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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
Selfinterstitial 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 (WileyInterscience,
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
6Al4V 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, facecentered cubic, or
bodycentered 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
molybdenumtungsten 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
highangle 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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