110年 - 110 國立臺灣大學_碩士班招生考試_部分系所:材料科學(A)#100703

(c) Compared to homogeneous nucleation, heterogeneous nucleation has a smaller critical free energy barrier (△G') and critical radius (r*) both. (2%)

(a) Write down all seven crystal systems. Which two systems do not have any perpendicular interaxial angles (that is,α≠ 90°， β≠ 90°， γ≠ 90°?(3%)

(b) The interplanar spacing is a function of the Miller indices and lattice parameters. For example, for crystal structures having cubic symmetry:
d Derive the interplanar spacing  for crystal structures having tetragonal symmetry. (3%)

(c) A BCT unit cell in martensitic steel is simply a body-centered cube that has been elongated along the c-axis. Due to the reduced symmetry from BCC, the martensite (002) and (200) peaks spit in X-ray diffraction pattern may be observed. Today a martensitic steel sampie with unknown carbon concentration is detected to have 2θ = 5.7° difference between (002) and (200) planes while using X-ray diffraction with Cr-Ka radiation (wavelength = 0.22897 nm). From a linear relationship between carbon content and cla ratio: , and lattice parameter a = 0.2868 nm, evaluate the carbon concentration of this martensitic steel. (4%)

(b) Zinc has an HCP crystal structure, a cla ratio of 1.856. In addition to slip on the basal plane, zinc has been observed to slip on a unique slip system. Draw one schematic HCP unit cell (such as the figure shown below) to illustrate basal slip AND another HCP unit cell to illustrate slip system. (2%)

(c) Zirconium also has an HCP crystal structure, a cla ratio of 1.593. It slips primarily on its prismatic plane instead of basal plane. Again, draw one schematic HCP unit cell to illustrate slip on the prismatic plane. (2%)

(c) You are requested to make a cast iron with volume percent of graphite in 14%. Additionally, the cast iron should consist of a martensite matrix where graphite is embedded. Calculate the proper carbon concentration, and describe the treatment necessary to produce such this microstructure. Assume densities of 7.87 and ferrite and graphite, respectively. (4%)

5. Suppose that CaCl₂ is added as an additive to NaCl, assuming thatsubstitute for Na⁺ and vacancy is formed. How many of this vacancy is created for every  added (10%)?

6. Both kaolinite and mullite are Al-Si-O compounds. The chemical formula of kaolinite is Al₂(Si₂O₅)(OH)₄, of mullite is 3Al₂O₃ 2SiO₂. Can we use kaolinite as the refractory for a 1600℃ furnace ? Explain brietly using the phase diagram for SiO₂-A1₂O₃ in the following (10%).
Note: the atomic weight of Al is 27, of Si is 14, of O is 8.

8. For the load-time cycle in figure (a), sketch schematic responses strain-versus-time for atactic poly(methy! methacrylate) at 0℃ and explain. (10%)