Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 5.7, Problem 24AAP
To determine
How long must be the diffusion time.
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The activation energy for the diffusion of atomic species A in metal B is 118 kJ/mol. Calculate the diffusion coefficient at 840°C, given that the value of D at 1140°C is 6.1 × 10-11 m2/s.
Problem 3. Phosphorus is diffused into a thick slice of silicon with no previous phosphorus in it at a
temperature of 1100°C. If the surface concentration of the phosphorus is 1 x 10 atoms/cm and its
concentration at 1 µm is 1 x 105 atoms/cm, how long must be the diffusion time? D = 3.0 x 10 cm?/s
for P diffusing in Si at 1100°C.
Vacancy diffusion vs interstitial diffusion (when they can happen?)
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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- Consider a 2-mm-thick silicon (Si) wafer to be doped using antimony (Sb). Assume that the dopant source (gas mixture of antimony chloride and other gases) provides a constant concentration of 1022 atoms/m3. We need a dopant profile such that the concentration of Sb at a depth of 1 micrometer is 5 x 1021 atoms/m3. What is the required time for the diffusion heat treatment? Assume that the silicon wafer initially contains no impurities or dopants. Assume that the activation energy for diffusion of Sb in silicon is 380 kJ/mole and D0 for Sb diffusion in Si is 1.3 x 10-3 m2/s. Assume T = 1250°C.arrow_forward3. 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_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
- 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:arrow_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_forwardempt in Progress Calculate the number of Frenkel defects per cubic meter in zinc oxide at 939°C. The energy for defect formation is 2.51 eV, while the density for ZnO is 5.55 g/cm³ at this temperature. The atomic weights of zinc and oxygen are 65.41 g/mol and 16.00 g/mol, respectively. N₁= 6.5e17 defects/m³ M Qu Mult Ques Multinarrow_forward
- What are the differences between Equimolar counter diffusion (EMD) and Uni molecular diffusionarrow_forwardWhy is the rate of interstitial diffusion mechanism higher than that of vacancy diffusion? * There are more interstitial sites and interstitial atoms are smaller. There are fewer interstitial sites and interstitial atoms are larger. There are more interstitial sites and interstitial atoms are larger. There are fewer interstitial sites and interstitial atoms are smaller.arrow_forwardQuestion 2: (Problem 2.6) An optical fiber for telecommunication is made of SIO2 glass (density 2.20 Mg/m) How many Si atoms and how many O atoms are present per millimeter of length (L 1 mm) of a fiber 10 um in diameter (d-10 mm)? Given M(Si)-28.09 g mole M(OF16gmole Avogadro's Number AN=0.6203 (10) Solution.arrow_forward
- You are examining two materials with the same density. One has a BCC crystal structure, and one has a HCP crystal structure. Which do you expect will have more rapid diffusion?arrow_forwardAnswer in a brief and concise essay. 1. Why does diffusion in solids important?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_forward
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Introduction to Diffusion in Solids; Author: Engineering and Design Solutions;https://www.youtube.com/watch?v=K_1QmKJvNjc;License: Standard youtube license