Hw3Solutions - EMS 164 Homework 3 Solutions 1 In a graphical representation show that diffusion occurs down the chemical potential gradient in a

EMS 164- Homework 3 Solutions 1. In a graphical representation show that diffusion occurs down the chemical potential gradient in a diffusion couple made of two solid solutions with compositions within a miscibility gap (class problem). (Not graded) Figure 2.1 in text book 2. In two clear schematics, show the octahedral and tetrahedral positions of interstitial atoms in an fcc structure. (10 points) Octahedral sites in a fcc crystal Total number of octahedrals: 12* ¼ +1= 4 octahedral sites in one fcc cubic structure. (2 points for drawing fcc, 2 points for the octahedral shape, 1 point for all the octahedral sites.) Tetrahedral sites in a fcc crystal Total number of tetrahedrals: 8*1= 8 tetrahedral sites in one fcc cubic structure. (2 points for drawing fcc, 2 points for the tetrahedral shape, 1 point for all the tetrahedral sites.) 3. At a particular temperature, the diffusion coefficient for Pb in naturally occurring ZrSiO 4 is D = 8.3 × 10 - 28 cm 2 s . Find the value of the concentration gradient where the flux of lead, J , is equal J = 5.0 × 10 - 30 g cm 2 ⋅ s       . (10 points) Ficks’ first law: J B = -D B * ∂C B ⁄∂x ( 2 points for equation) Where D B is the intrinsic diffusivity or the diffusion coefficient of B and has units [m