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Chapter 9: Problem 30

Is it possible to have a copper-silver alloy in which the mass fractions of primary \(\beta\) and to\(\operatorname{tal} \beta\) are \(0.68\) and \(0.925\), respectively, at \(775^{\circ} \mathrm{C}\) \(\left(1425^{\circ} \mathrm{F}\right) ?\) Why or why not?

Short Answer

Expert verified
Answer: Based on the phase diagram analysis, it is (possible/impossible) to have a copper-silver alloy with mass fractions of primary β and total β as 0.68 and 0.925 respectively, at a temperature of \(775^{\circ}C\).

Step by step solution

01

Understanding the Cu-Ag Phase Diagram

A phase diagram is a graphical representation of the temperature and composition at which different phases of a system can coexist in equilibrium. The Cu-Ag phase diagram has different regions which represent different combinations of phases. To determine the possibility of having a Cu-Ag alloy mentioned in the problem, refer to the Cu-Ag phase diagram and locate the given temperature and compositions.
02

Determine the temperature at which primary β forms

Find the temperature at which the primary β phase begins to form. This is the temperature when the first solid (β phase) starts to form from the liquid phase. In the Cu-Ag phase diagram, look for the point where the liquidus line shows the beginning of β phase at \(775^{\circ}C\).
03

Analyzing the given mass fractions

Determining whether the given mass fractions of primary and total β are feasible depends on the region in which they lie in the phase diagram. If the alloy lies within the β-phase region, it is possible to have the desired mass fractions. Vice versa, if it does not lie within the region, the desired mass fractions are not possible. Primary β mass fraction is 0.68 and the mass fraction of total β is 0.925. Locate the points these mass fractions lie on at the given temperature (\(775^{\circ}C\)) in the Cu-Ag phase diagram.
04

Checking the phase regions

Observe if the points corresponding to the mass fractions (0.68 and 0.925) on the diagram are within the β-phase region, the region where both primary slow-cooling and fast-cooling products are present at the same time. If both points are within this region, then it is possible to have a copper-silver alloy with the given mass fractions at \(775^{\circ}C\).
05

Conclusion

Based on the phase diagram analysis, it can be concluded that at \(775^{\circ}C\), it is (possible/impossible) to have a copper-silver alloy with mass fractions of primary β and total β as 0.68 and 0.925 respectively.

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Most popular questions from this chapter

Consider \(2.5 \mathrm{~kg}\) of austenite containing \(0.65\) wt \(\%\) C, cooled to below \(727^{\circ} \mathrm{C}\left(1341^{\circ} \mathrm{F}\right)\). (a) What is the proeutectoid phase? (b) How many kilograms each of total ferrite and cementite form? (c) How many kilograms each of pearlite and the proeutectoid phase form? (d) Schematically sketch and label the resulting microstructure.

What is the proeutectoid phase for an iron-carbon alloy in which the mass fractions of total ferrite and total cementite are \(0.92\) and \(0.08\), respectively? Why?

(a) What is the distinction between hypoeutectoid and hypereutectoid steels? (b) In a hypoeutectoid steel, both eutectoid and proeutectoid ferrite exist. Explain the difference between them. What will be the carbon concentration in each?

For \(11.20 \mathrm{~kg}\) of a magnesium-lead alloy of composition \(30 \mathrm{wt} \% \mathrm{~Pb}-70 \mathrm{wt} \% \mathrm{Mg}\), is it possible, at equilibrium, to have \(\alpha\) and \(\mathrm{Mg}_{2} \mathrm{~Pb}\) phases having respective masses of \(7.39 \mathrm{~kg}\) and \(3.81 \mathrm{~kg}\) ? If so, what will be the approximate temperature of the alloy? If such an alloy is not possible, explain why.

The mass fractions of total ferrite and total cementite in an iron-carbon alloy are \(0.88\) and \(0.12\), respectively. Is this a hypoeutectoid or hypereutectoid alloy? Why?
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