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Chapter 9: Problem 58

Is it possible to have an iron-carbon alloy for which the mass fractions of total ferrite and proeutectoid cementite are \(0.846\) and \(0.049\), respectively? Why or why not?

Short Answer

Expert verified
Explain your answer with reference to the step by step solution. Answer: Yes, it is possible to have an iron-carbon alloy with the given mass fractions of total ferrite and proeutectoid cementite. This is because the sum of these mass fractions (0.895) is less than or equal to 1, indicating that the alloy can exist with only these two phases present.

Step by step solution

01

Calculate the total mass fraction

Add the mass fractions of total ferrite and proeutectoid cementite: \(0.846 + 0.049 = 0.895\)
02

Compare the total mass fraction to 1

Check if the sum of the mass fractions is less than or equal to 1: \(0.895 \leq 1\)
03

Determine if the alloy is possible

Since the total mass fraction (0.895) is less than or equal to 1, it is possible to have an iron-carbon alloy with the given mass fractions of total ferrite and proeutectoid cementite.

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Most popular questions from this chapter

For a \(68 \mathrm{wt} \% \mathrm{Zn}-32 \mathrm{wt} \% \mathrm{Cu}\) alloy, make schematic sketches of the microstructure that would be observed for conditions of very slow cooling at the following temperatures: \(1000^{\circ} \mathrm{C}\) \(\left(1830^{\circ} \mathrm{F}\right), 760^{\circ} \mathrm{C}\left(1400^{\circ} \mathrm{F}\right), 600^{\circ} \mathrm{C}\left(1110^{\circ} \mathrm{F}\right)\), and \(400^{\circ} \mathrm{C}\left(750^{\circ} \mathrm{F}\right)\). Label all phases and indicate their approximate compositions.

Given here are the solidus and liquidus temperatures for the germanium-silicon system. Construct the phase diagram for this system and label each region. $$ \begin{array}{ccc} \hline \begin{array}{c} \text { Composition } \\ (\boldsymbol{w t} \% \text { Si) } \end{array} & \begin{array}{c} \text { Solidus } \\ \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) \end{array} & \begin{array}{c} \text { Liquidus } \\ \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) \end{array} \\ \hline 0 & 938 & 938 \\ 10 & 1005 & 1147 \\ 20 & 1065 & 1226 \\ 30 & 1123 & 1278 \\ 40 & 1178 & 1315 \\ 50 & 1232 & 1346 \\ 60 & 1282 & 1367 \\ 70 & 1326 & 1385 \\ 80 & 1359 & 1397 \\ 90 & 1390 & 1408 \\ 100 & 1414 & 1414 \\ \hline \end{array} $$

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

The mass fraction of eutectoid ferrite in an iron-carbon alloy is \(0.82\). On the basis of this information, is it possible to determine the composition of the alloy? If so, what is its composition? If this is not possible, explain why.

Is it possible to have a copper-silver alloy of composition \(50 \mathrm{wt} \%\) Ag-50 wt \% Cu that, at equilibrium, consists of \(\alpha\) and \(\beta\) phases having mass fractions \(W_{\alpha}=0.60\) and \(W_{\beta}=0.40\) ? If so, what will be the approximate temperature of the alloy? If such an alloy is not possible, explain why.
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