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 cu edges and across face diagonals.] Ra + Rc = (2Ra/(sqrt2)) Rc/Ra = (2/(sqrt2)-1) = 0.414 2. On the basis of ionic charge and ionic radii given in Table 12.3, predict crystal structures for the following materials: (a) CsI 0.170/.220 = 0.773 co-ordination number is 8 Cesium chloride structure (b) NiO 0.069/0.140 = 0.493 Co-ordination number is 6 Sodium chloride structure (c) KI 0.138/0.220 = 0.627 Co-ordination number is 6 sodium chloride structure (d) NiS 0.069/0.184 = 0.375 Co-ordination number is 4 Zinc blende structure 3. Calculate the density of FeO, given that it has the rock salt crystal structure. a = 2*(Rf +Ro) = 2*(0.077+0.140) = 4.34*10^-8 cm V= a^3 = (4.34*10^-8)^3 = 8.17*10^-23 4*71.85/(8.17*10^-23*6.022*10^23 = 5.85 g/cm^3 4. Magnesium oxide has the rock salt crystal structure and a density of 3.58 g/cm3. (a) Determine the unit cell edge length. a = ((4*40)/(3.58*6.022*10^23))^1/3 = 0.402 nm (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? a = (2*0.140+2*0.072) = 0.424nm 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 lbf). (3*290*(45*10^-3))/((2*10*10^-3)(5*10^-3)^2) = 78.3 MPa = 11,356.45Psi (b) The point of maximum deflection 4y occurs at the center of the specimen and is described by Ay = F13 (12.11) 48EI where E is the modulus of elasticity and I is the cross-sectional moment of inertia. Compute 4y a a load of 266 N (60 lbf). Ay = (266)(5*10^-3)^3/12 = 7.026*10^-5 = 0.07026 mm 4y = 0.002766 in
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