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ReserveQuestionsAndProblems

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Reserve Questions and Problems
CHAPTER 1 INTRODUCTION
Reserve Problem 01a (question pool)
Materials Science and Engineering is the study of
material behavior & performance and how this is
simultaneously related to structure, properties, and
processing. Which of the following is the best example
of a material property?
(a) Density
(b) Annealing
(c) Forging
(d) Single-crystal
(e) Crystalline
Reserve Problem 02a (question pool)
Materials Science and Engineering is the study of
material behavior & performance and how this is
simultaneously related to structure, properties, and
processing. Which of the following is the best example
of material processing?
(a) Extrusion
(b) Crystalline
(c) Amorphous
(d) Glassy
(e) Elastic Modulus
Reserve Problem 03a (question pool)
simultaneously related to structure, properties, and
processing. Which of the following is the best example
of material structure?
(a) Single-phase
(b) Elastic Modulus
(c) Sintering
(d) Magnetic Permeability
(e) Brittle
Reserve Problem 04a (question pool)
Which class of material is generally associated with
the highest density values at room temperature?
(a) Composites
(b) Ceramics
(c) Metals
(d) Polymers
Reserve Problem 05a (question pool)
By how many orders of magnitude (powers of ten,
approximately) does density vary for metals?
(a) 0.13
(b) 1.3
(c) 13
(d) 130
Materials Science and Engineering is the study of
material behavior & performance and how this is
CHAPTER 2 ATOMIC STRUCTURE AND INTERATOMIC BONDING
Reserve Question 01: Atomic mass
Reserve Question 02: Atomic nucleus
The atomic mass of an atom may be expressed as the
sum of the masses of
• Electrons
• Neutrons
• Protons
Choose all that apply.
The nucleus of an atom contains
• Electrons
• Neutrons
• Protons
Choose all that apply.
• R-1
R-2 • Reserve Questions and Problems
Reserve Question 03: Atomic number
The atomic number of an electrically neutral atom is
equal to the number of:
• protons
• electrons
• neutrons
Choose all that apply.
Reserve Problem 04
Hafnium has six naturally occurring isotopes: 0.16%
of 174Hf, with an atomic weight of 173.940 amu;
5.26% of 176Hf, with an atomic weight of 175.941 amu;
18.60% of 177Hf, with an atomic weight of 176.943
amu; 27.28% of 178Hf, with an atomic weight of
177.944 amu; 13.62% of 179Hf, with an atomic weight
of 178.946 amu; and 35.08% of 180Hf, with an atomic
weight of 179.947 amu. Calculate the average atomic
weight of Hf. Give your answer to three decimal
places.
Reserve Problem 05
Bromium has two naturally occurring isotopes: 79Br,
with an atomic weight of 78.918 amu, and 81Br, with
an atomic weight of 80.916 amu. If the average atomic
weight for Br is 79.903 amu, calculate the fraction-ofoccurrences of these two isotopes. Give your answer
to three decimal places.
Fraction-of-occurrence for 79Br: ______
Fraction-of-occurrence for 81Br: ______
Reserve Problem 06: Electron configuration
An element that has the electron configuration
1s22s22p6 has how many electrons? Enter numeric
values only.
Reserve Problem 07: The four electron subshells
M, K, L, N
Which subshells are found in each of the following
shells?
(a) Electron subshells—M shell
• s
• p
• d
• f
(b) Electron subshells—K shell
• s
• p
• d
• f
(c) Electron subshells—L shell
• s
• p
• d
• f
(d) Electron subshells—N shell
• s
• p
• d
• f
Reserve Problem 08: The number of electrons in
subshells M, K, L, N
What is the maximum number of electrons that each
of the following shells can contain?
(a) M shell ______ electrons
(b) K shell ______ electrons
(c) L shell ______ electrons
(d) N shell ______ electrons
Reserve Question 09: The electrons that occupy
the outermost…
The electrons that occupy the outermost filled shell
are called ______ electrons.
Reserve Question 10: When all the electrons in an
atom occupy…
When all the electrons in an atom occupy the lowest
possible energy states, the atom is said to be in its:
• ground state
• ionized state
• cold state
• regular state
Reserve Problem 11
How many p electrons at the outermost orbital do the
Group VIIA elements have?
Reserve Problem 12
To what group in the periodic table would an element
with atomic number 119 belong?
• Group 0 (or 18)
• Group IA (or 1)
• Group IIA (or 2)
• Group VIIA (or 17)
Reserve Problem 13
Ideally speaking, bonds tend to form between two
particles such that they are separated by a distance
Reserve Questions and Problems • R-3
where ______ net force is exerted on them, and their
overall energy is ______.
(a) a positive, maximized
(b) a negative, maximized
(c) a positive, minimized
(d) a negative, minimized
(e) zero, maximized
(f) zero, minimized
Reserve Problem 17
______ bonds are the only primary bonds that are
directionally dependent.
(a) Covalent
(c) Ionic
(b) Metallic
(d) Van der Waals
Reserve Problem 18
Calculate the force of attraction (in N) between a
cation with a valence of +2 and an anion with a valence of −3, the centers of which are separated by a
distance of 8.6 nm.
______ bonds are responsible for binding atoms
together within a molecule of propane, whereas ______
bonds bind separate propane molecules together in a
condensed state (liquid or crystal).
(a) Covalent, Ionic
(b) Ionic, Covalent
(c) Covalent, Metallic
(d) Metallic, Covalent
(e) Covalent, Van der Waals
(f) Van der Waals, Covalent
(g) Ionic, Van der Waals
(h) Van der Waals, Ionic
Reserve Problem 16
Reserve Problem 19
______ bonding is similar to ionic bonding, except
there are no high-electronegativity atoms present to
accept any electrons that the present atoms are willing to donate.
(a) Ionic
(c) Metallic
(b) Covalent
(d) Hydrogen
Materials whose constituent particles are bound by
which type of bond are generally expected to have the
lowest melting temperatures?
(a) Covalent
(d) Van der Waals
(b) Metallic
(e) Hydrogen
(c) Ionic
Reserve Problem 14: Attraction energy
Calculate the energy of attraction between a cation
with a valence of +2 and an anion with a valence of
−2, the centers of which are separated by a distance
of 3.7 nm.
Reserve Problem 15: Attraction force
Reserve Problem 20: Ionic character
Using the figure below, calculate the percent ionic character of the interatomic bonds for the following materials:
(a) CaCl2
(b) CsBr
0
IA
1
2
H
He
2.1
3
IIA
IIIA
IVA
VA
VIA
VIIA
4
5
6
7
8
9
–
10
Li
Be
B
C
N
O
F
Ne
1.0
11
1.5
12
2.0
13
2.5
14
3.0
15
3.5
16
4.0
17
–
18
Na
Mg
0.9
19
1.2
20
VIII
IIIB
IVB
VB
VIB
VIIB
21
22
23
24
25
26
27
28
IB
IIB
29
30
Al
Si
P
S
Cl
Ar
1.5
31
1.8
32
2.1
33
2.5
34
3.0
35
–
36
Kr
K
Ca
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Ge
As
Se
Br
0.8
1.0
1.3
1.5
1.6
1.6
1.5
1.8
1.8
1.8
1.9
1.6
1.6
1.8
2.0
2.4
2.8
–
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
Rb
Sr
Y
Zr
Nb
Mo
Tc
Ru
Rh
Pd
Ag
Cd
In
Sn
Sb
Te
I
Xe
0.8
55
1.0
56
1.2
57–71
1.4
72
1.6
73
1.8
74
1.9
75
2.2
76
2.2
77
2.2
78
1.9
79
1.7
80
1.7
81
1.8
82
1.9
83
2.1
84
2.5
85
–
86
Cs
Ba
La–Lu
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
Tl
Pb
Bi
Po
At
Rn
0.7
87
0.9
88
1.1–1.2
89–102
1.3
1.5
1.7
1.9
2.2
2.2
2.2
2.4
1.9
1.8
1.8
1.9
2.0
2.2
–
Fr
Ra
Ac–No
0.7
0.9
1.1–1.7
R-4 • Reserve Questions and Problems
Reserve Problem 21
(a) Calculate %IC of the interatomic bonds for
the intermetallic compound TiAl3.
(b) On the basis of this result, what type of interatomic bonding would you expect to be found
in TiAl3?
• Van der Waals
• metallic
• ionic
• covalent
CHAPTER 3 STRUCTURES OF METALS AND CERAMICS
Reserve Problem 01a (question pool)
Reserve Problem 02a (question pool)
Which structure is most consistent with a polycrystalline structure?
Which structure is most consistent with an amorphous
structure?
(a)
(a)
(b)
(b)
(c)
(c)
(d)
(d)
Reserve Questions and Problems • R-5
Reserve Problem 03
Reserve Problem 07a (question pool)
Which of the following microstructures is expected to
be most similar to a single crystal in terms of structure
and properties? Assume all of the options offer the
same volumes and only consider grain boundaries as a
crystalline defect for this question.
(a) Textured polycrystal with about 10,000 grains
Which of the following partial lattices does not exhibit
6-fold symmetry?
(a)
(b) Random polycrystal with about 1,000,000
grains
(c) Random polycrystal with about 1,000,000,000
grains
(d) Amorphous
Reserve Problem 04a (question pool)
Which of the following is the primitive unit cell for the
lattice that is depicted?
(b)
Reserve Problem 05a (question pool)
Which of the following candidate unit cells is invalid?
(c)
(d)
Reserve Problem 06a (question pool)
Which of the following unit cells exhibits the highest
symmetry?
R-6 • Reserve Questions and Problems
Reserve Problem 08
Reserve Problem 09c-1 (question pool)
Using atomic weight, crystal structure, and atomic
radius data tabulated inside the front cover, compute
the theoretical densities of lead, chromium, copper,
and cobalt, and then compare these values with the
measured densities listed in this same table. The c/a
ratio for cobalt is 1.623.
Which of the following options is consistent with the
unit cell plane depicted below?
Reserve Problem 09a-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
Reserve Problem 09d-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
Reserve Problem 09b-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
(a)
(b)
(c)
(d)
(e)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
(f)
(g)
(h)
(i)
FCC {110}
SC {111}
BCC {111}
FCC {111}
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
Reserve Questions and Problems • R-7
Reserve Problem 10a-1 (question pool)
Reserve Problem 10c-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
Which of the following options is consistent with the
unit cell plane depicted below?
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
Reserve Problem 10b-1 (question pool)
Reserve Problem 10d-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
Which of the following options is consistent with the
unit cell plane depicted below?
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
R-8 • Reserve Questions and Problems
Reserve Problem 11a-1 (question pool)
Reserve Problem 11c-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
Which of the following options is consistent with the
unit cell plane depicted below?
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
Reserve Problem 11b-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
Reserve Problem 11d-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
Reserve Questions and Problems • R-9
Reserve Problem 12a-1 (question pool)
Reserve Problem 12c-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
Which of the following options is consistent with the
unit cell plane depicted below?
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
Reserve Problem 12b-1 (question pool)
Reserve Problem 12d-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
Which of the following options is consistent with the
unit cell plane depicted below?
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
R-10 • Reserve Questions and Problems
Reserve Problem 13a-1 (question pool)
Reserve Problem 13c-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
Which of the following options is consistent with the
unit cell plane depicted below?
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
Reserve Problem 13b-1 (question pool)
Reserve Problem 13d-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
Which of the following options is consistent with the
unit cell plane depicted below?
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
Reserve Questions and Problems • R-11
Reserve Problem 14a-1 (question pool)
Reserve Problem 14c-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
Which of the following options is consistent with the
unit cell plane depicted below?
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
Reserve Problem 14b-1 (question pool)
Reserve Problem 14d-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
Which of the following options is consistent with the
unit cell plane depicted below?
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
SC {100}
BCC {100}
FCC {100}
SC {110}
BCC {110}
FCC {110}
SC {111}
BCC {111}
FCC {111}
R-12 • Reserve Questions and Problems
Reserve Problem 15a-1 (question pool)
Reserve Problem 15d-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
Which of the following options is consistent with the
unit cell plane depicted below?
(a) SC {100}
(b) SC {110}
(c) SC {111}
(d) FCC {100}
(e) FCC {110}
(f) FCC {111}
Reserve Problem 15b-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
(a)
(b)
(c)
(d)
(e)
(f)
SC {100}
SC {110}
SC {111}
FCC {100}
FCC {110}
FCC {111}
Reserve Problem 16a-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
(a) SC {100}
(b) SC {110}
(c) SC {111}
(d) FCC {100}
(e) FCC {110}
(f) FCC {111}
Reserve Problem 15c-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
(a)
(b)
(c)
(d)
(e)
(f)
(a) SC {100}
(b) SC {110}
(c) SC {111}
(d) FCC {100}
(e) FCC {110}
(f) FCC {111}
FCC {100}
FCC {110}
FCC {111}
SC {100}
SC {110}
SC {111}
Reserve Questions and Problems • R-13
Reserve Problem 16b-1 (question pool)
Reserve Problem 16d-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
Which of the following options is consistent with the
unit cell plane depicted below?
(a)
(b)
(c)
(d)
(e)
(f)
FCC {100}
FCC {110}
FCC {111}
SC {100}
SC {110}
SC {111}
Reserve Problem 16c-1 (question pool)
Which of the following options is consistent with the
unit cell plane depicted below?
(a) FCC {100}
(b) FCC {110}
(c) FCC {111}
(d) SC {100}
(e) SC {110}
(f) SC {111}
Reserve Problem 17a (question pool)
Certain crystal structures are sometimes similar to
other crystal structures in a variety of ways. This problem demonstrates one of the similarities that exists
between two of the cubic crystal structures discussed
in Chapter 3. Specifically, a family of planes in one
of these crystal structures is equivalent to a family of
planes in the other crystal structure.
For now, we are just considering how equal-sized
spheres, but you may also consider this as atoms of the
same element packing together to form two crystals,
each of which exhibits one of these different crystal
structures.
The figure below depicts a plane of atoms of radius
R in some crystal. The plane intersects the atoms
through their centers. Therefore, we do not see atoms
above and below this plane. We just see the circular
cross-sections of the atoms that lie within the plane.
(a)
(b)
(c)
(d)
(e)
(f)
FCC {100}
FCC {110}
FCC {111}
SC {100}
SC {110}
SC {111}
R-14 • Reserve Questions and Problems
If we consider only simple cubic (SC), body-centered
cubic (BCC), and face-centered cubic (FCC) crystal
structures as options, and we have no more information to rely on, what are the two possible identities for
the plane shown above?
Select all that apply.
(a) SC {100}
(b) BCC {100}
(c) FCC {100}
(d) SC {110}
(e) BCC {110}
(f) FCC {110}
(g) SC {111}
(h) BCC {111}
(i) FCC {111}
Reserve Problem 22: BCC unit cell volume
If the atomic radius of a metal that has the bodycentered cubic crystal structure is 0.181 nm, calculate
the volume of its unit cell.
Reserve Problem 23: FCC unit cell volume
Reserve Problem 18: Atomic radius–simple cubic
For a metal that has the simple cubic crystal structure,
calculate the atomic radius if the metal has a density of
2.05 g/cm3 and an atomic weight of 77.84 g/mol.
Reserve Problem 19: Cubic unit cell
Some metal is known to have a cubic unit cell with an
edge length of 0.437 nm. In addition, it has a density
of 4.37 g/cm3 and an atomic weight of 54.85 g/mol.
Indicate the letter of the metal listed in the following
table that has these characteristics.
Metal
Crystal Structure
Atomic Radius (nm)
A
B
C
D
BCC
FCC
FCC
HCP
0.219
0.309
0.155
0.125
Reserve Problem 20: Crystal Lengths III
In terms of the atomic radius, R, determine the distance between the centers of adjacent atoms for the
BCC crystal structure along the [110] direction.
4*R*
From the list below select all possible sets of indices
for this plane.
(a) (001)
(b) (11–1)
(c) (111)
(d) (–1–1–1)
(e) (101)
(f) (100)
√2
√3
Reserve Question 21: Miller indices III
Below is shown the atomic packing of a plane for the
simple cubic crystal structure; atoms drawn to full size
are represented by the circles.
If the atomic radius of a metal that has the facecentered cubic crystal structure is 0.123 nm, calculate
the volume of its unit cell.
Reserve Problem 24: Hexagonal close-packed
structure
For the hexagonal close-packed crystal structure:
(a) How many atoms are associated with the unit
cell?
(b) What is the coordination number?
(c) What is the atomic packing factor?
Reserve Problem 25: Orthorhombic unit cell
A hypothetical metal has an orthorhombic unit cell
for which the a, b, and c lattice parameters are 0.472,
0.732, and 0.826 nm, respectively.
(a) If there are 8 atoms per unit cell and the
atomic packing factor is 0.549, then determine
the atomic radius.
(b) If the density is 6.04 g/cm3, then calculate the
metal’s atomic weight.
Reserve Problem 26: Rhodium structure
Rhodium has an atomic radius of 0.1345 nm, a density
of 12.41 g/cm3 and an atomic weight of 102.91 g/mol.
What is rhodium’s crystal structure?
(a) Simple cubic
(b) BCC
(c) FCC
Reserve Problem 27: Unit cell length
A hypothetical metal has a cubic unit cell, a density of
6.79 g/cm3, a coordination number of 6, and an atomic
weight of 78.57 g/mol. Calculate the unit cell edge
length for this material.
Reserve Questions and Problems • R-15
Reserve Problem 28
Reserve Problem 34a (question pool)
Iron has a BCC crystal structure, an atomic radius
of 0.124 nm, and an atomic weight of 55.85 g/mol.
Compute and compare its theoretical density with the
experimental value found inside the front cover of the
book.
Consider the ideal barium titanate (BaTiO3) structure. What is the coordination number of the Ti4+ ion
in terms of surrounding O2– ions?
(a) 1
(e) 5
(b) 2
(f) 6
(c) 3
(g) 7
(d) 4
(h) 8
Reserve Problem 29
Niobium (Nb) has a BCC crystal structure, an atomic
radius of 0.143 nm and an atomic weight of 92.91 g/mol.
Calculate the theoretical density for Nb.
Reserve Problem 30
Rhenium has an HCP crystal structure, an atomic
radius of 0.137 nm, and a c/a ratio of 1.615. Compute
the volume of the unit cell for Re.
Reserve Problem 31
The unit cell for MgFe2O4 (MgO-Fe2O3) has cubic
symmetry with a unit cell edge length of 0.836 nm. If
the density of this material is 4.52 g/cm3, compute its
atomic packing factor. For this computation, you will
need to use ionic radii listed in Table 3.4.
Reserve Problem 35
Consider the ideal barium titanate (BaTiO3) structure. What is the coordination number of the Ba2+ ion
in terms of surrounding Ti4+ ions?
(a) 4
(d) 10
(b) 6
(e) 12
(c) 8
Reserve Problem 36
Which of the following options correctly depicts a
{110} plane from a diamond cubic unit cell?
(a)
Reserve Problem 32
For each statement below, choose the bonding type
that best completes each phrase.
(a) The crystal structures of ______ ceramics are
constrained by bond angles associated with
the locations of shared electrons within the
material.
(b) The coordination number of ______ ceramics
are constrained by the relative sizes of the
compound’s component species.
(c) The crystal structures of ______ ceramics are
constrained by the relative charges of the
compound’s component species.
(d) The crystal structures of ______ ceramics
are constrained by ratio of the compound’s
charged component species such that the
structure maintains charge neutrality.
(b)
Reserve Problem 33
Consider the fluorite (CaF2) crystal structure. The
coordination number of Ca2+ ions is __[a]__, and the
coordination number of F– ions is __[b]__.
(c)
R-16 • Reserve Questions and Problems
(d)
(e)
Reserve Problem 37
Compute the PPF of {110} planes for the diamond
cubic crystal structure.
(a) 0.29
(b) 0.34
(c) 0.42
(d) 0.56
(e) 0.68
(f) 0.71
(g) 0.74
(h) 0.82
Reserve Problem 38
Compute the planar density of atoms, in atoms per
square centimeter, on a {110} plane of a defect-free
diamond cubic crystal, whose atoms have a radius of
[R] nanometers.
Reserve Problem 39
(f)
Compute the PPF of {100} planes for the diamond cubic
crystal structure.
(a) 0.29
(b) 0.34
(c) 0.42
(d) 0.56
(e) 0.68
(f) 0.71
(g) 0.74
(h) 0.82
(g)
Reserve Problem 40
Compute the planar density of atoms, in atoms per
square centimeter, on a {100} plane of a defect-free
diamond cubic crystal, whose atoms have a radius of
[R] nanometers.
Reserve Question 41: Lattice parameters I
Which crystal system(s) listed below has (have) the
following relationship for the unit cell edge lengths?
(h)
a=b=c
(a) Cubic
(b) Hexagonal
(c) Tetragonal
(d) Rhombohedral
(e) Orthorhombic
(f) Monoclinic
(g) Triclinic
Reserve Questions and Problems • R-17
Reserve Question 42: Lattice parameters II
Reserve Question 46: Unit cell geometries III
Which crystal system(s) listed below has (have) the
following relationship for the unit cell edge lengths?
Which crystal system(s) listed below has (have) the
following interaxial angle relationship?
a=b≠c
(a) Cubic
(b) Hexagonal
(c) Tetragonal
(d) Rhombohedral
(e) Orthorhombic
(f) Monoclinic
(g) Triclinic
α = β = 90°, γ = 120°
(a) Cubic
(b) Hexagonal
(c) Tetragonal
(d) Rhombohedral
(e) Orthorhombic
(f) Monoclinic
(g) Triclinic
Reserve Question 43: Lattice parameters III
Which crystal system(s) listed below has (have) the
following relationship for the unit cell edge lengths?
a≠b≠c
(a) Cubic
(b) Hexagonal
(c) Tetragonal
(d) Rhombohedral
(e) Orthorhombic
(f) Monoclinic
(g) Triclinic
Reserve Question 47: Unit cell geometries IV
Which crystal system(s) listed below has (have) the
following interaxial angle relationship?
α = β = γ ≠ 90°
(a) Cubic
(b) Hexagonal
(c) Tetragonal
(d) Rhombohedral
(e) Orthorhombic
(f) Monoclinic
(g) Triclinic
Reserve Question 44: Unit cell geometries I
Which crystal system(s) listed below has (have) the
following interaxial angle relationship?
α ≠ β ≠ γ ≠ 90°
(a) Cubic
(b) Hexagonal
(c) Tetragonal
(d) Rhombohedral
(e) Orthorhombic
(f) Monoclinic
(g) Triclinic
Reserve Question 45: Unit cell geometries II
Which crystal system(s) listed below has (have) the
following interaxial angle relationship?
α = β = γ = 90°
(a) Cubic
(b) Hexagonal
(c) Tetragonal
(d) Rhombohedral
(e) Orthorhombic
(f) Monoclinic
(g) Triclinic
Reserve Question 48: Unit cell geometries V
Which crystal system(s) listed below has (have) the
following interaxial angle relationship?
α = γ = 90° ≠ β
(a) Cubic
(b) Hexagonal
(c) Tetragonal
(d) Rhombohedral
(e) Orthorhombic
(f) Monoclinic
(g) Triclinic
Reserve Problem 49
Sketch a tetragonal unit cell, and within that cell indi1
1
1 1 3
cate locations of the 2 1 2 and 4 2 4 point indices.
Reserve Problem 50
Sketch an orthorhombic unit cell, and within that cell
1
1 1 1
indicate locations of the 1 2 0 and 4 3 4 point indices.
R-18 • Reserve Questions and Problems
Reserve Problem 51: Crystal lengths II
Reserve Question 55: Cubic direction indices 03
In terms of the atomic radius, R, determine the distance between the centers of adjacent atoms for the
BCC crystal structure along the [111] direction.
What are the indices for the direction represented by
the vector that has been drawn within a unit cell?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
2*R
Reserve Problem 52: SC indices
z
For the simple cubic crystal structure, in terms of the
atomic radius, R, determine the distance between the
centers of adjacent atoms along the [120] direction.
2 * R * √5
c
Reserve Question 53: Cubic direction indices 01
What are the indices for the direction represented by
the vector that has been drawn within a unit cell?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
y
a
b
x
z
(a) [111]
c
(b) [1–11]
y
a
(c) [11–1]
(d) [–111]
b
Reserve Question 56: Cubic direction indices 04
x
What are the indices for the direction represented by
the vector that has been drawn within a unit cell?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
(a) [–102]
(b) [120]
(c) [121]
(d) 102
z
Reserve Question 54: Cubic direction indices 02
What are the indices for the direction represented by
the vector that has been drawn within a unit cell?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
c
z
a
b
x
c
(a) [0–11]
a
b
x
(a) [–002]
(b) [120]
(c) [101]
(d) [012]
y
(b) [1–11]
(c) [01–1]
(d) [–111]
y
Reserve Questions and Problems • R-19
Reserve Question 57: Cubic direction indices 05
What are the indices for the direction represented by
the vector that has been drawn within a unit cell?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
z
z
c
y
a
c
b
x
1
2
a
y
b
x
(a) [–0–2–1]
(c) [–0–1–1]
(b) [–1–1–1]
(d) [–0–0–2]
Reserve Question 60: Cubic direction indices 08
What are the indices for the direction represented by
the vector that has been drawn within a unit cell?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
(a) [210]
(b) [200]
(c) [–210]
(d) [2–11]
z
Reserve Question 58: Cubic direction indices 06
1, 1
2 2
What are the indices for the direction represented by
the vector that has been drawn within a unit cell?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
c
y
a
z
b
x
Reserve Question 61: Cubic direction indices 09
c
y
a
What are the indices for the direction represented by
the vector that has been drawn within a unit cell?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
z
b
x
(a)
(b)
(c)
(d)
1
3
[0–21]
[001]
[201]
[021]
1
2
a
Reserve Question 59: Cubic direction indices 07
What are the indices for the direction represented by
the vector that has been drawn within a unit cell?
c
b
x
(a) [–321]
(c) [–431]
(b) [–420]
(d) [–430]
y
R-20 • Reserve Questions and Problems
Reserve Question 62: Cubic direction indices 10
Reserve Problem 64
What are the indices for the direction represented by
the vector that has been drawn within a unit cell?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
Select the orthorhombic unit cell illustrating a [12– 1]
direction. Note: all angles are 90°.
z
(a)
z
c
O
c
1, 1
2 2
2
3
A
a
B
b
x
y
a
y
b
C
x
z
(b)
(a) [1–5–3]
O
(b) [1–4–2]
B
A
(c) [1–6–3]
c
(d) [1–6–4]
y
Reserve Question 63: Cubic direction indices 11
What are the indices for the direction represented by
the vector that has been drawn within a unit cell?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
C
a
b
x
z
(c)
z
c
O
c
1, 1
2 2
2, 2
3 3
a
a
b
B
x
y
C
b
x
y
A
z
(d)
(a) [–1– 43]
C
(b) [1–42]
c
(c) [0–43]
O
(d) [0–41]
B
A
b
x
y
a
Reserve Questions and Problems • R-21
Reserve Problem 65
Reserve Problem 67
Select a monoclinic unit cell illustrating a [0–11] direction.
z
(a)
Determine the indices for the directions shown in the
following cubic unit cell:
P
+z
c
O

y
2
3


1
2
1
3
A
b
1
3
C
a
2
3
x
B
D
z
(b)
2
3
O
c
y


+y
1, 1
2 2
1
3
+x
P

Reserve Problem 68
b
(a) What are the direction indices for a vector
1
1
1
that passes from point 10 3 to point 2 1 2 in a
tetragonal unit cell?
(b) Repeat part (a) for a rhombohedral unit cell.
a
x
z
(c)
Reserve Problem 69
P
For tetragonal crystals, cite the indices of directions
that are equivalent to each of the following directions:
(a) [001]
(b) [110]
(c) [010]
c

O


y
a
b
x
Reserve Problem 70
Reserve Problem 66
What are the indices for the directions indicated by
the two vectors in the sketch below?
+z
Direction 1
0.4 nm
+y
0.3 nm
+x
0.5 nm
Direction 2
Convert the [100] and [111] directions into the fourindex Miller–Bravais scheme for hexagonal unit cells.
R-22 • Reserve Questions and Problems
Reserve Problem 71
Reserve Problem 72
Determine indices for the directions shown in the following hexagonal unit cells.
1. Select the orthorhombic unit cell with a (210)
plane identified:
z
(a)
z
(a)
a2
c
a3
a1
z
(b)
y
a
b
x
a2
z
(b)
a3
a1
c
z
(c)
y
a
a2
x
b
a3
a1
z
(c)
z
(d)
c
a2
y
a3
a1
a
b
x
Reserve Questions and Problems • R-23
2. Select the monoclinic unit cell with a (002) plane
identified.
z
(a)
Reserve Problem 75
Determine the Miller indices for the planes shown in
the following unit cell:
+z
c



a
b
1
2
x
B
A
z
(b)
+y
2
3
c
+x



Reserve Problem 76
a
b
Find the indices of the direction that results from the
intersection of each of the following pairs of planes
within a cubic crystal:
(a) The (100) and (010) planes
(b) The (111) and (11–1) planes
(c) The (10–1) and (001) planes
x
z
(c)
c

Reserve Problem 77


Consider the reduced-sphere unit cell shown in the
figure, having an origin of the coordinate system positioned at the atom labeled O. For the following sets of
planes, determine which are equivalent:
a
b
x
+z
Reserve Problem 73
What are the indices for the two planes drawn in the
sketch below?
90°
+z
Plane 2
Plane 1
0.40 nm
O
90°
90°
0.30 nm
0.2 nm
+y
+x
+x
0.4 nm
0.4 nm
0.30 nm
(a) (00–1), (010), and (–100)
(b) (1–10), (10–1) and (–1–10)
(c) (–1–1–1), (–11–1), (–111) and (1–11)
+y
R-24 • Reserve Questions and Problems
Reserve Problem 81
The accompanying figure shows three different crystallographic planes for a unit cell of a hypothetical
metal. The circles represent atoms:
Identify the (a) (1−101) and (b) (11−20) planes in
hexagonal unit cell.
z
(a) 1.
0.46 nm
0.50 nm
0.40 nm
Reserve Problem 78
a2
0.30 nm
0.40 nm
0.35 nm
(001)
a1
(101)
(110)
a3
(a) To what crystal system does the unit cell
belong?
(b) What would this crystal structure be called?
(c) If the density of this metal is 8.95 g/cm3,
determine the atomic weight.
z
2.
Reserve Problem 79
Convert the (a) (010) and (b) (101) planes into the
four-index Miller–Bravais scheme for hexagonal unit
cells.
a2
a3
Reserve Problem 80
a1
Determine the indices for the planes shown in the following hexagonal unit cells:
z
3.
z
(a)
z
(c)
a2
a2
a1
a1
z
(b)
a2
a3
a3
a1
z
(d)
a3
z
4.
a2
a2
a3
a3
a1
a1
a2
a3
a1
Reserve Questions and Problems • R-25
z
(b) 1.
Reserve Question 82: Cubic plane indices 01
What are the Miller indices for the plane shown below?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
z
a2
a3
c
a1
z
2.
y
a
b
(a)
(b)
(c)
(d)
a2
a1
x
(–100)
(–110)
(011)
(010)
Reserve Question 83: Cubic plane indices 02
What are the Miller indices for the plane shown below?
a3
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
z
3.
z
c
a2
a3
a
b
a1
4.
z
(a)
(b)
(c)
(d)
a2
a1
a3
x
(110)
(–110)
(010)
(111)
y
R-26 • Reserve Questions and Problems
Reserve Question 84: Cubic plane indices 03
Reserve Question 87: Cubic plane indices 06
What are the Miller indices for the plane shown below?
What are the Miller indices for the plane shown below?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
z
z
c
c
1
2
a
b
(a) (110)
(b) (–110)
b
x
x
(a) (022)
(b) (013)
(c) (010)
(d) (111)
y
a
y
(c) (012)
(d) (103)
Reserve Question 88: Cubic Plane indices 07
Reserve Question 85: Cubic plane indices 04
What are the Miller indices for the plane shown below?
What are the Miller indices for the plane shown below?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
z
z
b
(a) (1–20)
(b) (1–10)
1
2
y
a
x
(a) (40–3)
(b) (41–3)
Reserve Question 86: Cubic plane indices 05
What are the Miller indices for the plane shown below?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
(c) (41–2)
(d) (40–2)
Reserve Question 89: Cubic plane indices 08
What are the Miller indices for the plane shown below?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
z
z
1
3
c
c
a
(a) (102)
(b) (1–13)
y
a
b
x
(c) (0–02)
(d) (0–10)
x
c
2
3
c
b
(c) (112)
(d) (103)
1
2
y
1
3
a
x
(a) (1–13)
(b) (–1–13)
b
(c) (–1–23)
(d) (1–23)
y
Reserve Questions and Problems • R-27
Reserve Question 90: Cubic plane indices 09
Reserve Question 93: Hexagonal plane indices
What are the Miller indices for the plane shown below?
What are the Miller-Bravais indices for the plane
shown below?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
z
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
z
2
3
c
a2
y
a
b
x
(a) (2–23)
(b) (1–23)
a3
a1
(c) (0–12)
(d) (2–32)
Reserve Question 91: Cubic plane indices 10
What are the Miller indices for the plane shown below?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
z
(a)
(b)
(c)
(d)
(000–1)
(0010)
(0101)
(0100)
Reserve Question 94: Miller indices I
Below is shown the atomic packing of a plane for the
simple cubic crystal structure; atoms drawn to full size
are represented by the circles.
c
2
3
1
2
x
y
a
b
2
3
(a) (42–2)
(b) (31–3)
(c) (43–3)
(d) (24–3)
Reserve Question 92: Cubic plane indices 11
What are the Miller indices for the plane shown below?
A negative index is indicated with a minus sign (“–”)
in front of (rather than over) the index number.
z
1
2
x
(a) (13–3)
(b) (24–3)
Reserve Problem 95
c
2
3
a
b
(c) (14–1)
(d) (15–4)
From the list below select all possible sets of indices
for this plane.
(a) (011)
(b) (1–10)
(c) (10–1)
(d) (–110)
(e) (0–11)
(f) (110)
y
(a) Derive linear density expressions for FCC
[100] and [111] directions in terms of the
atomic radius R.
(b) Compute and compare linear density values
for these same two directions for silver.
R-28 • Reserve Questions and Problems
Reserve Problem 96
Figure 3.39 shows the first four peaks of the x-ray diffraction pattern for copper, which has an FCC crystal
structure; monochromatic x-radiation having a wavelength of 0.1542 nm was used.
(a) Index (i.e., give h, k, and l indices) for each of these peaks.
(b) Determine the interplanar spacing for each of the peaks.
(c) For each peak, determine the atomic radius for Cu and compare these with the value presented in
Table 3.1.
Reserve Problem 97
Below are listed diffraction angles for the first three peaks (first-order) of the x-ray diffraction pattern for some
metal. Monochromatic x-radiation having a wavelength of 0.1254 nm was used.
(a) Determine whether this metal’s crystal structure is FCC, BCC, or neither FCC or BCC.
(b) If the crystal structure is either BCC or FCC, identify which of the metals in Table 3.1 gives this
diffraction pattern.
Peak Number
Diffraction Angle (2θ)
1
31.2°
2
44.6°
3
55.4°
Reserve Question 98: Noncrystalline: anisotropic
The properties of noncrystalline materials are anisotropic.
(a) True
(b) False
CHAPTER 4 POLYMER STRUCTURES
Reserve Question 01: Double/triple bonds
Reserve Question 02: Hydrocarbon bonding
Hydrocarbon molecules that contain double and/or
triple bonds are called
(a) unsaturated.
(b) saturated.
Which type(s) of bonding is (are) found within hydrocarbon molecules?
(a) Ionic bonding
(b) Hydrogen boning
(c) Covalent bonding
(d) Van der Waals bonding
(e) Metallic bonding
Reserve Questions and Problems • R-29
Reserve Question 03: Hydrocarbon groups
Reserve Question 06: Repeat unit structures
Select the correct name of each hydrocarbon group
that is shown below.
A. R
From the pull-down menus, select the correct name
for each repeat unit structure that is shown below.
C
A.
O
H
B.
R
O
C.
R
OH
D.
F
F
C
C
F
F
R′
B.
H
CH3
C
C
H
C
R
O
O
CH3
E.
OH
R
C.
C
O
Group A ______
Group B ______
Group C ______
Group D ______
Group E ______
D.
H
H
C
C
H
Cl
H
H
C
C
H
Reserve Question 04: Isomers
Hydrocarbon compounds that have the same composition but different atomic arrangements are
called ____.
E.
Reserve Question 05: Crystallinity comparisons
For the following two polymers:
Linear polyethylene
Lightly branched isotactic polypropylene
Is it possible to determine if one is more likely to
crystallize than the other?
(a) Yes. Linear polyethylene
(b) Yes. Lightly branched isotactic polypropylene
(c) No
F.
H
H
C
C
H
H
H
H
C
C
H
CH3
Repeat unit A ______
Repeat unit B ______
Repeat unit C ______
Repeat unit D ______
Repeat unit E ______
Repeat unit F ______
R-30 • Reserve Questions and Problems
Reserve Problem 07: Substitution of group
Reserve Question 11: Cis/trans identification
Polyethylene may be fluorinated by inducing the random substitution of fluorine atoms for hydrogen.
Indicate which structure has the cis configuration and
which has the trans configuration.
For this polymer, determine the following:
(a) The concentration of F (in wt%) that must be
added if this substitution occurs for 18.6% of
all of the original hydrogen atoms.
(b) The concentration of F (in wt%) that must
be added to completely fluorinate the material, i.e. to produce polytetrafluoroethylene
(PTFE).
Atomic weights for several elements are included in
the following table:
Carbon
12.01 g/mol
Chlorine
35.45 g/mol
Fluorine
19.00 g/mol
Hydrogen 1.008 g/mol
Oxygen
16.00 g/mol
Reserve Question 08: Linear polymers
Which of the following may form linear polymers?
(a) Rubber
(b) Epoxy
(c) Polyethylene
(d) Phenol-formaldehyde
(e) Polystyrene
(f) Nylon
Reserve Question 09: Network polymers
Which of the following form network polymers?
(a) Rubber
(b) Epoxy
H
H
C
C
H
H
C
C
H
H
H
H
H
H
C
C
C
C
H
H
______
______
Reserve Question 12: Isotactic/syndiotactic/atactic
Match the description of each stereoisomer with the
name of its configuration classification.
All R groups are on the same side. ______
R groups are alternate sides of the chain. ______
R groups are randomly positioned along the
chain. ______
Reserve Question 13: Polymer configuration
For most polymers, which configuration predominates?
(a) Head-to-head
(b) Head-to-tail
Reserve Problem 14
Five pieces of plastic, each one made of a different
polymer, feature the same degree of polymerization.
Which one will feature, on average, the shortest molecules when fully extended?
(a) PVC
(c) Polyethylene
(b) PE
(d) Phenol-formaldehyde
(c) PTFE
(e) Polystyrene
(d) PP
(f) Nylon
(e) PS
(f) They are equal lengths.
Reserve Question 10: Cis/Trans
Match the geometrical isomer descriptions with their
names.
Groups bonded to adjacent doubly-bonded chain
atoms are positioned on the same chain side. ______
Groups bonded to adjacent doubly-bonded chain
atoms are positioned on opposite chain sides. ______
Reserve Questions and Problems • R-31
Reserve Problem 15a (question pool)
Reserve Problem 16a (question pool)
Which of the following schematics is consistent with
a polymer architecture featuring PE grafted onto a
PTFE-PVC block-copolymer primary chain? Each
circle is considered to be a repeat unit.
(d)
(a)
Which of the following schematics is consistent with
a polymer architecture featuring PE grafted onto a
PP primary chain? Each circle is considered to be a
repeat unit.
(d)
(a)
(b)
(c)
(e)
(b)
(c)
(e)
R-32 • Reserve Questions and Problems
Reserve Problem 17a (question pool)
Reserve Problem 18a (question pool)
Which of the following schematics is consistent with
a polymer architecture featuring PE grafted onto a
PP primary chain? Each circle is considered to be a
repeat unit.
(d)
(a)
Which of the following schematics is consistent with
a polymer architecture featuring PE grafted onto a
PP-PVC alternating-copolymer primary chain? Each
circle is considered to be a repeat unit.
(d)
(a)
(b)
(c)
(e)
(b)
(c)
(e)
Reserve Questions and Problems • R-33
Reserve Problem 19a (question pool)
Reserve Problem 20a (question pool)
Which of the following schematics is consistent with
a polymer architecture featuring PP grafted onto a
PP-PVC alternating-copolymer primary chain? Each
circle is considered to be a repeat unit.
(d)
(a)
Which of the following schematics is consistent with a polymer architecture featuring PP-PVC grafted onto a PP primary chain? Each circle is considered to be a repeat unit.
(b)
(a)
(d)
(b)
(e)
(e)
(c)
(c)
Reserve Question 21: Polymer crystallinity
Is it possible to produce a polymer that is 100%
crystalline?
(a) True
(b) False
R-34 • Reserve Questions and Problems
CHAPTER 5 IMPERFECTIONS IN SOLIDS
Reserve Problem 01a (question pool)
Consider the schematic nanostructure depicted below.
Reserve Problem 02a (question pool)
Which of the following statements is FALSE regarding this schematic structure?
Which of the following statements is FALSE regarding this schematic structure?
Do not extrapolate the field of view. Consider only
what you are shown.
Do not extrapolate the field of view. Consider only
what you are shown.
(a) Each of the phases features a similar concentration of vacancies.
(b) The microstructure features exactly two components and two different phases.
(c) None of the phases present features interstitial impurities.
(d) Only one phase boundary is depicted.
(e) Two grain boundaries are depicted.
Consider the schematic nanostructure depicted below.
(a) Each of the phases features a similar concentration of vacancies.
(b) The microstructure features exactly two components and two different phases.
(c) One of the phases present features interstitial
impurities.
(d) Only one phase boundary is depicted.
(e) One grain boundary is depicted.
Reserve Questions and Problems • R-35
Reserve Problem 03a (question pool)
Consider the schematic nanostructure depicted
below.
Which of the following statements is FALSE regarding this schematic structure?
Do not extrapolate the field of view. Consider only
what you are shown.
Reserve Problem 05: Metallic vacancies–
temperature
The number of vacancies present in some metal at
864°C is 1.1 × 1024 m−3. Calculate the number of
vacancies at 463°C given that the energy for vacancy
formation is 1.25 eV/atom; assume that the density at
both temperatures is the same.
Reserve Question 06: Vacancies vs.
self-interstitials
In metals, there are significantly more vacancies than
self-interstitials.
(a) True
(b) False
Reserve Problem 07
Using the following data that relate to the formation
of Schottky defects in some oxide ceramic (having the
chemical formula MO), determine the following:
T ( °C)
(g/cm3)
Ns (m−3)
750
5.50
9.21 × 1019
1000
5.44
?
1250
5.37
5.0 × 1022
(a) The energy for defect formation (in eV).
(b) The equilibrium number of Schottky defects
per cubic meter at 1000°C.
(c) The identity of the oxide (i.e., what is the
metal M?).
Reserve Problem 08
(a) Each of the phases features a similar concentration of vacancies.
(b) The microstructure features exactly three
components and two different phases.
(c) Both of the phases present features interstitial
impurities.
(d) Only one phase boundary is depicted.
(e) One grain boundary is depicted.
Reserve Problem 04: Energy from temperature
The number of vacancies in some hypothetical metal
increases by a factor of 5 when the temperature is increased from 1040 K to 1150 K. Calculate the energy
(in kJ/mol) for vacancy formation assuming that the
density of the metal remains the same over this temperature range.
Which of the following oxides would you expect to
form substitutional solid solutions that have complete (i.e., 100%) solubility with MnO? Explain your
answers.
(a) MgO
(b) CaO
(c) BeO
(d) NiO
Reserve Problem 09
(a) Suppose that Li2O is added as an impurity
to CaO. If the Li+ substitutes for Ca2+, what
kind of vacancies would you expect to form?
How many of these vacancies are created for
every Li+ added?
(b) Suppose that CaCl2 is added as an impurity to
CaO. If the Cl− substitutes for O2−, what kind
of vacancies would you expect to form? How
many of the vacancies are created for every
Cl− added?
R-36 • Reserve Questions and Problems
Reserve Problem 10
Reserve Problem 11: Wt% to concentration
Atomic radius, crystal structure, electronegativity,
and the most common valence are given in the following table for several elements; for those that are
nonmetals, only atomic radii are indicated.
The concentration of carbon in an iron-carbon alloy
is 0.57 wt%. What is the concentration in kilograms
of carbon per cubic meter of alloy? The densities of
iron and carbon are 7.87 and 2.25 g/cm3, respectively.
Element
Atomic
Radius
(nm)
Crystal
Structure
Electronegativity
Valence
Cu
0.1278
FCC
1.9
+2
C
H
O
0.071
0.046
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
Ni
0.1246
FCC
1.8
+2
Pd
0.1376
FCC
2.2
+2
Pt
0.1387
FCC
2.2
+2
Zn
0.1332
HCP
1.6
+2
Reserve Problem 12
The concentration of gallium in silicon is 5.0 × 10−7
at%. What is the concentration in kilograms of gallium per cubic meter?
Reserve Problem 13
Choose which of these elements you would expect to
form the following with copper:
A substitutional solid solution having complete
solubility
• Ni
• C
• O
• Zn
• H
• Ag
• Pt
• Al
• Pd
• Cr
• Co
• Fe
A substitutional solid solution of incomplete solubility
• Pd
• Ni
• Al
• Zn
• Cr
• C
• Fe
• Ag
• H
• O
• Pt
• Co
An interstitial solid solution
• C
• Zn
• Pd
• Ag
• Pt
• Al
• H
• Co
• Cr
• Fe
• O
• Ni
Some hypothetical alloy is composed of 12.5 wt% of
metal A and 87.5 wt% of metal B. If the densities of metals A and B are 4.27 and 6.35 g/cm3, respectively, whereas
their respective atomic weights are 61.4 and 125.7 g/mol,
determine whether the crystal structure for this alloy is
simple cubic, face-centered cubic, or body-centered cubic. Assume a unit cell edge length of 0.395 nm.
Reserve Problem 14
For a BCC iron-carbon alloy that contains 0.15 wt%
C, calculate the fraction of unit cells that contain carbon atoms.
Reserve Problem 15
For Si to which has had added 1.5 × 10−6 at% of
arsenic, calculate the number of As atoms per cubic
meter.
Reserve Problem 16
Electronic devices found in integrated circuits are
composed of very high purity silicon to which has
been added small and very controlled concentrations of elements found in Groups IIIA and VA of
the periodic table. For Si that has had added 8.3 ×
1021 atoms per cubic meter of antimony, compute (a)
the weight percent and (b) the atom percent of Sb
present.
Reserve Problem 17
Iron and vanadium both have the BCC crystal structure and V forms a substitutional solid solution in Fe
for concentrations up to approximately 20 wt% V at
room temperature. Determine the concentration in
weight percent of V that must be added to iron to
yield a unit cell edge length of 0.289 nm.
Reserve Problem 18: Linear defects
Which of the following is a (are) linear defect(s)?
(a) An edge dislocation
(b) A Frenkel defect
(c) A Schottky defect
Reserve Questions and Problems • R-37
Reserve Problem 19: ASTM grain size I
Reserve Problem 20
A photomicrograph was taken of a specimen at a
magnification of 100×, and it was determined that the
average number of grains per square inch was 200.
What is this specimen’s ASTM grain size number?
For a single crystal of some hypothetical metal that
has the simple cubic crystal structure (Figure 3.3),
would you expect the surface energy for a (100) plane
to be greater, equal to, or less than a (110) plane?
CHAPTER 6 DIFFUSION
Reserve Question 01: Rate of Diffusion
Reserve Problem 04
Diffusion by which mechanism occurs more rapidly in
metal alloys?
(a) Vacancy diffusion
(b) Interstitial diffusion
If [m] atoms of helium pass through a [a] square meter
plate area every [t] hours, and if this flux is constant
with time, compute the flux of helium in units of atoms per square meter per second.
Reserve Question 02: Temperature effect in diffusion
As temperature decreases, the fraction of total number of atoms that are capable of diffusive motion
(a) increases.
(b) decreases.
Reserve Problem 03
A gas mixture is found to contain two diatomic A and
B species for which the partial pressures of both are
0.05065 MPa (0.5 atm). This mixture is to be enriched
in the partial pressure of the A species by passing both
gases through a thin sheet of some metal at an elevated
temperature. The resulting enriched mixture is to have a
partial pressure of 0.02026 MPa (0.2 atm) for gas A, and
0.01013 MPa (0.1 atm) for gas B. The concentrations of
A and B (CA and CB, in mol/m3) are functions of gas
partial pressures (pA2 and pB2, in MPa) and absolute
temperature according to the following expressions:
CA = 200 √pA2 exp(−
25.0 kJmol
)
RT
CB = 1.0 × 10−3 √pB2 exp(−
30.0 kJmol
RT
)
Furthermore, the diffusion coefficients for the diffusion of these gases in the metal are functions of the
absolute temperature as follows:
DA (m2s) = 4.0 × 10−7 exp −
(
DB (m2s) = 2.5 × 10−6 exp(−
15.0 kJmol
RT
)
24.0 kJmol
RT
)
Is it possible to purify the A gas in this manner? If
so, specify a temperature at which the process may be
carried out, and also the thickness of metal sheet that
would be required. If this procedure is not possible,
then state the reason(s) why.
Reserve Problem 05
If water molecules pass through a membrane with a
steady state flux of [j] mole/(m2 day), how long will it
take, in hours, for [m] kg of water to pass through a [a]
square centimeter of the membrane?
Reserve Problem 06a (question pool)
The cornea is the transparent outer layer of the human
eye. Because it must be transparent to light, it does not
normally contain blood vessels. Therefore, it must receive
its nutrients via diffusion. Oxygen from the surrounding air diffuses to the cornea through the surface tears,
whereas other nutrients diffuse to the cornea from the inner parts of the eye, such as the vitreous humor and lens.
During operation, the cornea produces waste in the
form of CO2 gas that must be expelled to keep the
eye healthy and functioning. This is accomplished by
the simultaneous diffusion of CO2 from the cornea to
the surrounding atmosphere, which generally features
a low CO2 concentration.
It is therefore critical that modern contact lens materials allow sufficient diffusion rates of oxygen and carbon
dioxide. Without oxygen, the cornea will warp, lose
transparency, and become susceptible to scarring. The
body may also react by growing additional blood vessels into the eye, which can damage the cornea.
If an increased steady-state flow rate of O2 (oxygen
molecules per second) to the cornea is desired, which
of the following contact lens/ambient condition modifications is not likely to be useful?
Note: the flow rate is equal to product of the diffusion flux
and an area of interest through which diffusion occurs.
(a) Increase the contact lens thickness
(b) Increase the diffusivity of oxygen gas by
decreasing the contact lens porosity
(c) Increase the ambient temperature
(d) Increase the ambient partial pressure of
oxygen gas
(e) All of the suggestions (a-d) are useful for
increasing the flow rate of oxygen
R-38 • Reserve Questions and Problems
Reserve Problem 07: Non-steady-state–Specific
concentration at different T
For a steel alloy it has been determined that a carburizing heat treatment of 16 h duration at 757°C will
raise the carbon concentration to 0.5 wt% at a point
2.3 mm from the surface. Estimate the time necessary
to achieve the same concentration at a 8 mm position
for an identical steel and at a carburizing temperature
of 1130°C. Assume that D0 is 4.6 × 10−5 m2/s and Qd
is 104 kJ/mol.
Reserve Problem 08a (question pool)
The figure below features diffusion profiles that developed within four separate plain-carbon steel specimens
of equivalent geometry after they separately experienced a carburization process. The specimens were
prepared such that the scenario of a one-dimensional
semi-infinite solid applies as a solution to Fick’s 2nd
Law of Diffusion. Each part originally contained a
uniform distribution of carbon, and each part was
processed using the same carburization temperature.
In the figure, x = 0 corresponds to the surfaces of
the steel parts that were exposed to the carbon-rich
atmosphere during the diffusion process.
Answer True or False for each of the following
statements.
(a) The carburization surface was maintained at
1.00 wt% carbon for each specimen.
(b) Comparing the finished specimens at a depth
of 0.75 mm, specimen A features the largest
carbon concentration.
(c) Comparing the finished specimens as a whole,
specimen A features the lowest overall
amount of carbon.
(d) Specimen B experienced a longer carburization time compared to specimen C.
(e) The initial concentration of carbon in each
part (prior to carburization) was a little less
than 0.25 wt% carbon.
Reserve Problem 09
The diffusion coefficient for aluminum in silicon is
DAl in Si = 3 × 10−16 cm2/s at 300 K (note that 300 K is
about room temperature).
What is a reasonable value for DAl in Si at 600 K ?
Note: Rather than performing a specific calculation,
you should be able to justify your answer from the options below based on the mathematical temperature
dependence of the diffusion coefficient.
(a) D < 3 × 10−16 cm2/s
(b) D = 3 × 10−16 cm2/s
(c) D = 6 × 10−16 cm2/s
(d) D = 1.5 × 10−16 cm2/s
(e) D > 6 × 10−16 cm2/s
(f) D = 6 × 10−17 cm2/s
Reserve Problem 10a (question pool)
Depicted below are five different steady-state concentration profiles for the same gas across five separate
and identical plastic membranes at the same temperature. Which concentration profile results in the lowest
diffusion flux through the membrane?
Reserve Problem 11
One integrated circuit design calls for the diffusion of
arsenic into silicon wafers; the background concentration of As in Si is 2.5 × 1020 atoms/m3. The predeposition heat treatment is to be conducted at 1000°C for
45 minutes, with a constant surface concentration of
8 × 1026 As atoms/m3. At a drive-in treatment temperature of 1100°C, determine the diffusion time required for a junction depth of 1.2 μm. For this system,
values of Qd and D0 are 4.10 eV and 2.29 × 10−3 m2/s,
respectively.
Reserve Questions and Problems • R-39
Reserve Problem 12
Reserve Problem 13
Phosphorus atoms are to be diffused into a silicon
wafer using both predeposition and drive-in heat
treatments; the background concentration of P in this
silicon material is known to be 5 × 1019 atoms/m3.
The predeposition treatment is to be conducted at
950°C for 45 minutes; the surface concentration of
P is to be maintained at a constant level of 1.5 ×
1026 atoms/m3. Drive-in diffusion will be carried out
at 1200°C for a period of 2.5 h. For the diffusion of
P in Si, values of Qd and D0 are 3.40 eV and 1.1 ×
10−4 m2/s, respectively.
(a) Calculate the value of Q0.
(b) Determine the value of xj for the drive-in diffusion treatment.
(c) Also for the drive-in treatment, compute the
position x at which the concentration of P
atoms is 1024 m−3.
Aluminum atoms are to be diffused into a silicon
wafer using both predeposition and drive-in heat
treatments; the background concentration of Al in
this silicon material is known to be 3 × 1019 atoms/m3.
The drive-in diffusion treatment is to be carried out
at 1050°C for a period of 4.0 h, which gives a junction depth xj of 3.0 μm. Compute the predeposition
diffusion time at 950°C if the surface concentration is
maintained at a constant level of 2 × 1025 atoms/m3.
For the diffusion of Al in Si, values of Qd and D0 are
3.41 eV and 1.38 × 10−4 m2/s, respectively.
CHAPTER 7 MECHANICAL PROPERTIES
Reserve Problem 01a-1 (question pool)
Reserve Problem 01c-1 (question pool)
Each of the rods depicted below were machined from
same stock metal. If the same force is applied axially
to each rod, which one will experience the highest
stress?
Each of the rods depicted below were machined from
same stock metal. If the same force is applied axially to
each rod, which one will experience the highest stress?
Reserve Problem 01d-1 (question pool)
Reserve Problem 01b-1 (question pool)
Each of the rods depicted below were machined from
same stock metal. If the same force is applied axially
to each rod, which one will experience the highest
stress?
Each of the rods depicted below were machined from
same stock metal. If the same force is applied axially to
each rod, which one will experience the highest stress?
R-40 • Reserve Questions and Problems
Reserve Problem 01e-1 (question pool)
(c)
(e)
(d)
(f)
Each of the rods depicted below were machined from
same stock metal. If the same force is applied axially to
each rod, which one will experience the highest stress?
Reserve Problem 01f-1 (question pool)
Each of the rods depicted below were machined from
same stock metal. If the same force is applied axially to
each rod, which one will experience the highest stress?
Reserve Problem 03: Stress-strain I
A specimen of some metal having a rectangular cross
section 11.2 mm × 12.4 mm is pulled in tension with
a force of 31200 N, which produces only elastic deformation. Given that the elastic modulus of this metal is
63 GPa, calculate the resulting strain.
Reserve Problem 02a (question pool)
Each of the rods depicted below were machined from
same stock metal. They were originally machined to
be the same length, but their cross-sectional areas
were different. Which plot correctly depicts the force
required to elastically elongate these specimens?
Reserve Problem 04: Maintaining plastic
deformation
For a bronze alloy, the stress at which plastic deformation begins is 277 MPa and the modulus of elasticity
is 117 GPa.
(a) What is the maximum load that may be applied to a specimen having a cross-sectional
area of 327 mm2 without plastic deformation?
(b) If the original specimen length is 148 mm, what
is the maximum length to which it may be
stretched without causing plastic deformation?
Reserve Problem 05
(a)
(b)
A steel bar 100 mm (4.0 in.) long and having a square
cross section 20 mm (0.8 in.) on an edge is pulled in
tension with a load of 89,000 N (20,000 lbf), and experiences an elongation of 0.10 mm (4.0 × 10−3 in.).
Assuming that the deformation is entirely elastic, calculate the elastic modulus of the steel.
Reserve Problem 06
Figure 7.35 shows, for a gray cast iron, the tensile engineering stress–strain curve in the elastic region. Determine
(a) the tangent modulus at 10.3 MPa (1500 psi), and
(b) the secant modulus taken to 6.9 MPa (1000 psi).
Reserve Questions and Problems • R-41
Reserve Question 07
Using the expression to which the modulus of elasticity is proportional,
dF
=−
( dr )r
0
2A
3(1−n)
A
( nB )
+
n(n + 1)B
A (n+2)(1−n)
( nB )
.
Reserve Problem 08c-1 (question pool)
Each of the rods depicted below were machined from
same stock metal. They were originally machined to
be the same length, but their cross-sectional areas
were different. If axial force is applied to each rod
such that they all change length by the same amount,
which rod experienced the largest force?
rank the magnitudes of the moduli of elasticity for
the following hypothetical X, Y, and Z materials from
the greatest to the least. The appropriate A, B and n
parameters (Equation 7.36) for these three materials
are tabulated below; they yield EN in units of electron
volts and r in nanometers:
Material
X
A
2.5
B
2.0 × 10
Y
2.3
8.0 × 10–6
10.5
Z
3.0
1.5 × 10–5
9
–5
n
8
The highest modulus of elasticity is Metal ______
The next highest modulus of elasticity is Metal ______
The least modulus of elasticity is Metal ______
Reserve Problem 08d-1 (question pool)
Each of the rods depicted below were machined from
same stock metal. They were originally machined to
be the same length, but their cross-sectional areas
were different. If axial force is applied to each rod
such that they all change length by the same amount,
which rod experienced the largest force?
Reserve Problem 08a-1 (question pool)
Each of the rods depicted below were machined from
same stock metal. They were originally machined to
be the same length, but their cross-sectional areas
were different. If axial force is applied to each rod
such that they all change length by the same amount,
which rod experienced the largest force?
Reserve Problem 09: Poisson’s ratio II
Reserve Problem 08b-1 (question pool)
Each of the rods depicted below were machined from
same stock metal. They were originally machined to
be the same length, but their cross-sectional areas
were different. If axial force is applied to each rod
such that they all change length by the same amount,
which rod experienced the largest force?
A cylindrical specimen of some metal alloy 10 mm in
diameter and 150 mm long has a modulus of elasticity of 100 GPa. Does it seem reasonable to expect a
tensile stress of 200 MPa to produce a reduction in
specimen diameter of 0.08 mm? Assume that the deformation is totally elastic.
(a) Yes
(b) No
Reserve Problem 12: Stress for tension test
Consider the brass alloy the stress-strain behavior
of which is shown in the Animated Figure 7.12. A
cylindrical specimen of this alloy 21 mm in diameter
and 224 mm long is to be pulled in tension. Calculate
the stress (in MPa) necessary to cause a 0.00832 mm
reduction in diameter. Assume a value of 0.33 for
Poisson’s ratio.
R-42 • Reserve Questions and Problems
Reserve Problem 13: Typical relationship between
E and G
Reserve Problem 16: Load for elongation
For most metals, the relationship between elastic and
shear moduli is approximately which of the following?
(a) G = 0.1 E
(d) G = 0.4 E
(b) G = 0.2 E
(e) G = 0.5 E
(c) G = 0.3 E
Consider the brass alloy the stress-strain behavior of
which is shown in the Animated Figure 7.12. A cylindrical specimen of this material 13.7 mm in diameter and
142.1 mm long is pulled in tension after which the tensile
load is released. After the load is released the total length
has still increased to 142.4 mm. Calculate the magnitude
of the load (in N) necessary to cause this elongation.
Reserve Problem 14
Reserve Problem 17
A cylindrical metal specimen 12.7 mm (0.5 in.) in diameter and 250 mm (10 in.) long is to be subjected to
a tensile stress of 28 MPa (4000 psi); at this stress level,
the resulting deformation will be totally elastic.
(a) If the elongation must be less than 0.080 mm
(3.2 × 10−3 in.), which of the metals in
Table 6.1 are suitable candidates?
• Brass
• Copper
• Tungsten
• Steel
• Titanium
• Nickel
• Magnesium
• Aluminum
(b) If, in addition, the maximum permissible
diameter decrease is 1.2 × 10−3 mm (4.7 ×
10−5 in.) when the tensile stress of 28 MPa is
applied, which of the metals that satisfy the
criterion in part (a) are suitable candidates?
• Aluminum
• Brass
• Steel
• Magnesium
• Copper
• Titanium
• Nickel
• Tungsten
A cylindrical specimen of aluminum having a diameter of 0.505 in. (12.8 mm) and a gauge length of
2.000 in. (50.800 mm) is pulled in tension. Use the
load–elongation characteristics shown in the following
table to complete parts (a) through (e).
Reserve Problem 15
A cylindrical rod 380 mm (15.0 in.) long and having a
diameter of 10.0 mm (0.40 in.), is to be subjected to a
tensile load. If the rod is to experience neither plastic
deformation nor an elongation of more than 0.9 mm
(0.035 in.) when the applied load is 24,500 N (5500 lbf),
which of the four metals or alloys listed below are
possible candidates?
Material
Aluminum alloy
Brass alloy
Copper
Steel alloy
•
•
•
•
Modulus of
Elasticity
(GPa)
70
100
110
207
Aluminum alloy
Brass alloy
Copper
Steel alloy
Yield
Strength
(MPa)
255
345
250
450
Tensile
Strength
(MPa)
420
420
290
550
Load
in N
Load
in lbf
Length
in mm
Length
in in.
0
7330
15,100
23,100
30,400
34,400
38,400
41,300
44,800
46,200
47,300
47,500
46,100
44,800
42,600
34,400
Fracture
0
1650
3400
5200
6850
7750
8650
9300
10,100
10,400
10,650
10,700
10,400
10,100
9600
8200
Fracture
50.800
50.851
50.902
50.952
51.003
51.054
51.308
51.816
52.832
53.848
54.864
55.880
56.896
57.658
58.420
59.182
Fracture
2.000
2.002
2.004
2.006
2.008
2.010
2.020
2.040
2.080
2.120
2.160
2.200
2.240
2.270
2.300
2.330
Fracture
Plot the data as engineering stress versus engineering
strain. Based on your plot,
(a) Compute the modulus of elasticity.
(b) Determine the yield strength at a strain offset
of 0.002.
(c) Determine the tensile strength of this alloy.
(d) What is the approximate ductility, in percent
elongation?
(e) Compute the modulus of resilience.
(a) ______ GPa
(d) ______ %EL
(b) ______ MPa
(e) ______ J/m3
(c) ______ MPa
Reserve Questions and Problems • R-43
Reserve Problem 18
Reserve Problem 19a-1 (question pool)
A specimen of ductile cast iron having a rectangular cross section of dimensions 4.8 mm × 15.9 mm
(3/16 in. × 5/8 in.) is deformed in tension. Using the
load–elongation data shown in the following table,
complete problems (a) through (e).
Three hypothetical tensile engineering stress-strain
curves through failure are depicted below.
Load
in N
Load
in lbf
Length
in mm
Length
in in.
0
4740
9140
12,920
16,540
18,300
20,170
22,900
25,070
26,800
28,640
30,240
31,100
31,280
30,820
29,180
27,190
24,140
18,970
Fracture
0
1065
2055
2900
3720
4110
4530
5145
5635
6025
6440
6800
7000
7030
6930
6560
6110
5430
4265
Fracture
75.000
75.025
75.050
75.075
75.113
75.150
75.225
75.375
75.525
75.750
76.500
78.000
79.500
81.000
82.500
84.000
85.500
87.000
88.725
Fracture
2.953
2.954
2.955
2.956
2.957
2.959
2.962
2.968
2.973
2.982
3.012
3.071
3.130
3.189
3.248
3.307
3.366
3.425
3.493
Fracture
Which response is considered to be the most brittle?
Reserve Problem 19b-1 (question pool)
Three hypothetical tensile engineering stress-strain
curves through failure are depicted below.
Which response is considered to be the most brittle?
Reserve Problem 19c-1 (question pool)
Plot the data as engineering stress versus engineering
strain.
(a) Compute the modulus of elasticity.
(b) Determine the yield strength at a strain offset
of 0.002.
(c) Determine the tensile strength of this alloy.
(d) Compute the modulus of resilience.
(e) What is the ductility, in percent elongation?
(a) ______ GPa
(b) ______ MPa
(c) ______ MPa
(d) ______ J/m3
(e) ______%EL
Three hypothetical tensile engineering stress-strain
curves through failure are depicted below.
Which response is considered to be the most brittle?
R-44 • Reserve Questions and Problems
Reserve Problem 19d-1 (question pool)
Reserve Problem 20a (question pool)
Three hypothetical tensile engineering stress-strain
curves through failure are depicted below.
Tensile engineering stress-strain curves through failure are depicted below.
Which response is considered to be the most brittle?
Which specimen features the most ductile response?
Reserve Problem 19e-1 (question pool)
Three hypothetical tensile engineering stress-strain
curves through failure are depicted below.
Which response is considered to be the most brittle?
(a) 1340 Steel, Water-Quenched & Tempered at
370oC
(b) Stainless Steel (18-8)
(c) Aluminum Alloy 2024-T81
(d) Structural Steel (Mild Steel)
(e) Magnesium
Reserve Problem 21: True strain
A tensile test is performed on a specimen of some metal
alloy, and it is found that a true plastic strain of 0.12 is produced when a true stress of 280 MPa is applied. For this
alloy, the value of the strain hardening exponent is 0.3.
On the basis of these data, what true plastic strain would
be expected for a total true plastic stress of 330 MPa?
Reserve Problem 22: True stress
Reserve Problem 19f-1 (question pool)
Three hypothetical tensile engineering stress-strain
curves through failure are depicted below.
Which response is considered to be the most brittle?
A cylindrical specimen of a metal alloy 48.8 mm long
and 9.09 mm in diameter is stressed in tension. A true
stress of 327 MPa causes the specimen to plastically
elongate to a length of 55 mm. If it is known that the
strain-hardening exponent for this alloy is 0.3, calculate the true stress (in MPa) necessary to plastically
elongate a specimen of this same material from a
length of 48.8 mm to a length of 57.6 mm.
Reserve Problem 23
A three-point transverse bending test is conducted
on a cylindrical specimen of aluminum oxide having
a reported flexural strength of 390 MPa (56,600 psi).
If the specimen radius is 2.5 mm (0.10 in.) and the
support point separation distance is 30 mm (1.2 in.),
predict whether or not you would expect the specimen
to fracture when a load of 620 N (140 lbf) is applied.
Calculate the value of flexural strength for this test.
Reserve Questions and Problems • R-45
Reserve Problem 24
Using the date in the table below, do the following:
(a) Determine the flexural strength for nonporous MgO assuming a value of 3.75 for n in Equation 7.22.
(b) Compute the volume fraction porosity at which the flexural strength for MgO is 62 MPa (9000 psi).
Material
Silicon nitride (Si3N4)
Zirconiaa (ZrO2)
Silicon carbide (SiC)
Aluminum oxide (Al2O3)
Glass-ceramic (Pyroceram)
Mullite (3Al2O3–2SiO2)
Spinel (MgAl2O4)
Magnesium oxide (MgO)
Fused silica (SiO2)
Soda-lime glass
Flexural Strength
MPa
ksi
250–1000
35–145
800–1500
115–215
100–820
15–120
275–700
40–100
247
36
185
27
110–245
16–35.5
15b
105b
110
16
69
10
Modulus of
Elasticity
GPa
106 psi
304
44
205
30
345
50
393
57
120
17
145
21
260
38
225
33
73
11
69
10
Reserve Problem 25
The flexural strength and associated volume fraction porosity for two specimens of the same ceramic material
are as follows:
σfs (MPa)
100
50
P
0.05
0.20
(a) Compute the flexural strength for a completely nonporous specimen of this material.
(b) Compute the flexural strength for a 0.10 volume fraction porosity.
Reserve Problem 26a (question pool)
Which polymer listed in the table below would feature the lowest tensile yield point?
Option
(a)
(b)
(c)
(d)
(e)
Identity
PP
PP
PP
PP
PP
Degree of
Polymerization
3,000
3,000
150,000
275,000
275,000
Architecture
Linear
Branched
Linear
Branched
Linear
% Crystalline
20
20
45
45
65
Reserve Problem 27a (question pool)
Which polymer listed in the table below would feature the highest tensile yield point?
Option
(a)
(b)
(c)
(d)
(e)
Identity
PP
PP
PP
PP
PP
Degree of
Polymerization
3,000
3,000
150,000
275,000
275,000
Architecture
Linear
Branched
Linear
Branched
Linear
% Crystalline
20
20
45
45
65
R-46 • Reserve Questions and Problems
Reserve Problem 28a (question pool)
Which polymer listed in the table below would feature the lowest elastic modulus?
Option
(a)
(b)
(c)
(d)
(e)
Identity
PP
PP
PP
PP
PP
Degree of
Polymerization
3,000
3,000
150,000
275,000
275,000
Architecture
Linear
Branched
Linear
Branched
Linear
% Crystalline
20
20
45
45
65
Reserve Problem 29a (question pool)
Which polymer listed in the table below would feature the highest elastic modulus?
Option
(a)
(b)
(c)
(d)
(e)
Identity
PP
PP
PP
PP
PP
Degree of
Polymerization
3,000
3,000
150,000
275,000
275,000
Architecture
Linear
Branched
Linear
Branched
Linear
% Crystalline
20
20
45
45
65
Reserve Problem 30a (question pool)
Which polymer listed in the table below would feature the lowest density?
Option
(a)
(b)
(c)
(d)
(e)
Identity
PP
PP
PP
PP
PP
Degree of
Polymerization
3,000
3,000
150,000
275,000
275,000
Architecture
Linear
Branched
Linear
Branched
Linear
% Crystalline
20
20
45
45
65
Reserve Problem 31a (question pool)
Which polymer listed in the table below would feature the highest density?
Option
(a)
(b)
(c)
(d)
(e)
Identity
PP
PP
PP
PP
PP
Degree of
Polymerization
3,000
3,000
150,000
275,000
275,000
Architecture
Linear
Branched
Linear
Branched
Linear
% Crystalline
20
20
45
45
65
Reserve Questions and Problems • R-47
Reserve Problem 32a (question pool)
Which polymer listed in the table below would feature the lowest thermal expansion coefficient?
Option
(a)
(b)
(c)
(d)
(e)
Degree of
Polymerization
3,000
3,000
150,000
275,000
275,000
Identity
PP
PP
PP
PP
PP
Architecture
Linear
Branched
Linear
Branched
Linear
% Crystalline
20
20
45
45
65
Reserve Problem 33a (question pool)
Which polymer listed in the table below would feature the highest thermal expansion coefficient?
Option
(a)
(b)
(c)
(d)
(e)
Degree of
Polymerization
3,000
3,000
150,000
275,000
275,000
Identity
PP
PP
PP
PP
PP
Architecture
Linear
Branched
Linear
Branched
Linear
% Crystalline
20
20
45
45
65
Reserve Problem 34a (question pool)
Reserve Problem 35a (question pool)
Assuming the stress-strain curves provide below all
correspond to the same polymer, which tensile test was
most likely performed at the highest temperature above
Tg? Choose (e) if no tests likely meet this condition.
Assuming the stress-strain curves provide below all
correspond to the same polymer tested at the same
temperature, which tensile test was most likely performed with the highest strain rate?
80
80
a
70
70
60
b
Stress (MPa)
Stress (MPa)
60
50
40
c
30
b
50
40
c
30
20
20
d
10
0
0
a
0.1
0.2
Strain
d
10
0.3
0
0
0.1
0.2
Strain
0.3
R-48 • Reserve Questions and Problems
Reserve Problem 36
(a) Consider a thin-walled cylindrical tube having
a radius of 65 mm that is to be used to transport pressurized gas. If inside and outside tube
pressures are 100 and 1.0 atm (10.13 and 0.1013
MPa), respectively, compute the minimum required thickness for each of the following metal
alloys. Assume a factor of safety of 3.5.
Alloy
Steel (plain)
Steel (alloy)
Cast iron
Aluminum
Magnesium
Yield
Strength,
σy (MPa)
375
1000
225
275
175
Density,
ρ (g/cm3)
7.8
7.8
7.1
2.7
1.80
Unit Mass
Cost,
cˉ ($US/kg)
1.65
4.00
2.50
7.50
15.00
• Steel (plain) ______
• Steel (alloy) ______
• Cast iron
______
• Aluminum ______
• Magnesium ______
(b) A tube constructed of which of the alloys will
cost the least amount?
• Cast iron
• Aluminum
• Magnesium
• Steel (plain)
• Steel (alloy)
CHAPTER 8 DEFORMATION AND STRENGTHENING MECHANISMS
Reserve Question 01: Atomic ordering with edge
dislocations
Reserve Question 06: Theoretical vs experimental
strength
After an edge dislocation has passed through some
region of a crystal, the atomic arrangement of that
region is disordered.
(a) True
(b) False
How does the theoretical strength of a solid material
compare with its experimental strength?
(a) Strengththeoretical < strengthexperimental
(b) Strengththeoretical = strengthexperimental
(c) Strengththeoretical > strengthexperimental
Reserve Question 02: Dislocation motion
The process by which plastic deformation is produced
by dislocation motion is called ______.
Reserve Question 03: Edge dislocation movement
Relative to the direction of an applied shear stress,
the direction of motion of an edge dislocation’s line is
(a) perpendicular.
(b) parallel.
Reserve Question 04: Screw dislocation movement
Relative to the direction of an applied shear stress,
the direction of motion of a screw dislocation’s line is
(a) perpendicular.
(b) parallel.
Reserve Question 07: Edge dislocation strain
The atoms surrounding an edge dislocation experience what kind(s) of strain(s)?
(a) Shear strains
(b) Tensile strains
(c) Compressive strains
Reserve Question 08: Screw dislocation strain
The atoms surrounding a screw dislocation experience
what kind(s) of strain(s)?
(a) Shear strains
(b) Tensile strains
(c) Compressive strains
Reserve Question 09: Ductility vs slip systems
Reserve Question 05: Edge dislocation stress
In response to an applied shear stress, an edge dislocation moves in which direction relative to its line?
(a) Perpendicular
(b) Parallel
A metal having a crystal structure with many operable
slip systems will be relatively
(a) ductile.
(b) brittle.
Reserve Questions and Problems • R-49
Reserve Question 10: Slip direction
Reserve Problem 15a (question pool)
For a particular crystal structure, the slip direction is
that direction in the slip plane having the
(a) lowest linear density.
(b) highest linear density.
Each option below depicts a candidate slip plane and
direction in a cubic crystal.
Reserve Question 11: Slip plane–atomic packing
Note: the loading axis is depicted with a BLACK dotted line and is always normal to a cube face.
(a)
For a particular crystal structure, the slip plane is that
plane having the
(a) least dense atomic packing.
(b) most dense atomic packing.
Which of the following slip system candidates is the
least likely to exhibit slip?
Reserve Question 12: Slip planes
Dislocations move with the same degree of ease on
all crystallographic planes of atoms and in all crystallographic directions.
(a) True
(b) False
(b)
Reserve Question 13: Slip systems
The slip system for a particular crystal structure is
that crystallographic plane-direction combination for
which atomic distortion accompanying the motion of
a dislocation is
(a) a minimum.
(b) a maximum.
Reserve Problem 14
Determine the angles α, β, and γ that are listed in the
cubic unit cell provided.
Enter the angles in degrees.
Note: You should be able to use basic facts about
cube geometry and crystallographic convention to
solve this, rather than elaborate direction cosine
equations.
(c)
(d)
(e)
R-50 • Reserve Questions and Problems
Reserve Problem 16a (question pool)
Reserve Problem 17a (question pool)
Each option below depicts a candidate slip plane and
direction in a cubic crystal.
The figures below depict hypothetical room-temperature
random polycrystalline grain structures (at the same
magnification) for the same single-component metal.
Which of these structures is expected to provide the
lowest yield stress?
(a)
Which of the following slip system candidates is the
least likely to exhibit slip?
Note: the loading axis is depicted with a BLACK dotted line and is always normal to a cube face.
(a)
(b)
(b)
(c)
(c)
(d)
(d)
(e)
Reserve Questions and Problems • R-51
Reserve Question 18: Twinning and crystal
structures
Mechanical twinning occurs in metals having which
type(s) of crystal structure(s)?
(a) BCC
(b) FCC
(c) HCP
Reserve Question 19: Grain size vs mechanical
properties
How does grain size influence strength of a polycrystalline material?
(a) Strengthfine-grained < strengthcourse-grained
(b) Strengthfine-grained = strengthcourse-grained
(c) Strengthfine-grained > strengthcourse-grained
Reserve Question 20: Grain size vs toughness
Reducing the grain size of metal improves toughness.
(a) true
(b) false
Reserve Question 21: Dislocation density
As dislocation density increases, the resistance to dislocation movement
(a) increases.
(b) decreases.
Reserve Question 22: Dislocation interactions
On the average, dislocation-dislocation strain interactions are
(a) repulsive.
(b) attractive.
Reserve Question 23: Ductility vs
strain hardening
As a metal is strain hardened, its ductility
(a) increases
(b) decreases
Reserve Question 24: Strain hardening
Most metals strain harden at room temperature.
(a) true
(b) false
Reserve Problem 25
It is necessary to select a metal alloy for an application that requires a yield strength of at least 345 MPa
(50,000 psi) while maintaining a minimum ductility
(%EL) of 20%. If the metal may be cold worked,
decide which of the following are candidates: copper,
brass, and a 1040 steel.
• Brass
• Copper
• 1040 steel
Reserve Problem 26
The average grain diameter and yield strength for a
brass material were measured as a function of time at
650°C. Given the following yield strengths for the two
specimens, compute the heat treatment time required
at 650°C to give a yield strength of 100 MPa. Assume
a value of 2 for n, the grain diameter exponent.
Time
(min)
Yield Strength
(MPa)
Grain Diameter
(mm)
30
90
3.9 × 10−2
90
75
6.6 × 10−2
Reserve Question 27: Recovery
During the recovery of a cold-worked material, which
of the following statement(s) is (are) true?
(a) Some of the internal strain energy is relieved.
(b) All of the internal strain energy is relieved.
(c) There is some reduction in the number of
dislocations.
(d) There is a significant reduction in the number
of dislocations, to approximately the number
found in the precold-worked state.
(e) The electrical conductivity is recovered to its
precold-worked state.
(f) The thermal conductivity is recovered to its
precold-worked state.
(g) The metal becomes more ductile, as in its
precold-worked state.
(h) Grains with high strains are replaced with
new, unstrained grains.
Reserve Question 28: Recrystallization
During the recrystallization of a cold-worked material,
which of the following statement(s) is (are) true?
(a) Some of the internal strain energy is relieved.
(b) All of the internal strain energy is relieved.
(c) There is some reduction in the number of
dislocations.
(d) There is a significant reduction in the number
of dislocations, to approximately the number
found in the precold-worked state.
(e) The electrical conductivity is recovered to its
precold-worked state.
(f) The thermal conductivity is recovered to its
precold-worked state.
(g) The metal becomes more ductile, as in its
precold-worked state.
(h) Grains with high strains are replaced with
new, unstrained grains.
R-52 • Reserve Questions and Problems
Reserve Question 29: Grain growth requirements
Reserve Question 33: Adhesive bonding
Grain growth must always be preceded by recovery
and recrystallization.
(a) True
(b) False
The bonding forces between adhesive and adherend
surfaces are thought to be
(a) Electrostatic
(b) Covalent
(c) Chemical
Reserve Problem 30
A hypothetical metal alloy has a grain diameter of
2.4 × 10−2 mm. After a heat treatment at 575°C for
500 min, the grain diameter has increased to 7.3 ×
10−2 mm. Compute the time required for a specimen
of this same material (i.e., d0 = 2.4 × 10−2 mm) to
achieve a grain diameter of 5.5 × 10−2 mm while being
heated at 575°C. Assume the n grain diameter exponent has a value of 2.2.
Reserve Problem 31: Tensile strength vs numberaverage molecular weight I
Tensile strengths and number-average molecular
weights for two polymers are as follows:
Tensile
strength
(MPa)
37.7
131
Number average
molecular weight
(g/mol)
36800
62400
Estimate the tensile strength (in MPa) for a numberaverage molecular weight of 51500 g/mol.
Reserve Problem 32: Tensile strength vs numberaverage molecular weight II
Tensile strengths and number-average molecular
weights for two polymers are as follows:
Tensile
strength
(MPa)
138
184
Number average
molecular weight
(g/mol)
12600
28100
Estimate number average molecular weight (in g/mol)
at a tensile strength of 141 Mpa.
Reserve Question 34: Anisotropy of
drawing
Deformation of a semicrystalline polymer by drawing
produces which of the following?
(a) Increase in strength in the direction of
drawing.
(b) Decrease in strength in the direction of
drawing.
(c) Increase in strength perpendicular to the
direction of drawing.
(d) Decrease in strength perpendicular to the
direction of drawing.
Reserve Question 35: Tensile strength–
Deformation
How does deformation by drawing of a semicrystalline polymer affect its tensile strength?
(a) Increases
(b) Decreases
Reserve Question 36: Tensile strength–
Degree of crystallinity
How does increasing the degree of crystallinity of a
semicrystalline polymer affect its tensile strength?
(a) Increases
(b) Decreases
Reserve Question 37: Tensile strength–
Molecular weight
How does increasing the molecular weight of a semicrysatlline polymer affect its tensile strength?
(a) Increases
(b) Decreases
CHAPTER 9 FAILURE
Reserve Question 01: Intergranular/transgranular
fracture types
Which kind of fracture (ductile or brittle) is associated
with each of the two crack propagation mechanisms?
• Intergranular ______
• Transgranular ______
Reserve Problem 02: Altering crack radii
The fracture strength of glass may be increased by
etching away a thin surface layer. It is believed that
the etching may alter the surface crack geometry (i.e.
reduce crack length and increase tip radius). Calculate
the ratio of the etched and original crack tip radii if
the fracture strength is increased by a factor of 7 when
28% of the crack length is removed.
Reserve Questions and Problems • R-53
Reserve Problem 03: Crack length in
plane strain
Reserve Question 07: Plane strain plate fracture
A structural component in the shape of a flat plate
27.3 mm thick is to be fabricated from a metal alloy
for which the yield strength and plane strain fracture
toughness values are 535 MPa and 31.3 MPa-m1/2,
respectively. For this particular geometry, the value
of Y is 1.8. Assuming a design stress of 0.5 times the
yield strength, calculate the critical length of a surface
flaw.
A plate of an alloy steel has a plane-strain fracture
toughness of 50 MPa-m1/2. If it is known that the largest surface crack is 0.5 mm long, and that the value of
Y is 1.1, which of the following can be said about this
plate when a tensile stress of 1200 MPa is applied?
(a) The plate will definitely fracture.
(b) The plate will definitely not fracture.
(c) It is not possible to determine whether or not
the plate will fracture.
Reserve Question 04: Effect of temp on fracture
toughness
Reserve Question 08: Stress raisers
How would the plane strain fracture toughness of a
metal be expected to change with rising temperature?
(a) Increase
(b) Decrease
(c) Remain constant
Reserve Question 05: Factors in brittle polymers
Which of the following factor(s) favor(s) brittle fracture in polymers?
(a) Increasing in temperature.
(b) Increasing in strain rate.
(c) The presence of a sharp notch.
(d) Decreasing specimen thickness.
Reserve Question 06: Fracture test–Charpy
The results of a laboratory test that is used to assess
the mechanical or failure characteristics of metals are
shown below. Select labels for both of the plot axes.
X-axis: ______
Y-axis: ______
The effect of a stress raiser is more significant for
which of the following types of materials?
(a) Brittle materials
(b) Ductile materials
Reserve Problem 09
A structural component is fabricated from an alloy
that has a plane strain fracture toughness of 45 MPa.
It has been determined that this component fails at a
stress of 300 MPa when the maximum length of a surface crack is 0.95 mm. What is the maximum allowable
surface crack length (in mm) without fracture for this
same component exposed to a stress of 300 MPa and
made from another alloy with a plane strain fracture
toughness of 100.0 MPa? The geometry factor Y is the
same in both cases.
Reserve Problem 10
Following are tabulated data that were gathered from
a series of Charpy impact tests on a ductile cast iron.
Temperature ( °C)
Impact Energy (J)
−25
−50
−75
−85
−100
−110
−125
−150
−175
124
123
115
100
73
52
26
9
6
(a) Determine a ductile-to-brittle transition temperature as that temperature corresponding
to the average of the maximum and minimum
impact energies.
(b) Determine a ductile-to-brittle transition temperature as that temperature at which the
impact energy is 80 J.
R-54 • Reserve Questions and Problems
Reserve Problem 11
Reserve Problem 14a (question pool)
Following are tabulated data that were gathered from
a series of Charpy impact tests on a tempered 4140
steel alloy.
The figure below depicts a brittle material featuring
four elliptical flaws, each featuring the same radius of
curvature at their tips. Based on the loading type and
the loading axis illustrated, which flaw is most likely
to propagate?
Temperature ( °C)
Impact Energy (J)
100
89.3
75
88.6
50
87.6
25
85.4
0
82.9
−25
78.9
−50
73.1
−65
66.0
−75
59.3
−85
47.9
−100
34.3
−125
29.3
−150
27.1
−175
25.0
(a) Determine a ductile-to-brittle transition temperature as that temperature corresponding
to the average of the maximum and minimum
impact energies.
(b) Determine a ductile-to-brittle transition temperature as that temperature at which the
impact energy is 70 J.
Reserve Question 15: Fracture test–Tensile
The results of a laboratory test that is used to assess
the mechanical or failure characteristics of metals
are shown below. Select labels for both of the plot
axes.
Reserve Problem 12
What is the maximum carbon content possible for a
plain carbon steel that must have an impact energy of
at least 150 J at 0°C?
Reserve Problem 13
Compute the minimum value of plane-strain fracture
toughness required of a material to satisfy the leakbefore-break criterion for a cylindrical pressure vessel
similar to that shown in Figure 9.11. The vessel radius
and wall thickness values are 250 mm and 10.5 mm, respectively, and the fluid pressure is 3.0 MPa. Assume
a value of 3.5 for the factor of safety.
X-axis ______
Y-axis ______
Reserve Questions and Problems • R-55
Reserve Question 16: Fracture test–fatigue
Reserve Question 19: Creep behavior
The results of a laboratory test that is used to assess
the mechanical or failure characteristics of metals are
shown below. Select labels for both of the plot axes.
Match each of the three stages of creep behavior with
the manner in which creep rate changes with increasing time.
Primary (transient creep)
• Decreasing creep rate
• Constant creep rate
• Increasing creep rate
Secondary creep
• Decreasing creep rate
• Constant creep rate
• Increasing creep rate
Tertiary creep
• Decreasing creep rate
• Constant creep rate
• Increasing creep rate
X-axis ______
Y-axis ______
Reserve Question 20: Fracture test–creep
Reserve Problem 17
A cylindrical rod of diameter 9.5 mm fabricated from
a 2014-T6 aluminum alloy is subjected to rotatingbending load cycling; test results (as S-N behavior) are
shown in Figure 9.27. If the maximum and minimum
loads are +400 N and –400 N, respectively, determine
its fatigue life. Assume that the separation between
loadbearing points is 72.5 mm.
The results of a laboratory test that is used to assess
the mechanical or failure characteristics of metals are
shown below. Select labels for both of the plot axes.
Reserve Problem 18
(a) Compare the fatigue limits for polystyrene
(Figure 9.29) and the cast iron for which fatigue data are given in the table below:
X-axis: ______
Y-axis: ______
Stress Amplitude
[MPa (ksi)]
Cycles to
Failure
248 (36.0)
1 × 105
Reserve Question 21: Creep elongation
236 (34.2)
3×
224 (32.5)
1 × 106
213 (30.9)
3 × 106
201 (29.1)
1 × 107
A specimen 667 mm long of a low carbon-nickel alloy
is to be exposed to a tensile stress of 37 MPa at 538°C.
Using the Animated Figure 9.40, determine its elongation after 5300 hours. Assume that the total of both instantaneous and primary creep elongations is 1.5 mm.
193 (28.0)
3 × 107
193 (28.0)
1 × 108
193 (28.0)
3 × 108
105
(b) Compare the fatigue strengths at 106 cycles
for poly(ethylene terephthalate) (PET, Figure
92.9) and 70Cu–30Zn brass (Figure 9.27).
Reserve Question 22: Creep tensile load
For a cylindrical low carbon-nickel alloy specimen
originally 11 mm in diameter and 503 mm long, what
tensile load (in N) is necessary to produce a total elongation of 4.8 mm after 19000 hours at 538°C? Assume
that the sum of instantaneous and primary creep
elongations is 0.86 mm. The logarithm stress versus
logarithm of steady-state creep rate plot for this alloy
is in the Animated Figure 9.40.
R-56 • Reserve Questions and Problems
Reserve Question 23: Factors affecting creep
Reserve Problem 26
Which of the following affect(s) the creep characteristics of metals?
(a) Melting temperature
(d) Ductility
A cylindrical component 75 mm long constructed
from an S-590 alloy (Figure 9.40) is to be exposed to
a tensile load of 20,000 N. What minimum diameter is
required for it to experience an elongation of no more
than 10.2 mm after an exposure for 1250 h at 815°C?
Assume that the sum of instantaneous and primary
creep elongations is 0.7 mm.
(e) Elastic modulus
Reserve Problem 27
(f) Resilience
A cylindrical specimen 7.5 mm in diameter of an S-590
alloy is to be exposed to a tensile load of 9000 N.
At approximately what temperature will the steadystate creep be 10−2 h−1?
(b) Grain size
(c) Yield strength
Reserve Question 24: Increasing stress or
temperature
If either stress or temperature is increased, indicate
which of the following consequences will result.
(a) The instantaneous strain at the time of stress
application decreases.
(b) The steady-state creep rate increases.
(c) The rupture lifetime is diminished.
Reserve Question 25: Temperature for creep
Above about what temperature does the creep
become an important failure mechanism for a metal?
(a) 0.1Tm
(b) 0.2Tm
(c) 0.3Tm
(d) 0.4Tm
(e) 0.5Tm
Reserve Problem 28
If a component fabricated from an S-590 alloy (Figure
9.39) is to be exposed to a tensile stress of 300 MPa
(43,500 psi) at 650°C (1200°F), estimate its rupture
lifetime.
Reserve Problem 29
A cylindrical component constructed from an S-590
alloy (Figure 9.39) is to be exposed to a tensile load
of 10,000 N. What minimum diameter is required for
it to have a rupture lifetime of at least 10 h at 730°C?
Reserve Problem 30
(a) Using Figure 9.39, compute the rupture lifetime for an S-590 alloy that is exposed to a
tensile stress of 100 MPa at 925°C.
(b) Compare this value to the one determined
from the Larson-Miller plot of Figure 9.41,
which is for this same S-590 alloy.
CHAPTER 10 PHASE DIAGRAMS
Reserve Problem 01
The mineral olivine is a solid solution of the silicate compounds forsterite (Mg2SiO4) and fayalite
(Fe2SiO4).
How many chemical components are there in a sample of olivine?
(a)
(b)
(c)
(d)
1
2
3
4
Reserve Questions and Problems • R-57
Reserve Problem 02a (question pool)
Which of the following depictions is consistent with a
single-component, single-phase 2D crystalline system?
(a)
(d)
(b)
(e)
(c)
Reserve Problem 03
Seawater, which covers the majority of the earth, is
composed primarily of molecules of H2O and equal
numbers of Na+ ions and Cl− ions. Suppose we have
a thoroughly mixed solution (containing these species
only) at 25oC. How many components and how many
phases are in such a system?
(a) 1 component, 1 phase
(f)
(g) 2 component, 3 phase
(h) 2 component, 4 phase
(i) 3 component, 1 phase
(j) 3 component, 2 phase
(k) 3 component, 3 phase
(l) 3 component, 4 phase
(b) 1 component, 2 phase
(m) 4 component, 1 phase
(c) 1 component, 3 phase
(n) 4 component, 2 phase
(d) 1 component, 4 phase
(o) 4 component, 3 phase
(e) 2 component, 1 phase
(p) 4 component, 4 phase
(f) 2 component, 2 phase
R-58 • Reserve Questions and Problems
Reserve Problem 04
Reserve Problem 08
Select all of the two-phase material systems from the
list below. Select all that apply.
(a) Solid ductile cast iron (ferrite solid solution +
embedded graphite spheres)
At a pressure of 0.01 atm, determine (a) the melting
temperature for ice, and (b) the boiling temperature
for water.
(b) Solid sodium chloride (salt, NaCl)
(c) Liquid bronze (Cu + Sn liquid solution)
(d) Solid gray cast iron (ferrite solid solution +
embedded graphite flakes)
(e) Solid aluminum featuring dissolved silicon
(f) Solid lead-tin solder (a mixture of Pb-rich and
Sn-rich solid solutions)
(g) Partially melted aluminum
(h) Frozen water with trapped air bubbles
(i) Epoxy embedded with carbon fibers
Reserve Problem 05
Complete the following statements regarding conditions that must be satisfied in order for a solid solution
to exhibit extensive solubility.
Reserve Question 09: Liquidus line
A liquidus line separates which of the following combinations of phase fields?
(a) Liquid and Liquid + α
(b) α and Liquid + α
(c) α and α + β
(d) Liquid + α and α + β
Reserve Question 10: Solvus line
A solvus line separates which of the following pairs of
phase fields?
(a) Liquid and Liquid + α
(b) α and Liquid + α
(c) α and α + β
(d) Liquid + α and α + β
The solute and host species must have very [w] sizes.
Reserve Problem 11
The solute and host species must attempt to pack with
[x] crystal structure.
How many kilograms of nickel must be added to
5.66ks of copper to yield a liquidus temperature of
1200°C? Use Animated Figure 10.3a.
The solute and host species must feature [y] valence
electron configuration.
The solute and host species must feature [z] ability to
attract electrons (electronegativity).
w = similar, different
x = a similar (or the same), a different
y = a similar (or the same), a different
z = a similar, a different
Reserve Question 06: Solvent/solute
For a solution, which of the following is present in the
higher concentration?
(a) Solvent
(b) Solute
Reserve Problem 07
Consider a specimen of ice that is at −10°C and 1 atm
pressure. Using Figure 10.2, the pressure–temperature
phase diagram for H2O, determine the pressure to
which the specimen must be raised or lowered to
cause it (a) to melt, and (b) to sublime.
Reserve Question 12: Information on phase
diagrams
Which of the following kinds of information may be
determined with the aid of a phase diagram?
(a) The phase(s) present at a specified temperature and composition.
(b) The composition(s) of phase(s) present at a
specified temperature and composition.
(c) The fraction(s) of phase(s) present at specified temperature and composition.
Reserve Questions and Problems • R-59
Reserve Problem 13: Pb-Sn phase diagram–
composition
In the Animated Figure 10.8 is shown the lead-tin
phase diagram. For an alloy of composition 25 wt%
Sn–75 wt% Pb, select the phase(s) present and their
composition(s) for each of the temperatures cited.
(a) 300°C?
• L = 25.0 wt% Sn–75.0 wt% Pb
• L = 25.0 wt% Sn–75.0 wt% Pb;
α = 10.0 wt% Sn–90.0 wt% Pb
• L = 10.0 wt% Sn–90.0 wt% Pb;
α = 10.0 wt% Sn–90.0 wt% Pb
• L = 90.0 wt% Sn–10.0 wt% Pb;
α = 10.0 wt% Sn–90.0 wt% Pb
(b) 200°C?
• α = 17.0 wt% Sn–83.0 wt% Pb;
L = 55.7 wt% Sn–44.3 wt% Pb
• α = 17.0 wt% Sn–83.0 wt% Pb;
β = 55.7 wt% Sn–44.3 wt% Pb
• α = 18.3 wt% Sn–81.7 wt% Pb;
β = 97.8 wt% Sn–2.2 wt% Pb
• L = 25.0 wt% Sn–75.0 wt% Pb;
α = 25.0 wt% Sn–75.0 wt% Pb
(c) 183°C?
• α = 25.0 wt% Sn–75.0 wt% Pb;
β = 25.0 wt% Sn–75.0 wt% Pb
• L = 25.0 wt% Sn–75.0 wt% Pb;
α = 25.0 wt% Sn–75.0 wt% Pb;
β = 25.0 wt% Sn–75.0 wt% Pb
• α = 18.3 wt% Sn–81.7 wt% Pb;
β = 97.8 wt% Sn–2.2 wt% Pb
• L = 61.9 wt% Sn–38.1 wt% Pb;
α = 18.3 wt% Sn–81.7 wt% Pb;
β = 97.8 wt% Sn–2.2 wt% Pb
(d) 100°C?
• α = 25.0 wt% Sn–75.0 wt% Pb;
β = 25.0 wt% Sn–75.0 wt% Pb
• L = 25.0 wt% Sn–75.0 wt% Pb;
α = 25.0 wt% Sn–75.0 wt% Pb;
β = 25.0 wt% Sn–75.0 wt% Pb
• α = 5.1 wt% Sn–94.9 wt% Pb;
β = 98.7 wt% Sn–1.3 wt% Pb
• L = 25.0 wt% Sn–75.0 wt% Pb;
α = 5.1 wt% Sn–94.9 wt% Pb;
β = 98.7 wt% Sn–1.3 wt% Pb
Reserve Problem 14: Pb-Sn phase diagram–Phases
In Animated Figure 10.8 is shown the lead-tin phase
diagram. Using this diagram, determine which of the
following phase(s)/phase combination(s) (alpha, beta,
liquid, alpha + liquid, beta + liquid, alpha + beta,
and alpha + beta + liquid) will be present for an alloy
of composition 61.9 wt% Sn–38.1 wt% Pb that is at
equilibrium at 185°C?
Reserve Question 15: Phases present at eutectic
point
At a eutectic point on a binary temperature-composition
phase diagrams, how many phases are present when
the system is at equilibrium?
(a) 0
(c) 2
(b) 1
(d) 3
Reserve Problem 16
A 45 wt% Pb–55 wt% Mg alloy is rapidly quenched
to room temperature from an elevated temperature
in such a way that the high-temperature microstructure is preserved. This microstructure is found to
consist of the phase and Mg2Pb, having respective
mass fractions of 0.65 and 0.35. Determine the approximate temperature from which the alloy was
quenched.
Reserve Problem 17
Two intermetallic compounds, AB and AB2, exist
for elements A and B. If the compositions for AB
and AB2 are 34.3 wt% A–65.7 wt% B and 20.7 wt%
A–79.3 wt% B, respectively, and element A is potassium, identify element B.
• Phosphorus
• Sulfur
• Arsenic
• Antimony
Reserve Problem 18
An intermetallic compound is found in the magnesiumgallium system that has a composition of 41.1 wt%
Mg–58.9 wt% Ga. Specify the formula for this compound.
• MgGa
• Mg2Ga
• MgGa2
• Mg3Ga2
R-60 • Reserve Questions and Problems
Reserve Problem 19
Reserve Problem 23
Specify the liquidus, solidus, and solvus temperatures
for the following alloy: 1.5 wt% C – 98.5 wt% Fe. If no
temperature, please put in “0.0”.
Liquidus temperature ______
Solidus temperature ______
Solvus temperature
______
Specify the number of degrees of freedom for the following alloys:
(a) 95 wt% Ag-5 wt% Cu at 780°C
(b) 80 wt% Ni-20 wt% Cu at 1400°C
(c) 44.9 wt% Ti-55.1 wt% Ni at 1310°C
(d) 61.9 wt% Sn-38.1 wt% Pb at 183°C
(e) 2.5 wt% C-97.5 wt% Fe at 1000°C
Reserve Question 20: Eutectoid reaction
A eutectoid reaction involves which of the following
phases?
(a) One liquid and one solid
(b) One liquid and two solid
(c) Two liquids and one solid
(d) Three solid
Reserve Question 21: Peritectic reaction
A peritectic reaction involves which of the following
combinations of phase fields?
(a) One liquid and one solid
(b) One liquid and two solid
(c) Two liquids and one solid
(d) Three solid
Reserve Question 22: Congruent transformations
For a congruent phase transformation there are
(a) no composition alterations.
(b) compositional alterations.
Reserve Problem 24
The mass fractions of total ferrite and total cementite
in an iron–carbon alloy are 0.88 and 0.12, respectively.
Is this a hypoeutectoid or hypereutectoid alloy?
Reserve Problem 25
A steel alloy is known to contain 93.8 wt% Fe, 6.0
wt% Ni, and 0.2 wt% C. Assume that there are no
alterations in the positions of other phase boundaries
with the addition of Ni.
(a) What is the approximate eutectoid temperature of this alloy?
(b) What is the proeutectoid phase when this
alloy is cooled at temperature below the
eutectoid?
(c) Compute the relative amounts of the proeutectoid phase and pearlite.
CHAPTER 11 PHASE TRANSFORMATIONS
Reserve Problem 01
It is known that the kinetics of some transformation obeys
the Avrami equation and that the value of k is 6.0 × 10−8
(for time in minutes). If the fraction transformed is 0.75
after 200 min, determine the rate of this transformation.
Diffusion-dependent with no change(s) in phase
composition(s)
• Eutectoid reaction
• Recrystallization
• Martensitic transformation
Reserve Question 02: Types of phase transformations
Match each transformation description below with
name of a transformation of this type.
Reserve Question 03: Equilibrium
in solid
Diffusion-dependent with change(s)
composition(s)
• Martensitic transformation
• Eutectoid reaction
• Recrystallization
Equilibrium structures are commonly achieved in
solid systems.
(a) True
(b) False
Diffusionless
• Recrystallization
• Martensitic transformation
• Eutectoid reaction
in
phase
Reserve Question 04: Heat treatment
Below is shown the isothermal transformation diagram for a 0.45 wt% C iron-carbon alloy. List the
microconstituent(s) present for the heat treatment
labeled (a) on this diagram. It is not necessary to state
the proportion(s) of the microconstituents.
Reserve Questions and Problems • R-61
900
1600
Temperature (°C)
700
(a)
A+F
300
1400
(c)
P
B
(c)
600
500
(b)
400
(a)
(c)
A
1200
A+P
1000
A+B
(b)
(c)
50%
800
M(start)
M(50%)
(b)
(c)
600
(b)
M(90%)
400
200
100
0
0.1
Temperature (°F)
800
200
(b)
1
(c)
10
102
103
(a)
104
(a) How long will it take for the austeniteto pearlite reaction to go to 50% completion?
To 100% completion?
50% completion: ______
100% completion: ______
(b) Estimate the hardness of the alloy that has
completely transformed to pearlite.
Reserve Question 06: Fe microstructures I
Schematic room temperature microstructures for four
iron-carbon alloys are shown below. Rank these alloy
microstructures (by letter) from most ductile to the
least ductile.
Fe3C
Fe3C
(b)
105
Fe3C
Time (s)
Reserve Problem 05
Suppose that a steel of eutectoid composition is
cooled to 550°C (1020°F) from 760°C (1400°F) in less
than 0.5 s and held at this temperature.
𝛼
𝛼
(A)
(a)
(b)
(c)
(d)
(B)
C, D, A, B
B, D, A, C
A, B, D, C
D, B, C, A
𝛼
Fe3C
Fe3C
𝛼
𝛼
Fe3C
(C)
(e)
(f)
(g)
(h)
(D)
C, A, B, D
B, A, D, C
A, B, C, D
D, C, B, A
CHAPTER 12 ELECTRICAL PROPERTIES
Reserve Problem 01
Reserve Question 03: Conductivities
Select the word combination that best completes this
statement.
Match each of the conductivity values/ranges with its
associated class of materials.
Electric current is a measure of [a] _______ passing
per unit [b]_______, and the base units of current
are [c]______ per [d]______, otherwise known as an
[e]_______.
• Time
• Volts
• Ampere
• Resistance
• Second
• Ohm
• Charge
• Coulomb
• Voltage
10−20 to 10−10 (Ω-m)−1
• Semiconductors
Reserve Problem 02a (question pool)
The current-voltage behavior of specimens [a]–[e] is
depicted in the figure below.
Which of these specimens features the lowest resistance?
• Metals
• Insulators
107 (Ω-m)−1
• Metals
• Insulators
• Semiconductors
10−6 to 104 (Ω-m)−1
• Insulators
• Semiconductors
• Metals
R-62 • Reserve Questions and Problems
Reserve Question 04: Band structures
Match each of the following energy band structures
with the type of material it represents.
(A)
Empty
conduction
band
Band gap
Filled
valence
band
• Semiconductor
• Metal
• Insulator
(B)
Empty
conduction
band
Band gap
Filled
valence
band
• Metal
• Insulator
• Semiconductor
Reserve Question 06: Energy name
______ energy is the name of energy corresponding to
the highest filled electron state at 0 K.
Reserve Question 07: Free electrons 01
Are energies for electrons that participate in the conduction process (i.e., free electrons) greater or less
than the Fermi energy?
(a) Greater than
(b) Less than
Reserve Question 08: Holes
Are energies for holes greater or less than the Fermi
energy?
(a) Greater than
(b) Less than
Reserve Question 09: Insulator band gap
An insulator has an energy band gap that is relatively
(a) wide.
(b) narrow.
Reserve Question 10: P band
For a material that contains N atoms, how many electron states will there be in a p band?
Reserve Question 11: S band
For a material that contains N atoms, how many electron states will there be in an s band?
Reserve Question 12: Semiconductor band gap
(C)
Empty
band
Band gap
Empty states
Filled states
• Insulator
• Semiconductor
• Metal
Reserve Question 05: Electrons for conductivity
All electrons present in a material are available to
participate in the conduction process.
(a) True
(b) False
A semiconductor has an energy band gap that is
relatively
(a) wide
(b) narrow
Reserve Question 13: Free electrons in metals
Electrons in metals do not require any excitation
before becoming conduction electrons that are free.
(a) True
(b) False
Reserve Question 14: Temperature vs band gap
For nonmetallic materials, which of the following is
true?
(a) The wider the band gap, the lower the electrical conductivity at a given temperature.
(b) The wider the band gap, the higher the electrical conductivity at a given temperature.
Reserve Questions and Problems • R-63
Reserve Question 15: Current in perfect crystal
Reserve Question 20: Resistivity contributions
In a perfect crystal (i.e., without any imperfections),
application of an electric field will result in a continuously increasing electric current with time.
(a) True
(b) False
Which of the following have a significant influence on
a material’s electrical resistivity?
(a) impurity concentration
(b) temperature
(c) grain size
(d) cold work
(e) vacancy concentration
Reserve Question 16: Electric field induced
electron movement
When an electric field is applied, in which direction
are the free electrons accelerated?
(a) Opposite to the direction of the electric
field.
(b) In the same direction as the electric field.
Reserve Question 17: Ion mobility
At temperatures between 775°C and 1100°C, the activation energy and preexponential for the diffusion
coefficient of A2+ in the metal oxide, AO, are 110 kJ/
mol and 7.1 × 10−7 m2/s, respectively. Compute the
mobility [in m2/(V-s)] of A2+ at 908°C.
Reserve Problem 21
(a) Using the data in Figure 12.8, determine the
values of ρ0 and a from Equation 12.10 for
pure copper. Take the temperature T to be in
degrees Celsius.
(b) Determine the value of A in Equation 12.11
for nickel as an impurity in copper, using the
data in Figure 12.8.
(c) Using the results of parts (a) and (b), estimate
the electrical resistivity of copper containing
1.75 at% Ni at 100°C.
Reserve Problem 22
Reserve Problem 18: Calculating resistivity
contributions
Conductivity in a metal is almost always reduced by
the introduction of defects into the lattice.
Estimate the electrical resistivity (in Ω-m) of metal Y
containing 1.3 at% of metal Z at 138°C, given the following data:
The factor primarily affected by defects is:
(a) free electron concentration
(b) electron charge
(c) electron mobility
(d) electron spin
ρ0
(Ω-m)
a
(Ω-m/°C)
A
(Ω-m)
1.5 × 10−7
6.7 × 10−11
1.2 × 10−6
Assume that all of the 1.3 at% of metal Z goes into
solid solution in metal Y. Use scientific notation.
Reserve Problem 23a (question pool)
Compute the number of electrons that each aluminum
atom donates, on average, to a bulk piece of aluminum metal. Room temperature data for aluminum:
The resistivity of aluminum is 2.63 × 10−8 Ω-m
Reserve Problem 19: Multi-component
conductivity
The electron mobility of aluminum is 0.0012 m2/(V-s)
Some two-phase metal alloy is known to be composed
of α and β phases; mass fractions of these phases are
0.74 and 0.26, respectively. Room-temperature electrical resistivity and density data for these phases are
tabulated below. Using this information, calculate the
electrical resistivity (in Ω-m) of the alloy at room temperature (use scientific notation).
The mass density of aluminum is 2.7 g/cm3
The atomic weight of aluminum is 27 g/mol
Reserve Problem 24
Compute the number of electrons that each atom
donates, on average, to a bulk piece of hypothetical
metal. Room temperature data for the metal:
The resistivity of the metal is [r] Ω-cm
Phase
Resistivity (Ω-m)
Density (g/cm2)
α
1.7 × 10−7
8.31
The electron mobility of the metal is [m] cm2/(V-s)
β
6.7 × 10−8
8.18
The mass density of the metal is [d] g/cm3
The atomic weight of the metal is [w] g/mol
R-64 • Reserve Questions and Problems
Reserve Question 25: Electric field induced hole
movement
Reserve Question 32: n-type semiconductor–
Conduction
When an electric field is applied, in which direction
are the free electrons accelerated?
(a) Opposite to the direction of the electric field.
(b) In the same direction as the electric field.
For an n-type semiconductor, which type of charge
carrier is present in the greater concentration?
(a) Hole
(b) Electron
Reserve Question 26: Intrinsic semiconductor
Reserve Question 33: n-type semiconductor–
electrons/holes
The electrical conductivity of an intrinsic semiconductor is
(a) characteristic of the high-purity metal.
(b) due to the presence of impurities.
For an n-type semiconductor
(a) Concentrationelectrons > concentrationholes
(b) Concentrationelectrons = concentrationholes
(c) Concentrationelectrons < concentrationholes
Reserve Question 27: Metals vs semiconductors
Reserve Question 34: p-type semiconductor–
conduction
How do the electrical conductivities of metals compare with those of semiconductors?
(a) σmetals > σsemiconductors
(b) σmetals = σsemiconductors
(c) σmetals < σsemiconductors
Reserve Question 28: Temperature vs electron/
hole concentrations–Intrinsic
How does increasing temperature affect the concentration of both electrons and holes in an intrinsic
semiconductor?
(a) Increases the concentration.
(b) Decreases the concentration.
(c) May increase and/or decrease the concentration, depending on the temperature range.
Reserve Question 29: Acceptor impurity
Which type of charge carrier will be introduced into
a semiconductor by the presence of an acceptor
impurity?
(a) Electron
(b) Hole
Reserve Question 30: Donor impurity
Which type of charge carrier will be introduced
into a semiconductor by the presence of a donor
impurity?
(a) Impurity
(b) Hole
For a p-type semiconductor, which type of charge
carrier is present in the greater concentration?
(a) Hole
(b) Electron
Reserve Question 35: p-type semiconductor–
electrons/holes
For a p-type semiconductor
(a) Concentrationelectrons > concentrationholes
(b) Concentrationelectrons = concentrationholes
(c) Concentrationelectrons < concentrationholes
Reserve Question 36: Required impurity
concentrations
In order for a semiconductor to exhibit extrinsic electrical characteristics, relatively high impurity concentrations are required.
(a) True
(b) False
Reserve Problem 37
The following electrical characteristics have been determined for both intrinsic and n-type extrinsic indium
phosphide (InP) at room temperature:
σ (Ω∙m)−1
n (m−3)
p (m−3)
Intrinsic
2.5 × 10−6
3.0 × 1013
3.0 × 1013
Extrinsic
(n-type)
3.6 × 10−5
4.5 × 1014
2.0 × 1012
Calculate electron and hole mobilities.
μe = ______
μh = ______
Reserve Question 31: Extrinsic semiconductor
Reserve Question 38: Semiconducting devices
The electrical conductivity of an extrinsic semiconductor is
(a) characteristic of the high-purity material.
(b) due to the presence of impurities.
Which of the following are preferred for semiconducting devices?
(a) Single crystals
(b) Polycrystalline materials
Reserve Questions and Problems • R-65
Reserve Problem 39
Reserve Question 40: Temperature vs conductivity
Which of the following current-voltage plots is consistent with the behavior of a p-n junction?
As temperature increases, the electrical conductivities
of polymers and ionic ceramics
(a) Increase
(b) Decrease
(a)
Reserve Question 41: Band gap of ionic ceramics/
polymers
(b)
Most polymers and ionic ceramics have energy band
gap structures that are most similar to those of
(a) Insulators
(b) Semiconductors
(c) Metals
Reserve Question 42: Charge carriers in ionic
ceramics/polymers
(c)
The charge carriers in ionic ceramics and polymers
can be
(a) Electrons
(b) Holes
(c) Anion
(d) Cations
Reserve Problem 43: Capacitor calculations I
(d)
Consider a parallel-plate capacitor having an area of
2300 mm2 and a plate separation of 3.6 mm, and with a
material of dielectric constant 5.8 positioned between
the plates. Also, the value of ε0 is 8.85 × 10−12 F/m.
(a) What is the capacitance of this capacitor?
(b) Compute the electric field that must be applied for a charge of 8.8 × 10−9 C to be stored
on each plate.
Reserve Problem 44: Capacitor spacing
(e)
A parallel-plate capacitor using a dielectric material
having an εr of 2.8 has a plate spacing of 2.6 mm. If
another material having a dielectric constant of 4.5 is
used and the capacitance is to not change, what is the
new spacing between the plates? The value of ε0 is
8.85 × 10−12 F/m.
R-66 • Reserve Questions and Problems
CHAPTER 13 TYPES AND APPLICATIONS OF MATERIALS
Reserve Question 01: Alloy designations I
Reserve Question 08: Cast irons–Typical C
Which type of steel has the designation 4330?
(a) Plain carbon steel (b) Alloy steel
Which of the following is the typical range of carbon
concentrations for cast iron?
(a) 1.0 wt%–1.5 wt% C
(b) 1.0 wt%–2.0 wt% C
(c) 2.0 wt%–3.0 wt% C
(d) 2.0 wt%–3.5 wt% C
(e) 3.0 wt%–4.0 wt% C
(f) 3.0 wt%–4.5 wt% C
Reserve Question 02: Alloy designations II
Which type of steel has the designation 1015?
(a) Plain carbon steel (b) Alloy steel
Reserve Question 03: Alloy designations III
What is the carbon concentration of a steel having
designation 1050?
(a) 0.01 wt% C
(d) 0.50 wt% C
(b) 0.05 wt% C
(e) Impossible to say
(c) 0.10 wt% C
Reserve Question 04: Alloying elements–stainless
steels
Which three elements in the list below are primary
alloying elements for the stainless steels?
(a) Copper
(e) Chromium
(b) Vanadium
(f) Tungsten
(c) Nickel
(g) Silicon
(d) Molybdenum
Reserve Question 05: Carbon constituent in white
cast iron
In what form is carbon found in white cast irons?
(a) Cementite
(b) Graphite
Reserve Question 06: Carbon steel strength
Which of the sequences below represents the various
steels types in order of decreasing hardness?
(a) High-carbon > Medium-carbon > Low-carbon
(b) High-carbon > Low-carbon > Medium-carbon
(c) Medium-carbon > High-carbon > Low-carbon
(d) Medium-carbon > Low-carbon > High-carbon
(e) Low-carbon > High-carbon > Medium-carbon
(f) Low-carbon > Medium-carbon > High-carbon
Reserve Question 07: Cast irons–Minimum C
Which of the following is the minimum carbon content for cast irons?
(a) 1.0 wt% C
(d) 2.14 wt% C
(b) 1.56 wt% C
(e) 3.42 wt% C
(c) 2.00 wt% C
(f) 4.96 wt% C
Reserve Question 09: Cold worked stainless
steels
Which of the following stainless steel types may be
strengthened/hardened only by cold working?
(a) Ferritic
(b) Martensitic
(c) Austenitic
Reserve Question 10: Conversion of gray to nodular
irons
Which two of the following elements may be added to
gray irons before casting so as to produce ductile (or
nodular) irons?
(a) Silicon
(c) Serium
(b) Magnesium
(d) Molybdenum
Reserve Question 11: Corrosion resistance: low-carbon
vs HSLA steels
Which type of steel has the greater resistance to
corrosion?
(a) plain low-carbon
(b) high-strength, low-alloy
Reserve Question 12: Disadvantages of
ferrous alloys
Which of the following factors restrict(s) the use of
ferrous alloys?
(a) Poor corrosion resistance.
(b) Poor mechanical properties.
(c) Ores containing iron are rare.
(d) Costly and difficult to process.
Reserve Question 13: Ferrous alloy structures
All ferrous alloys have similar microstructures.
(a) True
(b) False
Reserve Questions and Problems • R-67
Reserve Question 14: Ferrous alloys
Reserve Question 21: Magnetic stainless steels
______ is the primary constituent of ferrous alloys.
Which of the following stainless steel types may be
magnetized?
(a) Ferritic
(b) Martensitic
(c) Austenitic
Reserve Question 15: Gray iron structures
Which of the following microconstituents/phases is
(are) most commonly found in gray cast irons?
(a) Graphite
(d) Austenite
(b) Pearlite
(e) Martensite
(c) Ferrite
Reserve Question 16: Heat-treatable stainless
steels 01
Which of the following types of stainless steels may be
heat treated to improve their mechanical properties?
(a) Ferritic
(d) Austenitic
(b) Pearlitic
(e) Precipitation-hardenable
(c) Martensitic
Reserve Question 17: Heat treatment of
low-carbon steels
The strengths of typical low-carbon steels are often
improved by heat treatment.
(a) True
(b) False
Reserve Question 18: High-carbon steels
What is the range of carbon concentrations for highcarbon steels?
(a) 0.40 wt%–1.0 wt% C
(b) 0.50 wt%–1.1 wt% C
(c) 0.50 wt%–1.4 wt% C
(d) 0.65 wt%–1.4 wt% C
(e) 0.65 wt%–1.7 wt% C
Reserve Question 19: Low-carbon steel structures
Which of the following microconstituent(s)/phase(s) is
(are) typically found in a low-carbon steel?
(a) Ferrite
(d) Austenite
(b) Pearlite
(e) Tempered martensite
(c) Martensite
Reserve Question 20: Low-carbon steels
Which of the following is the typical carbon concentration for a low-carbon steel?
(a) 0.05 wt% C (d) 0.50 wt% C
(b) 0.10 wt% C (e) 0.75 wt% C
(c) 0.25 wt% C (f) 1.00 wt% C
Reserve Question 22: Mechanical properties of
white cast irons
Which of the following characteristics best describe
the mechanical properties of white cast irons?
(a) Hard
(c) Ductile
(b) Weak
(d) Brittle
Reserve Question 23: Medium-carbon steel
structures
Which of the following microconstituents/phases is
typically found in a medium-carbon steel?
(a) Ferrite
(d) Austenite
(b) Pearlite
(e) Tempered martensite
(c) Martensite
Reserve Question 24: Medium-carbon steels
What is the typical carbon concentration range for
medium-carbon steels?
(a) 0.05 wt%–1.00 wt% C
(b) 0.10 wt%–0.50 wt% C
(c) 0.25 wt%–0.65 wt% C
(d) 0.25 wt%–1.00 wt% C
(e) 0.50 wt%–0.75 wt% C
Reserve Question 25: Melting
Which of the following ferrous alloy types is most easily
melted?
(a) Cast irons
(b) Low-carbon steels
(c) Medium-carbon steels
(d) High-carbon steels
(e) Stainless steels
Reserve Question 26: Metal alloy production
Which metal alloy type is produced in the greatest
quantities?
(a) Ferrous
(b) Copper
(c) Aluminum
(d) Titanium
R-68 • Reserve Questions and Problems
Reserve Question 27: Most common steels
Which of the following steel types is produced in the
greatest quantities?
(a) Low-carbon
(b) Medium-carbon
(c) High-carbon
Reserve Question 28: Nodular iron structures
Which of the following microconstituents/phases are
generally found in nodular irons?
(a) Graphite
(b) Pearlite
(c) Ferrite
(d) Austenite
(e) Martensite
Reserve Question 29: Types of steels
Which type of steel contains only residual amounts of
alloying elements?
(a) Plain carbon steel
(b) Alloy steel
Reserve Question 30: white cast irons vs
malleable irons
Which of the following changes occur(s) when white
cast irons are converted to malleable irons?
(a) The cementite is converted into graphite.
(b) The graphite is converted into cementite.
(c) The ductility increases.
(d) The ductility remains about the same.
(e) The ductility decreases.
Reserve Question 31: Alloy selection
For each of the following applications, match the
metal or alloy that is most suitable.
Milling machine base
• Titanium alloy
• Plain carbon steel
• Tool steel
• Zinc
• Tungsten
•
•
•
•
•
Aluminum
Platinum
Gray cast iron
Stainless steel
Brass
Walls of steam boiler
• Plain carbon steel
• Tool steel
• Zinc
• Tungsten
• Aluminum
•
•
•
•
•
Platinum
Gray cast iron
Stainless steel
Brass
Titanium alloy
High-speed aircraft
• Brass
• Stainless steel
• Gray cast iron
• Platinum
• Aluminum
•
•
•
•
•
Tungsten
Zinc
Tool steel
Plain carbon steel
Titanium alloy
Drill bit
• Titanium alloy
• Brass
• Stainless steel
• Gray cast iron
• Platinum
•
•
•
•
•
Aluminum
Tungsten
Zinc
Tool steel
Plain carbon steel
Cryogenic (very low temperature) container
• Aluminum
• Titanium alloy
• Platinum
• Plain carbon steel
• Gray cast iron
• Tool steel
• Stainless steel
• Zinc
• Brass
• Tungsten
Pyrotechnic (i.e., flares or fireworks)
• Tungsten
• Aluminum
• Zinc
• Brass
• Tool steel
• Stainless steel
• Plain carbon steel
• Gray cast iron
• Titanium alloy
• Platinum
High-temperature furnace elements to be used in oxidizing environments
• Plain carbon steel
• Gray cast iron
• Tool steel
• Stainless steel
• Zinc
• Brass
• Tungsten
• Titanium alloy
• Aluminum
• Platinum
Reserve Question 32: Beryllium copper alloys
Which of the following elements, when alloyed
with copper, results in an alloy that is precipitation
hardenable?
(a) Beryllium
(b) Zinc
(c) Gold
(d) Tin
(e) Lead
Reserve Questions and Problems • R-69
Reserve Question 33: Brass
Reserve Question 40: Noble metal advantages
Which of the following are primary constituents of
brass?
(a) Copper and zinc
(c) Copper and lead
(b) Copper and iron
(d) Tin and zinc
Which of the following are desirable characteristics of
the noble metals?
(a) High strengths.
(b) High ductilities.
(c) Oxidation resistance.
(d) High electrical conductivities.
Reserve Question 34: Bronze compositions
Which four of the following elements are alloyed with
copper to produce bronze alloys?
(a) Zinc
(d) Silicon
(b) Tin
(e) Nickel
(c) Aluminum
(f) Lead
Reserve Question 35: Cast alloys 01
Which type of nonferrous alloy is amenable to mechanical deformation?
(a) Cast
(b) Wrought
Reserve Question 41: Noble metals
Which of the following are noble metals?
(a) silver
(g) iridium
(b) gold
(h) osmium
(c) platinum
(i) plutonium
(d) palladium
(j) zirconium
(e) rhodium
(k) lead
(f) ruthenium
Reserve Question 42: Refractory alloys
Reserve Question 36: Cast alloys 02
Which type of nonferrous alloy is not often amenable
to mechanical deformation?
(a) Cast
(b) Wrought
Reserve Question 37: Magnesium alloys
Which of the following is (are) desirable characteristics of magnesium and its alloys?
(a) Very corrosion resistant in a variety of environments.
(b) Low melting temperatures.
(c) Easily work-hardened.
(d) Very high specific strengths.
Reserve Question 38: Mg alloys replacing
plastics
For which of the following reasons have magnesium
alloys replaced engineered plastics having comparable
densities?
(a) Magnesium alloys are stiffer.
(b) Magnesium alloys are more recyclable.
(c) Magnesium alloys are cheaper to produce.
Reserve Question 39: Nickel alloys
In which of the following environments do nickel and
its alloys perform extremely well?
(a) Acidic
(b) Basic
Which of the following are refractory metals?
(a) niobium
(e) copper
(b) molybdenum (f) titanium
(c) tungsten
(g) iron
(d) tantalum
(h) aluminum
Reserve Question 43: Superalloys
Which of the following are the primary superalloy
metals?
(a) Irons
(d) Titanium
(b) Nickel
(e) Copper
(c) Cobalt
(f) Aluminum
Reserve Question 44: Titanium alloys
Which of the following are desirable characteristics of
titanium and its alloys?
(a) Corrosion resistant.
(b) Low melting temperatures.
(c) Easily processed, even at high temperatures.
(d) High strengths.
(e) High ductilities.
Reserve Question 45: Zinc content of brass
At room temperature, what is the approximate maximum zinc content of α-brass?
(a) 5 wt% Zn
(d) 35 wt% Zn
(b) 15 wt% Zn
(e) 45 wt% Zn
(c) 25 wt% Zn
R-70 • Reserve Questions and Problems
Reserve Problem 46a (question pool)
Reserve Problem 48a (question pool)
Select T/F for each of the following statements regarding aluminum/aluminum alloys:
(a) Aluminum alloys are generally not viable
as lightweight structural materials in humid
environments because they are highly susceptible to corrosion by water vapor.
(b) Aluminum alloys are generally superior to
pure aluminum, in terms of yield strength,
because their microstructures often contain
precipitate phases that strain the lattice,
thereby hardening the alloy relative to pure
aluminum.
(c) Aluminum is not very workable at high temperatures in air, in terms of extrusion and rolling, because a non-protective oxide grows and
consumes the metal, converting it to a hard
and brittle ceramic.
(d) Compared to most other metals, like steel,
pure aluminum is very resistant to creep
deformation.
(e) The relatively low melting point of aluminum
is often considered a significant limitation for
structural applications.
Select T/F for each of the following statements regarding copper & copper alloys:
(a) Copper has a higher elastic modulus than
aluminum.
(b) The density of copper is closer to that of
aluminum than it is to iron.
(c) Bronze is an alloy of copper and zinc.
(d) Copper and its alloys form a green tarnish over
time, consisting of sulfides and carbonates.
(e) Copper is relatively resistant to corrosion
by neutral and even mildly basic water,
making it useful for freshwater plumbing
applications.
Reserve Problem 47a (question pool)
Select T/F for each of the following statements regarding aluminum/aluminum alloys:
(a) Aluminum alloys are generally viable as lightweight structural materials in humid environments because they are not very susceptible
to corrosion by water vapor.
(b) Aluminum is not very workable at high temperatures in air, in terms of extrusion and rolling, because a non-protective oxide grows and
consumes the metal, converting it to a hard
and brittle ceramic.
(c) Aluminum alloys are generally superior to
pure aluminum, in terms of yield strength,
because their microstructures often contain
precipitate phases that strain the lattice,
thereby hardening the alloy relative to pure
aluminum.
(d) Compared to other metals, like steel, pure aluminum is very resistant to failure via fatigue.
(e) Aluminum exhibits one of the highest melting
points of all metals, which makes it difficult
and expensive to cast.
Reserve Problem 49a (question pool)
Select T/F for each of the following statements regarding copper & copper alloys:
(a) Copper is much more abundant in the earth’s
crust compared to iron or aluminum.
(b) Copper is one of just a few metals that can be
found in metallic form in nature.
(c) Pure and/or annealed copper is more difficult
to machine compared to its work-hardened
form or its alloys.
(d) Copper is a minor component (by weight) of
most brass & bronze alloys.
(e) Amongst metals and alloys copper is one of
the best conductors of heat.
Reserve Problem 50a (question pool)
Select T/F for each of the following statements regarding various metals & alloys:
(a) Nickel is majority component (by mass) in
certain superalloys such as WaspaloyTM.
(b) Tungsten is the lowest density metal that has
structural use.
(c) Tantalum offers extremely good corrosion
resistance, especially at low temperatures.
(d) Magnesium metal is very similar to aluminum
in terms of its physical and mechanical
properties.
(e) Beryllium metal is commonly used as an
alloying agent in copper metal.
Reserve Questions and Problems • R-71
Reserve Question 51: Alumina content of fireclays
Reserve Problem 57
Increasing the alumina (Al2O3) content of fireclays
results in
(a) an increase in maximum service temperature.
(b) a decrease in maximum service temperature.
Find the maximum temperature to which the following two magnesia–alumina refractory materials may
be heated before a liquid phase will appear.
(a) A spinel-bonded alumina material of composition 95 wt% Al2O3–5 wt% MgO.
(b) A magnesia–alumina spinel of composition 65 wt% Al2O3–35 wt% MgO. Consult
Figure 10.24.
Reserve Question 52: Alumina in silica refractories
The high-temperature performance of silica refractories is compromised by the presence of even small
concentrations of alumina (Al2O3).
(a) True
(b) False
Reserve Question 53: Porosity effects
As the porosity of refractory ceramic bricks increases,
(a) Strength decreases.
(b) Strength increases.
(c) Chemical resistance decreases.
(d) Chemical resistance increases.
(e) Thermal insulation decreases.
(f) Thermal insulation increases.
Reserve Question 54: Silica in basic refractories
The presence of silica (SiO2) in basic refractory
ceramics is beneficial to their high-temperature
performance.
(a) True
(b) False
Reserve Question 55: Slag application of basic
refractories
Basic refractory ceramics are often used for the containment of slags that are rich in
(a) silica.
(b) CaO.
(c) MgO.
Reserve Question 56: Slag application of silica
refractories
Silica refractory ceramics are often used for the containment of slags that are rich in
(a) silica.
(b) CaO.
(c) MgO.
Reserve Question 58: Abrasive materials
Materials that are used as abrasive ceramics include
which of the following?
(a) Diamond
(b) Silicon carbide
(c) Tungsten carbide
(d) Aluminum oxide
(e) Silica sand
(f) Titanium dioxide
Reserve Question 59: Abrasive properties
Which of the following are properties required for
abrasive ceramics?
(a) High wear resistance
(b) High temperature stability
(c) Low temperature stability
(d) High toughness
(e) High ductility
Reserve Question 60: Cement consumption
Which of the following cement materials is consumed
in the largest tonnages?
(a) Portland cement
(b) Plaster of Paris
(c) Lime
Reserve Question 61: Hardening mechanism
of lime
The hardening of lime is associated with
(a) a drying process.
(b) A chemical reaction involving water (i.e.
hydration).
(c) A chemical reaction involving compound
other than water.
R-72 • Reserve Questions and Problems
Reserve Question 62: Hardening mechanism of
Portland cement
The hardening of Portland cement is associated with
(a) a drying process.
(b) A chemical reaction involving water (i.e.
hydration).
(c) A chemical reaction involving a compound
other than water.
Reserve Question 63: Fluorocarbons
Which of these polymers are most resistant to attack by chemicals and, as such, are often used as
coatings?
(a) Fluorocarbons
(c) Polyethylene
(b) Polystyrene
(d) Rubber
Reserve Question 64: Optical transparency
For applications that require optical transparency, a
polymer must be which of the following:
(a) Amorphous.
(b) Semicrystalline with very small crystallites.
(c) Semicrystalline with very large crystallites.
(d) Crystalline.
Reserve Question 65: Plastics
Which of the following polymers are classified as plastics?
(a) Polyethylene
(b) Polypropylene
(c) Poly(vinyl chloride)
(d) Polystyrene
(e) The epoxies
(f) The polyesters
(g) Rubber
(h) Polyisoprene
(i) Polychloroprene
Reserve Question 66: Crosslinking of elastomers
Elastomers must have some crosslinking.
(a) True
(b) False
Reserve Question 67: Fiber molecular weight
For fiber applications, the molecular weight of a polymer should be
(a) Relatively high.
(b) Relatively low.
CHAPTER 14 SYNTHESIS, FABRICATION, AND PROCESSING OF MATERIALS
Reserve Question 01: Advantages of hot vs cold
working
Which type of forming operation produces a higher
quality surface finish, better mechanical properties,
and closer dimensional control of the finished piece?
(a) Cold working
(b) Hot working
Reserve Question 04: Forging
Reserve Question 02: Cold working
Hot working takes place at a temperature that is
above a metal’s
(a) melting temperature
(b) recrystallization temperature
(c) eutectoid temperature
(d) glass transition temperature
Cold working takes place at a temperature that is
below a metal’s
(a) Melting temperature
(b) Recrystallization temperature
(c) Eutectoid temperature
(d) Glass transition temperature
Reserve Question 03: Deformation in hot vs cold
working
Which type of forming operation has lower deformation energy requirements?
(a) Cold working
(b) Hot working
Forging operations normally take place at
(a) Low temperature
(b) Room temperature
(c) High temperature
Reserve Question 05: Hot working
Reserve Question 06: Metal forming
Which of the following are forming operations?
(a) Forging
(e) Powder metallurgy
(b) Rolling
(f) Welding
(c) Extrusion
(g) Continuous casting
(d) Drawing
(h) Die casting
Reserve Questions and Problems • R-73
Reserve Question 07: Annealing
Reserve Question 15: Normalizing cooling
Which of the following may occur during annealing?
(a) Stresses may be relieved.
(b) Ductility may be increased.
(c) Toughness may be increased.
(d) A specific microstructure may be produced.
A normalizing heat treatment is terminated by cooling in
(a) Air
(b) A furnace
Reserve Question 08: Annealing temperature
How does increasing the annealing temperature influence the rate of an annealing process?
(a) Increases the rate
(b) Decreases the rate
Reserve Question 09: Full annealing
Full annealing is used on which types of steels?
(a) Low-carbon steels
(b) Medium-carbon steels
(c) High-carbon steels
Reserve Question 10: Full annealing temperature
Full annealing is accomplished by heating at a temperature approximately how many degrees Celsius above
either A3 line (for compositions less than the eutectoid)
or A1 line (for compositions greater than the eutectoid)
(a) 25°C
(d) 55°C
(b) 40°C
(e) 70°C
(c) 50°C
Reserve Question 16: Powder metallurgy
The density of a piece produced by powder metallurgy
may be the same as the parent material.
(a) True
(b) False
Reserve Question 17: Spheroidizing
A spheroidizing heat treatment is normally used on
which type(s) of steels?
(a) Low-carbon steels
(b) Medium-carbon steels
(c) High-carbon steels
Reserve Problem 18
Give the approximate minimum temperature at
which it is possible to austenitize each of the following iron–carbon alloys during a normalizing heat
treatment:
(a) 0.20 wt% C
(b) 0.76 wt% C
(c) 0.95 wt% C.
Reserve Question 11: Full annealing cooling
Reserve Problem 19
A full annealing heat treatment is terminated by
cooling in
(a) Air
(b) A furnace
Give the approximate temperature at which it is desirable to heat each of the following iron–carbon alloys
during a full anneal heat treatment:
(a) 0.25 wt% C
(b) 0.45 wt% C
(c) 0.85 wt% C
(d) 1.10 wt% C.
Reserve Question 12: Metals for powder metallurgy
For which type of metals is powder metallurgy particularly suited?
(a) Metals having high melting temperatures
(b) Metals having low melting temperatures
Reserve Question 13: Normalizing
Normalizing of a ferrous alloy causes the average
grain size to
(a) Increase
(b) Decrease
Reserve Question 14: Normalizing temperature
Normalizing is accomplished by heating at a temperature at least how many degrees Celsius above the upper critical temperature?
(a) 25°C
(d) 55°C
(b) 40°C
(e) 70°C
(c) 50°C
Reserve Question 20: Cooling rate–Geometry I
The smaller the ratio of surface are to the mass of steel
specimen,
(a) The slower the cooling rate, and consequently,
the shallower the hardening effect
(b) The slower the cooling rate, and consequently,
the deeper the hardening effect
(c) The faster the cooling rate, and consequently,
the shallower the hardening effect
(d) The faster the cooling rate, and consequently,
the deeper the hardening effect
R-74 • Reserve Questions and Problems
Reserve Question 21: Cooling rate–
Geometry II
Based upon a specimen’s surface area-to-mass ratio,
which geometrical shape is more amenable to hardening by quenching?
(a) Irregular with edges and corners
(b) Regular and rounded
Reserve Question 22: Jominy end-quench test
composition
Reserve Question 27: Quenching media
Which of the following sequences correctly indicates
the severity of quench order of the three quenching
media, from least severe to most severe?
(a) Water; oil; air
(b) Water; air; oil
(c) Oil; water; air
(d) Air; oil; water
(e) Air; water; oil
An alloy steel (containing Ni, Cr, Mo, etc.) may be
hardened to a greater degree than an unalloyed steel.
This behavior is due to the presence of the alloying elements that delay austenite-to-pearlite and austeniteto-bainite reactions.
(a) True
(b) False
Reserve Question 28: Quenching media–steel
Reserve Question 23: Jominy end-quench test
cooling rate
Reserve Question 29: Severity of quench
The rate of heat transfer from the specimen during
a Jominy end-quench test is nearly independent of
composition.
(a) True
(b) False
Reserve Question 24: Martensitic content vs
strength I
For parts that are to be used in relatively high stress
applications, what percentage of the part’s interior
should be martensite?
(a) 40%
(e) 80%
(b) 50%
(f) 90%
(c) 60%
(g) 100%
(d) 70%
Reserve Question 25: Martensitic content vs
strength II
For parts that are to be used in moderately stressed
applications, what percentage of the part’s interior
should be martensite?
(a) 40%
(e) 80%
(b) 50%
(f) 90%
(c) 60%
(g) 100%
(d) 70%
Reserve Question 26: Quenching
During a quenching treatment, it is possible to cool the
specimen at a uniform rate throughout the entire piece.
(a) True
(b) False
Which of the three quenching media is most commonly used for alloy steels?
(a) Oil
(b) Water
(c) Air
The more “severe” a quench,
(a) The more rapid the quench.
(b) The less rapid the quench.
Reserve Question 30: Glass forming methods
Match each product with the glass forming method
that is used to produce it.
Dishes
• Drawing
• Blowing
• Pressing
• Fiber forming
Light bulbs
• Blowing
• Pressing
• Fiber forming
• Drawing
Rods
•
•
•
•
Pressing
Fiber forming
Drawing
Blowing
Fibers
• Blowing
• Drawing
• Fiber forming
• Pressing
Reserve Questions and Problems • R-75
Reserve Question 31: Glass phases
Which of the following represents the correct phase
transformation sequence as a glass material is heated?
(a) Solid; supercooled liquid; liquid
(b) Solid; liquid; supercooled liquid
(c) Supercooled liquid; solid; liquid
(d) Supercooled liquid; liquid; solid
(e) Liquid; supercooled liquid; solid
(f) Liquid; solid; supercooled liquid
Reserve Question 32: Temperature points relative
to glasses
Match the viscosity values with the names of their corresponding temperature points.
100 Pa-s
• Melting point
• Working point
• Softening point
• Annealing point
• Strain point
103 Pa-s
• Softening point
• Annealing point
• Strain point
• Working point
• Melting point
4 × 106 Pa-s
• Working point
• Softening point
• Annealing point
• Strain point
• Melting point
1012 Pa-s
• Softening point
• Melting point
• Working point
• Strain point
• Annealing point
3 × 1013 Pa-s
• Annealing point
• Strain point
• Working point
• Melting point
• Softening point
Reserve Question 33: Thermal stress reduction
Once thermal stresses have been introduced into a
ceramic piece, it is impossible to remove them.
(a) True
(b) False
Reserve Question 34: Thermal tempering
The strength of a glass piece may be improved by inducing thermal compressive residual surface stresses.
(a) True
(b) False
Reserve Question 35: Thermal tempering stresses
Thermal tempering results in the introduction of
(a) compressive stresses on the surface
(b) compressive stresses internally
(c) tensile stresses on the surface
(d) tensile stresses internally
Reserve Question 36: Thermal tempering
temperature
During thermal tempering, a glass piece is heated to
a temperature
(a) below the glass transition temperature
(b) above the glass transition temperature
(c) below the softening point
(d) above the softening point
Reserve Question 37: Particle size of clay products
The larger the initial particle size of a clay-based ceramic body that has been dried,
(a) the lower the shrinkage
(b) the greater the shrinkage
Reserve Question 38: Vitrification
As the vitrification of clay-based products increases,
which of the following also increase(s)?
(a) Shrinkage
(c) Durability
(b) Strength
(d) Density
Reserve Question 39: Water content of clay
products
During drying, the greater the initial water content of
a clay-based ceramic body,
(a) the greater the shrinkage
(b) the lower the shrinkage
Reserve Question 40: Plastic deformation in
powder pressing
During the powder pressing of ceramic pieces, plastic
deformation of the particles occurs.
(a) True
(b) False
R-76 • Reserve Questions and Problems
Reserve Question 41: Powder pressing
Reserve Question 42: Powder pressing techniques
Which of the following ceramic products are normally
produced using powder pressing?
(a) Clay ceramics
(b) Electronic ceramics
(c) Magnetic ceramics
(d) Refractory ceramics
(e) Glass ceramics
If a ceramic piece is desired that is dense and, in addition, is to experience very little or no grain growth
during its processing, which of the following powder
pressing techniques should be used?
(a) Uniaxial pressing, followed by firing.
(b) Isostatic pressing, followed by firing.
(c) Hot pressing.
CHAPTER 15 COMPOSTIES
Reserve Question 01: Hardness matrix vs dispersed
Reserve Question 06: Critical fiber length
For composite materials, which is phase is normally
harder?
(a) The matrix phase
(b) The dispersed phase
What is the order of magnitude critical length of glass
and carbon fibers in composites?
(a) 0.01 mm
(d) 10.0 mm
(b) 0.1 mm
(e) 100 mm
(c) 1.0 mm
Reserve Question 02: Particle content
As particle content is increased, how does the strength
a particle-reinforced composite change?
(a) it increases
(b) it decreases
Reserve Question 03: Cermets
In order to produce very hard cermet (ceramic-metal)
composites, what volume percent of the particulate
phase is normally used?
(a) > 50 vol%
(b) > 60 vol%
(c) > 70 vol%
(d) > 80 vol%
(e) > 90 vol%
Reserve Question 04: Dispersion-strengthened
composite vs precipitation-hardened alloy II
Which material retains its strength better at elevated
temperatures?
(a) A dispersion-strengthened composite
(b) A precipitation-hardened alloy
Reserve Question 05: Continuous fibers
The length of continuous fibers is typically
(a) l > 5 lc
(b) l > 15 lc
(c) l > 25 lc
(d) l > 35 lc
(e) l > 45 lc
Reserve Problem 07a (question pool)
Such that the bond strength across the fiber-epoxy interface is [s] MPa, and the shear yield strength of the
epoxy is [y] MPa, compute the minimum fiber length, in
millimeters, to guarantee that the fibers are conveying an
optimum fraction of force that is applied to the composite. The tensile strength of these carbon fibers is [f] MPa.
Reserve Problem 08: Reinforcement efficiency I
For an aligned fibrous composite, when a stress is applied in a direction that is parallel to the fibers, what
is the reinforcement efficiency?
(a) 0
(d) 3∕4
(b) 1∕5
(e) 1
3
(c) ∕8
Reserve Problem 09: Reinforcement efficiency II
For an aligned fibrous composite, when a stress is applied perpendicular to the fibers, what is the reinforcement efficiency?
(a) 0
(d) 3∕4
(b) 1∕5
(e) 1
3
(c) ∕8
Reserve Problem 10: Reinforcement efficiency III
For a fibrous composite with fibers that are randomly
and uniformly oriented within a specific plane, when
a stress is applied in any direction within the plane of
the fibers, what is the reinforcement efficiency?
(a) 0
(d) 3∕4
1
(b) ∕5
(e) 1
(c) 3∕8
Reserve Questions and Problems • R-77
Reserve Problem 11: Reinforcement efficiency IV
Reserve Problem 18a (question pool)
For a fibrous composite with fibers that are uniformly
distributed and randomly oriented in all directions,
when a stress is applied in any direction, what is the
reinforcement efficiency?
(a) 0
(d) 3∕4
1
(b) ∕5
(e) 1
(c) 3∕8
The figure below depicts a continuous aligned fiberreinforced composite featuring carbon fiber and
epoxy. If the elastic moduli of the composite components are [m] GPa and [f] GPa, what is the expected
modulus, in GPa, for the depicted loading scenario if
the fibers comprise [v] vol% of the composite?
Reserve Question 12: Applied load
A stress-strain test is performed on an aligned fibrous
composite such that the force is applied in the longitudinal direction. During the initial stage of the test,
which phase bears most of the load?
(a) Fibers
(b) Matrix
Reserve Question 13: Composite failure
Once the fibers fail in a fibrous composite, catastrophic failure of the piece takes place.
(a) True
(b) False
Reserve Question 14: Continuous fiber orientation
Reserve Problem 19a (question pool)
How are continuous fibers typically oriented in fibrous composites?
(a) Aligned
(b) Partially oriented
(c) Randomly oriented
The figure below depicts the elastic modulus rulesof-mixtures for an aligned and continuous fiber-reinforced epoxy composite. What is the composite modulus, measured parallel to the fiber alignment axis, for a
sample containing 80 vol% fiber? Note that the volume
fraction axis is intentionally unlabeled. You should be
able to discern this vol% label for yourself based on the
logic for producing a structural composite.
Reserve Question 15: Discontinuous fiber orientation
How are discontinuous fibers typically oriented in
fibrous composites?
(a) Aligned
(b) Partially oriented
(c) Randomly oriented
Reserve Question 16: Discontinuous vs continuous
fiber use
If the fiber orientation is random, which type of fibers
is normally used?
(a) Discontinuous
(b) Continuous
Reserve Problem 17a (question pool)
Select T/F for each of the following statements:
(a) Composites are single-phase materials by
definition.
(b) The term “composite” applies to materials
that feature polymeric materials only.
(c) Structural composites are, in general, highly
regarded for their specific strengths.
(d) Composites featuring continuous and aligned
fibers for reinforcement generally offer properties that are highly isotropic compared to
most metals (random polycrystals).
(a)
(b)
(c)
(d)
5 GPa
7.5 GPa
10 GPa
15 GPa
(e) 20 GPa
(f) 25 GPa
(g) 30 GPa
R-78 • Reserve Questions and Problems
Reserve Problem 20a (question pool)
Reserve Question 22: Fiber types
The figure below depicts the elastic modulus rulesof-mixtures for an aligned and continuous fiberreinforced epoxy composite. What is the composite
modulus, measured parallel to the fiber alignment
axis, for a sample containing 80 vol% fiber? Note that
the volume fraction axis is intentionally unlabeled.
You should be able to discern this vol% label for
yourself based on the logic for producing a structural
composite.
Match each fiber type with its description.
Whiskers
• Polycrystalline or amorphous materials with
small diameters
• Single crystals with extremely large length-todiameter ratios
• Metals having relatively large diameters
Fibers
• Single crystals with extremely large length-todiameter ratios
• Metals having relatively large diameters
• Polycrystalline or amorphous materials with
small diameters
Wires
• Metals having relatively large diameters
• Polycrystalline or amorphous materials with
small diameters
• Single crystals with extremely large length-todiameter ratios
Reserve Question 23: Fiber properties
(a)
(b)
(c)
(d)
(e)
(f)
(g)
5 GPa
7.5 GPa
10 GPa
15 GPa
20 GPa
25 GPa
30 GPa
For a composite material, which phase normally has
the higher elastic modulus?
(a) Fiber phase
(b) Matrix phase
Reserve Question 24: Matrix properties
For a composite material, how does the ductility of the
matrix phase normally compare with the ductility of
the dispersed phase?
(a) more ductile
(b) less ductile
Reserve Question 21: Fiber materials
Which of the following materials are typically used as
fibers?
(a) Graphite/carbon
(b) Silicon carbide
(c) Silicon nitride
(d) Aluminum oxide
(e) Glass
(f) Boron
(g) Steel
(h) Tungsten
(i) Molybdenum
Reserve Question 25: Aramid fiber
composites
Aramid fiber-reinforced composites have very high
tensile strengths and relatively low compressive
strengths.
(a) True
(b) False
Reserve Questions and Problems • R-79
Reserve Question 26: Aramid fibers
Which of aramid and metal fibers have higher strengthto-weight ratios?
(a) Aramid fibers
(b) Metal fibers
Reserve Question 27: Carbon fiber composites
Carbon fiber-reinforced composites have which of the
following properties?
(a) Relatively high strengths
(b) Relatively high stiffnesses
(c) High service temperatures (>200°C)
Reserve Question 28: Whisker materials
Which of the following materials are typically used as
whiskers?
(a) graphite/carbon
(b) silicon carbide
(c) silicon nitride
(d) aluminum oxide
(e) glass
(f) boron
(g) steel
(h) tungsten
(i) molybdenum
Reserve Question 29: Wire materials
Which of the following materials are typically used as
wires in composites?
(a) graphite/carbon
(b) silicon carbide
(c) silicon nitride
(d) aluminum oxide
(e) glass
(f) boron
(g) steel
(h) tungsten
(i) molybdenum
Reserve Question 30: Ceramic-matrix
composites
Compared to other ceramic materials, ceramic-matrix
composites have better/higher
(a) fracture toughnesses
(b) oxidation resistance
(c) stability at elevated temperatures
Reserve Question 31: Transformation-toughened
composites
Which of the following materials are typically used
as stabilizers in transformation-toughened ceramicmatrix composites?
(a) CaO
(b) MgO
(c) Y2O3
(d) CeO
(e) Al2O3
(f) SiC
Reserve Question 32: Carbon-carbon
composites
Carbon-carbon composites exhibit which of the following properties/characteristics?
(a) High tensile moduli at elevated temperatures
(b) High tensile strengths at elevated temperatures
(c) Resistance to creep
(d) Large fracture toughness values
(e) High thermal conductivities
(f) Low coefficients of thermal expansion
(g) Resistance to oxidation at elevated temperatures
(h) Low cost
Reserve Question 33: Laminar composites
Laminar composites have high strengths in all directions (in three dimensions).
(a) True
(b) False
R-80 • Reserve Questions and Problems
Reserve Problem 34a (question pool)
Reserve Problem 35a (question pool)
The figure below depicts four equal-sized composite
plates created by laminating separate sheets of unidirectional Kevlar reinforced polyester. Which of the
following laminate configurations would exhibit the
lowest strain if elastically loaded with an axial force F,
as depicted below? Select (e) if the strains for each of
the laminate configurations are equivalent.
The figure below depicts four equal-sized composite plates created by laminating separate sheets of
unidirectional Kevlar reinforced polyester. Which of
the following laminate configurations is expected to
exhibit the most anisotropic mechanical properties?
Select (e) if the laminate configurations exhibit an
equivalent degree of anisotropy.
(a)
(a)
(b)
(b)
(c)
(c)
(d)
(d)
Reserve Question 36: Sandwich panels
The strong outer sheets of sandwich panels are separated by a layer of material that is
(a) less dense than the outer sheet material
(b) more dense than the outer sheet material
Reserve Questions and Problems • R-81
CHAPTER 16 CORROSION AND DEGRADATION OF MATERIALS
Reserve Problem 01: Electrochemical cell
temperature
An electrochemical cell is constructed such that on one
side a pure lead electrode is in contact with a solution
containing Pb2+ ions at a concentration of 0.002 M.
The other cell half consists of a pure nickel electrode
that is immersed in a solution of Ni2+ ions having a
concentration of 0.5 M. Given that the standard electrode potentials for lead and nickel are −0.126 and
−0.250 V, respectively, at what temperature will the
potential between the two electrodes be −0.017 V?
Reserve Question 02: Chemical attack resistance
Reserve Question 05: Galvanic series I
Metals near the top of the galvanic series are
(a) Cathodic
(c) Unreactive
(b) Anodic
(d) Reactive
Reserve Question 06: Galvanic series II
Metals near the bottom of the galvanic series are
(a) Cathodic
(c) Unreactive
(b) Anodic
(d) Reactive
Reserve Question 07: Metal oxidation/
reduction
Which material type is more resistant to attack by
acidic and alkaline solutions?
(a) Polymeric materials
(b) Metallic materials
Metal ions in solution may only be oxidized.
(a) True
(b) False
Reserve Question 03: EMF–least reactive
In a corrosion process, only one reduction reaction is
possible.
(a) True
(b) False
Below are shown, for five metals, reduction reactions
and standard electrode potential values. Which of
these metals is the least reactive?
Electrode reaction
Standard electrode potential
(V )
Au3+ + 3 e− → Au
+1.420
Cu
2+
−
+ 2 e → Cu
Ni2+ + 2 e− → Ni
Fe
2+
+2
e−
→ Fe
Na+ + e− → Na
(a) Au
(b) Cu
(c) Ni
+0.340
−0.250
−0.440
−2.924
(d) Fe
(e) Na
Reserve Question 04: EMF–most reactive
Below are shown, for five metals, reduction reactions
and standard electrode potential values. Which of
these metals is the most reactive?
Electrode reaction
Standard electrode potential
(V )
Au3+ + 3 e− → Au
+1.420
Cu2+ + 2 e− → Cu
Reserve Question 08: Multiple reduction
reactions
Reserve Question 09: Overall electrochemical
reaction
An overall electrochemical reaction must consist of
at least
(a) A single reduction reaction
(b) A single oxidation reaction
(c) A single reduction reaction and a single oxidation reaction
Reserve Question 10: Oxidation I
Oxidation of an atom involves the
(a) Loss of electrons
(b) Gain of electrons
Reserve Question 11: Oxidation II
Oxidation takes place at the
(a) Anode
(b) Cathode
+0.340
Reserve Question 12: Oxidation III
2+
−
+ 2 e → Ni
−0.250
2+
−
−0.440
Which of the following is/are oxidation reactions?
(a) Fe → Fe2+ + 2 e−
(b) Al → Al3+ + 3 e−
(c) 2 H+ + 2 e− → H2
(d) H2 → 2 H+ + 2 e−
Ni
Fe
+
+ 2 e → Fe
−
Na + e → Na
(a) Au
(b) Cu
(c) Ni
−2.924
(d) Fe
(e) Na
R-82 • Reserve Questions and Problems
Reserve Question 13: Oxidation of metals
Reserve Question 20: Environmental effects
Most metals and alloys are subject to oxidation.
(a) True
(b) False
Which of the following factors may influence the
corrosion rates of materials?
(a) Fluid velocity
(b) Temperature
(c) Fluid composition
Reserve Question 14: Reduction I
Reduction of an atom involves the
(a) loss of electrons
(b) gain of electrons
Reserve Question 15: Reduction II
Reduction takes place at the
(a) anode
(b) cathode
Reserve Question 16: Reduction III
Which of the following are reduction reactions?
(a) Fe → Fe2+ + 2 e− (c) 2 H+ + 2 e− → H2
(b) Al → Al3+ + 3 e− (d) H2 → 2 H+ + 2 e−
Reserve Question 17: Activation and concentration
polarizations I
Match the polarization conditions with their
descriptions
Reaction rate is controlled by the slowest step in the
electrochemical reaction.
• Activation polarization
• Concentration polarization
Reaction rate is controlled by the diffusion of ions in
solution.
• Activation polarization
• Concentration polarization
Reserve Question 18: Passivity–maintenance
Once a metal has become passivated, it will always
remain so.
(a) True
(b) False
Reserve Question 19: Passivity–metals
Alloys of which of the following metals may passivate?
(a) Chromium
(b) Iron
(c) Nickel
(d) Titanium
(e) Copper
(f) Gold
Reserve Question 21: Forms of corrosion–crevice
corrosion
Which of the following describes crevice corrosion?
(a) Oxidation and reduction reactions occur
randomly over the surface.
(b) Two metals/alloys of different compositions
are coupled while exposed to an electrolyte.
(c) Corrosion that results from a difference in
concentration of ions or dissolved gases in the
electrolyte.
(d) Localized corrosion that may be initiated at
the surface defect.
(e) Corrosion that occurs preferentially along
grain boundaries.
(f) One element is preferentially removed as a
result of corrosion.
(g) Corrosion resulting from the combined action
of chemical attach and mechanical abrasion
or wear.
(h) Corrosion resulting from the combined action
of an applied tensile stress and a corrosive
environment.
Reserve Question 22: Forms of corrosion–erosion
corrosion
Which of the following describes erosion corrosion?
(a) Oxidation and reduction reactions occur randomly over the surface.
(b) Two metals/alloys of different compositions
are coupled while exposed to an electrolyte.
(c) Corrosion that results from a difference in
concentration of ions or dissolved gases in the
electrolyte.
(d) Localized corrosion that may be initiated at
the surface defect.
(e) Corrosion that occurs preferentially along
grain boundaries.
(f) One element is preferentially removed as a
result of corrosion.
(g) Corrosion resulting from the combined action
of chemical attach and mechanical abrasion
or wear.
(h) Corrosion resulting from the combined action
of an applied tensile stress and a corrosive
environment.
Reserve Questions and Problems • R-83
Reserve Question 23: Forms of corrosion–
galvanic corrosion
Reserve Question 25: Forms of corrosion–
pitting
Which of the following describes galvanic corrosion?
(a) Oxidation and reduction reactions occur randomly over the surface.
(b) Two metals/alloys of different compositions
are coupled while exposed to an electrolyte.
(c) Corrosion that results from a difference in
concentration of ions or dissolved gases in the
electrolyte.
(d) Localized corrosion that may be initiated at
the surface defect.
(e) Corrosion that occurs preferentially along
grain boundaries.
(f) One element is preferentially removed as a
result of corrosion.
(g) Corrosion resulting from the combined action
of chemical attach and mechanical abrasion
or wear.
(h) Corrosion resulting from the combined action
of an applied tensile stress and a corrosive
environment.
Which of the following describes pitting?
(a) Oxidation and reduction reactions occur randomly over the surface.
(b) Two metals/alloys of different compositions
are coupled while exposed to an electrolyte.
(c) Corrosion that results from a difference in
concentration of ions or dissolved gases in the
electrolyte.
(d) Localized corrosion that may be initiated at
the surface defect.
(e) Corrosion that occurs preferentially along
grain boundaries.
(f) One element is preferentially removed as a
result of corrosion.
(g) Corrosion resulting from the combined action
of chemical attach and mechanical abrasion
or wear.
(h) Corrosion resulting from the combined action
of an applied tensile stress and a corrosive
environment.
Reserve Question 24: Forms of corrosion–
intergranular corrosion
Which of the following describes intergranular
corrosion?
(a) Oxidation and reduction reactions occur randomly over the surface.
(b) Two metals/alloys of different compositions
are coupled while exposed to an electrolyte.
(c) Corrosion that results from a difference in
concentration of ions or dissolved gases in the
electrolyte.
(d) Localized corrosion that may be initiated at
the surface defect.
(e) Corrosion that occurs preferentially along
grain boundaries.
(f) One element is preferentially removed as a
result of corrosion.
(g) Corrosion resulting from the combined action
of chemical attach and mechanical abrasion
or wear.
(h) Corrosion resulting from the combined action
of an applied tensile stress and a corrosive
environment.
Reserve Question 26: Forms of corrosion–selective
leaching
Which of the following describes selective leaching?
(a) Oxidation and reduction reactions occur randomly over the surface.
(b) Two metals/alloys of different compositions
are coupled while exposed to an electrolyte.
(c) Corrosion that results from a difference in
concentration of ions or dissolved gases in the
electrolyte.
(d) Localized corrosion that may be initiated at
the surface defect.
(e) Corrosion that occurs preferentially along
grain boundaries.
(f) One element is preferentially removed as a
result of corrosion.
(g) Corrosion resulting from the combined action
of chemical attach and mechanical abrasion
or wear.
(h) Corrosion resulting from the combined action
of an applied tensile stress and a corrosive
environment.
R-84 • Reserve Questions and Problems
Reserve Question 27: Forms of corrosion–stress
corrosion
Reserve Question 30: Corrosion prevention–
cathodic protection
Which of the following describes stress corrosion?
(a) Oxidation and reduction reactions occur randomly over the surface.
(b) Two metals/alloys of different compositions
are coupled while exposed to an electrolyte.
(c) Corrosion that results from a difference in
concentration of ions or dissolved gases in the
electrolyte.
(d) Localized corrosion that may be initiated at
the surface defect.
(e) Corrosion that occurs preferentially along
grain boundaries.
(f) One element is preferentially removed as a
result of corrosion.
(g) Corrosion resulting from the combined action
of chemical attach and mechanical abrasion
or wear.
(h) Corrosion resulting from the combined action
of an applied tensile stress and a corrosive
environment.
Cathodic protection reduces the corrosion rate of a
metal when an electrical connection is made to another metal that is
(a) lower in the galvanic series
(b) higher in the galvanic series
Reserve Question 28: Forms of corrosion–uniform
corrosion
Which of the following describes uniform corrosion?
(a) Oxidation and reduction reactions occur randomly over the surface.
(b) Two metals/alloys of different compositions
are coupled while exposed to an electrolyte.
(c) Corrosion that results from a difference in
concentration of ions or dissolved gases in the
electrolyte.
(d) Localized corrosion that may be initiated at
the surface defect.
(e) Corrosion that occurs preferentially along
grain boundaries.
(f) One element is preferentially removed as a
result of corrosion.
(g) Corrosion resulting from the combined action
of chemical attach and mechanical abrasion
or wear.
(h) Corrosion resulting from the combined action
of an applied tensile stress and a corrosive
environment.
Reserve Question 29: Fresh vs seawater
Which water environment is more corrosive?
(a) Fresh water
(b) Seawater
Reserve Question 31: Corrosion prevention–
temperature
In most instances, one way to reduce the corrosion
rate is to
(a) Increase the fluid temperature.
(b) Decrease the fluid temperature.
Reserve Question 32: Galvanizing
Galvanizing involves applying a layer of what metal to
the surface of steel?
(a) zinc
(b) iron
(c) copper
(d) nickel
(e) aluminum
Reserve Question 33: Pilling–Bedworth ratio I
Given the following metal–Pilling-Bedworth ratio
combinations, which metals are expected to form protective coatings?
Metal
Aluminum
Chromium
Copper
Lithium
Molybdenum
Silicon
Sodium
(a)
(b)
(c)
(d)
(e)
(f)
(g)
aluminum
chromium
copper
lithium
molybdenum
silicon
sodium
P-B Ratio
1.28
1.99
1.68
0.57
3.40
2.27
0.57
Reserve Questions and Problems • R-85
Reserve Question 34: Pilling—Bedworth ratio II
Reserve Question 35: Polymer degradation
Given the following metal–Pilling-Bedworth ratio
combinations, which metals are not expected to form
protective coatings?
Polymer degradation may occur from exposure to or
as a result of which of the following?
(a) Electrochemical reactions
(b) Physiochemical reactions
(c) Swelling
(d) Heat
(e) Radiation
Metal
Aluminum
Chromium
Copper
Lithium
Molybdenum
Silicon
Sodium
(a)
(b)
(c)
(d)
(e)
(f)
(g)
P-B Ratio
1.28
1.99
1.68
0.57
3.40
2.27
0.57
aluminum
chromium
copper
lithium
molybdenum
silicon
sodium
Reserve Question 36: Swelling
The swelling of a polymer results in it becoming
(a) Softer
(b) Harder
Reserve Question 37: Swelling reduction
Polymer deterioration by swelling may be reduced by
(a) Increasing the degree of crosslinking
(b) Decreasing the degree of crosslinking
(c) Increasing the molecular weight
(d) Decreasing the molecular weight
(e) Increasing the degree of crystallinity
(f) Decreasing the degree of crystallinity
CHAPTER 17 THERMAL PROPERTIES
Reserve Question 01: Constant pressure vs
constant volume heat capacity
Reserve Question 05: Material thermal
expansion
For a given material, which heat capacity is greater?
(a) At constant pressure, Cp .
(b) At constant volume, Cv .
Which of the following material types typically
has the largest values of the coefficient of thermal
expansion?
(a) Polymers
(b) Metals
(c) Ceramics
Reserve Question 02: Debye temperature I
Below the Debye temperature, Cv is virtually independent of temperature.
(a) True
(b) False
Reserve Question 03: Debye temperature II
For most solid materials, the Debye temperature is
below room temperature.
(a) True
(b) False
Reserve Question 04: Electron contributions
In which of the following thermal phenomena do free
electrons play a role?
(a) Thermal conductivity
(b) Thermal expansion
Reserve Question 06: Thermal expansion and
atomic bonding energy
The greater the atomic bonding energy,
(a) The larger the interatomic spacing change
with increasing temperature.
(b) The smaller the interatomic spacing change
with increasing temperature.
(c) The larger the value of αl.
(d) The smaller the value of αl.
Reserve Question 07: Thermal expansion anisotropy
When heated, most materials expand equally in all
directions.
(a) True
(b) False
R-86 • Reserve Questions and Problems
Reserve Problem 08
Reserve Question 13: Thermal shock resistance
The difference between the specific heats at constant
pressure and volume is described by the expression
Which of the following properties lead to a high degree of thermal shock resistance?
(a) High fracture strength
(b) Low fracture strength
(c) High thermal conductivity
(d) Low thermal conductivity
(e) High modulus of elasticity
(f) Low modulus of elasticity
(g) High coefficient of thermal expansion
(h) Low coefficient of thermal expansion
Cp − Cv =
α2v v0 T
β
where αv is the volume coefficient of thermal expansion, v0 is the specific volume (i.e. volume per
unit mass, or the reciprocal of density), β is the
compressibility, and T is the absolute temperature.
Compute the values of Cv, at room temperature (293
K) for copper and nickel using the data in Table
17.1, assuming that αv = 3αl and given that the values for β for Cu and Ni are 8.35 × 10−12 and 5.51 ×
10−12(Pa)−1, respectively.
Reserve Question 09: Material thermal
conductivity
Which of the following material types typically has the
largest values of the thermal conductivity?
(a) Polymers
(b) Metals
(c) Ceramics
Reserve Question 10: Thermal conductivity
of ceramics
In the vicinity of room temperature, how do the thermal conductivities of ceramics change as the temperature increases?
(a) they decrease
(b) they increase
Reserve Question 11: Thermal conductivity of
polycrystalline vs single crystal
How do thermal conductivities of single crystals and
polycrystalline materials compare?
(a) ksingle crystal > kpolycrystalline
(b) ksingle crystal < kpolycrystalline
Reserve Question 12: Thermal shock in brittle
materials
Which of rapid heating or rapid cooling is more likely
to inflict thermal shock in brittle materials?
(a) Rapid cooling
(b) Rapid heating
Reserve Question 14: Thermal stress
The heating of a homogeneous and isotropic rod of
solid material for which axial motion is restrained,
results in which type of thermal stresses?
(a) Compressive
(b) Tensile
Reserve Problem 15
(a) If a rod of 1025 steel 0.5 m (19.7 in.) long is
heated from 20°C to 80°C (68°F to 176°F) while
its ends are maintained rigid, determine the
type and magnitude of stress that develops.
Assume that at 20°C the rod is stress-free.
(b) What will be the stress magnitude if a rod 1 m
(39.4 in.) long is used?
(c) If the rod in part (a) is cooled from 20°C to
−10°C (68°F to 14°F), what type and magnitude of stress will result?
Reserve Problem 16
To what temperature would 23.0 kg of some material at 100°C be raised if 255 kJ of heat is supplied?
Assume a cp value of 423 J/kg-K for this material.
(a) 26.2°C
(c) 126°C
(b) 73.8°C
(d) 152°C
Reserve Problem 17
A rod of some material 0.50 m long elongates 0.40
mm on heating from 50°C to 151°C. What is the value
of the linear coefficient of thermal expansion for this
material?
(a) 5.30 × 10–6 (°C)–1 (c) 1.60 × 10–5 (°C)–1
(b) 7.92 × 10–6 (°C)–1 (d) 1.24 × 10–6 (°C)–1
Reserve Questions and Problems • R-87
Reserve Problem 18
Reserve Problem 20a (question pool)
Which of the following sets of properties leads to a
high degree of thermal shock resistance?
(a) High fracture strength
High thermal conductivity
High modulus of elasticity
High coefficient of thermal expansion
(b) Low fracture strength
Low thermal conductivity
Low modulus of elasticity
Low coefficient of thermal expansion
(c) High fracture strength
High thermal conductivity
Low modulus of elasticity
Low coefficient of thermal expansion
(d) Low fracture strength
Low thermal conductivity
High modulus of elasticity
High coefficient of thermal expansion
Which of the following 1 kg samples is expected to
change temperature the least if 100 kJ of heat is perfectly transferred to each of them at a constant pressure of 1 atmosphere. The initial temperature of each
specimen is 25oC.
(a) Aluminum
(b) Copper
(c) Gold
(d) Borosilicate Glass
(e) Polystyrene
Reserve Problem 19a (question pool)
Reserve Problem 22
A 10 meter long square bar of 316 stainless steel (edge
length of 5 cm, with a modulus of 193 GPa and a yield
point of 290 MPa) was bolted securely in place when
its installation temperature was around [I]oC. What is
the expected thermal stress in the bar when its service
temperature reaches [F]oC? Enter a negative indicate
compressive stress, if necessary. The thermal expansion
coefficient of 316 stainless steel is 16.0 × 10−6 1/oC.
This ceramic outlier has the highest room-temperature
thermal conductivity of about 2,000 watts per meter
per kelvin, a value that is five time higher than the best
thermally conductive metals.
(d) SrTiO3
(a) Al2O3
(b) CaF2
(e) C (diamond)
(c) TiO2
Reserve Problem 21a (question pool)
If you were to locally heat identical geometry plates of
the materials listed below with the same heat source,
which would increase in temperature the fastest?
(a) Polystyrene
(b) Aluminum
(c) Copper
(d) Gold
(e) Borosilicate Glass
CHAPTER 18 MAGNETIC PROPERTIES
Reserve Question 01: Ferromagnetics
Reserve Question 02: Antiferromagnetics
Which two of the following are ferromagnetic materials?
(a) Aluminum oxide
Which of the following materials display(s) antiferromagnetic behavior?
(a) Aluminum oxide
(b) Copper
(c) Aluminum
(d) Titanium
(e) Iron (α ferrite)
(f) Nickel
(g) MnO
(h) Fe3O4
(i) NiFe204
(b) Copper
(c) Aluminum
(d) Titanium
(e) Iron (α ferrite)
(f) Nickel
(g) MnO
(h) Fe3O4
(i) NiFe204
R-88 • Reserve Questions and Problems
Reserve Question 03: Ferrimagnetics
Reserve Question 07: Domains and crystals
Which of the following are ferrimagnetic materials?
(a) Aluminum oxide
(b) Copper
(c) Aluminum
(d) Titanium
(e) Iron (α ferrite)
(f) Nickel
(g) MnO
(h) Fe3O4
(i) NiFe204
In a polycrystalline material, each grain will always
consist of just a single domain.
(a) True
(b) False
Reserve Problem 04
The formula for yttrium iron garnet (Y3Fe5O12) may
c
be written in the form Y3Fea2Fed3 O12 , where the superscripts a, c, and d represent different sites on which
the Y3+ and Fe3+ ions are located. The spin magnetic
moments for the Y3+ and Fe3+ ions positioned in the
a and c sites are oriented parallel to one another and
antiparallel to the Fe3+ ions in d sites. Compute the
number of Bohr magnetons associated with each Y3+
ion, given the following information: (1) each unit cell
consists of eight formula (Y3Fe5O12) units; (2) the unit
cell is cubic with an edge length of 1.2376 nm; (3) the
saturation magnetization for this material is 1.0 × 104
A/m; and (4) assume that there are 5 Bohr magnetons
associated with each Fe3+ ion.
Reserve Question 05: Curie temperature
At the Curie temperature, the saturation magnetization abruptly diminishes. Which of the following magnetic material types will have Curie temperatures?
(a) Diamagnetics
(b) Paramagnetics
(c) Ferromagnetics
(d) Antiferromagnetics
(e) Ferrimagnetics
Reserve Question 06: Neel temperature
With increasing temperature antiferromagnetic materials eventually become which of the following?
(a) Diamagnetics
(b) Paramagnetics
(c) Ferromagnetics
(d) Antiferromagnetics
(e) Ferrimagnetics
Reserve Problem 08
A coil of wire 0.1 m long and having 15 turns carries a
current of 1.0 A.
(a) Compute the flux density if the coil is within a
vacuum.
(b) A bar of an iron–silicon alloy, the B-H behavior for which is shown in Figure 18.29, is
positioned within the coil. What is the flux
density within this bar?
(c) Suppose that a bar of molybdenum is now
situated within the coil. What current must be
used to produce the same B field in the Mo as
was produced in the iron–silicon alloy part (b)
using 1.0 A?
Reserve Problem 09
The following data are for a transformer steel:
H (A/m)
0
10
20
50
100
150
B (tesla)
0
0.03
0.07
0.23
0.70
0.92
H (A/m)
200
400
600
800
1000
B (tesla)
1.04
1.28
1.36
1.39
1.41
(a) What are the values of the initial permeability
and initial relative permeability?
(b) What is the value of the maximum permeability?
(c) At about what H field does this maximum
permeability occur?
(d) To what magnetic susceptibility does this
maximum permeability correspond?
Reserve Problem 10
Estimate saturation values of H for single-crystal iron
in [100], [110], and [111] directions.
Reserve Questions and Problems • R-89
Reserve Question 11: Hard/soft materials
Reserve Question 13: Hard magnetic materials
Which type(s) of magnetic materials may be classified
as either soft or hard?
(a) Diamagnetic
(d) Antiferromagnetic
(b) Paramagnetic
(e) Ferrimagnetic
(c) Ferromagnetic
Which of the following characteristics are displayed
by hard magnetic materials?
(a) A relatively small hysteresis loop.
Reserve Question 12: Soft magnetic materials
Which of the following characteristics are displayed
by soft magnetic materials?
(a) A relatively small hysteresis loop.
(b) A relatively large hysteresis loop.
(c) Magnetization and demagnetization may be
achieved using relatively low applied fields.
(d) Magnetization and demagnetization require
relatively high applied fields.
(b) A relatively large hysteresis loop.
(c) Magnetization and demagnetization may
be achieved using relatively low applied
fields.
(d) Magnetization and demagnetization require
relatively high applied fields.
Reserve Problem 14
Using Equation 18.14, determine which of the superconducting elements in Table 20.7 are superconducting at 3 K and in a magnetic field of 15,000 A/m.
CHAPTER 19 OPTICAL PROPERTIES
Reserve Problem 01: Wavelength calculations
Reserve Question 05: Light transmission
What are (a) the frequency and (b) the energy
(in eV) of a photon of light having a wavelength of
8.8 × 10−7 m? The value for Planck’s constant is
4.13 × 10−15 eV-s. Express your answer to part (a) in
scientific notation.
Match the type of light transmission with its description.
Reserve Question 02: Visible wavelength
What is the order of magnitude wavelength for visible
light?
(a) 0.5 Angstroms
(b) 0.5 nanometers
(c) 0.5 micrometers
(d) 0.5 millimeters
(e) 0.5 meters
(f) 0.5 kilometers
Reserve Question 03: Bulk metal light transmission
In the visible spectrum, a thick metal specimen will be
(a) Transparent
(b) Translucent
(c) Opaque
Reserve Question 04: Insulator light transmission
In the visible spectrum, an electrical insulator that is a
single crystal and without porosity is normally
(a) Transparent
(b) Opaque
(c) Translucent
Transmits light with relative little absorption.
• Translucent
• Transparent
• Opaque
Transmits light diffusely.
• Opaque
• Translucent
• Transparent
Is impervious to light transmission.
• Transparent
• Opaque
• Translucent
Reserve Question 06: Semiconductor light
transmission
In the visible spectrum, a semiconductor that is a
single crystal and nonporous may be
(a) Transparent
(b) Translucent
(c) Opaque
Reserve Question 07: EM radiation and metals
To which of the following electromagnetic radiation
types are bulk metals opaque?
(a) radio waves
(d) ultraviolet radiation
(b) microwaves
(e) X-rays
(c) infrared radiation
R-90 • Reserve Questions and Problems
Reserve Question 08: Nonmetallic opaqueness
Reserve Problem 12a (question pool)
Every nonmetallic material becomes opaque to electromagnetic radiation having some wavelength.
(a) True
(b) False
A collimated beam containing two different frequencies of light travels through vacuum and is incident on
a piece of glass. Which of the schematics below depicts
the phenomenon of dispersion within the glass in a
qualitatively correct manner? Select (e) if none of the
options are qualitatively correct.
Reserve Question 09: Ceramics and light
transmission
(a)
Match the following material types with their light
transmission characteristics.
Single crystal electrical insulators
• Opaque
• Translucent
• Transparent
Polycrystalline and nonporous electrical insulators
• Translucent
• Transparent
• Opaque
(b)
Porous electrical insulators
• Transparent
• Opaque
• Translucent
(c)
Reserve Question 10: Index of refraction
For noncubic crystals, the index of refraction is lowest
in the crystallographic direction that has the
(a) Highest atomic packing density
(b) Lowest atomic packing density
Reserve Question 11: Polymer crystallinity and
light transmission
A completely amorphous and nonporous polymer
will be
(a) Transparent
(b) Translucent
(c) Opaque
(d)
Reserve Questions and Problems • R-91
Reserve Problem 13a (question pool)
A beam of light is shined on a thin (sub-millimeter
thick) single crystal wafer of material. The light source
is special since it can be tuned to provide any wavelength of visible light on demand. The specimen is illuminated such that the frequency of light is decreased
over time while the transmitted intensity of the light
is measured. If the sample becomes transparent when
the frequency is less than [F] THz, what is the band gap
of the material, in eV? Assume that an intrinsic excitation of electrons is responsible for the absorption.
Reserve Problem 14
Select the word combination that best completes this
statement.
When a semiconductor is exposed to a light source, its
intrinsic carrier concentration will increase if the [a]
of the light is [b] than band gap of the semiconductor.
[a] intensity, energy, wavelength, frequency,
voltage, current, resistance
[b] greater, less
Reserve Question 15: Fluorescence and
phosphorescence
Match the luminescence characteristics with their
descriptions.
Reemission of photons occurs in much less than one
second after excitation.
• Phosphorescence
• Fluorescence
Reemission of photons occurs in more than one second after excitation.
• Fluorescence
• Phosphorescence
Reserve Question 16: Luminescent materials
Only pure materials luminesce.
(a) True
(b) False
CHAPTER 20 ECONOMIC, ENVIRONMENTAL, AND SOCIETAL ISSUES IN
MATERIALS SCIENCE AND ENGINEERING
There are no Reserve Questions and Problems for this chapter.
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