2.7: Self-Assessment- Solid Solutions
- Page ID
- 408604
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(a) Construct the phase diagram \((\mathrm{T}, \mathrm{c})\) for \(\mathrm{Ag}-\mathrm{Cu}\) given the following data. (Assume all phase lines to be straight.)
\(\begin{array}{ll}\mathrm{T}_{\mathrm{M}} \mathrm{Ag}: & 960^{\circ} \mathrm{C} \\ \mathrm{T}_{\mathrm{M}} \mathrm{Cu}: & 1080^{\circ} \mathrm{C} \\ \mathrm{T}_{\mathrm{E}} \text { (Eutectic) } & 780^{\circ} \mathrm{C}: \alpha[9 \mathrm{wt} . \% \mathrm{Cu}] ; \beta[92 \mathrm{wt} . \% \mathrm{Cu}] ; \text { Eutectic comp. } 28 \mathrm{wt} . \% \mathrm{Cu} \\ & 400^{\circ} \mathrm{C}: \alpha[1 \mathrm{wt} . \% \mathrm{Cu}] ; \beta[100 \mathrm{wt} . \% \mathrm{Cu}]\end{array}\)
- Answer
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(b) Determine the liquidus temperature for a \(60 \mathrm{wt} . \% \mathrm{Ag}-40 \mathrm{wt} . \%\) Cu alloy.
- Answer
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From the phase diagram in (a) liquidus \(\mathrm{T}\) for \(40 \mathrm{wt} . \% \mathrm{Cu}\) alloy is \(\approx 840^{\circ} \mathrm{C}\)
(c) Determine which other Ag-Cu alloy composition has the same liquidus temperature as the one determined in (b).
- Answer
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From phase diagram in Prob. 3, other composition with same liquidus \(\mathrm{T}\) is \(\approx 20 \text{wt}.\% \mathrm{Cu}\)
(d) \(26 \mathrm{~g}\) of sterling silver (\(92.5 \text{wt}.\% \mathrm{Ag}-7.5 \mathrm{wt} . \% \mathrm{Cu})\) are melted together with \(376 \mathrm{~g}\) of pure copper \((\mathrm{Cu})\). Given the phase diagram for \(\mathrm{Ag}-\mathrm{Cu}\), determine:
(i) the liquidus temperature for the alloy formed;
(ii) the solidus temperature for this alloy;
(iii) the composition of the alloy formed.
- Answer
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(i) From phase diagram in part (a), liquidus \(\mathrm{T} \approx 1060^{\circ} \mathrm{C}\)
(ii) From phase diagram in part (a), solidus \(\mathrm{T} \approx 870^{\circ} \mathrm{C}\)
(iii) \(26 \mathrm{~g}\) of Sterling Silver has \((26)(0.925)=24.05 \mathrm{~g} \mathrm{Ag}\) and \((26)(0.075)= 1.95 \mathrm{~g} \mathrm{Cu}\). Total \(\mathrm{Cu}=1.95+376=378 \mathrm{~g}\).
\[\text { wt. } \% \mathrm{Cu}=\frac{378 \mathrm{~g} \mathrm{Cu}}{24 \mathrm{~g} \mathrm{Ag}+378 \mathrm{~g} \mathrm{Cu}}=94 \nonumber\]