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Chapter 9: Problem 52

Figure \(9.36\) is the tin-gold phase diagram, for which only single-phase regions are labeled. Specify temperature-composition points at which all eutectics, eutectoids, peritectics, and congruent phase transformations occur. Also, for each, write the reaction upon cooling.

Short Answer

Expert verified
Answer: At the eutectic point, the reaction upon cooling is: L -> α + β, where L is the liquid phase, and α and β are solid phases.

Step by step solution

01

Identify eutectic point

Eutectic points are the points on the phase diagram where a liquid phase forms a mix of two solid phases upon cooling. Look for the lowest temperature point on the diagram with a horizontal line connecting two single-phase regions.
02

Write eutectic reaction

Upon identifying the eutectic point, the reaction upon cooling can be written as follows: L -> α + β, where L is the liquid phase, and α and β are solid phases.
03

Identify eutectoid point

Eutectoid points are the points on the phase diagram where a single solid phase transforms into two other solid phases upon cooling. Look for a point on the diagram with three single-phase regions connected by a horizontal line.
04

Write eutectoid reaction

If there is a eutectoid point, upon identifying the eutectoid point, the reaction upon cooling can be written as follows: γ -> α + β, where γ is the original solid phase, and α and β are the resulting solid phases.
05

Identify peritectic point

Peritectic points are the points on the phase diagram where a primary solid phase and a liquid phase combine to form another solid phase upon cooling. Look for a point on the diagram where a liquid phase region and two solid phase regions meet.
06

Write peritectic reaction

Upon identifying the peritectic point, the reaction upon cooling can be written as follows: Liquid + α -> β, where α is the original solid phase, and β is the resulting solid phase.
07

Identify congruent phase transformation point

Congruent phase transformation points are the points on the phase diagram, where a phase change occurs without any change in composition. Look for a vertical line connecting two single-phase regions.
08

Write congruent phase transformation reaction

Upon identifying the congruent phase transformation point, the reaction upon cooling can be written as follows: α -> β, where α is the original phase (can be liquid or solid), and β is the resulting phase (can be liquid or solid).

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Most popular questions from this chapter

Cite the phases that are present and the phase compositions for the following alloys: (a) \(15 \mathrm{wt} \% \mathrm{Sn}-85 \mathrm{wt} \% \mathrm{~Pb}\) at \(100^{\circ} \mathrm{C}\left(212^{\circ} \mathrm{F}\right)\) (b) \(25 \mathrm{wt} \% \mathrm{~Pb}-75 \mathrm{wt} \% \mathrm{Mg}\) at \(425^{\circ} \mathrm{C}\left(800^{\circ} \mathrm{F}\right)\) (c) \(85 \mathrm{wt} \% \mathrm{Ag}-15 \mathrm{wt} \% \mathrm{Cu}\) at \(800^{\circ} \mathrm{C}\left(1470^{\circ} \mathrm{F}\right)\) (d) \(55 \mathrm{wt} \% \mathrm{Zn}-45 \mathrm{wt} \% \mathrm{Cu}\) at \(600^{\circ} \mathrm{C}\left(1110^{\circ} \mathrm{F}\right)\) (e) \(1.25 \mathrm{~kg} \mathrm{Sn}\) and \(14 \mathrm{~kg} \mathrm{~Pb}\) at \(200^{\circ} \mathrm{C}\left(390^{\circ} \mathrm{F}\right)\) (f) \(7.6 \mathrm{lb}_{\mathrm{m}} \mathrm{Cu}\) and \(144.4 \mathrm{lb}_{\mathrm{m}} \mathrm{Zn}\) at \(600^{\circ} \mathrm{C}\left(1110^{\circ} \mathrm{F}\right)\) (g) \(21.7 \mathrm{~mol} \mathrm{Mg}\) and \(35.4 \mathrm{~mol} \mathrm{~Pb}\) at \(350^{\circ} \mathrm{C}\left(660^{\circ} \mathrm{F}\right)\) (h) \(4.2 \mathrm{~mol} \mathrm{Cu}\) and \(1.1 \mathrm{~mol} \mathrm{Ag}\) at \(900^{\circ} \mathrm{C}\left(1650^{\circ} \mathrm{F}\right)\)

For a 64 wt \% Zn-36 wt\% Cu alloy, make schematic sketches of the microstructure that would be observed for conditions of very slow cooling at the following temperatures: \(900^{\circ} \mathrm{C}\left(1650^{\circ} \mathrm{F}\right), 820^{\circ} \mathrm{C}\) \(\left(1510^{\circ} \mathrm{F}\right), 750^{\circ} \mathrm{C}\left(1380^{\circ} \mathrm{F}\right)\), and \(600^{\circ} \mathrm{C}\left(1100^{\circ} \mathrm{F}\right)\) Label all phases and indicate their approximate compositions.

Often, the properties of multiphase alloys may be approximated by the relationship $$ E(\text { alloy })=E_{\alpha} V_{\alpha}+E_{\beta} V_{\beta} $$ where \(E\) represents a specific property (modulus of elasticity, hardness, etc.), and \(V\) is the volume fraction. The subscripts \(\alpha\) and \(\beta\) denote the existing phases or microconstituents. Use this relationship to determine the approximate Brinell hardness of a \(99.75 \mathrm{wt} \% \mathrm{Fe}-0.25 \mathrm{wt} \%\) C alloy. Assume Brinell hardnesses of 80 and 280 for ferrite and pearlite, respectively, and that volume fractions may be approximated by mass fractions.

The room-temperature tensile strengths of pure copper and pure silver are 209 and \(125 \mathrm{MPa}\), respectively. (a) Make a schematic graph of the room-temperature tensile strength versus composition for all compositions between pure copper and pure silver. (Hint: You may want to consult Sections \(9.10\) and 9.11, as well as Equation \(9.24\) in Problem 9.79.) (b) On this same graph, schematically plot tensile strength versus composition at \(600^{\circ} \mathrm{C}\). (c) Explain the shapes of these two curves as well as any differences between them.

What is the difference between a phase and a microconstituent?
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