Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 5.7, Problem 14AAP
The diffusion flux of copper solute atoms in aluminum solvent from point A to point B, 10 μm apart, is
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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.
3.
A BCC iron alloy containing 0.05 wt% C is carburized at 1050°C such that the carbon concentration is 0.5 wt% at a distance
2mm from the surface. Meanwhile, the carbon concentration at the surface is kept constant at 1.5 wt% C.
a. What is the value of the diffusion constant for carbon diffusing into BCC Fe at 1050 °C? Show all work.
Write the relevant equation for the diffusivity within this box:
Write the values of all of the parameters in the equation above within the box below:
Write your final answer for the diffusivity within this box:
b. Determine the diffusion time required to achieve the carbon profile described above. Show all work.
Write the relevant equation needed to
solve this problem within this box:
Write the values of all of the given parameters in the equation above within the box below:
Write the value for erf(z) within this box:
The diffusion coefficients for species A in metal B are given at two temperatures:
D (m²/s)
8.54 x 10-17
8.39× 10-16
i
(b) Determine the value of Do.
(a) Determine the value of the activation energy Qd (in J/mol).
i
J/mol
i
T (°C)
(c) What is the magnitude of D at 1190°C?
1020
1290
m²/s (Use scientific notation.)
m²/s (Use scientific notation.)
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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- The diffusion coefficients for species A in metal B are given at two temperatures: D (m²/s) 7.81 x 10-17 7.70x 10-16 i (b) Determine the value of Do. (a) Determine the value of the activation energy Qd (in J/mol). i T (°C) 1030 i 1260 J/mol m²/s (Use scientific notation.) (c) What is the magnitude of D at 1180°C? m²/s (Use scientific notation.)arrow_forwardCarbon is allowed to diffuse through a steel plate 11 mm thick. The concentrations of carbon at the two faces are 0.85 and 0.42 kg C/m³ in Fe, which are maintained constant. If the preexponential and activation energy are 6.2 x 107 m2/s and 80,000 J/mol, respectively, compute the temperature (in K) at which the diffusion flux is 6.5 x 10-10 kg/m2-s. Karrow_forwardDiffusion of carbon into the surface of BCC steel at 600oC for 10 hours results in a carbon concentration of 0.2wt% at a depth of 1.5 mm below the surface. At what depth will the same concentration be obtained if the diffusion time is increased to 20 hours, leaving the temperature at 600oarrow_forward
- Carbon 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_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_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 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.arrow_forward
- 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.arrow_forwardThe figure below shows five different steady-state concentration profiles from five separate tests, which had the same gas across identical membranes at the same temperature. Rank the diffusion flux of the five concentration profiles from lowest to highest. Using bullet points explain your answer. C(x)' (a) (b) (c) (d) (e) Membrane Thicknessarrow_forwardAt what temperature (in Kelvin) will the diffusion coefficient for the diffusion of species A in metal B have a value of 5.20 × 10-16 m2/s, assuming values of 1.3 x 10-5 m2/s and 224,000 J/mol for Do and Qa, respectively?arrow_forward
- A l-mm sheet of FCC iron is used to contain nitrogen in a heat exchanger at 1200°C. The concentration of N at one surface is 0.04 atomic percent and the concentration at the second surface is 0.005 atomic percent. Determine the flux of nitrogen through the foil in N atoms/cm2's. Hint: The diffusion coefficient D is related to temperature by an Arrhenius-type еquation D = Doexp(-) RT For the diffusion couple N in FCC iron, the activation energy Q is 8.269 kJ/mol and Do is 0.34 mm²/s. R is the gas constant 8.314 J/mol·K.arrow_forwardThe 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_forwardThe diffusion coefficients for carbon in nickel are given at two temperatures: T("C) D(m2/s) 600 5.5 x 10-14 700 3.9 x 10-13 (a) Determine the value of Do. i m2/s (Use scientific notation.) (b) Determine the value of Qd. kJ/mol (c) What is the magnitude of D? at 860°C. i m2/s (Use scientific notation.)arrow_forward
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