# Reading a Binary Phase Diagram (lever rule etc.)

Hello All,
Wanted to see if I am approaching this problem correctly, I have an exam coming up and am pretty sure something like this will show up.

Examine the phase diagram (phase.jpg) with a 20WT% A and 80WT%B which is allowed to cool slowly from liquid

A) what temp does the first solid appear?
B)What phase it is?
C)what is its composition?
D)What phases are present just below the eutectic temperature?
E) What are the compositions of these phases?
F) What are the weight fractions of these phases?

My attempt:

A) From the graph I would say about 820°C
B) The first solid is β phase (since the only things are L+β)
C)The composition is about 94%B and 6%A
D) The phases present just below the eutectic are α+β
E) 91%B and 9%A
F) This is where you have to use the lever rule:
For β phase:
wt%=$\frac{91-72}{91-9}$*100%=22.9%B
The composition of β: 22.9B and 77.1A

For α phase:
wt%=$\frac{72-8}{91-9}$*100%=78%A
The composition of α: 78%A and 22%B

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#### mjc123

A) To my eye, nearer 840 or 850, but just an estimate.
B) - D) OK
E) Question asks for composition of both phases.
F) The axis about which the lever pivots is not the eutectic composition, but the overall composition of the mixture. (Test your answer: if you have x% α with composition 8% B, and y% β with composition 91% B, do you have 80% B overall?)

"Reading a Binary Phase Diagram (lever rule etc.)"

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