1.The diffusion coefficient,D,in a solid is related to the rate at which an atom jumps from one site to another,w. (a)In a pure metal how are D and w related? (b)In a substitutional binary alloy the solute and vacancies are often attracted ("bound")to each other so that the solute atom's jump frequency,w2,is much greater than that of the base metal,w1.Under these conditions how is D2 related to w2 and wi? (c)For a very dilute interstitial alloy how is the interstitial jump frequency,wi, related to D? 2.An Fe-0.8%C alloy is decarburized in an atmosphere that keeps the surface essentially carbon free. (a)If the decarburization is carried out at 730 C a carbon-free layer of ferrite(alpha) forms on the surface of the austenitic (gamma)alloy.Set up an equation relating the movement of the alpha/gamma interface to the concentration difference across the ferrite layer and D in the ferrite. (b)Assume the solubility of carbon in equilibrium with austenite at 730 C is 0.02 w/o carbon and that D=10 cm /s for carbon in the ferrite.How long will it take to form a ferrite layer 0.01 cm thick? (c)If the decarburization is carried out at 800 C the c(x)curve crosses the alpha, alpha+aust.and aust.fields.Plot the c(x)curve across the diffusion zone.On the plot label the composition limits of the two-phase fields. 3.Consider a diffusion couple of Cu against an alpha solid solution of Cu-15a/o Al with fine inert markers initially placed in the interface between the two pieces of metal. (a)How would you measure the Kirkendall shift? (b)What is Kirkendall porosity,and where would one expect to find it? (c)How can this shift be related to the intrinsic diffusion coefficients Dint of Al and Cu in the alloy?(Are these values of Dint for all compositions in the couple,or for some particular composition?) (d)If the annihilation of vacancies was suddenly rendered impossible so that the vacancy chemical potential could locally rise,or fall,what would this do to the relative fluxes of Al and Cu? 4.Sulfur will segregate to grain boundaries in steel during annealing in the temperature range of 450-550C,causing grain boundary embrittlement. (a)If the sulfur atoms jump with a frequency of 10*/s at 500C,give an estimate of the diffusion coefficient D,in cm/s in the lattice. (b)If the atom fraction ofS in solution in the steel at 500C is 10,estimate how long it will take for enough diffusion to occur to form a monolayer of S on the grain boundary.(A monolayer consists of 1 sulfur atom per iron atom on die boundary.1. The diffusion coefficient, D, in a solid is related to the rate at which an atom jumps from one site to another, w. (a) In a pure metal how are D and w related? (b) In a substitutional binary alloy the solute and vacancies are often attracted (“bound”) to each other so that the solute atom’s jump frequency, w2, is much greater than that of the base metal, w1. Under these conditions how is D2 related to w2 and w1? (c) For a very dilute interstitial alloy how is the interstitial jump frequency, w1, related to D1? 2. An Fe-0.8% C alloy is decarburized in an atmosphere that keeps the surface essentially carbon free. (a) If the decarburization is carried out at 730 C a carbon-free layer of ferrite (alpha) forms on the surface of the austenitic (gamma) alloy. Set up an equation relating the movement of the alpha/gamma interface to the concentration difference across the ferrite layer and D in the ferrite. (b) Assume the solubility of carbon in equilibrium with austenite at 730 C is 0.02 w/o carbon and that D = 10-6 cm 2 /s for carbon in the ferrite. How long will it take to form a ferrite layer 0.01 cm thick? (c) If the decarburization is carried out at 800 C the c(x) curve crosses the alpha, alpha+aust. and aust. fields. Plot the c(x) curve across the diffusion zone. On the plot label the composition limits of the two-phase fields. 3. Consider a diffusion couple of Cu against an alpha solid solution of Cu-15a/o Al with fine inert markers initially placed in the interface between the two pieces of metal. (a) How would you measure the Kirkendall shift? (b) What is Kirkendall porosity, and where would one expect to find it? (c) How can this shift be related to the intrinsic diffusion coefficients Dint of Al and Cu in the alloy? (Are these values of Dint for all compositions in the couple, or for some particular composition?) (d) If the annihilation of vacancies was suddenly rendered impossible so that the vacancy chemical potential could locally rise, or fall, what would this do to the relative fluxes of Al and Cu? 4. Sulfur will segregate to grain boundaries in steel during annealing in the temperature range of 450 - 550°C, causing grain boundary embrittlement. (a) If the sulfur atoms jump with a frequency of 10*/s at 500°C, give an estimate of the diffusion coefficient D, in cm2 /s in the lattice. (b) If the atom fraction of S in solution in the steel at 500°C is 10-5, estimate how long it will take for enough diffusion to occur to form a monolayer of S on the grain boundary. (A monolayer consists of 1 sulfur atom per iron atom on die boundary.)