lable at ScienceDirect

Intermetallics 16 (2008) 1142–1148

Contents lists avai

Intermetallics

journal homepage: www.elsevier .com/locate/ intermet

Growth mechanism of bulk Ag3Sn intermetallic compoundsin Sn–Ag solder during solidification

J. Shen a, Y.C. Chan a,*, S.Y. Liu b

a Department of Electronic Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong, Chinab Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong, China

a r t i c l e i n f o

Article history:Received 5 March 2008Received in revised form 21 May 2008Accepted 29 June 2008Available online 12 August 2008

Keywords:A. Intermetallics, miscellaneousB. Thermal propertiesC. Crystal growthD. Microstructure

* Corresponding author. Tel.: þ852 2788 7130; fax:E-mail address: eeycchan@cityu.edu.hk (Y.C. Chan

0966-9795/$ – see front matter � 2008 Elsevier Ltd.doi:10.1016/j.intermet.2008.06.016

a b s t r a c t

Thermal analysis was used to clarify the growth mechanism of bulk Ag3Sn IMCs in Sn–Ag lead-freesolders and compared with Pandat software calculations and theoretical calculations. In slowly-cooledSn–Ag lead-free solders, bulk Ag3Sn IMCs formed when Ag3Sn crystal nuclei formed at the onset of theeutectic reaction. The fractions of bulk Ag3Sn IMCs in hypereutectic Sn–4.4 mol%Ag solders, measured bythermal analysis, are larger than those predicted by the equilibrium phase diagram and softwarecalculations. The reasons for this could be attributed to eutectic Ag3Sn phases clinging to the primaryAg3Sn crystals during the eutectic reaction with their matching crystalline orientation relationship. Thedriving force for the growth of the faceted bulk Ag3Sn IMCs phase is proportional to the degree ofundercooling achieved, which fits with the prediction of classical solidification theory. The resultexplains the formation and rapid growth of bulk Ag3Sn IMCs in slowly-cooled eutectic Sn–Ag solder witha minimal degree of undercooling during solidification.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Solder materials play crucial roles in the reliability of jointassemblies in electronic packaging. Increasing environmental andhealth concerns over the toxicity of lead combined with strictlegislation to ban the use of lead-based solders have provided aninevitable driving force for the development of lead-free solderalloys. Sn–Ag alloy has been identified as a lead-free solder candi-date to replace Pb-bearing solders in microelectronic applicationsbecause of its enhanced strength, improved creep and thermalfatigue characteristics, as compared with other lead-free soldersystems [1]. However, recent investigations on the processingbehavior and solder joint reliability have revealed several potentialrisk factors associated with this alloy. The formation of plate-like(three-dimensional imaging) or needle-like (two-dimensionalimaging) bulk Ag3Sn intermetallic compounds (IMCs) in Sn–Agalloy joints, especially when solidified at a relatively slow coolingrate, is one issue of concern [2–5]. Bulk Ag3Sn plates can adverselyaffect the plastic deformation properties of the solder and causeplastic-strain localization at the boundary between the Ag3Snplates and the bounding b-Sn phase [4].

However, explanations for the formation of this bulk Ag3Sn IMCsare ambiguous [2–5]. If they are just the primary Ag3Sn crystals due

þ852 2788 8803.).

All rights reserved.

to the high Ag concentration of the solder, how does one explainthat this bulk Ag3Sn IMCs formed even in slowly-cooled eutecticSn–Ag and Sn–Ag–Cu solders. In our previous study, we discussedthe formation mechanism of bulk Ag3Sn IMCs in hypereutecticSn–Ag alloy [6]. But this still does not explain why bulk Ag3Sn IMCsformed even in slowly-cooled eutectic Sn–Ag and Sn–Ag–Cusolders. Hence, the relationship between bulk Ag3Sn IMCs andAg3Sn crystal nuclei, particularly, the rapid growth mechanism ofthese bulk IMCs in eutectic Sn–Ag alloy is still not clear.

This study deals with the thermal analysis and microstructuralobservations of the solidification of molten eutectic Sn–3.8 mol%Agand hypereutectic Sn–4.4 mol%Ag alloys in order to clarify thegrowth mechanism of bulk Ag3Sn IMCs in eutectic Sn–3.8 mol%Agsolder. A Pandat 7.0 Demo software was used for phase diagram,phase equilibria and solidification process calculations. The rela-tionship between undercooling and the growth velocity was clar-ified and used to explain the rapid growth phenomenon of bulkAg3Sn IMCs in slowly-cooled eutectic Sn–Ag solder.

2. Experimental procedures

Sn–3.8 mol%Ag and Sn–4.4 mol%Ag alloys were prepared frombulk rods of pure Sn and Ag (their purities were all above 99.99%).After weighing the individual pure metals, they were mixed andmelted in a vacuum arc furnace under a high-purity argon atmo-sphere to produce button-like specimens with a diameter of about3.5 cm. In order to get a homogeneous composition, the ingots were

Fig. 1. Binary phase diagram of Sn–Ag system calculated by Pandat 7.0 Demo.

J. Shen et al. / Intermetallics 16 (2008) 1142–1148 1143

remelted 4 times. Finally they were solidified in a water-cooledcopper mould with a cooling rate of about 20 K s�1. The solidifiedalloys were then cut into small specimens with dimensions of45� 2 mm, and a Netzsch DSC 404C apparatus was adopted fordifferential thermal analysis (DTA) measurements. The isochronalmeasurement DTA signals were calibrated and corrected by theCurie point of pure Fe and heat capacity of sapphire according to themethod described in Ref. [7]. The temperature difference (smear-ing) was corrected as follow:

Tm ¼ Tm;s ��Tc;Fe;s � Tc;Fe

�(1)

where Tm is the actual liquid/solid point of the alloy, Tm,s is themeasured liquid/solid point of the alloy, Tc,Fe is the literature valuefor the Curie point of pure Fe (1043.15 K) and Tc,Fe,s is the measuredCurie point of pure Fe (1024.42 K (5 K min�1), 1029.5 K (10 K min�1)and 1020.00 K (20 K min�1)). A common method of heat capacitycalibration in non-isothermal DTA was used to calculate the valueof the apparent heat capacity of a sample ðCapp

p;s Þ assuming that themeasured temperature difference is proportional to the heatcapacity of the specimen:

Cappp;s ¼ Cp;cal

DTt;s

DTt;cal(2)

where Cp,cal is the literature value for the molar heat capacity ofsapphire (Cp;cal ¼ a0 þ a1ðT � T0Þ þ a2ðT � T0Þ2 þ a3ðT � T0Þ3þa4ðT � T0Þ4 þ a5ðT � T0Þ5, here, T0¼ 273.15 K, a0¼ 73.10 J mol�1

K�1, a1¼0.2477 J mol�1 K�2, a2¼�6.321�10�4 J mol�1 K�3,a3¼ 9.760�10�7 J mol�1 K�4, a4¼�7.967�10�10 J mol�1 K�5 anda5¼ 2.624�10�13 J mol�1 K�6), DTt,s and DTt,cal are the signals fromthe DTA measurements on the sapphire and on the sample,respectively. Thus, the value determined for the heat capacity is anapparent heat capacity because the influence of smearing over timeis neglected.

DTA measurements were performed under the protection ofhigh-purity argon to avoid any unexpected oxidation. The appliedthermal treatment procedure in the calorimetric experiments wasas follows: the specimens were firstly heated up from roomtemperature to 543 K with a constant rate (5, 10 and 20 K min�1)and kept at this temperature for 10 min. Then they were cooled toroom temperature (w300 K) with a rate of 5, 10 and 20 K min�1.Specimens of water-cooled (namely rapidly-cooled) and DSC(namely slowly-cooled) were prepared by standard metallographicprocedures. The specimens were mechanically polished with1 mm diamond paste and etched with a solution of 5 vol.%HNO3þ 95 vol.% C2H5OH. Scanning electron microscopy (FEI,Inc. NOVA 400 NanoSEM) was used for the observation ofmicrostructures.

A Pandat 7.0 Demo software was used for the thermodynamiccalculations. The thermodynamic parameters used were adopteddirectly from the parameters of the binary constituent systemsdetermined by the thermodynamic database.

3. Results and discussions

3.1. Microstructural observation

The phase diagram of the Sn–Ag system was calculated by thePandat 7.0 Demo software and is given in Fig. 1 and the phaseequilibria data are listed in Table 1. According to the phase equi-libria data of the Sn–Ag system, eutectic Sn–Ag alloy(0.038436 mol%Ag) experiences a eutectic reaction at 494.31 K. So,the Sn–3.8 mol%Ag and Sn–4.4 mol%Ag alloys should experiencea eutectic and hypereutectic solidification reaction in our DTA testsand the equilibrium solidification paths can be described as:

Sn—3:8 mol%Ag : L / Ag3Sn D b

� Sn body centred tetragonal ðBCTÞ:

Sn—4:4 mol%Ag : L / L D primary Ag3Sn crystals and

L / Ag3Sn D b� Sn ðBCTÞ:

Fig. 2(a) and (b) illustrates the typical microstructures of the Sn–3.8 mol%Ag and Sn–4.4 mol%Ag alloys solidified at a cooling rate of5 K min�1, which have nearly followed the corresponding equilib-rium solidification path. It is obvious that the slowly-cooled alloysexhibit eutectic (rod-like and particle-like eutectic Ag3Sn and b-Snphase) and hypereutectic (bulk Ag3Sn IMCs and eutectic colonies)structures, which fit with the prediction of the phase equilibriacalculations. While for the rapid cooling cases, the degree of kineticundercooling achieved, leads to the metastable eutectic concen-tration shifting to higher Ag concentration [6]. Although the b-Snphase requires a larger undercooling than that of Ag3Sn duringsolidification, the kinetic undercooling obtained is large enough forthe formation of the primary b-Sn phase. Thus, all eutecticSn–3.8 mol%Ag and hypereutectic Sn–4.4 mol%Ag alloy specimensexhibit microstructures which are the same as the microstructureof the hypoeutectic alloy solidified under equilibrium solidificationconditions, which consists of a mixture of primary b-Sn dendritesand eutectic colonies (see Fig. 2(c) and (d)).

3.2. Theoretical and software calculation

Microstructural observations indicate that bulk Ag3Sn IMCsformed in the slowly-cooled Sn–4.4 mol%Ag alloy. If they are theprimary Ag3Sn crystals formed in the Sn–4.4 mol%Ag alloy duringsolidification, following the equilibrium solidification process, thevolume fraction of them could be determined by the ‘‘lever rule’’according to the phase equilibria. During the hypereutectic solidi-fication process, the Sn–4.4 mol%Ag liquid alloy matches with theeutectic composition after the pro-eutectic reaction (i.e., the end ofprimary Ag3Sn crystal formation). The concentration for the equi-librium eutectic reaction can be determined as:

Table 1Phase equilibria data and the invariant reaction of Sn–Ag system calculated byPandat 7.0 Demo

Temperature (K) 974.74 757.96 494.31Invariant

reactionFccþ liquid /

HcpHcpþ liquid /

Ag3SnLiquid /

Ag3Snþ BCT_SnX(Ag(Fcc)) 0.883522X(Sn(Fcc)) 0.116478X(Ag(Liquid)) 0.766245 0.508288 0.038436X(Sn(Liquid)) 0.233755 0.491712 0.961564X(Ag(Hcp)) 0.871209 0.765837X(Sn(Hcp)) 0.128791 0.234163X(Ag(Ag3Sn)) 0.750000 0.750000X(Sn(Ag3Sn)) 0.250000 0.250000X(Ag(BCT_Sn))X(Sn(BCT_Sn)) 1.000000

J. Shen et al. / Intermetallics 16 (2008) 1142–11481144

CAg � Cp

CSn � 13Cp¼ 3:8

96:2(3)

where CAg is the Ag concentration and CSn is the Sn concentration inthe Sn–4.4 mol%Ag alloy. Here, Cpis the Ag concentration in primaryAg3Sn crystals in the solidified Sn–4.4 mol%Ag alloy. The Snconcentration in the primary Ag3Sn crystals in the solidified Sn–4.4 mol%Ag alloy is 1/3 Cp. From Eq. (3), Cp becomes approximately0.63 mol%. Since the actual solidification process (under slowcooling) is slightly removed from the equilibrium state, thevolume fraction of primary Ag3Sn crystals in the slowly-cooledSn–4.4 mol%Ag alloy must be smaller than 0.63.

Pandat 7.0 Demo software was also used to simulate the equi-librium solidification process of Sn–3.8 mol%Ag, Sn–4.4 mol%Agalloys and the supposed Sn–3.8436 mol%Ag alloy. Fig. 3 showsthe relationship between the solid fraction and temperature

Fig. 2. SEM micrographs of slowly-cooled (a) Sn–3.8 mol%Ag and (b) Sn–4.4 mol%A

of Sn–3.8 mol%Ag, Sn–4.4 mol%Ag alloys and the supposed Sn–3.8436 mol%Ag alloy as determined from software calculations. Forthe Sn–3.8 mol%Ag and Sn–4.4 mol%Ag alloys, an inflection pointscould be recognized in the curves (see Fig. 3(a) and (b)). Analyzingthe results of this simulation, it is found that the inflection point ofSn–3.8 mol%Ag is mainly from the formation of primary b-Sncrystals at 494.33 K because the composition of the Sn–3.8 mol%Agalloy deviates from the eutectic point of the Sn–Ag system.However, the equilibrium solidification curve of the supposed Sn–3.8436 mol%Ag alloy shows no inflection point and this proved thatthere is no primary phase formed in the eutectic Sn–Ag alloy at theeutectic temperature (494.31 K) during solidification (see Fig. 3(c)).The inflection point in the equilibrium solidification curve of theSn–4.4 mol%Ag alloy is the end point of primary Ag3Sn IMCsformation and the corresponding solid fraction is 0.71, which isclose to the theoretical calculated value by the ‘‘lever rule’’ (0.63). Infact, the difference of solid fraction achieved by the ‘‘lever rule’’ andthe software calculation is attributed to the adapted eutecticcomponent point in the ‘‘lever rule’’ calculation for 3.8 mol%Ag,which is not 3.8436 mol%Ag.

3.3. Thermodynamic calculation by DTA

A general procedure for the determination of the transformationrate to solid phase fractions in solidified alloys from the apparentheat capacity curves recorded was adopted to determine thetransformed fraction of bulk Ag3Sn IMCs in the alloys [8]. The liquidfraction, fl, and the enthalpy difference between the liquid and solidDHsl, have been determined as a function of temperature in themeasured curves of the apparent heat capacity. The apparent heatcapacity, Cp,m, includes the heat of transformation and the change

g alloys, and rapidly-cooled (c) Sn–3.8 mol%Ag and (d) Sn–4.4 mol%Ag alloys.

Fig. 3. Solidification process of (a) Sn–3.8 mol%Ag, (b) Sn–4.4 mol%Ag alloys and (c) the supposed Sn–3.8436 mol%Ag simulated by Pandat 7.0 Demo.

Fig. 4. Apparent heat capacities of Sn–4.4 mol%Ag alloys measured at different coolingrates of 5, 10 and 20 K min�1.

J. Shen et al. / Intermetallics 16 (2008) 1142–1148 1145

in the heat capacity of the liquid, Cp,l, and of the solid, Cp,s, inducedby the temperature change:

Cp;mðTÞ ¼ flCp;lðTÞ þ fsCp;sðTÞ þdfsdT

DHslðTÞ (4)

where the solid fraction, fs, equals 1� fl. The first two terms on theright-hand side of the above equation state that the heat capacity ofboth liquid and solid phases can be given as the weighted(according to the amounts of the individual phases) average of theheat capacities of the individual phases. The last term on the right-hand side represents the (reaction) enthalpy released duringsolidification. The values of Cp,l and Cp,s can be determined byextrapolation from the measured Cp,m outside the temperaturerange where the solidification takes place.

The temperature-dependent enthalpy difference is caused bythe difference between the temperature-dependent heat capacitiesof the separate phases:

DHslðTÞ ¼ H0 þZ T2

T1

�Cp;sðTÞ � Cp;lðTÞ

�dT (5)

where T1 is the starting temperature of the transformation; T2 is thetemperature where the transformation has just been completed(i.e., fs¼ 1); H0, the value of DHsl at T1. H0 can be determinedaccording to the following procedure. The starting point of thetransformation, where fl equals 1, is estimated by comparing themeasured Cp,s curve with the extrapolated curve for Cp,l. By

prescribing H0, DHsl can be calculated as a function of temperaturefrom T1 to T2. These values of DHsl are used as inputs to evaluate flfrom the measured Cp,s. Then the value of H0 is adjusted in order tosatisfy the requirement that the fraction fs equals 1 at T¼ T2.

Fig. 5. The relationship between the transformation rate and temperature of Sn–4.4 mol%Ag alloys as determined from DTA measurements.

J. Shen et al. / Intermetallics 16 (2008) 1142–11481146

Using the above method, the fraction of solid phase and thetransformation rate were obtained from the measured apparentheat capacities (Fig. 4). The transformation rates of the solid phasein the Sn–4.4 mol%Ag alloy investigated were calculated and arepresented as a function of temperature in Fig. 5. For all the appliedcooling rates, two inflection points could be recognized in thecurves obtained from the transformation rate. After comparing with

Fig. 6. The relationship between the solid fraction and temperature as determined from D20 K min�1.

the phase diagram, it is found that the low inflection point is mainlyfrom the formation of bulk Ag3Sn IMCs, and the high inflection pointis from the eutectic reaction (see Fig. 2(b)). Hence, the first inflectionpoint is likely to be the end point of bulk Ag3Sn IMCs formation.

Fig. 6 shows the relationship between the solid fraction andtemperature as determined from DSC measurements of the Sn–4.4 mol%Ag alloy. Using Fig. 5, the end temperature point of bulkAg3Sn IMCs formation was determined, and it was used to deter-mine the volume fraction of the bulk Ag3Sn IMCs. The volumefraction of bulk Ag3Sn IMCs, determined from the measuredapparent heat capacity, are 2.78 (5 K min�1), 4.03 (10 K min�1) and4.43 (20 K min�1) (see Fig. 6). These values are larger than thevolume fraction of primary Ag3Sn crystal in the solidified Sn–4.4 mol%Ag alloy predicted by the theoretical calculation (0.63) andsoftware calculation (0.71). Hence, the bulk Ag3Sn IMCs formed inthe Sn–4.4 mol%Ag alloy are not totally from the primary Ag3Sncrystals predicted by the phase equilibria calculations.

3.4. Growth mechanism of bulk Ag3Sn IMCs

An inherent mechanism for the formation of excess bulk Ag3SnIMCs in slowly-cooled Sn–4.4 mol%Ag alloy could be explained bythe schematic diagram shown in Fig. 7. The two phases involvedpossess different growth velocities, and the leading phase is Ag3Snduring the eutectic reaction of the Sn–Ag alloy [9]. Hence, ifprimary Ag3Sn crystals formed before the onset of the eutecticreaction (such as in the slowly-cooled Sn–4.4 mol%Ag alloy), moreAg3Sn phase could nucleate adjacent to the primary Ag3Sn crystalswith a match in their crystalline orientation relationships, which

SC measurements of Sn–4.4 mol%Ag alloys at the cooling rates of (a) 5, (b) 10 and (c)

Fig. 7. Schematical diagram of the formation and growth process of bulk Ag3Sn IMCs.

J. Shen et al. / Intermetallics 16 (2008) 1142–1148 1147

would result in the formation of bulk Ag3Sn IMCs. Thus the solid-ified volume fraction of bulk Ag3Sn IMCs becomes larger than theamount of primary Ag3Sn crystals predicted by the phase equilibriacalculations. To prove this, the relationship between undercoolingand the growth velocity needs to be clarified.

The degrees of undercooling of Sn–4.4 mol%Ag alloy at differentcooling rates were achieved by correction and calibration of theliquid/solid point with the Curie point of pure Fe and determinedas follows: 7.5 K (5 K min�1), 9.7 K (10 K min�1) and 10.1 K(20 K min�1). In the classical theory of a faceted crystal growthmechanism, the relationship between growth velocity y and thedegree of melt undercooling is [10]:

y ¼ msðDTÞ2 (6)

where ms is a material constant.Since the growth velocity y is proportional to the volume frac-

tion of bulk Ag3Sn IMCs, the variation of the volume fraction withthe square of the degree of melt undercooling, DT , was linearlyfitted and given in Fig. 8. Linear regression analysis of the experi-mental data yields an equation for the volume fraction of the bulkAg3Sn IMCs in the form:

f ¼ 0:79þ 0:035�

DT2�

(7)

Fig. 8. Variation of the volume fraction of bulk Ag3Sn IMCs with the square of thedegree of undercooling DT .

The correlation coefficient of this fit is better than 0.99. By linearregression analysis, the volume fraction of primary Ag3Sn IMCs is0.79, which is close to the volume fraction of primary Ag3Sn IMCsdetermined by phase equilibria calculations. Hence, this showedthat the bulk Ag3Sn IMCs formed by the excess growth of primaryAg3Sn IMCs and the driving force for the growth of this facetedAg3Sn IMCs phase is proportional to the degree of undercooling thealloy during solidification. Increasing the cooling rate will increasethe fraction of bulk Ag3Sn IMCs, which is in accord with the thermalanalysis (see Fig. 6).

For the slowly-cooled eutectic Sn–Ag and Sn–Ag–Cu alloys, thedegree of undercooling required for b-Sn is larger than that for theAg3Sn phase [11]. Hence, the Ag3Sn crystal nuclei are likely to format the onset of the eutectic reaction due to the movement of Agatoms during slow solidification of the alloy. The pre-nucleatedAg3Sn phase could then become an epitaxial sink for the eutecticAg3Sn phase, leading to the formation of bulk Ag3Sn IMCs. The rod-like Ag3Sn phase in the slowly-cooled eutectic Sn–3.8 mol%Ag alloysample (see Fig. 2(a)), which can be regarded as a transition fromparticle-like Ag3Sn phase to bulk Ag3Sn IMCs, is a demonstration ofthis proposal. Note in our study that the solder alloys wereprepared from high-purity Sn and Ag elements. For other researchconditions, when eutectic Sn–Ag and Sn–Ag–Cu solder pastes wereused for solidification studies, bulk Ag3Sn IMCs usually formedbecause the impurities can be act as nucleation agents for thenucleation of Ag3Sn crystal nuclei, and the growth velocity of bulkAg3Sn IMCs increases with the square of the degree of undercoolingof the alloy achieved. This is the reason that many researchers havereported bulk Ag3Sn IMCs formed even in slowly-cooled eutecticSn–Ag and Sn–Ag–Cu solders.

When the b-Sn phase acts as the primary phase (such as in therapidly-cooled Sn–3.8 mol%Ag and Sn–4.4 mol%Ag alloys), thekinetic undercooling obtained is large enough for the formation ofthe primary b-Sn phase. More driving force is required for theAg3Sn phase to separate through a eutectic reaction and formaround primary b-Sn crystals. This is caused by the mismatchedcrystalline orientation relationships (Ag3Sn has a faceted structure,but b-Sn possesses a non-faceted structure). In this case, the Ag3Snphase has to nucleate more or less homogenously, and no bulkAg3Sn IMCs separates out through the eutectic reaction.

4. Conclusions

In conclusion, by thermal analysis technology and phase equi-libria calculation, we have clarified the rapid growth mechanism of

J. Shen et al. / Intermetallics 16 (2008) 1142–11481148

bulk Ag3Sn IMCs in Sn–Ag solders. The fraction difference betweenthe bulk Ag3Sn IMCs in solders measured by thermal analysis andthe primary Ag3Sn phase predicted by phase equilibria calculationsis caused by the epitaxial growth of the eutectic Ag3Sn phase at theleading Ag3Sn phase’s surfaces due to the match in their crystallineorientation relationship. The formation of bulk Ag3Sn IMCs inslowly-cooled eutectic Sn–Ag and Sn–Ag–Cu solders is attributed tothe formation of fine Ag3Sn crystal nuclei at the onset of theeutectic reaction and the high driving force for the growth of thisfaceted bulk Ag3Sn IMCs phase in Sn–Ag solder with a minimaldegree of undercooling during solidification.

Acknowledgements

This work was financial supported by an RGC Competitive Ear-marked Research Grant (Project no. 9041222 CityU.111307). Theauthors would like to thank K.N. Tu at UCLA for helpful discussion.

Special thanks to Prof. B. Ralph at Brunel University for his coop-eration in this study.

References

[1] Abtew M, Selvaduray G. Mater Sci Eng R 2000;27:95.[2] Henderson DW, Gosselin T, Sarkhel A. J Mater Res 2002;17:2775.[3] Ochoa F, Willlams JJ, Chawla N. J Electron Mater 2003;32:1414.[4] Kim KS, Huh SH, Suganuma K. Mater Sci Eng A 2002;333:106.[5] Kang SK, Choi WK, Shih DY, Henderson DW, Gosselin T, Sarkhel A, et al. JOM

2003;55:61.[6] Shen J, Liu YC, Gao HX, Wei C, Yang YQ. J Electron Mater 2005;34:1591.[7] Kempen ATW, Sommer F, Mittemeijer EJ. Thermochim Acta 2002;383:21.[8] Kempen ATW, Sommer F, Mittemeijer EJ. Acta Mater 2002;50:3545.[9] Davies V. J Inst Metals 1964;93:10.

[10] Flemings MC. Solidification processing. New York: McGRAW-HILL; 1974.p. 1–24.

[11] Ohnuma I, Miyashita M, Anzai K, Liu XJ, Ohtani H, Kainuma R, et al. J ElectronMater 2000;29:1137.