghraby A. Study of some mechanical properties and wetting behavior with addition Bi to SnCu solder alloys. International Journal of Innovative Research in Science, Engineering and Technology. 2014;3(2):9439-9446.. There are numerous works on low solute content (Cu) Sn-based alloys⁸8 Silva BL, Garcia A, Spinelli JE. Complex eutectic growth and Bi precipitation in ternary Sn-Bi-Cu and Sn-Bi-Ag alloys. Journal of Alloys and Compounds. 2017;691:600-605.^,2323 Hu X, Li Y, Liu Y, Min Z. Developments of high strength Bi-containing Sn0.7Cu lead-free solder alloys prepared by directional solidification. Journal of Alloys and Compounds. 2015;625:241-250.

24 Zhang X, Matsuura H, Tsukihashi F, Yuan Z. Wettability of Sn-Zn, Sn-Ag-Cu and Sn-Bi-Cu alloys on copper subsrates. Materials Transactions. 2012;53(5):926-931.

25 Cheng HC, Yu CF, Chen WH. Strain- and strain-rate-dependent mechanical properties and behaviors of Cu3Sn compound using molecular dynamics simulation. Journal of Materials Science. 2012;47(7):3103-3114.

26 Hu X, Li K, Min Z. Microstructure evolution and mechanical properties of Sn0.7Cu0.7Bi lead-free solders produced by directional solidification. Journal of Alloys and Compounds. 2013;566:239-245.

27 Mohammed S, El-Maghraby A. Study of some mechanical properties and wetting behavior with addition Bi to SnCu solder alloys. International Journal of Innovative Research in Science, Engineering and Technology. 2014;3(2):9439-9446.

28 Silva BL, Garcia A, Spinelli JE. Cooling thermal parameters and microstructure features of directionally solidified ternary Sn-Bi-(Cu,Ag) solder alloys. Materials Characterization. 2016;114:30-42.

29 Yang TL, Wu JY, Li CC, Yang S, Kao CR. Low temperature bonding for high temperature applications by using SnBi solders. Journal of Alloys and Compounds. 2015;647:681-685.

30 Spinelli JE, Garcia A. Microstructural development and mechanical properties of hypereutectic Sn-Cu solder alloys. Materials Science and Engineering: A. 2013;568:195-201.^-3131 Wang KK, Gan D, Hsieh KC. The orientation relationships of the Cu3Sn/Cu interfaces and a discussion of the formation sequence of Cu3Sn and Cu6Sn5. Thin Solid Films. 2014;562:398-404.. Nevertheless, there has been only a limited amount of data about the mechanical properties of directionally solidified high solute content (Cu) Sn-based alloy. In this study, Sn-Bi-Cu ternary alloy containing high Cu is preferred. Similar alloys are used as soldering or brazing material depending on the content of copper. The aim of the present work is to investigate the effect of solidification rate (V) on microstructure (λ), microhardness (HV) and compressive strength (σ) of the directionally solidified Sn-36Bi-22Cu (wt.%) ternary eutectic alloy. The dependence of microhardness on the lamellar spacing (Bi-rich phase) and the Cu₃Sn IMC phase spacing were also determined.

2. Experimental Procedure

2.1. 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 work³²32 Sahin M. The directional solidification of binary and ternary metallic alloys and investigation the physical properties of them. [Thesis]. Nigde: Nigde University; 2012..

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 H₂O, 2.5 ml HNO₃, 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 phase) and the Cu₃Sn intermetallic phase spacings (λ_I) 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 elsewhere³²32 Sahin M. The directional solidification of binary and ternary metallic alloys and investigation the physical properties of them. [Thesis]. Nigde: Nigde University; 2012..

2.2. 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

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.

2.3. 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.

3. Results and Discussion

3.1 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°C³³33 Hansen M, Anderko K. Constitutions of Binary Alloys. New York: McGraw-Hill; 1958.. 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°C³³33 Hansen M, Anderko K. Constitutions of Binary Alloys. New York: McGraw-Hill; 1958.. Previous work³⁴34 Chang LS, Straumal BB, Rabkin E, Gust W, Sommer F. The Solidus Line of the Cu-Bi Phase Diagram. Journal of Phase Equilibria. 1997;18(2):128-135. 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 material³⁴34 Chang LS, Straumal BB, Rabkin E, Gust W, Sommer F. The Solidus Line of the Cu-Bi Phase Diagram. Journal of Phase Equilibria. 1997;18(2):128-135..

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 (Cu₃Sn intermetallic) and dark gray phase (Cu₆Sn₅ 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-24.16 wt.% 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, Cu₃Sn and Cu₆Sn₅, respectively. For the Cu₃Sn IMC, its growth is governed by the reaction between Cu and Sn atoms. Clevenger et al.³⁵35 Clevenger LA, Arcot B, Ziegler W, Colgan EG, Hong QZ, d'Heurle FM, et al. Interdiffusion and phase formation in Cu(Sn) alloy films. Journal of Applied Physics. 1998;83(1):90-99. reported the onset of Cu₃Sn formation from the reaction between Cu₆Sn₅ and Cu. The Cu₃Sn phase can be formed by conventional casting³⁶36 Sakuyama S, Akamatsu T, Uenishi K, Sato T. Effects of a Third Element on Microstructure and Mechanical Properties of Eutectic Sn-Bi Solder. Transactions of The Japan Institute of Electronics Packaging. 2009;2(1):98-103.^,3737 Wang KK, Gan D, Hsieh KC. The orientation relationships of the Cu3Sn/Cu interfaces and a discussion of the formation sequence of Cu3Sn and Cu6Sn5. Thin Solid Films. 2014;562:398-404., directional solidification⁸8 Silva BL, Garcia A, Spinelli JE. Complex eutectic growth and Bi precipitation in ternary Sn-Bi-Cu and Sn-Bi-Ag alloys. Journal of Alloys and Compounds. 2017;691:600-605.^,2323 Hu X, Li Y, Liu Y, Min Z. Developments of high strength Bi-containing Sn0.7Cu lead-free solder alloys prepared by directional solidification. Journal of Alloys and Compounds. 2015;625:241-250.^,2626 Hu X, Li K, Min Z. Microstructure evolution and mechanical properties of Sn0.7Cu0.7Bi lead-free solders produced by directional solidification. Journal of Alloys and Compounds. 2013;566:239-245. and rapid solidification methods³⁸38 Shen J, Liu YC, Gao HX. Formation of bulk Cu6Sn5 intermetallic compounds in Sn-Cu lead-free solders during solidification. Journal of Materials Science. 2007;42(14):5375-5380.

39 El Ashram T, Shalaby RM. Effect of rapid solidification and small additions of Zn and Bi on the structure and properties of Sn-Cu eutectic alloy. Journal of Electronic Materials. 2005;34(2):212-215.^-4040 Zhai W, Wang BJ, Lu XY, Wei B. Rapid solidification mechanism of highly undercooled ternary Cu40Sn45Sb15 alloy. Applied Physics A. 2015;121(1):273-281.. Due to the solidification temperature differences, initially the Cu-rich Cu₃Sn and Cu₆Sn₅ 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, Cu₃Sn particles with a thickness about 4 µm were surrounded by Cu₆Sn₅ phase and these two phases are coherent with each other very well. During the eutectic reaction, the Cu₃Sn 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=1.5405 A°) 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 Cu₃Sn and Cu₆Sn₅ is confirmed due to the high number of peaks corresponding to these phases. Bi was not observed present in the Cu₃Sn and Cu₆Sn₅ IMC phases, and Bi did not form IMCs in the interfacial reactions. The Cu₃Sn and Cu₆Sn₅ intermetallics have rod-like morphologies, being characterized as faceted phases. Cu₃Sn IMC is a more stable phase than Cu₆Sn₅ IMC. The Cu₃Sn intermetallic particles may grow in a rod-like form without branches, as shown in Figure 4. Kim et al.⁴¹41 Kim KS, Huh SH, Suganuma K. Effects of intermetallic compounds on properties of Sn-Ag-Cu lead-free soldered joints. Journal of Alloys and Compounds. 2003;352(1-2):226-236. reported similar morphologies for the Cu₆Sn₅ and Ag₃Sn particles in Sn-Ag-Cu alloys.

3. 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 Cu₃Sn within Sn-rich and Bi-rich phases. Cu₃Sn 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 Cu₃Sn 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 (Cu₃Sn) 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' results⁴²42 Ochoa F, Williams JJ, Chawla N. Effects of cooling rate on the microstructure and tensile behavior of a Sn-3.5wt.%Ag solder. Journal of Electronic Materials. 2003;32(12):1414-1420.^,4343 Deng X, Piotrowski G, Williams JJ, Chawla N. Influence of initial morphology and thickness of Cu6Sn5and Cu3Sn intermetallics on growth and evolution during thermal aging of Sn-Ag solder/Cu joints. Journal of Electronic Materials. 2003;32(12):1403-1413.. Because of its mechanical properties, Cu₃Sn is also more suitable than Cu₆Sn₅ and Sn as a joint material for microbumps⁴⁴44 Bosco NS, Zok FW. Critical interlayer thickness for transient liquid phase bonding in the Cu-Sn system. Acta Materialia. 2004;52(10):2965-2972.^,4545 Deng X, Chawla N, Chawla KK, Koopman M. Deformation behavior of (Cu, Ag)-Sn intermetallics by nanoindentation. Acta Materialia. 2004;52(14):4291-4303..

Rod-like Cu₃Sn particles prevailed along the Bi-rich eutectic matrix, as can be seen in Fig. 4. These hard and brittle Cu₃Sn particles are normally alternated with the Bi-rich phase permitting the eutectic mixture to be characterized. According to Figure 4, The primary Cu₃Sn intermetallic phases with a thickness about 4 µm were surrounded by Cu₆Sn₅ intermetallic phases for lowest solidification rate (8.3 µm/s) and these two phases are coherent with each other very well. With increasing the solidification rate from 8.3 to 166 µm/s, the thickness of Cu₆Sn₅ intermetallic phase decreased from 4.15 µm to 0.75 µm. The thickness of the Cu₆Sn₅ phase agrees with the thickness found by Chen⁴⁶46 Chen Z. Micro-mechanical characteristics and dimensional change of Cu-Sn interconnects due to growth of interfacial intermetallic compounds. [Thesis]. Loughborough: Loughborough University; 2014., Le et al.⁴⁷47 Lee HT, Chen MH, Jao HM, Liao TL. Influence of interfacial intermetallic compound on fracture behavior of solder joints. Materials Science and Engineering: A. 2003;358(1-2):134-141. and Rao et al.⁴⁸48 Chandra Rao BSS, Weng J, Shen L, Lee TK, Zeng KY. Morphology and mechanical properties of intermetallic compounds in SnAgCu solder joints. Microelectronic Engineering. 2010;87(11):2416-2422.. The variation of lamellar spacing (λ) and Cu₃Sn 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 1.41 µm, λ_T (lamellar) decreased from 2.89 to 1.50 µm, λ_IL (for Cu₃Sn phase) decreased from 98.3 to 18.6 µm and λ_IT (for Cu₃Sn phase) decreased from 108.0 to 25.4 µm. The exponent value (0.24-0.25) of the V is in good agreement with the values of 0.22-0.26, 0.25 obtained by Şahin and Çadırlı⁴⁹49 Şahin M, Çadırlı E. Mechanical, electrical, and thermal properties of the directionally solidified Bi-Zn-Al ternary eutectic alloy. International Journal of Minerals, Metallurgy, and Materials. 2014;21(10):999-1008. for Bi-2.0Zn-0.2Al (wt.%) eutectic alloy, by Yan et al.⁵⁰50 Yan Y, Ding H, Kang Y, Song J. Microstructure evolution and mechanical properties of Nb-Si based alloy processed by electromagnetic cold crucible directional solidification. Materials & Design. 2014;55:450-455. for 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 theory⁵¹51 Jackson KA, Hunt JD. Lamellar and rod eutectic growth. Transactions of the Metallurgical Society of AIME. 1966;236:1129-1142. 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 Cu₃Sn phase spacings related to solidification rate.

3.3. 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 (Cu₃Sn phase) increased from 3054.8 to 3436.4 MPa and HV_IT (Cu₃Sn phase) increased from 2663.4 to 3144.1 MPa. The measured microhardness values for the Cu₃Sn 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 4231.1-4184.9 MPa (1.96-4.9 N load) obtained by Lee et al.⁵²52 Lee CC, Wang PJ, Kim JS. Are Intermetallics in Solder Joints Really Brittle? In: Proceedings of the 57th Electronic Components and Technology Conference; 2007 May 29-Jun 1; Reno, NV, USA., Liu et al.⁵³53 Liu CY, Hu YJ, Liu YS, Tseng HW, Huang TS, Lu CT, et al. Epitaxial Cu-Sn bulk crystals grown by electric current. Acta Materialia. 2013;61(15):5713-5719., Frear et al.⁵⁴54 Frear DR, Burchett SN, Morgan HS, Lau JH. The Mechanics of Solder Alloy Interconnects. New York: Van Nostrand Reinhold; 1994. and Ghosh⁵⁵55 Ghosh G. Elastic properties, hardness, and indentation fracture toughness of intermetallics relevant to electronic packaging. Journal of Materials Research. 2004;19(5):1439-1454., 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.⁷7 Zhang B, Li X, Wang T, Liu Z. Microstructures and mechanical properties of directionally solidified Ni-25%Si full lamellar in situ composites. Materials Science and Engineering: A. 2016;674:242-249. for Ni-25at.%Si alloy, by Hu et al.⁵⁶56 Hu X, Chen W, Wu B. Microstructure and tensile properties of Sn-1Cu lead-free solder alloy produced by directional solidification. Materials Science and Engineering: A. 2012;556:816-823. for Sn-1.0 wt.% Cu, by Fan et al.⁵⁷57 Fan J, Li X, Su Y, Guo J, Fu H. Dependency of microhardness on solidification processing parameters and microstructure characteristics in the directionally solidified Ti-46Al-0.5W-0.5Si alloy. Journal of Alloys and Compounds. 2010;504(1):60-64. for Ti-46Al-0.5W-0.5Si alloy (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 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.

The increment of the solidification rate not only decrease the Cu₃Sn IMC spacings but also refines the Cu₃Sn IMC phases. The finer microstructure causes an increment on the mechanical properties. The microhardness values of the Cu₃Sn 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 Cu₃Sn 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 Cu₃Sn 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.³⁰30 Spinelli JE, Garcia A. Microstructural development and mechanical properties of hypereutectic Sn-Cu solder alloys. Materials Science and Engineering: A. 2013;568:195-201. for Sn-Cu solder alloys

3.4 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.²³23 Hu X, Li Y, Liu Y, Min Z. Developments of high strength Bi-containing Sn0.7Cu lead-free solder alloys prepared by directional solidification. Journal of Alloys and Compounds. 2015;625:241-250. for Sn-0.7Cu-0.7Bi (wt.%) alloy, by Hosch and Napolitano⁵⁸58 Hosch T, Napolitano RE. The effect of the flake to fiber transition in silicon morphology on the tensile properties of Al-Si eutectic alloys. Materials Science and Engineering: A. 2010;528(1):226-232. for Al-12wt.%Si alloy, by Çadırlı et al.⁵⁹59 Çadırlı E, Sahin M, Turgut Y. Characterization of a directionally solidified Sn-Pb-Sb ternary eutectic alloy. Metallography, Microstructure, and Analysis. 2015;4(4):286-297. 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.²³23 Hu X, Li Y, Liu Y, Min Z. Developments of high strength Bi-containing Sn0.7Cu lead-free solder alloys prepared by directional solidification. Journal of Alloys and Compounds. 2015;625:241-250. 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.²³23 Hu X, Li Y, Liu Y, Min Z. Developments of high strength Bi-containing Sn0.7Cu lead-free solder alloys prepared by directional solidification. Journal of Alloys and Compounds. 2015;625:241-250. 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.²⁶26 Hu X, Li K, Min Z. Microstructure evolution and mechanical properties of Sn0.7Cu0.7Bi lead-free solders produced by directional solidification. Journal of Alloys and Compounds. 2013;566:239-245. 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.³⁶36 Sakuyama S, Akamatsu T, Uenishi K, Sato T. Effects of a Third Element on Microstructure and Mechanical Properties of Eutectic Sn-Bi Solder. Transactions of The Japan Institute of Electronics Packaging. 2009;2(1):98-103. found that, the elongation of the Bi-41.8Sn-0.5Cu is higher than the Bi-41.8Sn-0.5Ag, Bi-41.8Sn-0.5Zn and Bi-42Sn alloys. This situations improve the importance of the material for technological applications.

According to the literature⁶⁰60 Zhang Q, Zou H, Zhang ZF. Improving tensile and fatigue properties of Sn-58Bi/Cu solder joints through alloying substrate. Journal of Materials Research. 2010;25(2):303-314., it is well established that the two IMCs are the ε-phase (Cu₃Sn) and η-phase (Cu₆Sn₅). 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 Cu₃Sn 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 Cu₃Sn and Cu₆Sn₅ 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.

4. 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 Cu₃Sn 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 Cu₃Sn 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).

5. References

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