Page 165 - Materials Science and Engineering An Introduction

Questions and Problems • 137

4.28 Molybdenum (Mo) forms a substitutional been added small and very controlled concentra-
solid solution with tungsten (W). Compute the tions of elements found in Groups IIIA and VA of
number of molybdenum atoms per cubic cen- the periodic table. For Si to which has been added
timeter for a molybdenum–tungsten alloy that 6.5 10 21 atoms per cubic meter of phosphorus,
contains 16.4 wt% Mo and 83.6 wt% W. The compute (a) the weight percent and (b) the atom
densities of pure molybdenum and tungsten are percent of P present.
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10.22 and 19.30 g/cm , respectively.
4.37 Iron and vanadium both have the BCC crystal
4.29 Niobium forms a substitutional solid solution with structure, and V forms a substitutional solid
vanadium. Compute the number of niobium atoms solution for concentrations up to approximately
per cubic centimeter for a niobium–vanadium alloy 20 wt% V at room temperature. Compute the
that contains 24 wt% Nb and 76 wt% V. The den- unit cell edge length for a 90 wt% Fe–10 wt%
sities of pure niobium and vanadium are 8.57 and V alloy.
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6.10 g/cm , respectively.
4.30 Consider an iron–carbon alloy that contains Dislocations—Linear Defects
0.2 wt% C, in which all the carbon atoms reside in 4.38 Cite the relative Burgers vector–dislocation line
tetrahedral interstitial sites. Compute the fraction orientations for edge, screw, and mixed disloca-
of these sites that are occupied by carbon atoms. tions.
4.31 For a BCC iron–carbon alloy that contains 0.1 wt%
C, calculate the fraction of unit cells that contain Interfacial Defects
carbon atoms. 4.39 For an FCC single crystal, would you expect the
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4.32 For Si to which has been added 1.0 10 at% of surface energy for a (100) plane to be greater or
aluminum (Al), calculate the number of Al atoms less than that for a (111) plane? Why? (Note: You
per cubic meter. may want to consult the solution to Problem 3.60
at the end of Chapter 3.)
4.33 Sometimes it is desirable to determine the weight
percent of one element, C 1 , that will produce a 4.40 For a BCC single crystal, would you expect the
specified concentration in terms of the number of surface energy for a (100) plane to be greater or
atoms per cubic centimeter, N 1 , for an alloy com- less than that for a (110) plane? Why? (Note: You
posed of two types of atoms. This computation is may want to consult the solution to Problem 3.61
possible using the following expression: at the end of Chapter 3.)
4.41 For a single crystal of some hypothetical
100
C 1 = (4.22) metal that has the simple cubic crystal structure
N A r 2 r 2 (Figure 3.3), would you expect the surface en-
1 + -
N 1 A 1 r 1 ergy for a (100) plane to be greater, equal to, or
less than a (110) plane. Why?
where N A is Avogadro’s number, r 1 and r 2 are the
densities of the two elements, and A 1 is the atomic 4.42 (a) For a given material, would you expect the
weight of element 1. surface energy to be greater than, the same as, or
Derive Equation 4.22 using Equation 4.2 and less than the grain boundary energy? Why?
expressions contained in Section 4.4. (b) The grain boundary energy of a small-angle
grain boundary is less than for a high-angle one.
4.34 Gold (Au) forms a substitutional solid solution
with silver (Ag). Compute the weight percent of Why is this so?
gold that must be added to silver to yield an al- 4.43 (a) Briefly describe a twin and a twin boundary.
loy that contains 5.5 10 21 Au atoms per cubic (b) Cite the difference between mechanical and
centimeter. The densities of pure Au and Ag are annealing twins.
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19.32 and 10.49 g/cm , respectively.
4.44 For each of the following stacking sequences
4.35 Germanium (Ge) forms a substitutional solid found in FCC metals, cite the type of planar de-
solution with silicon (Si). Compute the weight fect that exists:
percent of germanium that must be added to sili-
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con to yield an alloy that contains 2.43 10 Ge (a) . . . A B C A B C B A C B A . . .
atoms per cubic centimeter. The densities of pure (b) . . . A B C A B C B C A B C . . .
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Ge and Si are 5.32 and 2.33 g/cm , respectively.
Copy the stacking sequences and indicate the
4.36 Electronic devices found in integrated circuits are position(s) of planar defect(s) with a vertical
composed of very high purity silicon to which has dashed line.