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 5.82DP
Design a spherical tank, with a will thickness of 2 cm that will ensure that no more than 50 kg of hydrogen will be lost per year. The tank, which will operate at 500°C, can be made from nickel, aluminum, copper, or iron. The diffusion coefficient of hydrogen and the cost per pound for each available material is listed below.
Diffusion Data for Problem 5-82
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Design a spherical tank, with a wall thickness of 2 cm that will assure that no more than 50 kg of hydrogen will be lost per year. The tank, which will operate at 500 °C, can be made of nickel, aluminum, copper, or iron. The diffusion coefficient of hydrogen and the cost per kg for each available material is listed here. (Assume that the tank capacity is 15 kg)
Diffusion Data
Material Do (cm2/s) Q (cal/mol) Cost ($/kg)Nickel 0.0055 8900 9.0Aluminium 0.16 10340 1.32Copper 0.011 9380 2.43Iron (BCC) 0.0012 3600 0.33
A plate of iron is exposed to a carburizing atmosphere on one side and a decarburizing atmosphere on the other side. If a condition of steady state is achieved, calculate the diffusion flux of carbon through the plate if the concentrations of carbon at positions of 5 and 10 mm beneath the carburizing surface are 1.2 and 0.6 kg/m3, respectively. Assume a diffusion coefficient of 2.4 x 10-12 m2/s at this temperature.
Consider a diffusion couple setup between pure tungsten
and a tungsten alloy containing 1 at% thorium. After
several minutes of exposure at 2000 C, a transition zone of
0.01 cm thickness is established. What is the flux of
thorium atoms at this time if diffusion is due to (a) volume
diffusion, (b) grain boundary diffusion, and (c) surface
diffusion?
TABLE 5-2 I The effect of the type of diffusion for thorium in tungsten and for self-diffusion in
silver*
Diffusion Coefficient (D)
Diffusion Type
Thorium in Tungsten
Silver in Silver
Do cm?/s
Q cal/mole
Do cm2/s
Q cal/mole
66,400
90,000
120,000
0.47
0.068
8,900
22,750
45,700
Surface
Grain boundary
0.74
0.24
Volume
1.00
0.99
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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- 2. For the image, label the region indicated by the arrow and the expected mechanical response for that region (i.e. is it soft, hard, brittle, ductile), then name the diffusion mechanism to create it White region Phase: Behavior: Dark region Phase: Behavior: Mechanism:arrow_forwardWhat 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.arrow_forwardThe preexponential and activation energy for the diffusion of chromium in nickel are 1.1 x 10-4 m²/s and 272,000 J/mol, respectively. At what temperature (in "C) will the diffusion coefficient have a value of 1.1 x 10-14 m²/s? i °Carrow_forward
- 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.arrow_forwardCompare the diffusion coefficients (in cm²/s) of nitrogen in BCC and FCC iron at the allotropic transformation temperature of 912°C. Decc -153606 X Your response differs from the correct answer by more than 10%. Double check your calculations, cm²/s -1976-7 Dicc x Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. cm2/sarrow_forwardAluminum atoms are to be diffused into a silicon wafer using both predeposition and drive-in heat treatments; the background concentration of Al in this silicon material is known to be 3.5 × 101⁹ atoms/m³. The drive-in diffusion treatment is to be carried out at 1050°C for a period of 4.0 h, which gives a junction depth x; of 3.0 µm. Compute the predeposition diffusion time at 950°C if the surface concentration is maintained at a constant level of 2 x 1025 atoms/m³. For the diffusion of Al in Si, values of Qd and Do are 3.41 eV and 1.38 × 10-4 m²/s, respectively.arrow_forward
- The outer surface of a steel alloy is to be hardened by increasing its carbon content. The carbon is to be supplied from an external carbon-rich atmosphere, which is maintained at an elevated temperature. A diffusion heat treatment at 837°C for 11 min increases the carbon concentration to 0.79 wt% at a position 1.9 mm below the surface. Estimate the diffusion time required at 680°C to achieve this same concentration also at a 1.9 mm position. Assume that the surface carbon content is the same for both heat treatments, which is maintained constant. The preexponential and activation energy values for the diffusion of carbon in the iron are 8.1 x 108 m²/s and 75.9 kJ/mol, respectively. i minarrow_forwardDefine the General Heat/Diffusion Equation ?arrow_forwardYou are asked to determine the concentration of a diffusing gas at a given depth on a metal surface after a given time. If you know the temperature of the metal, the surface concentration of the gas, and the diffusion coefficient, describe how you would approach this problem.arrow_forward
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Ficks First and Second Law for diffusion (mass transport); Author: Taylor Sparks;https://www.youtube.com/watch?v=c3KMpkmZWyo;License: Standard Youtube License