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18 SMT007 MAGAZINE I JULY 2019 stantial part of the SAC ball alloy remains after the soldering process, the joints have adequate reli- ability. The distribution of strain in a typical assem- bly means that it tends to be concentrated in the outer areas of solder close to the interface with the component package. If the solder in that area is an alloy that is known to deliver the required ser- vice life under the expected conditions, then the reliability of the mixed alloy joint is comparable with that of a joint that is reflowed with the same alloy as the BGA ball. The challenge with this technique has been determining how to complete the mixed alloy reflow soldering process with sufficient of the original ball alloy remaining on the compo- nent that an adequate level of reliability can be achieved. While there has been much discussion about "Bi diffusion" from the low-melting-point sol- der into the SAC alloy, the purpose of this arti- cle is to explain that the extent to which the BGA ball is lost to the mixed alloy is deter- mined by the thermodynamics of the alloy sys- tem made up of the solder ball and the solder paste. Those thermodynamics are neatly sum- marized in one of the basic tools of the mate- rial scientist—the equilibrium phase diagram. The Equilibrium Phase Diagram The equilibrium phase diagram can be con- sidered a map of the location of phases—liquid or solid—in space defined by the dimensions of composition and temperature. Where vapor pressures are significant, a third dimension is pressure. But in the case being considered here, at the process temperatures being used, the alloy constituents have relatively low vapor pressures so that dimension need not be considered. For a particular composition at a specific temperature, an equilibrium phase diagram will show what phases are present and their composition. With the application of the "lever rule," the relative proportions of the phases present at any such point can be calculated. For a binary system (i.e., in the case of an alloy, a mixture of two metals), the phase dia- gram is two-dimensional. The phase equilibria for three elements can be presented in a three- dimensional diagram, or if the level of one ele- ment is fixed, as a two-dimensional pseudo- binary plot. For more than three elements the level of one or more of the elements has to be fixed to reduce the number of dimensions to three or two. Figure 3 is the equilibrium phase diagram for the binary Sn-Bi system on which the low- melting-point alloys used in mixed alloy reflow are currently based. An alloy with the compo- sition and temperature at Point A would be entirely liquid. An alloy with the composition and temperature at Point B would be a roughly 50/50 mixture of liquid and solid Sn-Bi alloy with about 10wt% Bi in solid solution. An alloy with the composition and temperature Point C would be completely solid with about 5wt% Bi in solid solution. An alloy at the composition and temperature Point D would be completely solid with a roughly 50/50 mix of nearly pure Bi and Sn with about 15% Bi in solid solution. Figure 3: The Sn-Bi equilibrium phase diagram.