280a
Introduction MatSE to Engineering Materials
1. (5.1) Calculate the fraction of atom sites that are vacant for copper at its melting temperature of 1084 C (1357K). Assume an energy for vacancy formation of 0.9eV. 2. (5.3) Calculate the fraction of lattice sites that are Schottky defects for cesium chloride at its melting temperature (645 C). Assume an energy for defect formation of 1.86eV. 3. (5.5) Below, atomic radius, crystal structure, electronegativity, and the most common valence are tabulated, for several elements; for those that are nonmetals, only atomic radii are given. Element Ni C H O Ag Al Co Cr Fe Pt Zn Radius [nm] 0.1246 0.071 0.046 0.060 0.1445 0.1431 0.1253 0.1249 0.1241 0.1387 0.1332 Structure FCC Electronegativity 1.8 Valence +2
FCC FCC HCP BCC BCC FCC HCP
1.9 1.5 1.8 1.6 1.8 2.2 1.6
+1 +3 +2 +3 +2 +2 +2
Which of these elements would you expect to form the following with nickel: (a) A substitutional solid solution having complete solubility. (b) A substitutional solid solution of incomplete solubility. (c) An interstitial solid solution. 4. (W5.6) For both FCC and BCC crystal structures, there are two different types of interstitial sites. In each case, one site is larger than the other, and is normally occupied by impurity toms. For FCC, this larger one is located at the center of each edge of the unit cell; it is termed an 11 octahedral interstitial site. On the other hand, with BCC the larger site type is found at 0 2 4 positions--that is, lying on {100} faces, and situated midway between two unit cell edges on this face, and one-quarter of the distance between the other two unit cell edges; it is termed a tetrahedral interstitial site. For both and FCC BCC crystal structures, compute the radius r of an impurity atom that will just fit into one of these sites in terms of the atomic radius R of the host atom. 5. (5.6) (a) Suppose that CaO is added as an impurity to Li2 O. If the Ca2+ substitutes for Li+ , what kind of vacancies would you expect to form? How many of these vacancies are created for every Ca2+ added? (b) Suppose that CaO is added as an impurity to CaCl2 . If the O2- substitutes for Cl- , what kind of vacancies would you expect to form? How many of these vacancies are created for every O2- added?
Homework 3
1
2009 February 25
MatSE 280a
Introduction to Engineering Materials
6. (W5.2) Would you expect Frenkel defects for anions to exist is ionic ceramics in relatively large concentrations? Why or why not? 7. (5.11) Determine the approximate density of a Ti-6Al-4V titanium alloy that has a composition of 90 wt% Ti, 6 wt% Al, and 4 wt% V. 8. (5.D2) Gallium arsenide (GaAs) and indium arsenide (InAs) both have the zincblende crystal structure and are soluble in each other at all concentrations. Determine the concentration in weight percent of InAs that must be added to GaAs to yield a unit cell edge length of 0.5820nm. The densities of GaAs and InAs are 5.316g/cm3 and 5.668g/cm3 , respectively. 9. (5.18) (a) For a given material, would you expect the surface energy to be greater than, the same as, or less than the grain boundary energy? Why? (b) The grain boundary energy of a small-angle grain boundary is less than for a high-angle one. Why is this so? 10. (W5.21) Cite the relative Burgers vector-dislocation line orientations for edge, screw, and mixed dislocations.
Homework 3
2
2009 February 25