I continue to get much interest in the solder alloy density calculator I developed. It is now online here. It assumes no chemical interaction between the metals and no formation of interstitials. It works well for solder alloys.
Many people have an incorrect idea of how to perform this calculation. The most common incorrect concept is to multiply the % by weight of each alloy times its density and add them together. Using this incorrect approach one would calculate the density of tin-lead eutectic solder as 8.79 g/cc (0.63 x 7.29 + 0.37 x 11.34) vs the correct 8.4 g/cc. The correct derivation follows.
We want to find the density of an alloy composed of three metals. Assume the mass of the alloy is M. Metal A has a mass ma and a density da, Metal B has a mass mb and a density db and Metal C has a mass mc and a density dc. The total volume, V, of the three metals is va + vb+ vc.
However, since v = m/d, the total volume can be expressed:
V = ma/da + mb/db +mc/dc (Eq. 1)
The density of the resulting alloy is D = M/V, hence 1/D = V/M, therefore:
1/D = V/M = (ma/M)/da + (mb/M)/db +(mc/M)/dc (Eq. 2)
Now ma/M is the mass fraction of a, which we will call Xa, and similarly Xb and Xc for metals B and C.
Eq. 2 then becomes:
1/D = Xa/da + Xb/db +Xc/dc
which is our solution.
This principle also can be applied to alloys of more than three metals.