(b) Write the equation for the total free-energy change involved in the solidification of liquid to produce a strain-free solid nucleus with a radius of R by homogencous nucleation. (4%)

(a) Detcrmine the three-axis Miller index and four-axis Miller-Bravais index for the plane ABCD. (4%)

(b) Determine the three-axis Miller index and four-axis Miller-Bravais index for the direction. (4%)

(c) Determine the planar packing fraction for the CDE planc. (4%)

(a) Why the critical resolved shear stress in a BCC (body-centered cubic) metal is higher than that in a FCC (face-centered cubic) metal? (3%)

(b) A single crystal of a BCC metal is oricnted such that the [120] direction is parallel to an applied tensile stress. If' slip occurs on a (112) plane, and the critical resolved shear stress is 48 MPa, Compute the yield streneth of the single crystal.

(c) Is the (111) plane a possible slip plane in a BCC metals? Explain why. (3%) (6%)

(a) During the solidification of pure metal, what are the two energics involved in the transformation? (4%)

(c) Describe and explain the change of the two energies during solidification transformalion.(4%)

4. Consider the impurity diffusion of phosphorus into a silicon wafer. If phosphorus is diffused into a thick silicon waler with no previous phosphorus in it at a temperature of 1100℃. If the surface concentr tration of the phosphorus is 1 x atoms/cm3and its eoncentration at ce of 1.2 Jum below the surface is atoms/cm3, how long must be required for the impurity diffusion? The difiusion coeficient for phosphorus diffusing in silicon at 1 100*C is 3.0 x. (10%) 

(a) Estimate the engincering strain just before yield. (3%)

110年 - 110 國立臺北科技大學_碩士班招生考試_材料科學與工程研究所：材料科學與工程導論#108255