Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 9: Problem 66

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 \(725^{\circ} \mathrm{C}\).

Short Answer

Expert verified
Question: Calculate and plot the mass fractions of proeutectoid ferrite and pearlite, and ferrite and cementite for a series of Fe-Fe3C alloys with compositions ranging between 0.022 and 0.76 wt% C at 725°C. Use the lever rule and the Fe-Fe3C phase diagram to do this.

Step by step solution

01

Identify the phases

At 725°C, the two phases present, according to the Fe-Fe3C phase diagram, are proeutectoid ferrite and pearlite.
02

Apply the lever rule to calculate mass fractions

Using the lever rule, we can calculate the mass fractions of proeutectoid ferrite and pearlite. For a specific composition, find the corresponding tie line on the Fe-Fe3C phase diagram at 725°C, and use the lever rule formula to determine the mass fractions.
03

Create a table of data

After identifying the mass fractions of pearlite and proeutectoid ferrite at 725°C for various alloys with carbon concentrations between 0.022 and 0.76 wt% C, create a table to organize this data. Ensure to include the carbon concentration, mass fraction of proeutectoid ferrite, and mass fraction of pearlite in the table.
04

Plot Graph (a)

Plot a graph with carbon concentration on the x-axis, and mass fractions of proeutectoid ferrite and pearlite on the y-axis. The result should be Graph (a): Mass fractions of proeutectoid ferrite and pearlite versus carbon concentration at 725°C. Now, let's plot the mass fractions of ferrite and cementite at 725°C:
05

Identify the phases

At 725°C, within the pearlite phase, there are ferrite and cementite phases present, according to the Fe-Fe3C phase diagram.
06

Calculate the mass fractions within pearlite

Using the lever rule, determine the mass fractions of ferrite and cementite within the pearlite phase. Calculate these mass fractions for each carbon concentration in the specified range (0.022 to 0.76 wt% C), using the Fe-Fe3C phase diagram.
07

Combine calculated mass fractions

Multiply the mass fractions of ferrite and cementite within pearlite by the pearlite mass fraction (obtained during Steps 2 and 3 of the previous part) to obtain the total mass fractions of ferrite and cementite in the alloy.
08

Create another table of data

After identifying the mass fractions of ferrite and cementite in the alloy for various carbon concentrations between 0.022 and 0.76 wt% C, create another table to organize this data. Ensure to include the carbon concentration, mass fraction of ferrite, and mass fraction of cementite in the table.
09

Plot Graph (b)

Plot a graph with carbon concentration on the x-axis, and mass fractions of ferrite and cementite on the y-axis. The final output should be Graph (b): Mass fractions of ferrite and cementite versus carbon concentration at 725°C.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

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.

What thermodynamic condition must be met for a state of equilibrium to exist?

Consider \(1.5 \mathrm{~kg}\) of a \(99.7 \mathrm{wt} \% \mathrm{Fe}-0.3 \mathrm{wt} \%\) C alloy that is cooled to a temperature just below the eutectoid. (a) How many kilograms of proeutectoid ferrite form? (b) How many kilograms of eutectoid ferrite form? (c) How many kilograms of cementite form?

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.

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 \(900^{\circ} \mathrm{C}\left(1650^{\circ} \mathrm{F}\right)\)
See all solutions

Recommended explanations on Physics Textbooks

Oscillations

Read Explanation

Classical Mechanics

Read Explanation

Magnetism

Read Explanation

Thermodynamics

Read Explanation

Nuclear Physics

Read Explanation

Work Energy and Power

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free