Callister - An introduction - 8th edition

120 • Chapter 4 / Imperfections in Solids
germanium–silicon alloy that contains 15 wt%
Ge and 85 wt% Si. The densities of pure
germanium and silicon are 5.32 and 2.33 g/cm 3 ,
respectively.
4.22 Sometimes it is desirable to determine the
weight percent of one element, C 1 , that will
produce a specified concentration in terms of
the number of atoms per cubic centimeter, N 1 ,
for an alloy composed of two types of atoms.
This computation is possible using the following
expression:
100
C 1
(4.19)
1 N Ar 2
r 2
N 1 A 1 r 1
where
N A Avogadro’s number
r 1 and r 2 densities of the two elements
A 1 and A 2 the atomic weights of the two
elements
Derive Equation 4.19 using Equation 4.2 and
expressions contained in Section 4.4.
4.23 Molybdenum forms a substitutional solid solution
with tungsten. Compute the weight percent
of molybdenum that must be added to
tungsten to yield an alloy that contains 1.0
10 22 Mo atoms per cubic centimeter. The densities
of pure Mo and W are 10.22 and 19.30
g/cm 3 , respectively.
4.24 Niobium forms a substitutional solid solution
with vanadium. Compute the weight percent
of niobium that must be added to vanadium
to yield an alloy that contains 1.55 10 22 Nb
atoms per cubic centimeter. The densities of
pure Nb and V are 8.57 and 6.10 g/cm 3 ,
respectively.
4.25 Silver and palladium both have the FCC crystal
structure, and Pd forms a substitutional
solid solution for all concentrations at room
temperature. Compute the unit cell edge
length for a 75 wt% Ag–25 wt% Pd alloy. The
room-temperature density of Pd is 12.02 g/cm 3 ,
and its atomic weight and atomic radius are
106.4 g/mol and 0.138 nm, respectively.
Dislocations—Linear Defects
4.26 Cite the relative Burgers vector–dislocation
line orientations for edge, screw, and mixed
dislocations.
Interfacial Defects
4.27 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 solution to Problem
3.54 at the end of Chapter 3.)
4.28 For a BCC single crystal, would you expect the
surface energy for a (100) plane to be greater
or less than that for a (110) plane? Why?
(Note: You may want to consult the solution
to Problem 3.55 at the end of Chapter 3.)
4.29 (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 smallangle
grain boundary is less than for a highangle
one. Why is this so?
4.30 (a) Briefly describe a twin and a twin
boundary.
(b) Cite the difference between mechanical
and annealing twins.
4.31 For each of the following stacking sequences
found in FCC metals, cite the type of planar
defect that exists:
(a) ...A B C A B C B A C B A ...
(b) ...A B C A B C B C A B C ...
Now, copy the stacking sequences and indicate
the position(s) of planar defect(s) with a
vertical dashed line.
Grain Size Determination
4.32 (a) Using the intercept method, determine the
average grain size, in millimeters, of the specimen
whose microstructure is shown in Figure
4.14(b); use at least seven straight-line
segments.
(b) Estimate the ASTM grain size number for
this material.
4.33 (a) Employing the intercept technique, determine
the average grain size for the steel specimen
whose microstructure is shown in Figure
9.25(a); use at least seven straight-line
segments.
(b) Estimate the ASTM grain size number for
this material.
4.34 For an ASTM grain size of 8,approximately how
many grains would there be per square inch