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Chapter 9: Problem 67

The microstructure of an iron-carbon alloy consists of proeutectoid ferrite and pearlite; the mass fractions of these two microconstituents are \(0.174\) and \(0.826\), respectively. Determine the concentration of carbon in this alloy.

Short Answer

Expert verified
Answer: The concentration of carbon in this iron-carbon alloy is approximately 0.6314%.

Step by step solution

01

Recall the mass fraction and carbon concentration of both microconstituents

The mass fractions of proeutectoid ferrite and pearlite are given as 0.174 and 0.826, respectively. The carbon concentration in proeutectoid ferrite is 0.022% and in pearlite, it is 0.76%.
02

Calculate the weighted average of carbon concentration for each microconstituent

To find the overall carbon concentration in the alloy, we need to calculate the weighted average of carbon concentration for each microconstituent. This is done by multiplying the mass fraction of each microconstituent with its respective carbon concentration, and then summing the products. Carbon concentration in alloy = (mass fraction of proeutectoid ferrite × carbon concentration of proeutectoid ferrite) + (mass fraction of pearlite × carbon concentration of pearlite)
03

Calculate the carbon concentration in the alloy

Now, we can plug in the given values and calculate the carbon concentration in the alloy. Carbon concentration in alloy = (0.174 × 0.022) + (0.826 × 0.76) Carbon concentration in alloy = 0.003828 + 0.6276 Carbon concentration in alloy = 0.631428 The concentration of carbon in this iron-carbon alloy is approximately 0.6314%.

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Most popular questions from this chapter

An intermetallic compound is found in the aluminum-zirconium system that has a composition of \(22.8 \mathrm{wt} \%\) Al-77.2 wt \(\% \mathrm{Zr}\). Specify the formula for this compound.

Compute the mass fractions of proeutectoid ferrite and pearlite that form in an iron-carbon alloy containing \(0.35 \mathrm{wt} \% \mathrm{C}\).

The mass fraction of eutectoid ferrite in an ironcarbon alloy is \(0.71\). 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.

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.

Construct the hypothetical phase diagram for metals \(\mathrm{A}\) and \(\mathrm{B}\) between room temperature \(\left(20^{\circ} \mathrm{C}\right)\) and \(700^{\circ} \mathrm{C}\), given the following information: \- The melting temperature of metal \(\mathrm{A}\) is \(480^{\circ} \mathrm{C}\). \- The maximum solubility of \(B\) in \(A\) is 4 wt \(\%\) B, which occurs at \(420^{\circ} \mathrm{C}\). \- The solubility of \(\mathrm{B}\) in \(\mathrm{A}\) at room temperature is 0 wt \(\%\) B. \- One eutectic occurs at \(420^{\circ} \mathrm{C}\) and \(18 \mathrm{wt} \%\) B-82 wt \(\%\) A. \- A second eutectic occurs at \(475^{\circ} \mathrm{C}\) and \(42 \mathrm{wt} \%\) B- \(58 \mathrm{wt} \% \mathrm{~A}\) \- The intermetallic compound AB exists at a composition of \(30 \mathrm{wt} \% \mathrm{~B}-70 \mathrm{wt} \% \mathrm{~A}\), and melts congruently at \(525^{\circ} \mathrm{C}\). \- The melting temperature of metal B is \(600^{\circ} \mathrm{C} .\) \- The maximum solubility of \(\mathrm{A}\) in \(\mathrm{B}\) is \(13 \mathrm{wt} \% \mathrm{~A}\), which occurs at \(475^{\circ} \mathrm{C}\). \- The solubility of \(\mathrm{A}\) in \(\mathrm{B}\) at room temperature is \(3 \mathrm{wt} \% \mathrm{~A}\)
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