FE Other Disciplines Materials Practice Problems

The current FE Other Disciplines specification assigns 6-9 of the 110 exam questions to Materials. Form A contains 7 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A binary alloy of overall composition 40 wt% B is held at a temperature at which solid $α$ and liquid coexist. At that temperature the $α$ solidus boundary lies at 12 wt% B and the liquidus lies at 62 wt% B. The mass fraction of liquid present is most nearly:

(A)0.30
(B)0.44
(C)0.45
(D)0.56

Show worked solution

Answer: (D)

Slightly more than half the alloy is molten, because the lever arm opposite the liquid spans 28 of the 50 wt% tie line.

Tie-line geometry sets the phase amounts: the fraction of one phase uses the arm on the far side of the overall composition.

W_{L} = \frac{C _{0} - C _{α}}{C _{L} - C _{α}}

With the tie line running from 12 to 62 wt% B, the full length is 50 wt% and the arm opposite the liquid measures 28 wt%.

W_{L} = \frac{40 - 12}{62 - 12} = 0.56

FE Reference Handbook — Materials Science/Structure of Matter: Binary Phase Diagrams, Lever Rule

Why the other choices appear

(A)Forms the ratio of the $α$ boundary composition to the overall composition, $12/40 = 0.30$ , instead of using a lever arm.
(B)Inverts the lever and reports the arm adjacent to the liquidus, $(62 - 40) /50 = 0.44$ , which is the $α$ fraction.
(C)Divides the correct arm by the liquidus composition rather than the tie-line length, $28/62 = 0.45$ .