The technique to calculate density of an alloy still attracts interest about a year after I first discussed it. Although I am pleased to share my Excel software that calculates solder alloy densities, being an educator, I can't help but want to share the fundamentals of how to solve this problem. A simple explanation follows&thanks to my Indium colleague Bob Jarrett for this approach.
Say you want to calculate the density of an alloy of 60% by weight tin (Sn) and 40% lead (Pb). The density of tin is Dsn = 7.29 g/cc and that of lead Dpb = 11.34 g/cc. Let's say you make a 100 g sample of this alloy, 60 g will be Sn, 40 g will be Pb. The total volume of the alloy will be 60 g Sn/Dsn + 40 g Pb/Dpb = 60/7.29 + 40/11.34 = 8.23 cc + 3.53 cc = 11.76 cc. The density of the alloy is its mass (100g) divided by its volume (11.76 cc) or 100/11.76 g/cc = 8.50 g/cc.
In general then, the equation to calculate density is 1/Dalloy = Mass Fraction Metal 1/Dmetal 1 + Mass Fraction Metal 2/Dmetal 2. The equations continues for metals 3, 4 etc.