Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 5.7, Problem 21AAP
To determine
What depth in millimeters will the carbon content be.
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Consider the gas carburizing of a gear of 1020 steel at 927°C (1700°F) as in Example
Problem 5.2. Only in this problem calculate the carbon content at 0.50 mm beneath the sur-
face of the gear after 5 h carburizing time. Assume that the carbon content of the surface of
the gear is 0.90%, and that the steel has a nominal carbon content of 0.20%.
Danin=1.28 x 10-11 m2/s
1Solution
Maximum solubility
in FCC austenite at
1147 °C is
2.04 wt%
2.14 wt%
14.2 wt% O
0.022 wt% O
Consider de-oxidation by the addition of
ferromanganese (60 percent Mn) to molten
steel at 1600°C.The initial oxygen content is
0.04 wt%. It has to be brought down to 0.02
wt%. Calculate the quantity of
ferromanganese required per tonne of steel.
The manganese content of steel before de-
oxidation is 0.1 wt%.
(MnO) + [Fe] = [Mn] + (FeO)
Given: K Mn at 1873 K = 0.4
K Fe-Mn at 1873 K = 0.156
Assumptions: Fe and Mn form ideal solutions
Chapter 5 Solutions
Foundations of Materials Science and Engineering
Ch. 5.7 - Prob. 1KCPCh. 5.7 - Write an equation for the number of vacancies...Ch. 5.7 - Prob. 3KCPCh. 5.7 - Prob. 4KCPCh. 5.7 - Describe the substitutional and interstitial...Ch. 5.7 - Prob. 6KCPCh. 5.7 - What factors affect the diffusion rate in solid...Ch. 5.7 - Write the equation for Ficks second law of...Ch. 5.7 - Prob. 9KCPCh. 5.7 - Prob. 10KCP
Ch. 5.7 - (a) Calculate the equilibrium concentration of...Ch. 5.7 - Prob. 12AAPCh. 5.7 - Determine the diffusion flux of zinc atoms in a...Ch. 5.7 - The diffusion flux of copper solute atoms in...Ch. 5.7 - Prob. 15AAPCh. 5.7 - Prob. 16AAPCh. 5.7 - Prob. 17AAPCh. 5.7 - A gear made of 1020 steel (0.20 wt% C) is to be...Ch. 5.7 - Prob. 19AAPCh. 5.7 - The surface of a steel gear made of 1020 steel...Ch. 5.7 - Prob. 21AAPCh. 5.7 - If boron is diffused into a thick slice of silicon...Ch. 5.7 - Prob. 23AAPCh. 5.7 - Prob. 24AAPCh. 5.7 - Prob. 25AAPCh. 5.7 - Prob. 26AAPCh. 5.7 - Prob. 27AAPCh. 5.7 - Prob. 28AAPCh. 5.7 - Prob. 29AAPCh. 5.7 - Prob. 30AAPCh. 5.7 - The diffusivity of copper atoms in the aluminum...Ch. 5.7 - Prob. 32AAPCh. 5.7 - Prob. 33SEPCh. 5.7 - Prob. 34SEPCh. 5.7 - Prob. 37SEPCh. 5.7 - Prob. 38SEPCh. 5.7 - The activation energy of nickel atoms in FCC iron...Ch. 5.7 - Prob. 40SEPCh. 5.7 - The self-diffusion of iron atoms in BCC iron is...Ch. 5.7 - Would you expect the diffusion rate of copper...Ch. 5.7 - Would you expect the diffusion rate of copper...Ch. 5.7 - Prob. 44SEPCh. 5.7 - Prob. 45SEPCh. 5.7 - Prob. 46SEPCh. 5.7 - Prob. 47SEPCh. 5.7 - Prob. 48SEPCh. 5.7 - Prob. 49SEPCh. 5.7 - Prob. 50SEP
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- In a binary Fe-Fe3C system, what is a transformation that occurs when cooling an austenistic mixture of 2% C by weight from 1100°C to below the eutectoid temperature? What is the microstructure, and how is it formed? What are the total and partial phases? Given:Eutectoid temperature=723°C; Eutectoid concentration=0.76% C; Limit concentration of ferrite=0.022%; Limiting concentration of cementite: 6.7%.arrow_forwardProblem 2. In carburizing of a piece of low carbon steel with the initial carbon centration 0.2 wt%, the carbon concentration at the surface is maintained at 1.0 wt%. The diffusivity of C in Fe is 2.98 x 10-¹¹ m²/s, and the carburizing time is 3.68 x 104 seconds. Calculate the carbon concentration at a distance of (a) 0.5 mm and (b) 2 mm from the surface.arrow_forwardProblem 2 Consider the gas carburizing of a gear 1020 steel at 927°C. Calculate the time (in minute) necessary to increase the carbon content to 0.40 wt% at 0.5 mm below the surface. Assume that the carbon content at the surface 0.9 wt% and that the steel has a nominal carbon content of 0.2 wt%. Given: Diffusivity of C in Fe at 9270C is 1.28 x 10-11 m²s-1, activation energy is 148 kJmol-1, gas constant is 8.31 Jmol-1K-1, if erf (Z) = 0.7143, Z = 0.755. %3Darrow_forward
- Determine the carburizing time necessary to achieve a carbon concentration of 0.50 wt% at a position 1.2 mm into an iron-carbon alloy that initially contains 0.18 wt% C. The surface concentration is to be maintained at 1.1 wt% C, and the treatment is to be conducted at 1200°C. Assume that Do 6.5 x 10-5 m2/s and Qd = 168 kJ/mol. The following table may be useful. %3D Table 5.1 Tabulation of Error Function Values erf(z) erf(z) erf(z) 0.55 0.5633 1.3 0.9340 0.0282 0.0564 0.025 0.60 0.6039 1.4 0.9523 0.05 0.10 0.65 0.70 0.75 0.6420 1.5 0.9661 0.1125 0.6778 1.6 0.9763 0.15 0.1680 0.7112 1.7 0.9838 0.20 0.2227 0.80 0.7421 1.8 0.9891 0.85 0.90 0.25 0.2763 0.7707 1.9 0.9928 0.9953 0.9981 0.30 0.3286 0.7970 2.0 0.35 0.3794 0.95 0.8209 2.2 0.8427 0.8802 0.40 0.4284 1.0 2.4 0.9993 0.45 0.4755 1.1 2.6 0.9998 0.50 0.5205 1.2 0.9103 2.8 0.9999arrow_forwardAn FCC iron–carbon alloy initially containing 0.25 wt% C is exposed to an oxygen-rich and carbon-free atmosphere at 1400 K. Under these circumstances the carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere; that is, the carbon concentration at the surface position is maintained essentially at 0 wt% C. (This process of carbon depletion is termed decarburization.) At what position (x, in mm) will the carbon concentration 0.10 wt% after a 8-h treatment? The value of D at 1400 K is 6.9 x10-11 m2/s. Round your answer to 2 decimal place.arrow_forwardA certain component is to be carburized to obtain 0.592 wt % C at a depth of 2.0 mm. After carburizing (for 1.2 hours) the heat treater finds that he achieved 0.4 wt % C at a depth of 2.0 mm His furnace only operates at a 900 *C and maintains a constant atmosphere of 1 wt % C. The steel used has an initial carbon content of 0.2 wt %. How long (in hours) should he carburize to achieve his goal?arrow_forward
- Problem 3 An FCC iron-carbon alloy initially containing 0.35 wt% C is exposed to an oxygen-rich and virtually carbon- free atmosphere at 1400 K (1127 °C). Under these circumstances the carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere; that is, the carbon concentration at the surface position is maintained essentially at 0 wt% C. (This process of carbon depletion is termed decarburization.) At what position will the carbon concentration be 0.15 wt% after a 10-h treatment? The value of D at 1400 K is 6.9 x 10¹¹ m²/s.arrow_forward25. A sample of an alkali metal that has a bcc unit cell is found to have a mass of 1.000 g.and a volume of 1.0298 cubic meter. When the metal reacts with excess water, the reaction produces 539.29 mL of hydrogen gas at 0.980 atm and 23°C. Identify the metal, determine the unit cell dimensions, and give the approximate size of the atom in picometers.arrow_forwardDetermine the carburizing time necessary to achieve a carbon concentration of 0.50 wt% at a position 3.1 mm into an iron-carbon alloy that initially contains 0.12 wt% C. The surface concentration is to be maintained at 1.2 wt% C, and the treatment is to be conducted at 1080°C. Assume that Do = 5.8 x 10-5 m²/s and Qd = 156 kJ/mol. The table Tabulation Error Function Values may be useful.arrow_forward
- 3. A block of pure iron needs to be converted to steel. The density of iron is 7.86x10^3kg/m^3, and the atomic weight is 0.0558kg/mol. The concentration of carbon at position A is 4x10^26 at/m^3. The carbon atomic weight is 0.012kg/mol. Carbon must be diffused into the iron to convert it to steel. It is desired to have 1025 atoms of carbon per m' at point B. Position A is 1mm from position B. Assume that you have 1m^3 of iron. You heat the material uniformly to 1200°C. Do, carton = 79x10 * m/sec, Ea = 83kJ/mol, and the density of carbon is 2260kg/m^3. (4pts) 1mm Fe block A What is Dearbon at 1200°C in m?/sec? i. ii. Calculate the FLUX (J) of carbon atoms in atoms per m²-sec at 1200°C? B.arrow_forwardWhat is the volume of 3.00 moles of copper? Molar mass of copper is 63.546 g/mol and its density is 8.9 x 103 kg/m3.arrow_forwardGiven that a component is made of 0.1 wt.%C steel is carburized by introducing 1.0 wt.% carbon at its surface at 980ºC. Calculate the carbon content at 0.5 mm below the surface of this component after 1 hour.Do= 0.2 cm^2/s and Qd=40,000 cal/mol.arrow_forward
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