Folks,
I continue to get much interest in the solder alloy density calculator I developed some years ago. It is now online at http://www.indium.com/densityCalc/. 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 . The correct derivation is below:
We want to find the density of an alloy composed of 3 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 m c and a density dc. The total volume, V, of the 3 metals is va + vb+ vc, however since v = m/d, the total volume can be expressed:
1) V = ma/da + mb/db +mc/dc The density of the resulting alloy is D = M/V, hence 1/D = V/M, therefore:
2) 1/D = V/M = (ma/M)/da + (mb/M)/db +(mc/M)/dc
Now ma/M is the mass fraction of a, which we will call Xa, and similarly Xb and Xc for metals B and C.
Equation 2 then becomes:
1/D = Xa/da + Xb/db +Xc/dc which is our solution.
This principle can be applied to alloys of more than 3 metals.
Cheers,
Dr. Ron