4) Consider the diffusion of metal A atoms taken place into the polycrystalline metal B. Depending on the temperature, either grain boundary (g.b.) diffusion or lattice (L) diffusion of A into B will be the dominant mechanism. The Arrhenius variation of diffusion coefficients with temperature for both mechanisms are as follows : (32 points) D9.b.=3.1106exp(Qg.b./RT)andDL=4.7102exp(QL/RT)whereQg.b.=17,500calories/molandQL=34,000calories/mol The average thickness of the grain boundaries of metal B is about 0.5nm(=0.5nm). a) Determine the apparent diffusion coefficient (Detr) as a function of temperature for a B metal with an average grain size of 10m(d=10m). Sketch log(Dgb),log(/dD9b),log (DL) and log(Deff) versus (1/T) on the same plot. Determine the transition temperature at which one mechanism dominates over the other. b) Now, determine the apparent diffusion coefficient (Dott) as a function of temperature for a B metal with an average grain size of 50m(d=50m) and determine the transition temperature at which one mechanism dominates over the other. Note :R=1.987cal/(molK)=8.134Joules/(molK),N0=6.021023 atoms /mole,1 calories =4.186 Joules, 1 Joules =107 ergs