HW-CH5 - 158 'i ChapurS i Imperfections in Solids...

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Unformatted text preview: 158 'i ChapurS i Imperfections in Solids preference is dictated by the nature of the specimen as well as the structural element or defect to be examined. More recent scanning probe microscopic techniques have been developed that generate topographical maps representing the surface features and characteristics of the specimen. Examinations on the atomic and molecular levels are possible using these techniques. Grain Size Determination Grain size of polycrystalline materials is frequently determined using photomicro- graphic techniques Two methods are commonly employed: intercept and standard comparison charts. IMPORTANT TERMS CONCEPTS Alloy Atom percent Imperfection Interstitial solid solution Screw dislocation Self-interstitial Atomic vibration Microscopy Solid solution Boltzmann’s constant Microstructure Solute Burgers vector Mixed dislocation Solvent Composition Photomicrograph Stoichiometry Defect structure Point defect Substitutional solid solution Dislocation line Scanning electron microscope Transmission electron Edge dislocation (SEM) microscope (TEM) Electroneutrality Scanning probe microscope Vacancy Frenkel defect (5PM) Weight percent Grain size Schottky defect R E F E RE N C ES ASM Handbook, Vol. 9, Metaiiography and Micro- structures, ASM International, Materials Park. OH, 2004. Brandon. D. and W. D. Kaplan, Microstructural Characterization of Materials, Wiley. New York, 1999. Chiang, Y. M., D. P. Birnie, III, and W. D. Kingery, Physical Ceramics: Principles for Ceramic Science and Engineering. Wiley, New York, 1997. Clarke, A. R. and C. N. Eberhardt, Microscopy QUESTIONS AND PROBLEMS Techniques for Materials Science, CRC Press, Boca Raton, FL, 2002. Kingery, W. D., H. K. Bowen, and D. R. Uhlmann, Introduction to Ceramics, 2nd edition, Wiley, New York, 1976. Chapters 4 and 5. Van Bueren, H. (3., imperfections in Crystals, North- Holland, Amsterdam (Wiley-Interscience, New York), 1960. Vander Voort. G. F., Metaliograph y, Principles and Practice. ASM International, Materials Park, OH, 1984. Additional problems and questions for this chapter may be found on both Student and Instructor Companion Sites at Willeycom/coiiege/coiifiter. Point Defects in Metal: 5.1 Calculate the fraction of atom sites that are vacant for copper at its melting temperature of 1084"C(1357 K). Assume an energy for va— cancy formation of 0.90 eWatom. 5.2 Calculate the energy for vacancy formation in Silver, given that the equilibrium num- ber of vacancies at 800°C (1073 K) is 3.6 x 1023 m‘3. The atomic weight and density (at 800°C) for silver are, respectively, 107.9 g/mol and 9.5 glcma. Point Defects in Ceramic: 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 1.86 eV. 5.4 Using the data given below that relate to the formation of Schottky defects in some oxide ceramic (having the chemical formula MO), determine the following: (a) the energy for defect formation (in eV), (b) the equilibrium number of Schottky defects per cubic meter at 1000‘” C. and (c) the identity of the oxide (i.e., what is the metal M?) ICC} _ n!§!£flfl__ “Iain—"32 750 3.50 5.7 x 109 1000 3.45 '? 1500 ._ _. 354.0 _ __5_-3__ P”. Impurities in Solids 5.5 Below, atomic radius, crystal structure, elec- tronegalivity. and the most common valence are tabulated, for several elements; for those that are nonmetals, only atomic radii are indi- cated. Atomic Crystal Electro- Elemem __R_edi_us_tn_m_] 5:11.1ch negativity Valence Ni 0.1246 FCC 1.3 +2 C 0071 H 0.046 0 0.060 Ag 0.1445 FCC 1.9 +1 Al 0.1431 FCC 1.5 +3 Co 0.1253 HCP 1.8 +2 Cr 0.1249 BCC 1.6 +3 Fe 0.1241 BCC 1.8 +2 p1 0.1387 FCC 2.2 +2 211 0.1332 HCP 1.0 +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 incom- plete solubility (1:) An interstitial solid solution Questions and Problems 0 159 5.6 (a) Suppose that CaO is added as an impurity to Li20. 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 CaClz. If the 02' substitutes for C1“, what kind of vacancies would you expect to form? How many of these vacancies are created for every 02' added? Specification of Composition 5.? What is the composition, in atom percent, of an alloy that consists of 92.5 wt% Ag and 7.5 wt% Cu? 5.8 Calculate the composition, in weight percent, of an alloy that contains 105 kg of iron. 0.2 kg of carbon, and 1.0 kg of chromium. 5.9 What is the composition, in atom percent. of an alloy that contains 44.5 lbIn of silver, 83.? lbljll of gold, and 5.3 lbm of Cu? 5.10 Convert the atom percent compositiOn in Problem 5.9 to weight percent. 5.11 Determine the approximate density of a T1- 6Al-4V titanium alloy that has a composition of 90 wt% "11,6 wt% Al, and 4 wt% V. 5.12 Some hypothetical alloy is composed of 25 wt% of metal A and 75 wt% of metal B. If the densities of metals A and B are 6.17 and 8.00 g/cm3, respectively, whereas their respective atomic weights are 171.3 and 162.0 gfmol, de- termine whether the crystal structure for this alloy is simple cubic, face-centered cubic, or body-centered cubic. Assume a unit cell edge length of 0.332 nm. 5.13 Molybdenum forms a substitutional solid so- lution with tungsten. Compute the number of molybdenum atoms per cubic centimeter for a molybdenum-tungsten alloy that contains 16.4 wt% Mo and 83.6 wt% W. The densities of pure molybdenum and tungsten are 10.22 and 19.30 gr‘cm3, respectively. [Hint you may want to consult Problem W5.16 (Equation 5.21), which is found on the book’s Web site] 5.14 Sometimes it is desirable to be able to de— termine the weight percent of one element, C1, that will produce a specified concentra— tion in terms of the number of atoms per cubic 160 ' Chapter 5 l‘ Imperfections in Solids centimeter, N1, for an alloy composed of two types of atoms. This computation is possible using the following expression: 100 C1 = fiN— (5.22) 1 + A” — E NlAl .01 where NA = Avogadro’s number ,0] and p2 = densities of the two elements A] andA; = the atomic weights of the two el— cments Derive Equation 5.22 using Equation 5.2 and expressions contained in Section 5.6. 5.15 Germanium forms a substitutional solid solu- tion with silicon. Compute the weight percent of germanium that must be added to silicon to yield an alloy that contains 2.43 x 1021 Ge atoms per cubic centimeter. The densities of pure Ge and Si are 5.32 and 2.33 gfcm3, re- spectively. 5.16 Iron and vanadium both have the BCC crys- tal structure, and V forms a substitutional solid solution for concentrations up to approx- imately 20 wt% V at room temperature. Com- pute the unit cell edge length for a 90 wt% Fe—10 wt% V alloy. lnterfacial Defects 5.17 For an FCC single crystal, would you expect the surface energy for a (100) plane to be greater or less than that for a (111) plane? Why? (Note: You may want to consult the DESIGN PROBLEMS _ Specification of Composition 5.131 Aluminum—lithium alloys have been devel- oped by the aircraft industry to reduce the weight and improve the performance of its aircraft. A commercial aircraft skin material having a density of 2.47 gem3 is desired. Com- pute the concentration of Li (in wt%) that is required. solution to Problem W345, found on the book‘s Web site.) 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 50? 5.19 For each of the following stacking sequences found in FCC metals, cite the type of planar defect that exists: (a) A BCABCBA CBA (h) ABCABCBCABC... Now, copy the stacking sequences and indicate the position(s) of planar defect(s) with a ver- tical dashed line. ' Grain Size Detemtination 5.20 (a) Employing the intercept technique, de- termine the average grain size for the steel specimen whose rnicrostructure is shown in Figure 10.2903); use at least seven straight—line segments. (I3) Estimate the ASTM grain size number for this material. 5.21 For an ASTM grain size of 6. approximately how many grains would there be per square _ inch at (a) a magnification of 100, and 03) without any magnification? 5.22 Determine the ASTM grain size number if 25 grains per square inch are measured at a mag- nification of 75. 5.D2 Gallium arsenide (GaAs) and indium ar- senide (InAs) both have the zinc blende crys- tal structure and are soluble in each other at all concentrations. Determine the concentra- tion in weight percent of InAs that must be added to GaAs to yield a unit cell edge length of 0.5820 nm. The densities of GaAs and InAs are 5.316 and 5.668 g/cm3, respectively. ...
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HW-CH5 - 158 'i ChapurS i Imperfections in Solids...

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