# hw7 - 1 MSE Homework#7 Michael Mark 22838947 9.32(a This...

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1 MSE Homework #7 Michael Mark, 22838947, 3/9/2009 9.32 (a) This portion of the problem asks that we determine the mass fractions of α and β phases for an 80 wt% Sn-20 wt% Pb alloy (at 180 ° C). In order to do this it is necessary to employ the lever rule using a tie line that extends entirely across the α + β phase field. At 180 ° C, C α = 18.3 wt% Sn, C β = 97.8 wt% Sn, and C eutectic = 61.9 wt% Sn. Therefore, the two lever-rule expressions are as follows: W α = C β - C 0 C β - C α = 97 . 8 - 80 97 . 8 - 18 . 3 = 0.224 W β = C 0 - C α C β - C α = 80 - 18 . 3 97 . 8 - 18 . 3 = 0.776 (b) Now it is necessary to determine the mass fractions of primary β and eutectic microconstituents for this same alloy. This requires that we utilize the lever rule and a tie line that extends from the maximum solubility of Pb in the β phase at 180 ° C (i.e., 97.8 wt% Sn) to the eutectic composition (61.9 wt% Sn). Thus W β ' = C 0 - C eutectic C β - C eutectic = 80 . 0 - 61 . 9 97 . 8 - 61 . 9 = 0.504 W e = C β - C 0 C β - C eutectic = 97 . 8 - 80 . 0 97 . 8 - 61 . 9 = 0.496 (c) And, finally, we are asked to compute the mass fraction of eutectic β , W e β . This quantity is simply the

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