The Science and Engineering of Materials (MindTap Course List)
7th Edition
ISBN: 9781305076761
Author: Donald R. Askeland, Wendelin J. Wright
Publisher: Cengage Learning
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Chapter 5, Problem 5.55P
To determine
The carburizing time.
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What temperature is required to obtain 0.4%C at a
distance of 0.3 mm beneath the surface of a 0.22% C
steel in 2h, when 1.1% C is present at the surface?
Assume that the iron is FCC. (Please see figure 5.12
below for diffusion coefficient data. Please use your notes
for a table of erf() function values
Diffusion coefficient D (cm²/s)
ܐ
ܐ
ܐ
ܐ
10-
10-5
10-
10-10
10-11
10-12
10-13
10-14
10-15
Temperature (°C)
2000 1500 1200 1000 900 800 700 600
Cin graphite
Mg in MgO
Ca in Cao
Hin FCC iron
C in FCC iron
Fe in FCC iron
Fe in BCC iron
H in BCC iron
C in BCC iron
Fe in FeO
500
5 6 7 8 9 10 11 12 13
104
T(K)
Figure 5-12 The diffusion coefficient D as a function of reciprocal temperature for some
metals and ceramics. In this Arrhenius plot, D represents the rate of the diffusion process.
A steep slope denotes a high activation energy.
The diffusion coefficient for carbon in BCC iron at 400C and 900C is given as 3.80x10-13 and 1.70x-10m2/s respectively. Determine the temperature (in degrees C) at which a specimen of BCC iron has to be carburized for 150 minutes to produce the same diffusion result as at 900C for one hour.
What temperature is required to obtain 0.4%C at a
distance of 0.3 mm beneath the surface of a 0.22% C
steel in 2h, when 1.1% C is present at the surface?
Assume that the iron is FCC. (Please see figure 5.12
below for diffusion coefficient data. Please use your notes
for a table of erf() function values
table of erf() fun
Diffusion coefficient D (cm²/s)
10-3
!! ! ! ! !
10-
10-5
10-9
10-10
10-11
10-12
10-13
10-14
Temperature (°C)
2000 1500 1200 1000 900 800 700 600
wwwwwwwwwwwwwww
in graphite
Mg in MgO
Ca in CaO
H in FCC iron
Cin FCC iron
Fe in FCC iron
Fe in BCC iron
H in BCC iron
104
T(K)
C in BCC iron
Fe in FeO
500
10-15
4 5 6 7 8 9 10 11 12 13
Figure 5-12 The diffusion coefficient D as a function of reciprocal temperature for some
metals and ceramics. In this Arrhenius plot, D represents the rate of the diffusion process.
A steep slope denotes a high activation energy.
Chapter 5 Solutions
The Science and Engineering of Materials (MindTap Course List)
Ch. 5 - What is the driving force for diffusion?Ch. 5 - Give three examples of materials processes that...Ch. 5 - In the carburization treatment of steels, what are...Ch. 5 - Prob. 5.4PCh. 5 - Prob. 5.5PCh. 5 - Prob. 5.6PCh. 5 - Prob. 5.7PCh. 5 - A certain mechanical component is heat treated...Ch. 5 - Prob. 5.9PCh. 5 - Prob. 5.10P
Ch. 5 - Prob. 5.11PCh. 5 - Prob. 5.12PCh. 5 - Prob. 5.13PCh. 5 - Prob. 5.14PCh. 5 - Prob. 5.15PCh. 5 - Prob. 5.16PCh. 5 - Compare the diffusion coefficients of carb on in...Ch. 5 - Prob. 5.18PCh. 5 - Activation energy is sometimes expressed as...Ch. 5 - Prob. 5.20PCh. 5 - The activation energy for the diffusion of copper...Ch. 5 - Prob. 5.22PCh. 5 - Prob. 5.23PCh. 5 - Prob. 5.24PCh. 5 - Prob. 5.25PCh. 5 - Write down Fick’s first law of diffusion. Clearly...Ch. 5 - Prob. 5.27PCh. 5 - Prob. 5.28PCh. 5 - Prob. 5.29PCh. 5 - Prob. 5.30PCh. 5 - A 1-mm-thick BCC iron foil is used to separate a...Ch. 5 - Prob. 5.32PCh. 5 - Prob. 5.33PCh. 5 - A 0.001 in. BCC iron foil is used to separate a...Ch. 5 - Prob. 5.35PCh. 5 - Prob. 5.36PCh. 5 - Prob. 5.37PCh. 5 - Prob. 5.38PCh. 5 - Prob. 5.39PCh. 5 - Prob. 5.40PCh. 5 - Prob. 5.41PCh. 5 - Prob. 5.42PCh. 5 - Prob. 5.43PCh. 5 - Prob. 5.44PCh. 5 - Prob. 5.45PCh. 5 - Prob. 5.46PCh. 5 - Prob. 5.47PCh. 5 - Prob. 5.48PCh. 5 - Pure zinc is to be diffused into copper by dipping...Ch. 5 - Nitriding is a process in which nitrogen is...Ch. 5 - Determine the carburizing time necessary to...Ch. 5 - Prob. 5.52PCh. 5 - Prob. 5.53PCh. 5 - Prob. 5.54PCh. 5 - Prob. 5.55PCh. 5 - Prob. 5.56PCh. 5 - Prob. 5.57PCh. 5 - Prob. 5.58PCh. 5 - Compare the rate at which oxygen ions diffuse in...Ch. 5 - Prob. 5.60PCh. 5 - Prob. 5.61PCh. 5 - Prob. 5.62PCh. 5 - Prob. 5.63PCh. 5 - Prob. 5.64PCh. 5 - Prob. 5.65PCh. 5 - A 0.80% C steel must operate at 950°C in an...Ch. 5 - Prob. 5.67PCh. 5 - Prob. 5.68PCh. 5 - Prob. 5.69PCh. 5 - Prob. 5.70PCh. 5 - Prob. 5.71PCh. 5 - Prob. 5.72PCh. 5 - Most metals and alloys can be processed using the...Ch. 5 - Prob. 5.74PCh. 5 - Prob. 5.75PCh. 5 - Prob. 5.76PCh. 5 - A ceramic part made from MgO is sintered...Ch. 5 - Prob. 5.78PCh. 5 - What are the advantages of using hot pressing and...Ch. 5 - Prob. 5.80PCh. 5 - Prob. 5.81DPCh. 5 - Design a spherical tank, with a will thickness of...Ch. 5 - Prob. 5.83DPCh. 5 - Prob. 5.84DPCh. 5 - Prob. 5.85DPCh. 5 - Prob. 5.86CPCh. 5 - Prob. 5.87CPCh. 5 - Prob. 5.88CPCh. 5 - Prob. 5.1KP
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- The surface of a solid sphere is covered by a monolayer of receptors for a ligand. When the ligands diffuse to the surface of the sphere, they are captured instantaneously by the receptors. The ligand diffusion coefficient is 4.8*10-9m2/s. Assume the bulk concentration far away from the sphere is constant of 1.2nM and the sphere radius is 2.8 μm. (a) Find the ligand concentration C at the location of r=2.7 μm at steady state, where r is the distance to the surface of the sphere. Please enter the numerical value with a unit of nM.arrow_forwardThe surface of a solid sphere is covered by a monolayer of receptors for a ligand. When the ligands diffuse to the surface of the sphere, they are captured instantaneously by the receptors. The ligand diffusion coefficient is 2.3*10-9m2/s. Assume the bulk concentration far away from the sphere is constant of 1.5nM and the sphere radius is 1.8 μm. (a) Find the total ligand flux onto the surface of the sphere. The answer is in the form of A*10-18 mole/s. Please enter the value of A in the box.arrow_forwardConsider an alloy that is undergoing carburizing process, initially has a uniform carbon concentration of 0.27 wt% and is to be treated at 950°C (1750°F). If the concentration of carbon at the surface is suddenly brought to and maintained at 1.32 (c) wt%, how long will it take to achieve a carbon content of 0.85% at a position 0.7 mm below the surface? The diffusion coefficient for carbon in iron at this temperature is 1.6 x 10-11 m2/s; assume that the steel piece is semi-finite.arrow_forward
- 6. A sheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at 1200C and is permitted to achieve a steady-state diffusion condition. The diffusion coefficient for nitrogen in steel at this temperature is 6 10-11 m2/s, and the diffusion flux is found to be 1.2 10-7 kg/m2-s. Also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 4 kg/m3. How far into the sheet from this high-pressure side will the concentration be 2.0 kg/m3? Assume a linear concentration profile.arrow_forwardConsider steady 2D diffusion through a funnel. The funnel radius varies linearly with the distance along the funnel axis according to the following formula: rx=r0*(1+x/L). r0 = 1mm, L=1cm.arrow_forwardCarbon is being diffused into chromium at 1400 K (1127°C). The diffusion coefficient at this temperature for the system is 6.25 x 10-11 m/s. Based on this information, calculate the diffusion coefficient of carbon in chromium at a temperature 1300 K (827°C). The activation energy for the diffusion of carbon in chromium is 111,000 J/mol.arrow_forward
- Question 8 A sheet of steel 3 mm thick is exposed on one side to a nitrogen-rich atmosphere at 1200°C and is permitted to achieve a steady-state diffusion condition. It is known that from the high- pressure nitrogen-rich side, the concentration of nitrogen on the steel surface is 6 kg/m³. The diffusion coefficient for nitrogen in steel at this temperature is 5x10-11 m²/s, and the diffusion flux is found to be 1.6 x 107 kg/m² s. How far into the sheet from this high-pressure side will the concentration be 2.0 kg/m³? Assume a linear concentration profile. The Fick's first law is given by the equation: dC J = - D dxarrow_forwardThe diffusion coefficient of Ni in Cu at 1025 C is 10-9 cm2 s-1. How long does it take for the mean square root of the distance to be 1 cm?arrow_forwardCalculate the value of the diffusion coefficient D (in m^2/s) at 694°C for the diffusion of some species in a metal; assume that the values of D0 and Qd are 5.6 x 10^-5 m^2/s and 177 kJ/mol, respectively. R=8.314 J/(mol*K)arrow_forward
- Diffusion of carbon into BCC iron for 12 hours at a temperature of 500 °C results in a carbon concentration of 0.2 wt% at a depth 2 mm from the surface. How long would it take to get a concentration of 0.2 wt% at a depth 3 mm from the surface at 500 °C?arrow_forward6. (20%) Pure zinc is to be diffused into the copper by dipping copper into molten zinc at 450°C. Calculate how long would take to obtain 10wt% zinc at a depth of 0.5 mm beneath the copper surface. Is this commercially feasible? What practical problems might arise if we raise the temperature to 1000°C ? Use Table below for error function values as needed. At 450°C, the diffusion coefficient D = 6.3 10-17 m²/s.arrow_forwardThe diffusion coefficients for carbon in nickel are given at two temperatures: T(°C) D (m²/s) (a) Determine the value of Do. i (b) Determine the value of Qd. i i kJ/mol (c) What is the magnitude of D? at 810°C. 600 700 ! m²/s (Use scientific notation.) 5.5 x 10-14 3.9 × 10-13 m²/s (Use scientific notation.)arrow_forward
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