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Chapter 9: Problem 10

Is it possible to have a copper-silver alloy that, at equilibrium, consists of an \(\alpha\) phase of composition 4 wt \(\%\) Ag- 96 wt \(\%\) Cu, and also a \(\beta\) phase of composition 95 wt \(\%\) Ag-5 wt \(\%\) Cu? If so, what will be the approximate temperature of the alloy? If this is not possible, explain why.

Short Answer

Expert verified
Based on the provided information about the copper-silver alloy, analyze whether it is possible for the given α phase (4 wt% Ag and 96 wt% Cu) and β phase (95 wt% Ag and 5 wt% Cu) to exist in equilibrium. If so, also calculate the approximate temperature of the alloy at equilibrium using the copper-silver phase diagram.

Step by step solution

01

Understanding Phase Diagrams for Alloys

A phase diagram is a graphical representation of the equilibrium conditions between different phases of an alloy system as a function of temperature, pressure, and composition. For this problem, we will primarily focus on temperature and composition.
02

Locate the Copper-Silver Phase Diagram

To solve this problem, we need to find the phase diagram for the copper-silver system. It can be found in textbooks or reliable online resources. The phase diagram will display the equilibrium phases of the copper-silver alloy system as a function of temperature and composition.
03

Identify the α and β Phases on the Phase Diagram

Once you have the copper-silver phase diagram in front of you, identify the α and β phase regions. These are labeled directly on the diagram, and they help determine the existence of the given compositions at equilibrium.
04

Check for the Given Compositions on the Phase Diagram

Now, locate the compositions given in the problem which are 4 wt% Ag- 96 wt% Cu (α phase) and 95 wt% Ag-5 wt% Cu (β phase). If the given compositions fall within the α phase and β phase regions of the phase diagram, respectively, it implies that it is possible to have the alloy at equilibrium with these respective compositions.
05

Confirm Whether the Compositions Exist on the Phase Diagram

If both the given compositions exist on the phase diagram in their respective α andβ phase regions, then it is possible to have a copper-silver alloy at equilibrium with these given compositions. However, if either or both the compositions do not fall within their respective phase regions on the phase diagram, then it is not possible to have an equilibrium alloy with the given compositions.
06

Determine the Approximate Temperature (if possible)

If the given compositions are possible at equilibrium (both found in their respective phase regions on the phase diagram), find the approximate temperature by following the line perpendicular to the temperature axis where the compositions intersect the respective phase boundaries. This temperature will correspond to the approximate temperature of the alloy at the given compositions. If the given compositions are not within their respective phase regions on the phase diagram, then it is not possible to approximate the temperature since equilibrium with these compositions does not exist.

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Most popular questions from this chapter

Cite three variables that determine the microstructure of an alloy.

It is desirable to produce a copper-nickel alloy that has a minimum noncold- worked tensile strength of \(380 \mathrm{MPa}(55,000 \mathrm{psi})\) and a ductility of at least \(45 \%\) EL. Is such an alloy possible? If so, what must be its composition? If this is not possible, then explain why.

What thermodynamic condition must be met for a state of equilibrium to exist?

A \(2.0-\mathrm{kg}\) specimen of an \(85 \mathrm{wt} \% \mathrm{Pb}-15 \mathrm{wt} \%\) Sn alloy is heated to \(200^{\circ} \mathrm{C}\left(390^{\circ} \mathrm{F}\right)\); at this temperature it is entirely an \(\alpha\) -phase solid solution (Figure 9.8 ). The alloy is to be melted to the extent that \(50 \%\) of the specimen is liquid, the remainder being the \(\alpha\) phase. This may be accomplished by heating the alloy or changing its composition while holding the temperature constant. (a) To what temperature must the specimen be heated? (b) How much tin must be added to the \(2.0-\mathrm{kg}\) specimen at \(200^{\circ} \mathrm{C}\) to achieve this state?

Is it possible to have a copper-silver alloy of composition 20 wt \(\%\) Ag -80 wt \(\%\) Cu that, at equilibrium, consists of \(\alpha\) and liquid phases having mass fractions \(W_{\alpha}=0.80\) and \(W_{L}=\) \(0.20 ?\) If \(\mathrm{so},\) what will be the approximate temperature of the alloy? If such an alloy is not possible, explain why.
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