1) Using the Sn-Pb equilibrium phase diagram shown in the figure below and apply

Question

1) Using the Sn-Pb equilibrium phase diagram shown in the figure below and applying the lever rule, answer the following question.

--- a) What is the eutectic composition?

--- b) What are the compositions of the solid phases in equilibrium at the eutectic temperature?

--- c) For an alloy containing 90 wt% Sn, what fraction exists as the  phase at 220 o C? 

--- d) What fraction of this alloy is liquid just above the eutectic temperature?

--- e) Determine the fractions of  and  phases just below the eutectic temperature in the 90 wt% Sn alloy and the eutectic alloy.

--- f) What fraction of the total weight of the 90 wt% Sn alloy will have the eutectic structure, just below the eutectic temperature?

Explanation / Answer

a) The Eutectic composition is Ce on the graph, 61.9. (My graph has slightly more clear numbers so using those but if you guesstimate around these numbers you'll get the same answers.) b) The composition of Alpha at the Eutectic temperature (~Tc~180 degrees C or so) is 18.3% Tin (you simply go to the solid phase, and then down.) The composition of the Beta phase is 97.8% Tin (same method as Alpha.) c) At 90 wt% Sn 220 degrees C, it looks like you're in the B + L phase or all L phase, which means there is no alpha. It's kind of hard to read on the small picture so confirm with a ruler on the graph. d) So part D is where you have to start doing a little more work. At 90 degrees C just above the eutectic temperature... you have B + L To find the fraction of L, you do (97.8 - 90) / (97.8 - 61.9) ~ 22% To find the fraction of B, you do (90-61.9) / (97.8 - 61.9) - 1-22% = 88% The best way to confirm these is to look at where the point on the graph would be. The point at 90 degrees just about Tc is much closer to Beta than it is to Liquid, which means there is more beta than liquid... and the fractions agree. e) Just below, you're looking for Beta (on the right) and Alpha (on the left) at 90% Sn you would expect there to be much more Beta (it's much closer to Beta) than Alpha. Alpha = (97.8 - 90) / (97.8 - 18.3) = 9.8% Beta = (90 - 18.3) / (97.8 - 18.3) = 90.2% f) For this problem, you really need a diagram to understand- but basically you have to split the sections up. We (Weight of Eutectic) is based on the amount of Liquid you have turning into Eutectic so you can look just above the eutectic temperature Tc to figure out what that fraction would be. So you have (97.8-90)/(97.8-61.9) = 22%, which makes sense... if you look again at the 90 % Sn mark right above the eutectic... it's really close to Beta, meaning most of what you have is Beta... the liquid that is there ~ 20% turns into Eutectic with Primary blobs Beta in it.

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