ENGR 220 Homework Problems: Week 6 - Chapter 12 1. Show that the minimum cation-to-anion radius ratio for a coordination number of 6 is 0.414. [Hint: Use the NaCl crystal structure (Figure 12.2), and assume that anions and cations are just touching along cube edges and across face diagonals.] 2. On the basis of ionic charge and ionic radii given in Table 12.3, predict crystal structures for the following materials: (a) CsI (b) NiO (c) KI (d) NiS Justify your selections. 3. Calculate the density of FeO, given that it has the rock salt crystal structure. 4. Magnesium oxide has the rock salt crystal structure and a density of 3.58 g/cm3. (a) Determine the unit cell edge length. (b) How does this result compare with the edge length as determined from the radii in Table 12.3, assuming that the Mg 2+ and O 2- ions just touch each other along the edges? 5. A three-point bending test is performed on a glass specimen having a rectangular cross section of height d = 5 mm (0.2 in.) and width b = 10 mm (0.4 in.); the distance between support points is 45 mm (1.75 in.). (a) Compute the flexural strength if the load at fracture is 290 N (65 lbs). (b) The point of maximum deflection 4y occurs at the center of the specimen and is described by Ay = FL3 48EI (12.11) where E is the modulus of elasticity and I is the cross-sectional moment of inertia. Compute Ay at a load of 266 N (60 lbs). 6. An AX ceramic compound has the rock salt crystal structure. If the radii of the A and X ions are 0.137 and 0.241 nm, respectively, and the respective atomic weights are 22.7 and 91.4 g/mol, what is the density (in g/cm3) of this material? (A) 0.438 g/cm3 (B) 0.571 g/cm3 (C) 1.75 g/cm3 (D) 3.50 g/cm3 1