# Excel Software Tool to Determine Mass Fractions in Binary Alloy

Folks,

Recently, I posted a derivation of the equations to determine the mass fractions of two metals in a binary alloy. I thought it may be helpful to develop an Excel software tool to perform these calculations.

To use the tool, you enter the densities of the two metals and the density of the alloy in the blue cells as seen in Figure 1 below. The calculated mass fraction of each metal is shown in the gray cells.

Figure 1. The data entry for the mass fraction calculator. The densities are entered into the blue cells and the mass fractions are calculated and shown in the gray cells.

As an example, let’s assume you purchase some 14 karat gold. Unfortunately, to your eye it looks more like 10 karat gold, so you want to check it out. As a reminder, when gold is expressed in karats, the alloying metal is copper. First you need to measure the density of the gold alloy. An easy way to do this is the wet gold technique as discussed in a past blog post. From using this technique, you determine that the density of the alloy is 11.53 g/cc. The density of gold is 19.3 g/cc and that of copper is 8.96 g/cc. You will recall that 14 karat gold is (14/24) gold or a mass fraction of 0.5833.

The weight fraction of gold is shown to be 0.4167 or 10/24, as shown in Figure 1, indicating that the gold is 10 karat, not 14 karat.

Time to complain to the seller!

Cheers,

Dr. Ron

# Some Consensus on SAC

Back in November, I posted comments on lead-free availability. In this post, I mentioned that I chaired a session at SMTAI on Alternate Alloys. At this session, Greg Henshall presented a paper on the  Low Silver BGA Sphere Metallurgy Project. This paper was a collaborative effort of six companies.  In addition, Richard Coyle presented an overview of the work of three companies titled “The Effect of Silver Content on the Solder Joint Reliability of a Pb-free PBGA Package.” Both projects evaluated Pb-free thermal cycle reliability as a function of silver content and compared the results to SnPb reliability.

Both papers concluded that, as far as 0oC to 100 oC thermal cycle reliability is concerned, in their experiments

SnPb < SAC105 < SAC305 < SAC405

Coyle’s presentation summed it up best: “Each of the SAC alloys outperformed the SnPb eutectic alloy in every test, including the long, 60 min. dwell time test. This tends to diminish the argument that SAC is less reliable than SnPb.”

To be clear, it was two papers by two different groups coming to the same conclusion. It would probably be a stretch to say that the conclusions of either group were “almost unique”.

Denny Fritz responded to this blog post with this point: “No one I know will dispute your ranking of SAC better than SnPb solder using the commercial temperature cycle Henshall uses – 0C to 100C. But, harsh environment electronics have to perform to either -40C or -55C, and most use a top end cycling temperature of 125C. IT IS IN THAT WIDE THERMAL CYCLE TESTING THAT SnPb outperforms SAC solders.”

Denny’s point is well- taken. I believe it can be said that SAC alloys have demonstrated acceptable reliability in commercial, non harsh environments (i.e., mobile phones, PCs, consumer electronics, etc.). However, it cannot be said that acceptable reliability for SAC has been established for military (RoHS exempt) and harsh (i.e., automobile engine compartment) environments.

A short time ago, Werner Engelmaier wrote an article on this topic (Global SMT, vol. 11, no. 1, January 2011, pp. 38-40), referring to my post he said: “Of course, ‘Dr. Ron’ selectively picks data agreeing with the point of view he held from the inception of the Pb-ban under RoHS on a plot with an expanded x-axis overemphasizing the differences and supporting a solder joint reliability ranking of SnPb < SAC105 < SAC305 < SAC405.”

Ouch! My motives were not quite so nefarious, I chaired a session and wanted to share the conclusions.

However, Werner makes good points in his article, data exist disagreeing with this reliability ranking and he suggests some good points on how to conduct reliability tests so that comparisons can be made between data sets.

In reading some of his other articles, I was delighted to find that we actually agree on the state of lead-free reliability in thermal cycle testing. Here is a statement of his circa 2008 (Global SMT, vol 8., no. 8, August 2008, pp. 46-48.): “It has been 2 years since the infamous ban of Pb-solders under RoHS. What have we learned? For solder joints, no dramatic differences in reliability are apparent. The data bases for LF-solders have grown, the favored LF-solders might be shifting, and no reliability model exists as of yet. Nevertheless, progress has been made.”

Best Wishes,

Dr. Ron

# Calculating Solder Alloy Density

Folks,

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.