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24 SMT007 MAGAZINE I JULY 2019 der ball will be used as an example. A num- ber of other simplifying assumptions are made in constructing this model, but in its practical application to the selection of assembly param- eters, actual data would be used. As in the earlier example, the paste alloy will be a 50wt% Sn Sn-Bi solder. This alloy is slightly hypereutectic with respect to Sn but still has a relatively low liquidus temperature of around 155°C (Figure 4). Because of the large difference in density between the solder and flux medium, a stencil- printable solder paste is typically about 50% solder by volume. The density of a 50wt% Bi Sn-Bi solder can be estimated by calculation at about 8.4g/cm 3 . For simplicity, the paste deposit will be assumed to be circular so that the volume of paste is can be calculated as Equation 2: Where d is the diameter of the paste deposit and t the thickness. With the chosen volume frac- tion of solder in the paste deposit and the esti- mated density of the low-melting-point alloy, the weight of solder can be estimated as a function of the thickness and/or diameter of the deposit. For a reflow temperature of 165°C, the wt% Sn at which the mixed alloy will reach its sol- idus composition can be calculated by Equa- tion 1 as around 84.5wt%. The amount of Sn required to raise the Sn level in the molten solder can be calculated on the basis of the weight of solder in the paste deposit. It is the dissolution of that Sn that will determine how much of the original solder ball will be lost to the mixed alloy phase in the final joint. A com- plication is that, in calculating the amount of Sn that will be dissolved from the solder ball to reach the solidus composition at the reflow temperature, allowance has to be made for the diluting effect of the increase in the volume of the molten phase. The calculations made on this basis for a range of paste deposit thick- nesses are set out in Table 1. Table 1: Calculation of dissolution of Sn from solder ball as a function of the thickness of the solder paste deposit.