230
HW9 MSE (due 03/25, 03/26)
Spring 2010
1. The important refractory ceramic MgO has the NaCl crystal structure. (a) Neglecting the small effect of CN on ionic radius, how much larger would the Mg2+ cation have to be in order for MgO to possibly have the CsCl crystal structure? (b) Based on equation 2.8 (including associated footnote), which factor, ion valence or ion separation (r = rcation + ranion), contributes more to the higher melting temperature of MgO compared to NaCl (Table 2.3)? Do not calculate absolute EA values, but show the relative effects using ratios. 2. One form of the important abrasive ceramic SiC has the ZnS crystal structure (see Fig. 12.4). (a) From an electronic structure standpoint, explain briefly why the coordination number in SiC is 4. (b) Calculate the lattice parameter of this structure based on the true density (pore-free) of 3.22 g/cm3. (c) Bulk SiC, like many bulk ceramics, often contains residual porosity (small voids) due to incomplete sintering. What volume fraction (i.e., 0 to 1) of porosity would be in a sintered SiC ceramic having a bulk density of 3.10 g/cm3? 3. Ceramics based on the Al2O3-SiO2 system (p. 442) are used for processing molten metals. The maximum use temperature is limited by the formation of any amount of liquid phase. (a) On a copy or tracing of the Al2O3-SiO2 phase diagram draw a heavy line indicating the maximum use temperature versus composition over the entire range. (b) Why is about 80 wt.% alumina the minimum alumina content in alumina-silica refractories handling for molten steel? 4. Five rectangular bend test bars 5 mm x 5 mm x 50 mm long are cut from a sintered silicon nitride and tested in 3-point bending according to Fig. 12.32 with L = 40 mm. The test bars fracture at the mid-point (L/2) under loads, Ff = 934, 1313, 1170, 850, and 1099 N, respectively. (a) Calculate the average flexural strength of this silicon nitride. (b) For the highest and lowest test result, estimate the size of the flaw that caused fracture, assuming surface cracks of length a, Y = 1.2 and the appropriate fracture toughness from Appendix B. (c) Explain briefly why the average strength would increase if the test specimen size were decreased. (d) Explain briefly why the average strength would decrease if the specimens were tested in uniaxial tension. 5. Thermal tempering is commonly used to strengthen glass components. (a) Describe the process of tempering glass and explain the origin(s) of the strengthening effect. (b) Compare and contrast the tempering of glass with the tempering of steel. 6. Callister 13.14: For many viscous materials, the viscosity may be defined in terms of the expression, = ,
d dt
where and d/dt are, respectively, the tensile stress and (tensile) strain rate. A cylindrical specimen of borosilicate glass of diameter 4 mm and length 125 mm is subjected to a tensile force of 2 N along its axis. If its deformation (displacement) is to be less than 2.5 mm over a weeks time, using Fig. 13.7, determine the maximum temperature to which the specimen may be heated.