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Chapter 9: Problem 71

Compute the maximum mass fraction of proeutectoid cementite possible for a hypereutectoid iron-carbon alloy.

Short Answer

Expert verified
Answer: The maximum mass fraction of proeutectoid cementite in hypereutectoid iron-carbon alloys is 1, which indicates that for a hypereutectoid iron-carbon alloy with 6.67 wt% carbon, it's completely composed of proeutectoid cementite.

Step by step solution

01

Understanding the iron-carbon phase diagram

The iron-carbon phase diagram represents the equilibrium phases of iron-carbon alloys at various carbon concentrations and temperatures. In particular, we will focus on the eutectoid point. For an iron-carbon alloy, the eutectoid point is at 0.76 wt% carbon and a temperature of 727°C. The hypereutectoid alloys contain carbon concentrations higher than the eutectoid point.
02

Identify the hypereutectoid phase boundaries

In the phase diagram, the hypereutectoid phase boundary is where we have a mixture of proeutectoid cementite and the eutectoid structure (pearlite). It is between the eutectoid composition (0.76 wt% C) and the maximum solubility of carbon in cementite (6.67 wt% C).
03

Apply the lever rule

The lever rule helps us to determine the mass fraction of each phase present using the phase diagram. To compute the maximum mass fraction of proeutectoid cementite in hypereutectoid iron-carbon alloys, we will apply the lever rule at the hypereutectoid phase boundary. The lever rule is given by: Mass fraction of proeutectoid cementite = \(\frac{(C_0 - C_\alpha)}{(C_\beta - C_\alpha)}\) where \(C_0\) is the overall concentration of carbon in the alloy, \(C_\alpha\) is the carbon concentration at the eutectoid point (0.76 wt% C), and \(C_\beta\) is the carbon concentration at the cementite phase boundary (6.67 wt% C).
04

Calculate the mass fraction

In order to find the maximum mass fraction of proeutectoid cementite, we will consider the maximum carbon concentration in cementite. Let's assume a hypereutectoid iron-carbon alloy with 6.67 wt% carbon to calculate the mass fraction. Mass fraction of proeutectoid cementite = \(\frac{(C_0 - C_\alpha)}{(C_\beta - C_\alpha)}\) = \(\frac{(6.67 - 0.76)}{(6.67 - 0.76)}\) = 1 The maximum mass fraction of proeutectoid cementite is 1, which indicates that for a hypereutectoid iron-carbon alloy with 6.67 wt% carbon, it's completely composed of proeutectoid cementite.

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Most popular questions from this chapter

Cite three variables that determine the microstructure of an alloy.

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

Is it possible to have a copper-silver alloy that, at equilibrium, consists of a \(\beta\) phase of composition \(92 \mathrm{wt} \%\) Ag-8 \(\mathrm{wt} \% \mathrm{Cu}\) and also a liquid phase of composition \(76 \mathrm{wt} \%\) Ag-24 wt \(\% \mathrm{Cu}\) ? If so, what will be the approximate temperature of the alloy? If this is not possible, explain why.

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.

For a series of \(\mathrm{Fe}-\mathrm{Fe}_{3} \mathrm{C}\) alloys with compositions ranging between \(0.022\) and \(0.76 \mathrm{wt} \% \mathrm{C}\) that have been cooled slowly from \(1000^{\circ} \mathrm{C}\), plot the following: (a) mass fractions of proeutectoid ferrite and pearlite versus carbon concentration at \(725^{\circ} \mathrm{C}\) (b) mass fractions of ferrite and cementite versus carbon concentration at \(725^{\circ} \mathrm{C}\).
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