Page 163 - Materials Science and Engineering An Introduction

Questions and Problems • 135

Important Terms and Concepts

alloy imperfection screw dislocation
atomic vibration interstitial solid solution self-interstitial
atom percent microscopy solid solution
Boltzmann’s constant microstructure solute
Burgers vector mixed dislocation solvent
composition photomicrograph substitutional solid solution
dislocation line point defect transmission electron microscope (TEM)
edge dislocation scanning electron microscope (SEM) vacancy
grain size scanning probe microscope (SPM) weight percent

REFERENCES

ASM Handbook, Vol. 9, Metallography and Microstructures, Tilley, R. J. D., Defects in Solids, Wiley-Interscience, Hoboken,
ASM International, Materials Park, OH, 2004. NJ, 2008.
Brandon, D., and W. D. Kaplan, Microstructural Characterization Van Bueren, H. G., Imperfections in Crystals, North-Holland,
of Materials, 2nd edition, Wiley, Hoboken, NJ, 2008. Amsterdam, 1960.
Clarke, A. R., and C. N. Eberhardt, Microscopy Techniques Vander Voort, G. F., Metallography, Principles and Practice,
for Materials Science, CRC Press, Boca Raton, FL, 2002. ASM International, Materials Park, OH, 1999.
Kelly, A., G. W. Groves, and P. Kidd, Crystallography and
Crystal Defects, Wiley, Hoboken, NJ, 2000.

QUESTIONS AND PROBLEMS
Problem available (at instructor’s discretion) in WileyPLUS
Vacancies and Self-Interstitials Impurities in Solids
4.1 The equilibrium fraction of lattice sites that are va- 4.6 Atomic radius, crystal structure, electronegativity,
6
cant in silver (Ag) at 700 C is 2 10 . Calculate and the most common valence are given in the
the number of vacancies (per meter cubed) at following table for several elements; for those that
3
700 C. Assume a density of 10.35 g/cm for Ag. are nonmetals, only atomic radii are indicated.
4.2 For some hypothetical metal, the equilibrium Atomic
25
3
number of vacancies at 900 C is 2.3 10 m . Radius Crystal Electro-
If the density and atomic weight of this metal Element (nm) Structure negativity Valence
3
are 7.40 g/cm and 85.5 g/mol, respectively, cal- Ni 0.1246 FCC 1.8 2
culate the fraction of vacancies for this metal at
900 C. C 0.071
4.3 (a) Calculate the fraction of atom sites that are H 0.046
vacant for copper (Cu) at its melting temperature O 0.060
of 1084 C (1357 K). Assume an energy for va- Ag 0.1445 FCC 1.9 1
cancy formation of 0.90 eV/atom.
Al 0.1431 FCC 1.5 3
(b) Repeat this calculation at room temperature Co 0.1253 HCP 1.8 2
(298 K).
Cr 0.1249 BCC 1.6 3
(c) What is the ratio of N y /N (1357 K) and N y /N
(298 K)? Fe 0.1241 BCC 1.8 2
Pt 0.1387 FCC 2.2 2
4.4 Calculate the number of vacancies per cubic me-
ter in gold (Au) at 900 C. The energy for vacancy Zn 0.1332 HCP 1.6 2
formation is 0.98 eV/atom. Furthermore, the den- Which of these elements would you expect to
3
sity and atomic weight for Au are 18.63 g/cm (at form the following with nickel:
900 C) and 196.9 g/mol, respectively.
(a) a substitutional solid solution having com-
4.5 Calculate the energy for vacancy formation in plete solubility
nickel (Ni), given that the equilibrium number of
22
3
vacancies at 850 C (1123 K) is 4.7 10 m . The (b) a substitutional solid solution of incomplete
atomic weight and density (at 850 C) for Ni are, solubility
3
respectively, 58.69 g/mol and 8.80 g/cm . (c) an interstitial solid solution