Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Chapter 5.7, Problem 9KCP
To determine
Write the equation for the solution to Fick’s second law for the diffusion of a gas into the surface of a solid metal crystal lattice.
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Compare interstitial and vacancy atomic mechanisms for diffusion and cite two reasons why interstitial diffusion is normally more rapid than vacancy diffusion.
6. (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.
Please kindly help. I will give a like. Thank you!
a. Describe the S-curve model of diffusion on how does ‘rate of adoption’ change over time? At which-point is the rate of diffusion the fastest?
b. S-curve model of diffusion: (true/false) and reasoning
- k = 0, the rate of diffusion is instantaneous?
- fixed k ≥ 0, the carrying capacity is determined only by the ratio of a and b?
- fixed k ≥ 0, the rate of diffusion is determined only by the ratio of a and b?
c. The diffusion of hybrid corn in the 1940s, who or which region seems to have adopted the hybrids more quickly and why?
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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- Diffusion Mechanisms 5. (a) Compare interstitial and vacancy atomic mechanisms for diffusion. (b) Cite two reasons why interstitial diffusion is normally more rapid than vacancy diffusion.arrow_forwardWrite down the [units] for the following terms: Diffusion coefficient, [D] = ______________ Coagulation coefficient, [K] = _____________ Electrical mobility, [Zp] = __________________ Slip correction factor, [C] = _____________arrow_forwardRank the magnitudes of the diffusion coefficients from greatest to least for the following systems: N in Fe at 700°C Cr in Fe at 700°C N in Fe at 900°C Cr in Fe at 900°C Now justify this ranking. (Note: Both Fe and Cr have the BCC crystal structure, and the atomic radii for Fe, Cr, and N are 0.124, 0.125, and 0.065 nm, respectively. You may also want to refer to Section 5.4.)arrow_forward
- A thin plastic membrane is used to separate helium from a current.gaseous. Under steady-state conditions, a concentration of helium in the membrane is known to be 0.02 and 0.005 kmol/m³ on the inner and outer surfaces, respectively. If the membrane has a thickness of 1 mm and the coefficient ofbinary diffusion of helium to plastic is 10^(-9) m²/ s, what is the value of the flow diffusive?arrow_forwardIn precipitation hardening, after being quenched into solution, overcooling is done and then either artificial aging is done at 180-250°C or natural aging is done at room temperature, both of which occur through diffusion, where temperature and time parameters are dominant. While 180°C and 250°C provide sufficient temperature for diffusion, is it not interesting that diffusion occurs at room temperature? This is because of the thermal energy of atoms causing them to move, which may facilitate diffusion at room temperature.arrow_forwardThe 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.arrow_forward
- Answer in 2 to 3 sentences. How does point defect affects the property of a material. Why does diffusion in solids important? Why do we need to study the mechanical properties of a metal?arrow_forwardAnswer in a brief and concise essay. 1. Why does diffusion in solids important?arrow_forwardPhosphorus atoms are to be diffused into a siliconwafer using both predeposition and drive-in heat treatments; the backgroundconcentration of P in this silicon material is known to be 7.5 x 10^19 atoms/m^3. Thepredeposition treatment is to be conducted at 950 degree C for 50 minutes; thesurface concentration of P is to be maintained at a constant level of 2.0 x 10^26 atoms/m^3.Drive-in diffusion will be carried out at 1200 degree C for a period of 3.0 h.For the diffusion of P in Si, values of Qd and D0 are 3.40eV/atom and 1.1 x 10^4 m^2/s, respectively. Calculate the value of Q0.arrow_forward
- Interstitial diffusion requires the solute atom to be ___________ than the matrix atomsarrow_forwardGive three examples of materials processes that rely on diffusion in solids and explain how diffusion plays a critical role for one of those processes.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_forward
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