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Chapter 9: Problem 7

Given here are the solidus and liquidus temperatures for the copper-gold system. Construct the phase diagram for this system and label each region. $$ \begin{array}{ccc} \hline \begin{array}{c} \text { Composition } \\ \text { (wt\% Au) } \end{array} & \begin{array}{c} \text { Solidus } \\ \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) \end{array} & \begin{array}{c} \text { Liquidus } \\ \text { Temperature }\left({ }^{\circ} \boldsymbol{C}\right) \\ \hline 0 \end{array} & 1085 & 1085 \\ \hline 20 & 1019 & 1042 \\ \hline 40 & 972 & 996 \\ \hline 60 & 934 & 946 \\ \hline 80 & 911 & 911 \\ \hline 90 & 928 & 942 \\ \hline 95 & 974 & 984 \\ \hline 100 & 1064 & 1064 \\ \hline \end{array} $$

Short Answer

Expert verified
Question: Based on the given data points for the copper-gold system, construct the phase diagram and label each region. Answer: The phase diagram for the copper-gold system consists of three regions: solid, liquid, and solid-liquid mixture. The solid region is located on the left side of the solidus curve, the liquid region is on the right side of the liquidus curve, and the solid-liquid mixture region is between the two curves.

Step by step solution

01

Identify given data points

We have the following data points provided for the copper-gold system: Composition (wt% Au), Solidus Temperature (\(^{\circ} \mathrm{C}\)), Liquidus Temperature (\(^{\circ} \mathrm{C}\)) 0, 1085, 1085 20, 1019, 1042 40, 972, 996 60, 934, 946 80, 911, 911 90, 928, 942 95, 974, 984 100, 1064, 1064
02

Plot the data points on a graph

Using the data points, we can plot the solidus and liquidus temperatures on a graph, with Composition (wt% Au) on the x-axis and Temperature (\(^{\circ} \mathrm{C}\)) on the y-axis.
03

Connect the points to form the phase diagram

Connect the solidus temperature data points (left side of the line) and liquidus temperature data points (right side of the line) to form the phase boundary between the solid and liquid regions. For compositions with matching solidus and liquidus temperatures, the line will be a vertical line.
04

Identify and label the different regions of the phase diagram

There are three regions in the phase diagram: 1. Pure solid: This region is located on the left side of the solidus curve (the lower temperature side). Label this region as "Solid." 2. Pure liquid: This region is located on the right side of the liquidus curve (the higher temperature side). Label this region as "Liquid." 3. Solid-liquid mixture: This region is located between the solidus and liquidus curves. Label this region as "Solid + Liquid." With these steps completed, the phase diagram has been constructed and labeled.

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Most popular questions from this chapter

Plot the mass fraction of phases present versus temperature for a \(40 \mathrm{wt} \% \mathrm{Sn}-60 \mathrm{wt} \% \mathrm{~Pb}\) alloy as it is slowly cooled from \(250^{\circ} \mathrm{C}\) to \(150^{\circ} \mathrm{C}\).

For alloys of two hypothetical metals \(\mathrm{A}\) and \(\mathrm{B}\), there exist an \(\alpha\), A-rich phase and a \(\beta\), B-rich phase. From the mass fractions of both phases for two different alloys provided in the following table (which are at the same temperature), determine the composition of the phase boundary (or solubility limit) for both \(\alpha\) and \(\beta\) phases at this temperature. $$ \begin{array}{lcc} \hline \begin{array}{c} \text { Alloy } \\ \text { Composition } \end{array} & \begin{array}{c} \text { Fraction } \\ \boldsymbol{\alpha} \text { Phase } \end{array} & \text { Fraction } \\ \hline 70 \mathrm{wt} \% \mathrm{~A}-30 \mathrm{wt} \% \mathrm{~B} & 0.78 & 0.22 \\ \hline 35 \mathrm{wt} \% \mathrm{~A}-65 \mathrm{wt} \% \mathrm{~B} & 0.36 & 0.64 \\ \hline \end{array} $$

How many kilograms of nickel must be added to \(1.75 \mathrm{~kg}\) of copper to yield a liquidus temperature of \(1300^{\circ} \mathrm{C} ?\)

For a \(76 \mathrm{wt} \%\) Pb-24 wt \% Mg alloy, make schematic sketches of the microstructure that would be observed for conditions of very slow cooling at the following temperatures: \(575^{\circ} \mathrm{C}\left(1070^{\circ} \mathrm{F}\right)\), \(500^{\circ} \mathrm{C}\left(930^{\circ} \mathrm{F}\right), 450^{\circ} \mathrm{C}\left(840^{\circ} \mathrm{F}\right)\), and \(300^{\circ} \mathrm{C}\left(570^{\circ} \mathrm{F}\right)\) Label all phases and indicate their approximate compositions.

Briefly explain why, upon solidification, an alloy of eutectic composition forms a microstructure consisting of alternating layers of the two solid phases.
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