JOM-0212-45

452002 December • JOM

The need for new, improved solder alloys and a better understanding of reactions during the soldering process grows steadily as the need for smaller and more reliable electronic products increases. Information obtained from phase equilibria data and thermody-namic calculations has proven to be an important tool in the design and understanding of new lead-free solder alloys. A wide range of candidate alloys can be rapidly evaluated for proper freezing ranges, susceptibility to contamination effects, and reactions with substrate materials before the expensive process of preparing and testing candidate alloys is initiated.

INTRODUCTION

Intense international competition makes it necessary for microelectronics and supporting industries to design and produce smaller, more functional, and reliable electronic products more economically. At the same time, there is growing global interest in eliminating toxic elements, such as lead, from electronic products. In recent years, substantial efforts were made to develop lead-free solders that are suitable substitutes for classic tin-lead eutectic solders. Simultaneously, there is a growing need for solders that can be used for applications with more demanding service conditions such as in automotive, avionic, military, or oil-exploration industries. For these purposes, it is necessary to evaluate the properties of candidate solder alloys that are related to manufacturing and reliability. Of particular interest are properties such as freezing range (liquidus and solidus), the effects from

Phase Diagrams for Lead-Free Solder Alloys

Ursula R. Kattner

possible contamination from other solder materials such as the formation of low-melting eutectics, and reactions with various substrates. A recent study

Author’s Note: The identification of any commercial product or trade name does not imply endorsement or recommendation by the National Institute of Standards and Technology.

and flux compatibility) were tin-based. Common alloying additions are low-melting metals, such as bismuth, antimony, and indium, or metals forming a eutectic reaction with (Sn), such as silver and copper. (The elemental symbol in parenthesis is used to distinguish the disordered solid solution based on this element from the pure element.) Substrate materials may consist of copper, copper that has been coated or plated with tin-lead or tin-bismuth solders, nickel-tin, nickel-gold, or nickel-platinum alloys. Knowledge of the phase equilibria of solder/alloy and solder/substrate systems provides the basic roadmap for the initial selection of candidate solders and contributes to the understanding of solder wetting and spreading. Phase equilibria data provide not only informa-tion about the liquidus and solidus temperatures of a candidate solder alloy, but also information about possible intermetallic phase formation, either within the solder during solidification or in reaction with the substrate mate-rial by a combination of isothermal solidification and solid-state reaction. Reaction of substrate material that has been pre-tinned with a tin-lead or tin-bismuth alloy with a solder of a different composition may result in the formation of a low-melting higher-component eutectic. In this case, the multi-component phase diagram can be used to evaluate the possible effects resulting from such a contamination. Traditionally, phase diagrams are determined from thermal analysis, examination of microstructure, and other experimental methods. However, the experimental determination of phase diagrams is a time-consuming, costly task since the number of possible systems

Figure 1. The calculated phase diagram of the Sn-Pb system.16

Knowledge of the phase equilibria of solder-alloy and solder/substrate systems provides the basic roadmap for the initial selection of candidate solders and contributes to the understanding of solder wetting and spreading.

of high-temperature lead-free candidate solder alloys1 showed that the only lead-free alloys that fulfilled the initial selection criteria (toxicity, cost, oxida-tion resistance, solidus temperature,

Overview Phase Diagrams

46 JOM • December 2002

increases drastically as the number of elements increases. For example, increasing the number of elements under consideration from six to seven increases the number of binary systems from 15 to 21, the number of ternary systems from 20 to 35, and the number of quaternary systems from 15 to 35. Experimental information for the entire phase diagram is available for most of the binary systems that are of interest for solders, but experimental information becomes increasingly sparse as the number of constituent elements increases (i.e., for ternary, quaternary, and higher-component systems). It has been shown that thermodynamic calculation of phase equilibria with the CALPHAD method2,3 is extremely useful for obtaining quantitative information about these higher-component systems.

The thermodynamic descriptions that are used with the CALPHAD method can also be used to obtain data of other properties that are important for under-standing the wetting behavior of a molten solder, such as surface tension and viscosity.4,5 In addition, Lee et al.6 used the calculation of metastable equilibria and the driving forces for phase forma-tion to predict the phase that forms first at a solder/substrate interface. Further-more, thermodynamic calculation also provides information that is needed for the simulation of kinetic processes. For example, tie-line information (i.e., the compositions of two phases in equilib-rium) and thermodynamic factors for the calculation of diffusion coefficients are necessary for the simulation of diffusion processes.7

THE CALPHAD METHOD

The CALPHAD method uses a series of models to describe the concentration, temperature dependence, and, if neces-sary, pressure dependence of the Gibbs energy functions of each individual phase in a system.2,3 Commercial and public domain software packages are available for the calculation of phase equilibria from these Gibbs energy functions.2,3 One of these, Thermo-Calc,8 was used for the calculation of the phase diagrams shown in Figures 1 to 10. The most common models for the description of the concentration dependence are the regular solution model for disordered solution phases and the sublattice model for ordered compounds. The choice of the sublattice model description for solid phases depends on their crystal structure.9 If the homogeneity range of a phase is narrow, this phase can also be described as a stoichiometric phase. The usual strategy for the assessment of a multi-component system is to first derive thermodynamic model descriptions that are consistent with the experimental data of the binary systems. These descriptions are then used together with a standard thermodynamic extrapolation method to calculate ternary and higher-order systems. If indicated by experimental data, it is possible to add ternary interaction terms to the thermodynamic models to obtain a more accurate calculation of the ternary system. This strategy is usually followed until the constituent systems of a higher-order system have been assessed. Experience has shown that no or very minor corrections are necessary for a reasonable prediction of quaternary and higher-component systems. The quality of the results that are obtained from calculations with the CALPHAD method depends not only on the quality of the thermodynamic models but also on the quality of the available experimental information that was used to derive the model parameters of the individual phases. The quality of the extrapolation of a ternary system from the three constituent binary systems depends on the magnitude of possible ternary interactions and the occurrence of ternary intermetallic compounds. For most binary systems that are relevant

for solder, the magnitude of the binary excess Gibbs energies is fairly small,10 indicating that ternary interactions may not be significant. Therefore, the accuracy of the calculated constituent binary systems is of crucial importance for obtaining quality calculations of ternary and higher-component systems.11

The efforts in the development of thermodynamic descriptions for systems that are relevant to solders have resulted in several thermodynamic databases that are either available in the public domain4,12 or are commercial.5

ACCURACY REQUIREMENT

The knowledge of temperatures and compositions of the invariant equilibria and regimes of primary phase solidifica-tion is of significant importance for the design of new solder alloys and for the specification of manufacturing tolerances of these solders. The liquidus temperature changes little with composi-tion in many tin-based systems when (Sn) forms as a primary phase, while the temperature dependence on composition can be relatively large for other phases, especially for intermetallic compounds. If the liquidus is steep, composition fluctuations in the solder alloy can cause the solder to have a significantly higher liquidus temperature than for the nominal composition. The invariant temperatures of solder alloys are usually known with fairly high accuracy while there is usually a larger variation in the reported composition of the liquid phase at the invariant temperature. This is, in part, due to the

Figure 2. The calculated phase diagram of the Sn-Bi system.19

Figure 3. The calculated phase diagram of the Sn-In system.19

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fact that temperatures between 50°C and 300°C can be easily measured with high accuracy. However, the interpretation of the microstructure of an alloy with near-eutectic composition is not always a straightforward task. The phase observation may be misleading due to a phenomenon caused by a skewed coupled zone.13 In this case, the fast growth kinetics of the unfaceted phase, (Sn) in most solder alloys, may lead to the formation of dendrites of this phase even on the other side of the eutectic composition where the faceted, frequently intermetallic phase, should form primary dendrites. This phenom-enon may result in an overestimation of the extent of the primary solidifica-tion area of the unfaceted phase. The interpretation of the microstructure in higher-component alloys can be even more difficult. Moon et al.11 found that the remaining liquid phase had a tendency for supercooling after the initial formation of the primary intermetallic phase in tin-rich alloys of the Sn-Ag-Cu system. The sequence of solidification of this supercooled liquid consisted of dendritic (Sn), coupled formation of non-faceted (Sn), and a faceted intermetallic phase (Ag3Sn or Cu6Sn5, depending on alloy composi-tion), followed by the ternary eutectic reaction. This solidification behavior resulted in microstructures with a smaller amount of eutectic structure than is expected from the equilibrium phase diagram. The fact that the slope of the liquidus in tin-based systems with intermetallic phases is usually very steep may lead

to insufficiently accurate calculation of a system. Moon et al.11 showed that, although the agreement between the calculated and measured liquidus data for the binary Ag-Sn and Cu-Sn system is satisfactory, it was not possible to use the descriptions of these binary systems to obtain an accurate fit of the ternary tin-rich part of the Ag-Cu-Sn system. It is known that the results of the calculation of higher component systems indicate whether further refinements of the thermodynamic description of a binary system are needed.14

BINARY SYSTEMS

A summary of the evaluated phase diagrams and available assessments of binary and ternary systems in the literature has been compiled.12 Most binary phase diagrams that are of interest for solder alloys are fairly simple and most of the phase boundaries are well established. Since the binary tin-based systems are key systems for the evaluation of candidate solder alloys, important features of these systems will be briefly discussed. The elements that are most often considered as alloying elements to tin for lead-free solders are Ag, Bi, Cu, In, and Sb. Although its susceptibility to corrosion is a concern, zinc is occasionally considered as an alloying element for solders because the temperature of the binary Sn-Zn eutectic is similar to that of the Sn-Pb eutectic. The elements gold and nickel are of interest since they are frequently used in substrate materials. Although the present goal is to eliminate lead from solder alloys because of its toxicity, the knowledge of this system is still relevant for either the study of the mechanisms that take place during soldering or the effects that may be caused in new lead-free solders that are applied to components that were pre-tinned with classical Sn-Pb solder. The transforma-tion from the high-temperature form, βSn, to the low-temperature form, αSn (Tβ α = 13°C), can be neglected since it does not affect the equilibria with other phases. Also, the transformation, which is kinetically inhibited, rarely occurs in solders.15

Sn-Pb

The phase diagram of this system is well established and a number of

thermodynamic assessments are avail-able for this simple eutectic system. At 183°C, the liquid with xSn = 0.619 decomposes into the two terminal solid solutions, (Pb) and (Sn). (All composi-tions are given in weight fraction unless otherwise noted.) In addition to the stable phase equilibria data, the thermodynamic assessments of Fecht et al.16 and Ohtani et al.17 also used data for metastable equilibria. The major differences between the two assessments are that Ohtani et al. also considered the pressure dependence of the phases while Fecht et al. empha-sized an accurate reproduction of the experimental quantities at atmospheric pressure. The phase diagram obtained from the assessment of Fecht et al. is shown in Figure 1.

Sn-Bi

Most parts of the phase diagram of this simple eutectic system are well established. At 138°C, the liquid with xSn = 0.43 decomposes into the two terminal solid solutions, (Bi) and (Sn). However, the solubility limit of tin in (Bi) is not reliably known although a lower value is preferred.18 Lee et al.19 accepted this lower value for the (Bi) homogeneity range and also used experimental data of the Sn-Bi-In system for the refinement of the description of the Sn-Bi system. The phase diagram obtained from this assessment is shown in Figure 2.

Sn-In

In addition to liquid and the two terminal solution phases (In) and (Sn),

Figure 4. The calculated phase diagram of the Sn-Sb system.22

Figure 5. The calculated phase diagram of the Sn-Ag system.24

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this system has two intermediate phases, β and γ. Both intermediate phases form through a peritectic reaction from the liquid and one of the terminal solution phases. At a temperature of 120°C, the liquid with xSn = 0.491 decomposes into the two intermediate phases. The evaluation by Okamoto20 concludes that most of the boundaries of the solid phases need to be better established for concentrations with xSn ≥ 0.75. The two thermodynamic assessments19,21 avail-able are based on the evaluation by Okamoto. The phase diagram obtained from the assessment of Lee et al.19 is shown in Figure 3.

Sn-Sb

In addition to liquid and the two terminal solution phases, (Sb) and (Sn), this system has two intermediate phases, SbSn (β) and Sb3Sn2. Both intermediate phases, as well as (Sn), form by peritectic reactions. The peritectic reaction forming (Sn) occurs at a temperature of 250°C. The two available thermodynamic assessments17,22 are based on the experi-mental work of Predel and Schwer-mann.23 The phase diagram obtained from the assessment of Jönsson and Ågren22 is shown in Figure 4.

Sn-Ag

In addition to liquid and the two terminal solution phases, (Ag) and (Sn), this system has two intermediate phases, (ζAg) and Ag3Sn. Both intermediate phases form by peritectic reactions. The eutectic reaction in which liquid with xSn = 0.965 decomposes into Ag3Sn and (Sn) at a temperature of 221°C is well

established. The two available thermody-namic assessments10,24 give very similar results. Moon et al.11 pointed out that in both assessments, the liquidus for primary Ag3Sn formation needs further refinement. The phase diagram obtained from the assessment of Oh et al.24 is shown in Figure 5.

Sn-Zn

The phase diagram of this system is relatively well established and a number of thermodynamic assessments are available for this simple eutectic system. At 198.5°C, the liquid decomposes into the two terminal solid solutions, (Zn) and (Sn). However, the composition reported for the liquid phase at the eutectic temperature varies between xSn = 0.906 and xSn = 0.921. The phase diagram obtained from the assessment of Lee25 is shown in Figure 7.

Sn-Cu

In addition to liquid and the two terminal solution phases, (Cu) and (Sn), this system has seven intermediate phases, β, γ, Cu41Sn11 (δ), Cu10Sn3 (ζ), Cu3Sn (γ), and Cu6Sn5/Cu6Sn5’ (η/η1, high- and low-temperature forms). All of the intermediate phases form by peritectic or peritectoid reactions. All of the copper-rich intermediate phases decompose in eutectoid reactions at temperatures above 350°C and, there-fore, only the Cu3Sn and Cu6Sn5/Cu6Sn5´ phases are of interest for solder applica-tions. The temperature of 227°C for the eutectic reaction, where liquid decom-poses into Cu6Sn5 and (Sn), is well established. However, various evalua-tions of this system disagree on the exact composition of the liquid phase, either xSn = 0.91 or xSn = 0.93. Moon et al.11 showed that the composition of xSn = 0.91 is consistent with the eutectic temperature and the slope of the liquidus for primary (Sn) formation. The two available thermodynamic assess-ments26,27 give very similar results. Moon et al.11 pointed out that the liquidus for primary Cu6Sn5 formation needs further refinement. The phase diagram obtained from the assessment of Shim et al.26 is shown in Figure 7.

Sn-Au

In addition to liquid and the two terminal solution phases, (Au) and (Sn),

this system has six intermediate phases, Au10Sn (β), (ζAu), Au5Sn (ζ´), AuSn (δ), AuSn2 (γ), and AuSn4 (η). Except for the ζ´ phase, which forms peritectoidally, and the δ (AuSn) phase, which forms congruently, the other intermediate phases form by peritectic reactions. The phase diagram obtained from the thermodynamic assessment by Cheva-lier28 is consistent with the phase diagram that was accepted by Okamoto and Massalski.29 Since then, the phase equilibria involving the Au10Sn, (ζAu), and Au5Sn phases were revised,30 extending their stability ranges to lower temperatures. However, only the AuSn, AuSn2, and AuSn4 phases are of interest for solder applications. The tin-rich eutectic occurs at a temperature of 217°C and a liquid composition of xSn = 0.90 (xSn = 0.918 calculated). The tin-rich AuSn4 phase decomposes eutectoidally at a temperature above room tempera-ture, according to the diagram of Okamoto and Massalski. Although the exact temperature is not known, the calculated decomposition temperature is 104°C. The phase diagram obtained from the assessment by Chevalier28 is shown in Figure 8.

Sn-Ni

In addition to liquid and the two terminal solution phases, (Ni) and (Sn), this system has five intermediate phases: Ni3Sn (high- and low-temperature forms), Ni3Sn2 (high- and low-temperature forms), and Ni3Sn4. The high-temperature forms of Ni3Sn and Ni3Sn2 form congruently from the liquid phase and Ni3Sn4 forms by a peritectic

Figure 6. The calculated phase diagram of the Sn-Zn system.25

Figure 7. The calculated phase diagram of the Sn-Cu system.26

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reaction. The tin-rich eutectic occurs at a temperature of 231.2°C and a liquid composition of xSn = 0.998. The only available thermodynamic assessment of this system was carried out by Ghosh;31 the calculated phase diagram is shown in Figure 9.

TERNARY AND HIGHER COMPONENT SYSTEMS

Critical evaluations of experimental data are available for ternary Ag, Al, and Au systems,32 and Cu systems.33 Also, Villars et al.34 compiled a summary of the available experimental data for most ternary systems. Many solder alloys are included in these references and, therefore, only systems that are most relevant for solder applications will be discussed here.

Sn-Ag-Bi

The phase diagram of this system was experimentally determined by Hassam et al.35 No ternary phases have been reported, and the solid phases have fairly small ternary homogeneity ranges. The ternary eutectic is reported to occur at 138.4°C where the liquid with xAg = 0.010 and xBi = 0.563 decomposes into the two terminal solid solutions, (Bi) and (Sn), and the binary Ag-Sn phase, Ag3Sn. The experimental phase diagram is in good agreement with the one predicted by Kattner and Boettinger10 using thermodynamic extrapolation of the descriptions of the binary systems. The tin-rich part of the liquidus projec-tion obtained from this calculation is shown in Figure 10a. Ohtani et al.36 used the available experimental data

for a refinement of the description of the ternary systems. However, the differences between the results for the tin-rich part of the system from the two calculations are not significant.

Sn-Ag-Cu

The phase diagram of this system was experimentally determined by Gebhardt and Petzow.37 No ternary phases have been reported and the solid phases have fairly small ternary homogeneity ranges. The invariant reaction in the tin-rich corner was first reported to be non-eutectic. More recent work38,39 showed that this reaction is eutectic with a temperature of 217 ± 0.2°C, and the liquid decomposes into (Sn) and the binary intermediate compounds Ag3Sn and Cu6Sn5. However, there was disagreement on the composition of the liquid phase at the eutectic temperature. The experimental work of Moon et al.11 confirmed the composition of the liquid phase as xAg = 0.035 and xCu = 0.009 and the temperature as 217.2°C. The calculated tin-rich part of the liquidus projection is shown in Figure 10b.

Sn-Ag-In

Few experimental phase diagram data are available for this system. Korhonen and Kivilahti21 used six ternary alloys that were annealed at 250°C to gain information about phase boundary locations and differential scanning calorimetry (DSC) to investigate the melting/solidification behavior of the alloys. The temperature of the ternary eutectic where the liquid decomposes into Ag2In and the intermediate Sn-In phases β and γ was reported to be about 113°C.

Sn-Ag-Sb

A series of 21 alloys was studied with differential thermal analysis (DTA) and electron microprobe analysis (EMPA) and used for the construction of a liquidus surface.40 The intermediate phases of the Ag-Sn ((ζAg) and Ag3Sn) and Ag-Sb systems ((ζAg) and Ag3Sb) were found to form continuous homo-geneity ranges in the ternary system. The tin-rich invariant reaction was reported as a transition (type II) reaction, L + SbSn Ag3(Sb,Sn) + (Sn), at 234.8°C with xAg = 0.05 and xSb = 0.06 as the composition of the

liquid phase. However, it should be noted that the intermediate phase, Sb2Sn3, of the binary Sn-Sb system was not detected in this experimental work.

Sn-Bi-Cu

No experimental phase diagram data are available for this system. It can be expected that the thermodynamic extrapolation of the description of the binary systems gives a fairly accurate prediction of the ternary phase diagram, as was the case for the Sn-Ag-Bi system. The liquidus projection obtained from the binary descriptions19,26,41 is shown in Figure 10c. The predicted tin-rich eutectic occurs at a temperature of 138.8°C and the composition of the eutectic liquid phase is xBi = 0.428 and xCu = 0.0004.

Sn-Cu-Ni

Extensive phase diagram data are available for the Cu- and Cu,Ni-rich part of this system.34 The experimental data show that the binary Sn-Cu and Sn-Ni phases have extended ternary homogeneity ranges. A series of ternary phases has been reported but it is not clear whether these phases are true ternary phases or extended ternary homogeneity ranges of the binary phases. No experimental data are available for tin concentrations larger than an atomic fraction of 0.6. Gupta et al.42 proposed that a transition (type II) reaction, L + Ni3Sn4 Cu6Sn5 + (Sn), occurs in the tin-rich corner. However, without experimental evidence this is rather speculative. A thermodynamic

Figure 8. The calculated phase diagram of the Sn-Au system.28

Figure 9. The calculated phase diagram of the Sn-Ni system.31

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extrapolation of the description of the binary systems is not likely to give a reliable prediction for the ternary system since the extrapolation cannot predict the ternary homogeneity of the solid phases. However, once the parameters for the description of the liquid and solid phases in the ternary system have been established utilizing the available experimental data, the calculation should reliably predict the liquidus for the tin-rich corner of the system.

APPLICATION EXAMPLES

Freezing range evaluation is the most basic application of phase diagram information for the selection of new candidate solder alloys. The maximum acceptable component temperature during assembly depends on the device, package, and PCB material being used, establishing the maximum temperature for a candidate solder. The processing temperature of a solder should be at least 10°C to 20°C above its liquidus temperature. The combination of these criteria limits the maximum liquidus temperature for most solders to 225°C43 and 260°C for high-temperature, fatigue-resistant solders.44 Solders for high-temperature applications are required to perform at operating temperatures up to 160°C. This require-ment results in a minimum solidus temperature of 208°C if the operating temperature is set to be 90% or less of the absolute melting temperature of the solder.1 At the same time, the solidus temperature should not be much more than 30°C lower than

its liquidus temperature in order to avoid manufacturing problems, such as defective joints caused by vibrations during cooling from the soldering temperature.43 Alloy compositions that fulfill the freezing range criterion are shown as shaded areas for the Sn-Ag-Bi, Sn-Ag-Cu, and Sn-Bi-Cu systems in Figure 10. However, it should be noted that in systems that show noticeable changes in the maximum solubility of the alloying element in (Sn) during cooling, the amount of liquid phase during cooling can be larger than predicted by the equilibrium diagram.2

Support of experimental design through the calculation of phase equilib-ria can reduce the number of experiments that are necessary for the determina-tion of a higher-component system. Moon et al.11 presented an example where experimental and computational methods were used to complement each other in the determination of the tin-rich part of the Sn-Ag-Cu system. The phase equilibria information was used to understand which signals are likely to be observed during the thermal analysis so that special attention could be paid

to the sensitivity of the measurement technique. This strategy resulted in a highly accurate determination of the eutectic temperature and composition of the liquid phase, as well as two temperature-concentration sections. The experimental results were then used to refine the thermodynamic description. Analysis of contamination effects is of great importance in avoiding detrimental effects such as the forma-tion of low-melting eutectics. Moon et al.45 showed that even though the contamination level of a Sn-Bi solder with lead was not high enough to show the formation of the equilibrium ternary eutectic, which occurs at 95°C, the effects of non-equilibrium solidifica-tion occurred at fairly low levels of contamination. It was also shown that the experimental observation was in accord with predictions obtained assuming the worst case of microsegregation, the so-called Scheil path. Moon et al. performed Scheil calculations for a range of Sn-Bi solders with a very low level (< 1%) of lead contamination (Figure 11). They found that a 0.1% lead

Figure 10. The composition regimes (shaded) with suitable freezing ranges (<35°C) for candidate solder alloys in the systems (a) Sn-Ag-Bi,10 (b) Sn-Ag-Cu,11 and (c) Sn-Bi-Cu.12

a b c

Figure 11. The effect of lead contamina-tion on the lowest possible freezing temperature pre-dicted from Scheil path calculations for Sn-Bi solders.45

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contamination promotes the formation of ternary eutectic in Sn-Bi solder with xBi ≥ 0.005, although, according to the equilibrium diagram, eutectic formation should only occur for concentrations larger than xBi = 0.113 and xPb = 0.007. Kattner and Handwerker9 applied the Scheil analysis to a series of solder alloys and found that the combination of bismuth and lead was especially detri-mental to the final freezing temperature of solders. Reaction with substrate materials is a strong function of processing and services temperatures and depends on substrate metallization and solder composition. It is highly desirable to control these interfacial reactions to optimize joint properties. For example, it was shown that the kind of intermediate phase formation on nickel substrates is very sensitive to the copper concentra-tion in Sn-Cu46 and Sn-Ag-Cu47 solders. The formation of the Ni3Sn4 phase was only observed for fairly low copper concentrations in the solder and the interface was dominated by the forma-tion of Cu6Sn5. The observations were rationalized by diffusion path analysis. The prediction of other properties is another advantage of the thermodynamic description of phases, since quantities such as the partial excess Gibbs energies are readily available. For example, Lee and Lee4 used the correlation between the partial excess Gibbs energies and the surface tension to calculate the surface tension of binary solder liquids. In addition to the prediction of the surface tension, Ohnuma et al.5 used thermo-dynamic properties to predict the activation energy of viscosity. Both of these properties are important for understanding the wetting behavior of a molten solder.

CONCLUSION

Phase diagram information provides basic information for the design and understanding of solder alloys and is not limited to the application of equilibrium processes. The calculation of phase equilibria is a powerful tool for developing new solders since a

wide range of potential alloys can be relatively rapidly evaluated. The power of the calculation is that information can be provided for higher-component systems using thermodynamic extrapo-lation methods where no or little experimental information is available. In addition, the thermodynamic quantities provide the key to the prediction of other solder properties, such as surface tension and viscosity. The coupling of phase diagram calculation and experimental determination of phase equilibria provides useful information for interpret-ing experimental observations and the experimental results can be used to further improve the thermodynamic description of the system.

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Ursula R. Kattner is a physical scientist with the Materials Science and Engineering Laboratory at the National Institute of Standards and Technology.

For more information, contact Ursula R. Kattner, National Institute of Standards and Technology, Materials Science and Engineering Laboratory, 100 Bureau Drive, Stop 8555, Gaithersburg, Maryland 20899; e-mail [email protected].