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Published in Z. Metallkd. 92 (2001) July issue

Ursula R. Kattner and Carol A. Handwerker

Metallurgy Division, National Institute of Standards and Technology, Gaithersburg, U.S.A.

Calculation of Phase Equilibria in Candidate Solder AlloysDedicated to Prof. Dr. Dr. h.c. mult. Günter Petzow on the occasion of his 75th birthday

Abstract

New solder alloys are being developed forelectronic assemblies as replacements fortraditional Pb-containing solder materials as aresult of international pressure to remove Pb fromthe waste stream. In the transition period from Pb-containing to Pb-free solder alloys, componentleads and copper interconnections on circuit boardwill continue to be pre-tinned with a Pb-containing solder to improve solderabili ty. Phaseequili bria information is needed for the evaluationof candidate Pb-free solder alloys in terms of theirmelting behavior and of the possible effects of Pb-contamination on manufacturing and reliabilit y.The CALPHAD method of phase equili briacalculation using thermodynamic descriptionsfrom databases provides a powerful tool forobtaining such information. The reliabil ity of thecalculation, however, depends on the quality ofthe thermodynamic descriptions of the individualphases. Criteria for the evaluation of thesedescriptions and the available thermodynamicdatabases are discussed. The effect of Pb-contamination on four solder alloys is analyzed.

1 Introduction

In the last five years the microelectronicsindustry has been moving away from Pb-containing solder alloys for two reasons. First,there is a growing interest worldwide in removingtoxic elements, including Pb, from the solid wastestream for electronic equipment. Second, theautomotive industry is developing solders thatwithstand higher service temperaturescharacteristic of under-the-hood applications. Forthese purposes it is necessary to evaluate theproperties of candidate solders related tomanufacturing and reliabilit y, such as freezing

range (liquidus, solidus), effects from possiblecontamination from other solder materials andreactions with various substrates, andsolderabilit y. Most Pb-free solders are Sn-basedalloys with additions of low melting metals suchas Bi, Sb and In or metals forming a eutecticreaction with (Sn)*, such as Ag and Cu. Sincecommon substrate materials consist of Cu, Cucoated or plated with Sn-Pb or Sn-Bi solders, Ni-Sn, Ni-Au and Ni-Pd, the systems containing theseelements in combination with the solder elementsalso need to be evaluated.

Although extensive research has been carriedout on the phase diagrams of most binary Sn-systems, data may be not available for everyhigher-order Sn-based system. However, when thebinary sub-systems are known, thermodynamiccalculation provides an extremely useful tool forobtaining quantitative information about thehigher-order (ternary, quaternary, etc.) systems.For a ternary system, for example, thermodynamicmodels consistent with the experimental binarydata are first obtained, then a standardthermodynamic extrapolation method is used tocalculate the ternary system. This approach is partof the CALPHAD method [1,2]. From thecalculated phase diagram, the melting temperaturerange for solder, the solidification path, as well asthe susceptibilit y to intermetalli c formation withvarious substrates, can be estimated. TheCALPHAD method also allows the calculation ofequili bria for compositions and temperatureswhere data are not available, as well as calculationof metastable equili bria.

Thermodynamic calculation also provides datafor the analysis of other alloy properties. Analysis

* The elemental symbol in parenthesis is used to distinguishthe disordered solid solution based on this element from thepure element.

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of multi-component diffusion requires that tie-lineinformation, i.e., the compositions of two phasesin equili brium, be available [3]. Tie-line data arerarely measured but can be easily obtained fromthe calculated phase equili brium.

The wetting behavior of a molten solder is animportant property which partially depends on thesurface tension and viscosity of the liquid phase.Lee and Lee [4] used the correlation between thepartial excess Gibbs energies and the surfacetension to calculate the surface tension of binarysolder liquids. The partial excess Gibbs energiesare quantities that are readily available from thethermodynamic calculation. The correlationbetween the thermodynamic properties of theliquid phase and surface tension, as well as theviscosity, was also used by Ohnuma et al. [5].

The subject of this paper is to give criteria forthe evaluation of the thermodynamic assessmentsof binary and ternary systems relevant to solderalloys and to give a survey of the availablethermodynamic databases. Examples of theutili zation of information from the phasediagrams, as well as the thermodynamiccalculation, for the evaluation the effect of Pb-contamination on the freezing ranges of solderalloys will be presented.

2 The Calculation of Phase Equilibria

2.1 Choice of Models

The CALPHAD method [1,2] employs avariety of models for the descriptions of thevarious phases. The choice of model used for thedescription of each phase is important since itdetermines the compatibilit y of all possible binarysystems in which phases with the same or similarcrystal structures occur. The crystallographicrelationship between two phases of differentbinary systems is sometimes obscured by the factthat they have different stoichiometries. Forexample, the high- and low-temperature η and η'phases of the Cu-In and the Cu-Sn systems occurat 33-38 % In and 43.5-45 % Sn (atomic fraction),respectively, and are, therefore, associated withdifferent stoichiometries, i.e., Cu2In and Cu5Sn6.Despite their apparently different stoichiometries,the need for the same model for the two phases isnecessary for the Cu-In-Sn system since the high-temperature phase shows a continuous ternarysolid solution [6]. The crystal structure of both ofthese phases belongs to the B81/B82 (NiAs/Ni2In)structure type family and can be successfullydescribed with the same model description [7].Another family of related structures are the D82

and D83 structures (Cu5Zn8 and Cu9Al4,respectively). These two phases form continuousternary solutions in the Al-Cu-Zn system [8] aswell as in the Cu-Ga-Zn (Cu5Zn8 and Cu9Ga4)system [9]. The modeling of these two structureswith the sublattice model would require a complexdescription with 4 sublattices [10]. In order tosimpli fy the description of this phase, Liang andChang [11] modeled it as a disordered solution. Itis not uncommon to make such simpli fications inthe thermodynamic assessment of a complexsystem. Other common simpli fications are: todescribe a solid phase with a narrow homogeneityrange as a stoichiometric compound; to omit aphase which is only stable in a narrow temperatureinterval and assess the metastable diagram instead;and to treat two or more phases with relatedcrystal structures as one phase, thus ignoring thetransformation between them. Thesesimpli fications are acceptable as long as care istaken not to compromise general and importantfeatures of the system.

2.2 Selection Criteria for Assessments

It is desirable to utili ze as many of the existingbinary assessments as possible in order to allowrapid assessment of higher-component systems.Therefore, it is necessary to select a set of binaryassessments as a basis for a database for soldersystems. An obvious requirement is that calculatedphase equili bria data reproduce the experimentaldata within the limits of the experimentalaccuracy. In the case of solder alloy systems,where the invariant temperatures are known withina few tenths of degrees, it is paramount that thesetemperatures are reproduced within this limit.However, the true test of the quality of thethermodynamic description is the extrapolation toa ternary system. One example where the qualityof the thermodynamic description was found to beinsuff icient is the Sn-rich part of the Sn-Ag-Cusystem. In this case, the calculation does notreproduce the ternary eutectic within the limits ofthe experimental error [12]. Moon et al. [12]found that the description of the liquid + Ag3Snand liquid + Cu6Sn5 equil ibria in the binary Ag-Snand Cu-Sn systems is in need of further refinementin order to obtain better agreement with theternary system. However, the availableexperimental data for the Sn-rich part of these twobinary systems scatter noticeably. Therefore, thefurther refinement of these description must eitherutil ize ternary data or improved new experimentaldata of the binary systems.

Extrapolation to higher-component systems isone reason why a large number of terms in the

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concentration dependence of a solution phase isundesirable. In an extrapolation, a large number ofterms can result in a "bumpy" Gibbs energyfunction, creating unlikely shapes in phaseboundaries. Alternatively, a phase may appear tobe stable in a composition/temperature region ofthe system where it is not observed in theequilibrium diagram. In order to combine ternaryassessments for the extrapolation to a higher-component system, all of the ternary assessmentsmust be based on the same binary descriptions.The substitution of one binary description byanother in a ternary assessment will require areevaluation of the ternary description in mostcases.

2.3 Advantages of Calculated PhaseDiagrams

If all of the above criteria are fulfill ed, thephase diagram that is obtained from a ternaryassessment can actually be more accurate than theone from a critical evaluation, as is the case forthe Ag-Cu-Pb system. The calculated liquidussurface [13] differs from the one proposed inevaluations [8,14,15] where the liquidus surfacewas based on the early interpretation of the resultsof Friedrich and Leroux [16]. Jänecke [14] basedhis evaluation on the then accepted Cu-Pb phasediagram for which the miscibilit y gap in the binaryliquid phase was greatly overestimated and,accordingly, resulted in an overestimation of theternary miscibilit y gap in the liquid phase. Thisevaluation was later accepted in the evaluations byChang et al. [8] and Hayes [15]. The calculationof Hayes et al. [13] is based on a revised Cu-Pbsystem with a much less pronounced liquidmiscibilit y gap and the original data of Friedrichand Leroux [16] as well as thermodynamic data.Since both phase diagram data andthermodynamic quantities are generated from thesame thermodynamic description and are,therefore, consistent, the calculated liquidussurface is more realistic than the criticallyevaluated liquidus data.

3 Available Phase Equilibria Information forCandidate Solders

3.1 Binary Systems

Several of the phase diagrams of binary soldersystems are fairly simple. However, almost twothirds of the binary systems have at least oneintermetalli c compound. A summary of binaryintermetalli c phases and their structures for themost common elements in solder alloys is given in

Table 1. For the binary systems which do notcontain intermetalli c compounds, there exist atmost three phases (the low-temperaturemodification of Sn, αSn, can be neglected forsolder applications). The simplest of these systemsis the Bi-Sb system where both the liquid and thesolid phases form continuous solid solutions.Many of these simple systems, e.g., Ag-Bi, Ag-Cu, Ag-Pb, Bi-Cu, Bi-Sn, Ga-In, Ga-Sn, Ga-Zn,In-Zn, Pb-Sb, Pb-Sn and Sn-Zn, are eutectic. Inother systems, such as Ag-Cu, Ag-Pb and Cu-Pb,the solid two-phase equili bria are the result of amiscibilit y gap in the fcc phase. Other systemsform miscibilit y gaps in the liquid phase,including Bi-Ga, Bi-Zn, Cu-Pb, Ga-Pb and Pb-Zn.Thermodynamic assessments with SGTEcompatible lattice stabiliti es [17] for thedescription of the pure elements are available formost of these systems.

Many of the binary systems relevant to soldersform intermetalli c compounds, making theirdescription fairly complex since several phaseswith ordered structures exist. In a few systems,one or two of the intermetalli c phases have adisordered site occupation in their crystalstructure, e.g., Bi-Pb, Ag-Sn, In-Pb and In-Sn.These disordered phases frequently showsignificant homogeneity ranges. Since the crystalstructures of these phases can be the same asdisordered elemental structures, the same modeldescriptions as for the corresponding elementalphases should be used. Other systems, such as Ga-Sb and In-Sb, have only one compound with avery narrow homogeneity range.

3.2 Ternary and Higher-Component Systems

Including the most common 8 elements forsolder alloys, Ag, Bi, Cu, In, Pb, Sb, Sn and Zn,results in consideration of 56 ternary systems thatare relevant to solders. Since the experimentaldetermination of a ternary system is extremelytime consuming, a suff icient number ofexperiments has been carried out for only about aquarter of these systems to establish their phasediagrams reasonably well . Some experimentaldata are available establishing a partial phasediagram for almost half of the remaining systems.No experimental information is available for theremaining quarter of the systems. Criticalevaluations of the experimental data are availablefor ternary Ag-, Al- and Au-systems [18] and Cu-systems [8]. Vill ars et al. [19] compiled asummary of the available experimental phasediagram data for ternary systems.

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If thermodynamic descriptions of all of theconstituent binary systems are available, it ispossible to estimate a phase diagram of a higher-component system from the extrapolation of thebinary systems. The quality of the extrapolation toa ternary system from the descriptions of the threebinary systems depends not only on the accuracyof the calculation of each binary system, but alsoon the magnitude of possible ternary interactionsand the occurrence of ternary intermetalli ccompounds. The probable magnitude of theseternary interactions can be estimated from theproperties of the binary systems. In most cases theexcess Gibbs energies of the solution phases in thebinary systems relevant to solder alloys arerelatively small i n magnitude, indicating thatternary interactions are probably not significant.This was demonstrated by Kattner and Boettingerfor the case of the Cu-Pb-Sn system [20]. Many ofthe binary systems show no tendency to formintermetalli c compounds, suggesting that theformation of ternary intermetalli c compounds inhigher-component systems based on these systemsis also unlikely. In fact, only two ternaryintermetalli c compounds have so far been reportedfor those of the 56 ternary systems which havebeen experimentally measured. In the Cu-In-Snsystem [6] the structure of the Cu11In2Sn phase isan ordered bcc structure and can, therefore, berelated to binary intermetallic phases of the Cu-Inand Cu-Sn systems. In the Sb-Sn-Zn system [21]the structural relation of the Sb2SnZn phase to thebinary phases is not known.

3.3 Available Thermodynamic Databases

The efforts in the development ofthermodynamic descriptions for systems that arerelevant to solders have resulted in severalthermodynamic databases that are either availablein the public domain [4,22] or are commercial†[5]. These databases are usually built from theassessed descriptions of all binary constituentssystems but not necessarily all ternary systems.The database described by Lee and Lee [4]includes seven elements (Sn, Ag, Bi, Cu, In, Sb,Zn) and the assessments of all constituent binarysystems and selected ternary systems. Thedatabase described by Ohnuma et al. [5] includesassessed descriptions for all binary and ternarysystems including elements Sn, Ag, Bi, Cu. Pb,Sb, Zn and selected systems containing In. The

† Commercial products are referenced for completeness.Such identification does not imply recommendation orendorsement by the National Institute of Standards andTechnology, nor does it imply that these products arenecessarily the best available for the purpose.

description of the Sn-Pb systems includes also thepressure dependence of the Gibbs energy of thephases. Another database under development [22]currently includes assessed descriptions of allbinary systems and selected ternary systems forthe elements Sn, Ag, Bi, Cu, Pb.

4 Freezing Temperature Ranges

4.1 Equilibrium Solidification

A basic requirement for a candidate solderalloy to replace a Pb-containing solder is to havea specific freezing range, the temperature rangeover which both solid and liquid co-exist; thisfreezing range is dictated by the application. Toreplace the Pb-Sn eutectic alloy, the ideal solderalloy would be eutectic or near-eutectic, with aliquidus temperature low enough to avoiddamaging components and a solidus temperaturehigh enough to maintain joint reliabilit y duringthermomechanical fatigue.

One limiting case for describing solidificationbehavior is solidification obeying the lever rule(thermodynamic equili brium). For equili briumsolidification (lever rule) it is assumed that at eachtemperature during cooling, complete diffusionoccurs in the solid as well as in the liquid and,therefore, all phases are in thermodynamicequilibrium at each temperature. The equilibriumfreezing range of a binary alloy can be easily readfrom a phase diagram or from the isopleths forhigher-component systems. However, isoplethsprovide information only for one section throughthe multi -component phase diagram and, since thetie-lines are usually not in the plane of theisopleth, there is no information on phasecompositions and amounts. In the case of ternarysystems this information can be obtained fromsimultaneously examining the liquidus and solidusprojections of the ternary system. These diagramsdo not provide information about the onset of theformation of a second solid phase.Thermodynamic calculations, however, can beused to calculate the equili brium solidificationpath for individual alloys and to generate tableswith the desired numerical quantities, such as tie-line data, phase amounts or enthalpy content.

4.2 Non-Equilibrium Solidification

Even if the phase diagram shows that aspecific alloy has the desired freezing range, it ispossible, and quite likely for non-eutecticfreezing, that a larger freezing range is observedin experiments. This is the case when non-equili brium solidification occurs. Since the degree

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to which non-equili brium solidification occurs isdetermined by kinetic factors, it is diff icult topredict. The limiting case describing thissolidification behavior is the Scheil path, wherediffusion in the solid is forbidden.Thermodynamic equili brium exists only as localequili brium at the liquid/solid interface. Thisproduces the worst case of microsegregation withthe lowest final freezing temperature. Since thecomposition of the remaining liquid phase variesaccording to the tie-lines it is usually not possibleto obtain the Scheil path from an isopleth.However, the Scheil path can be easily obtainedfrom thermodynamic calculation. Althoughmodeling of real solidification behavior requiresthe incorporation of a kinetic analysis ofmicrosegregation and back diffusion, thepredictions of the Scheil model are close to realityfor many alloys for the time scales found insoldering.

4.3 Contamination of Pb-free Solders

The use of a pre-tinning alloy for componentleads and copper circuit board interconnects withcomponents and pads with different compositionthan that used for the solder may result indegraded properties of the solder joints. Forexample, when Pb-free solder alloys arecontaminated by Pb from the pre-tinned layer,these alloys may form a low melting higher-component eutectic. This case was studied indetail for Pb-contaminated Sn-Bi solders by Moonet al. [23] using experimental methods inconjunction with calculations of the equili briumphase diagram and Scheil solidification. Theyfound that a small amount of contamination by Pbresults in the formation of this low meltingeutectic at 98°C. The predictions from the Scheilpath calculations were in accord with theirexperimental observations.

Since the freezing ranges of other Pb-freesolder alloys may be similarly susceptible to Pb-contamination, the freezing behavior of foursolder alloys was studied from the calculation ofthe lever rule and Scheil freezing path of theoriginal solder alloy and the contaminated solder.Moon et al. estimated a Pb-concentration of 6 %(mass fraction) in the solder from contaminationby the component lead and board pre-tinning.The original solder compositions and thoseresulting from contamination are listed in Table 2.The calculations were carried out using the NISTsolder database [22], the Thermo-Calc softwarepackage [24] and the Scheil and Lever programs[25].

Fig. 1 shows the calculated isopleths from theoriginal solder composition to the composition ofthe contaminant for sections through the multi -component solder system. The phases that areformed during equili brium solidification can beobtained from these sections. The diagrams showalso that Pb-contamination for solders without Biresults in the formation of eutectic equilibria withslightly lower temperatures than the binary Sn-Pbeutectic (Ag-Pb-Sn: 177 °C, Ag-Cu-Pb-Sn: 176°C). However, as previously mentioned, phasecompositions, i.e., tie-line information, phasefractions as well as information about Scheil pathsolidification, cannot be obtained from thesediagrams.

Lever rule and Scheil path calculations wereperformed for each of the alloy compositionslisted in Table 2. The results of these calculationsare summarized in Fig. 2 and Tables 3 and 4. Thecompositions of the Bi-free solders are identicalor close to the compositions of the Sn-richeutectics of the Ag-Sn and Ag-Cu-Sn systems.Thus, the freezing ranges of these alloys are smalland essentially identical for lever rule and Scheilsolidification. Pb-contamination of these alloysresults for both alloys in the formation of higher-component eutectics where solid (Pb) is formed.Since freezing of the Pb-contaminated alloys endsfor both lever rule and Scheil solidification withthe eutectic reaction the solidification behaviorsare similar. The effect of Pb-contamination on thesolders with Bi is different. The combination ofSn, Bi and Pb results in the formation of lowmelting eutectics (T = 98 °C) that are very close tothe Bi-Pb-Sn ternary system and do not extend tocompositions of the isopleths (Fig. 1). However,depending on the Pb-concentration, the liquidphase is stable at fairly low temperatures. Sincethe lever rule solidification is not terminated byeutectic freezing it can be expected that Scheilsolidification will result in lower final freezingtemperatures which can be as low as the low-melting eutectics of these systems. Eutectic finalfreezing is observed for the Scheil path for the Sn-2.9Ag-4Bi-6Pb alloy but not for the Sn-2.8Ag-0.8Cu-2.8Bi-6Pb alloy and is a consequence ofthe lower Bi concentration in that alloy. Thisbehavior is in accord with the observations byMoon et al. [23].

In a recent summary of fatigue resistant, hightemperature solders Gayle[26] gave a targetstorage and operating temperature of -55 °C to+160 °C and noted that the Bi concentration forthese alloys must be kept below 3.5 % to avoidproblems with low melting eutectic in case of Pb-

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contamination. Although the present resultsconfirm that the formation of the low meltingeutectic does not occur during Scheilsolidification of an alloy with a lower Bi-concentration after Pb-contamination, the liquidphase is a stable phase at temperatures below 160°C. Bi containing solders should, therefore,completely be avoided for these applications ifthere is the possibilit y of Pb-contamination.

Contamination of solders is not a problemassociated only with Pb but will always pose apossible problem when the constituent elementsfrom the solder and the pre-tinning material aredifferent. For example, pre-tinning with a Bi-containing alloy could cause the formation of thelow melting eutectics in which solid (Sn) and (Bi)form. However, current practices use pre-tinningalloys with fairly low Bi-concentrations comparedto 37 % Pb of the Sn-Pb alloy, therefore, theeffect from the contamination can be expected tobe much less pronounced than found for Pb-containing pre-tinning alloys.

5 Conclusion

The calculation of phase diagrams andproperties from thermodynamic databases is apowerful tool for the development of new soldersneeded worldwide for Pb-free electronicassembly. A wide range of potential alloys can berelatively rapidly evaluated and potentialproblems with non-equili brium freezing orcontamination with other elements can beanalyzed provided adequate thermodynamicdatabases exist. Thermodynamic calculationsfurther provide data that are needed for theprediction of other solder properties such assurface tension and viscosity of the liquid phase.

Correspondence Address

Ursula R. Kattner and Carol A. HandwerkerNational Institute of Standards and Technology100 Bureau Dr., Stop 8555Gaithersburg, MD 20899-8555U.S.A.

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References

1. Kaufman, L.: CALPHAD Analysis ofMaterials Processing and Performance, in:M. Doyama, T. Suzuki, J. Kihara, R.Yamamoto (eds.), Computer AidedInnovation of New Materials, Elsevier,Amsterdam (1991) p. 773-778.

2. Kattner, U.R.: JOM (12) 49 (1997) 14-19.

3. Andersson, J.-O.; Ågren, J.: J. Appl. Phys.72 (1992) 1350-1355.

4. Lee, B.-J.; Lee, H.M.: Alloy Design of Sn-Ag-In-Bi-Sb Solder System UsingThermodynamic Calculations, in: R.K.Mahidhara, D.R. Frear, S.M.L. Sastry, K.L.Murtym, P.K. Liaw, W. Winterbottom(eds.), Design and Reliabilit y of Solder andSolder Interconnections, TMS, Warrendale,PA (1991), p. 129-136.

5. Ohnuma, I.; Liu, X.J.; Ohtani H.; Ishida, K.:J. Electron. Mater. 28 (1999) 1164-1171.

6. Köster, W. Gödecke,T.; Heine, D.: Z.Metallkde. 63 (1972) 802-807

7. Kao, C.R.; Bolcavage, A.; Chen, S.-L.;Chen, S.W.; Chang, Y.A.; Roming, A.D. Jr.:J. Phase Equili bria 14 (1993) 22-30.

8. Chang, Y.A.; Neumann, J.P.; Mikula, A.;Goldberg, D.: Phase Diagrams andThermodynamic Properties of TernaryCopper-Metal Systems, INCRA MonographSeries VI, The International CopperResearch Assn., New York, (1979).

9. Massalski, T.B.; Raynor, G.V.: J. Inst.Metals, London 82 (1954) 539-544.

10. Ansara, I.; Burton, B.; Chen, Q.; Hill ert,M.; Fernadez Guill ermet, A.; Fries, S.G.;Lukas, H.L.; Seifert, H.J.; Oates, W.A.:CALPHAD 24 (2000) 19-40.

11. Liang, H.; Chang, Y.A.: J. Phase Equilibria19 (1998) 25-37.

12. Moon, K.-W.; Boettinger, W.J.; Kattner,U.R.; Biancaniello, F.S.; Handwerker, C.A.:J. Electron. Mater. 29 (2000) 1122-1136.

13. Hayes, F.H.; Lukas, H.L.; Effenberg, G.;Petzow, G.: Z. Metallkde. 77 (1986)749-754.

14. Jänecke, E.: Kurzgefaßtes Handbuch allerLegierungen, 2nd edition, Carl WinterUniversitätsverlag, Heidelberg, Germany,(1949).

15. Hayes, F.: Silver-Copper-Lead, in: G.Petzow, G. Effenberg (eds.), Ternary Alloys,Vol. 2, VCH, Weinheim, Germany, (1988),p. 1-13.

16. Friedrich, K.; Leroux, A.: Metallurgie 4(1907) 293-315.

17. Dinsdale, A.T.: CALPHAD 15 (1991) 317-425.

18. Petzow, G.; Effenberg, G. (eds.): TernaryAlloys, Vol. 1-13, VCH, Weinheim,Germany, (1988-1995).

19. Vill ars, P.; Prince, A.; Okamoto, H.:Handbook of Ternary Alloy PhaseDiagrams, Vol. 3-10, ASM International,Materials Park, OH, (1995).

20. Kattner, U.R.; Boettinger, W.J.: J. Electron.Mater. 23 (1994) 603-610.

21. Khudolii , V.A.; Golovei, M.I.; Novoselova,A.V.: Dokl. Chem. 228 (1976) 430-431.

22. Kattner, U.R.: unpublished research, NIST,Gaithersburg, MD, (2001); see alsohttp://www.metallurgy.nist.gov/phase

23. Moon, K.-W.; Boettinger, W.J.; Kattner,U.R.; Handwerker, C.A.; Lee, D.-J.: J.Electron. Mater. 30 (2001) 45-52.

24. Sundman, B.; Jansson, B.; Andersson, J.-O.:CALPHAD 9 (1985) 153-190.

25. Kattner, U.R.; Boettinger, W.J.; Coriell ,S.R.: Z. Metallkd. 87 (1996) 522-528.

26. Gayle, F.W.: Advanced Mater. & Processes(4) 159 (2001) 43-44.

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Table 1: Crystal Structures of the Solid Phases in Binary Solder Systems

disordered phases ordered phasesSystem

A1: fcc A2: bcc A3: hcp A5: βSn A6: In A7: αAs fcc bcc hcp other

Ag-Bi (Ag) (Bi)

Ag-Cu (Ag), (Cu)

Ag-In (Ag) β ζ (In) L12: Ag3In D83: Ag2In C16: AgIn2

?: α'

Ag-Pb (Ag), (Pb)

Ag-Sb (Ag) ζ (Sb) L60: Ag3Sb

Ag-Sn (Ag) ζ (Sn) D0a: Ag3Sn?: ε'

Ag-Zn (Ag) β ε, (Zn) D82: Ag5Zn8 Bb: ζAgZn

Bi-Cu (Cu) (Bi)

Bi-In (In),ε?

(Bi) B82: BiIn2 B10: BiInD81: Bi3In5

Bi-Pb (Pb) ε (Bi)

Bi-Sb (Bi,Sb)

Bi-Sn (Sn) (Bi)

Bi-Zn (Zn) (Bi)

Cu-In (Cu) β (In) InMn3: γ B81: Cu2In.hB82: Cu2In.l ?

Cu7In3: Cu7In3

AlCu: Cu11In9

Cu-Pb (Cu), (Pb)

Cu-Sb (Cu) γ (Sb) D03: β ?: δ D0a: Cu3SbCu10Sb3: Cu10Sb3

C38: Cu2Sb

Cu-Sn (Cu) β (Sn) D03: γCu41Sn11: Cu41Sn11

B81: Cu6Sn5.hB82: Cu6Sn5.l ?Cu10Sn3: Cu10Sn3

Cu3Sn: Cu3Sn

Cu-Zn (Cu) β ε, (Zn) B2: β'D82: Cu5Zn8

?: δ

In-Pb (Pb) (In), α

In-Sb (In) (Sb) B3: InSb

In-Sn (Sn) (In), β hex: γ

In-Zn (Zn) (In)

Pb-Sb (Pb) (Sb)

Pb-Sn (Pb) (Sn)

Pb-Zn (Pb) (Zn)

Sb-Sn (Sn) (Sb) B1: β ?: Sb2Sn3

Sb-Zn (Zn) (Sb) Be: SbSn?: γ, ε, δ, ζ, η

Sn-Zn (Zn) (Sn)

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Table 2: Modified solder compositions as a result from contamination with 16.2 % of Sn - 37 % Pbsolder. (Compositions are in % of mass fraction)

Original Solder Composition Contaminated Solder CompositionSn - 3.5 % Ag Sn - 2.9 % Ag - 6 % PbSn - 4 % Ag - 1 % Cu Sn - 3.4 % Ag - 0.8 % Cu - 6 % PbSn - 3.5 % Ag - 4.8 % Bi Sn - 2.9 % Ag - 4 % Bi - 6 % PbSn - 3.4 % Ag - 1 % Cu - 3.3 % Bi Sn - 2.8 % Ag - 0.8 % Cu - 2.8 % Bi - 6 % Pb

Table 3: Liquidus, final freezing temperatures, and mass fraction of low-melting eutectic from thelever rule and Scheil calculations without and with Pb-contamination.

Sn-3.5Ag Sn-4Ag-1Cu Sn-3.5Ag-4.8Bi Sn-3.4Ag-1Cu-3.3BiT (°C) fe T (°C) fe T (°C) fe T (°C) fe

SolderLever 221 - 225-215 - 215-201 - 233-204 -Scheil 221 - 225-215 - 215-137 0.03 233-137 0.02ContaminatedLever 213-177 0.09 227-176 0.09 208-144 - 234-155 -Scheil 213-177 0.13 227-177* 0.09 208-97 0.01 234-109 -

*Note: During Scheil solidification the remaining liquid phase is depleted of Cu which results in that the finalfreezing occurs at the temperature of the Ag-Pb-Sn eutectic.

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Table 4: Sequence of phase formation during lever rule and Scheil freezing without and with Pb-contamination.

Lever rule T (°C) Scheil T (°C)Sn-3.5AgSolder L → (Sn) + ε 221 L → (Sn) + ε 221Contaminated L + (Sn)

L + (Sn) + ε(Sn) + ε + (Pb)

213211177

L → (Sn)L → (Sn) + εL → (Sn) + ε + (Pb)

213211177

Sn-4Ag-1CuSolder L + η

L + η + ε(Sn) + η + ε

225221215

L → ηL → η + εL → (Sn) + η + ε

225221215

Contaminated L + ηL + η + εL + η + ε + (Sn)(η → η')L + η' + ε + (Sn)η' + ε + (Sn) + (Pb)

227210208

187176

L → ηL → η + εL → η + ε + (Sn)(η → η')L → η' + ε + (Sn)L → ε + (Sn) + (Pb)

227210208

187177

Sn-3.5Ag-4.8BiSolder L + ε

L + ε + (Sn)ε + (Sn)

215214201

L → εL → ε + (Sn)

215214

Contaminated L + (Sn)L + (Sn) + εL + (Sn) + ε + (Pb)(Sn) + ε + (Pb)

208207154144

L → (Sn)L → (Sn) + εL → (Sn) + ε + (Pb)L → (Sn) + ε + (Pb) + (Bi)

20820714697

Sn-3.4Ag-1Cu-3.3BiSolder L + η

L + η + (Sn) + εη + (Sn) + ε

233212204

L → ηL → η + (Sn) + ε(η → η')L → η' + (Sn) + εL → η' + (Sn) + ε + (Bi)

233212

187137

Contaminated L + ηL + η + (Sn)L + η + (Sn) + ε(η → η')L + η' + (Sn) + εL + η' + (Sn) + ε + (Pb)η' + (Sn) + ε + (Pb)

234206205

187165155

L → ηL → η + (Sn)L → η + (Sn) + ε(η → η')L → η' + (Sn) + εL → η' + (Sn) + ε + (Pb)L → η' + (Sn) + ε + θ

234206205

187160136

11

Figure 1: Isopleths from the original solder composition to the composition of the contaminant. (a) Sn -3.5 % Ag to Sn - 37 % Pb, (b) Sn - 4 % Ag - 1 % Cu to Sn - 37 % Pb, (c) Sn - 3.5 % Ag - 4.8 % Bi to Sn -37 % Pb, (d) Sn - 3.4 % Ag - 1 % Cu - 3.3 % Bi to Sn - 37 % Pb. The dotted lines represent a Pbconcentration of 6 %.

12

Figure 2: Calculated fraction solid vs. temperature curves from lever rule and Scheil calculations for thepure and contaminated solder alloys. (a) Sn - 3.5 % Ag and Sn - 2.9 % Ag - 6 % Pb, (b) Sn - 4 % Ag - 1 %Cu and Sn - 3.4 % Ag - 0.8 % Cu - 6 % Pb, (c) Sn - 3.5 % Ag - 4.8 % Bi and Sn - 2.9 Ag - 4 Bi - 6 % Pb, (d)Sn - 3.4 % Ag - 1 % Cu - 3.3 % Bi and Sn - 2.8 % Ag - 0.8 % Cu - 6 % Pb.