5.The existence of dislocations in a crystal invariably affects the diffusion of a solute.In each of the following cases,tell whether adding dislocations will enhance, or retard,the effective diffusivity for the solute.Also,explain how this occurs. (a)Diffusion of Cd*through a single crystal of Ag at a temperature of half the melting point. (b)Diffusion of Cu in Ge,or Au in Si. (c)Permeation of H through a sheet of Fe at room temperature. 6.(a)A carbon atom in iron jumps from one site to another with a frequency of once per second at 25 C.Estimate the most probable distance a carbon atom will be found from its initial position after 24 hours. (b)The activation energy for the motion of carbon in bcc iron is 20.45 kcal/mol (170 kJ/mol).What is the value of D at 750 C? (c)Given an Fe-0.01%C alloy exposed to a decarburizing gas on both sides, how thick a sheet could be decarburized in one day at 750 C? 7.Consider a one-dimensional heat conduction situation with thermal conductivity, k=1 and source term,s=2(in appropriate units)everywhere.If four grid points at x =0,1,2,3 are used to span the domain of length 3 units,write the four discretization equations (including the half-control-volume equations).Solve the equations by the TDMA (Tri-Diagonal Matrix Algorithm)using the following boundary conditions:Temperature at x=0 is 100 and at x =3 is 25,in arbitrary units. 8 If the tracer diffusivity of Fe in magnetite (Fe304)is measured as a function of oxygen partial pressure between 900 and 1400 C plots of log D vs.log (oxygen activity) consist of two segments,one with a slope of about 2/3 and the other with a slope of-2/3 (see fig.for an example). Tell the mechanism that operates in each leg of the curve,and explain why the sign of the slope is positive Log(activ.oxygen) or negative for that mechanism. 9.(a)Derive an expression for diffusion of SiH4 gas through the boundary layer to the substrate in a CVD process as shown below.The process is diffusion controlled,i.e.,the following reaction taking place at the substrate is very fast. SiH4(g)=Si(s)+2H2(g)5. The existence of dislocations in a crystal invariably affects the diffusion of a solute. In each of the following cases, tell whether adding dislocations will enhance, or retard, the effective diffusivity for the solute. Also, explain how this occurs. (a) Diffusion of Cd* through a single crystal of Ag at a temperature of half the melting point. (b) Diffusion of Cu in Ge, or Au in Si. (c) Permeation of H through a sheet of Fe at room temperature. 6. (a) A carbon atom in iron jumps from one site to another with a frequency of once per second at 25 C. Estimate the most probable distance a carbon atom will be found from its initial position after 24 hours. (b) The activation energy for the motion of carbon in bcc iron is 20.45 kcal/mol (170 kJ/mol). What is the value of D at 750 C? (c) Given an Fe-0.01% C alloy exposed to a decarburizing gas on both sides, how thick a sheet could be decarburized in one day at 750 C? 7. Consider a one-dimensional heat conduction situation with thermal conductivity, k = 1 and source term, s = 2 (in appropriate units) everywhere. If four grid points at x = 0, 1, 2, 3 are used to span the domain of length 3 units, write the four discretization equations (including the half-control-volume equations). Solve the equations by the TDMA (Tri-Diagonal Matrix Algorithm) using the following boundary conditions: Temperature at x = 0 is 100 and at x = 3 is 25, in arbitrary units. 8. If the tracer diffusivity of Fe in magnetite (Fe304) is measured as a function of oxygen partial pressure between 900 and 1400 C plots of log D vs. log (oxygen activity) consist of two segments, one with a slope of about 2/3 and the other with a slope of -2/3 (see fig. for an example). Tell the mechanism that operates in each leg of the curve, and explain why the sign of the slope is positive or negative for that mechanism. 9. (a) Derive an expression for diffusion of SiH4 gas through the boundary layer to the substrate in a CVD process as shown below. The process is diffusion controlled, i.e., the following reaction taking place at the substrate is very fast. SiH4(g) = Si(s) + 2H2(g)