INTRODUCTION TO
ENGINEERING MATERIALS
Chapter 3 -
Materials Science
- Study of the properties of solid
materials and how those properties
are determined by the material's
composition and structure, both
macroscopic and microscopic
Chapter 3 -
Materials of Engineering
- refers to selecting the correct
materials for the application in which
the engineered part is being used.
- This selection process includes
choosing the material, paying attention
to its specific type or grade based on
the required properties.
Chapter 3 -
Materials
• Over 70,000 different kinds and grades of engineering
materials
• This number grows daily
• 1,000 different materials
make up an
automobile
Chapter 3 -
The Three Basics:
• Metals
• Polymers
– Composites
• Ceramics
Chapter 3 -
Metal
• Cast Iron
• Steel
– Mild steel, medium carbon steel, high carbon steel
• Specialty steel
– Stainless (tin plated or galvanized)
• Alloys (two or more pure metals)
– Steel= iron & carbon
– Brass= copper & zinc
– Bronze= copper & tin
Chapter 3 -
Polymers
• Natural
–Animal cellulose
• Synthetic–Thermoplastics
–Thermosets
Chapter 3 -
Natural Composites
• Hardwood
–Deciduous Trees
• Softwood
–Coniferous
Chapter 3 -
Hardwoods
•
•
•
•
•
•
•
•
•
Ash
Beech
Birch
Cherry
Mahogany
Maple
Oak
Poplar
walnut
Chapter 3 -
Softwoods
•
•
•
•
•
•
Cedar
Cypress
Fir
Pine
Redwood
Spruce
Chapter 3 -
Ceramics
• Clay based
– Structural clay-tile, brick
– Porcelain
• Refractories
– Heat resistant (fire bricks)
• Glasses
• Inorganic cements
Chapter 3 -
Manufactured Wood
• Particle Board
–flake board, particle board
• Laminar
–plywood, laminated beams
Chapter 3 -
Composite
Lamborghini carbon
fiber materials
chassis. Carbon
Fiber Reinforced
Plastics
Space Shuttle Reusable
Ceramic Tiles
Chapter 3 -
Semiconductor
Chapter 3 -
Biomaterials
Chapter 3 -
Nano engineered material
Chapter 3 -
The Structure of Crystalline Solids
• How do atoms assemble into solid structures?
• How does the density of a material depend on
its structure?
• When do material properties vary with the
sample (i.e., part) orientation?
Chapter 3 -
17
Energy and Packing
• Non dense, random packing
Energy
typical neighbor
bond length
typical neighbor
bond energy
r
Energy
• Dense, ordered packing
typical neighbor
bond length
typical neighbor
bond energy
r
Dense, ordered packed structures tend to have
lower energies.
Chapter 3 -
18
Materials and Packing
Crystalline materials...
• atoms pack in periodic, 3D arrays
• typical of: -metals
-many ceramics
-some polymers
crystalline SiO2
Adapted from Fig. 3.23(a),
Callister & Rethwisch 8e.
Noncrystalline materials...
• atoms have no periodic packing
• occurs for: -complex structures
-rapid cooling
"Amorphous" = Noncrystalline
Si
Oxygen
noncrystalline SiO2
Adapted from Fig. 3.23(b),
Callister & Rethwisch 8e.
Chapter 3 -
19
Metallic Crystal Structures
• How can we stack metal atoms to minimize
empty space?
2-dimensions
vs.
Now stack these 2-D layers to make 3-D structures
Chapter 3 -
20
Simple Cubic Structure (SC)
• Rare due to low packing density (only Po has this structure)
• Close-packed directions are cube edges.
• Coordination # = 6
(# nearest neighbors)
Click once on image to start animation
(Courtesy P.M. Anderson)
Chapter 3 -
21
Atomic Packing Factor (APF)
Volume of atoms in unit cell*
APF =
Volume of unit cell
*assume hard spheres
• APF for a simple cubic structure = 0.52
atoms
unit cell
a
R=0.5a
APF =
volume
atom
4
p (0.5a) 3
1
3
a3
close-packed directions
contains 8 x 1/8 =
1 atom/unit cell
Adapted from Fig. 3.24,
Callister & Rethwisch 8e.
volume
unit cell
Chapter 3 -
22
Body Centered Cubic Structure (BCC)
• Atoms touch each other along cube diagonals.
--Note: All atoms are identical; the center atom is shaded
differently only for ease of viewing.
ex: Cr, W, Fe (), Tantalum, Molybdenum
• Coordination # = 8
Click once on image to start animation
(Courtesy P.M. Anderson)
Adapted from Fig. 3.2,
Callister & Rethwisch 8e.
2 atoms/unit cell: 1 center + 8 corners x 1/8
Chapter 3 -
23
Atomic Packing Factor: BCC
• APF for a body-centered cubic structure = 0.68
3a
a
2a
Adapted from
Fig. 3.2(a), Callister &
Rethwisch 8e.
R
a
Close-packed directions:
length = 4R = 3 a
atoms
volume
4
p ( 3a/4) 3
2
unit cell
atom
3
APF =
volume
3
a
unit cell
Chapter 3 -
24
Face Centered Cubic Structure (FCC)
• Atoms touch each other along face diagonals.
--Note: All atoms are identical; the face-centered atoms are shaded
differently only for ease of viewing.
ex: Al, Cu, Au, Pb, Ni, Pt, Ag
• Coordination # = 12
Adapted from Fig. 3.1, Callister & Rethwisch 8e.
Click once on image to start animation
(Courtesy P.M. Anderson)
4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8
Chapter 3 -
25
Atomic Packing Factor: FCC
• APF for a face-centered cubic structure = 0.74
maximum achievable APF
Close-packed directions:
length = 4R = 2 a
2a
a
Adapted from
Fig. 3.1(a),
Callister &
Rethwisch 8e.
Unit cell contains:
6 x 1/2 + 8 x 1/8
= 4 atoms/unit cell
atoms
volume
4
3
p ( 2a/4)
4
unit cell
atom
3
APF =
volume
3
a
unit cell
Chapter 3 -
26
FCC Stacking Sequence
• ABCABC... Stacking Sequence
• 2D Projection
B
B
C
A
B
B
B
A sites
C
C
B sites
B
B
C sites
• FCC Unit Cell
A
B
C
Chapter 3 -
27
Hexagonal Close-Packed Structure
(HCP)
• ABAB... Stacking Sequence
• 3D Projection
c
a
• 2D Projection
A sites
Top layer
B sites
Middle layer
A sites
Bottom layer
Adapted from Fig. 3.3(a),
Callister & Rethwisch 8e.
• Coordination # = 12
• APF = 0.74
• c/a = 1.633
6 atoms/unit cell
ex: Cd, Mg, Ti, Zn
Chapter 3 -
28
Theoretical Density, r
Density = r =
r =
where
Mass of Atoms in Unit Cell
Total Volume of Unit Cell
nA
VC NA
n = number of atoms/unit cell
A = atomic weight
VC = Volume of unit cell = a3 for cubic
NA = Avogadro’s number
= 6.022 x 1023 atoms/mol
Chapter 3 -
29
Theoretical Density, r
• Ex: Cr (BCC)
A = 52.00 g/mol
R = 0.125 nm
n = 2 atoms/unit cell
Adapted from
Fig. 3.2(a), Callister &
Rethwisch 8e.
atoms
unit cell
r=
volume
unit cell
R
a
2 52.00
a3 6.022 x 1023
a = 4R/ 3 = 0.2887 nm
g
mol
rtheoretical = 7.18 g/cm3
ractual
atoms
mol
= 7.19 g/cm3
Chapter 3 -
30
Densities of Material Classes
In general
rmetals > rceramics > rpolymers
30
Why?
Metals have...
Ceramics have...
• less dense packing
• often lighter elements
Polymers have...
r (g/cm3 )
• close-packing
(metallic bonding)
• often large atomic masses
• low packing density
(often amorphous)
• lighter elements (C,H,O)
Composites have...
• intermediate values
Metals/
Alloys
20
Platinum
Gold, W
Tantalum
10
Silver, Mo
Cu,Ni
Steels
Tin, Zinc
5
4
3
2
1
0.5
0.4
0.3
Titanium
Aluminum
Magnesium
Graphite/
Ceramics/
Semicond
Polymers
Composites/
fibers
Based on data in Table B1, Callister
*GFRE, CFRE, & AFRE are Glass,
Carbon, & Aramid Fiber-Reinforced
Epoxy composites (values based on
60% volume fraction of aligned fibers
in an epoxy matrix).
Zirconia
Al oxide
Diamond
Si nitride
Glass -soda
Concrete
Silicon
Graphite
PTFE
Silicone
PVC
PET
PC
HDPE, PS
PP, LDPE
Glass fibers
GFRE*
Carbon fibers
CFRE*
Aramid fibers
AFRE*
Wood
Data from Table B.1, Callister & Rethwisch, 8e.
Chapter 3 -
31
Single vs Polycrystals
• Single Crystals
E (diagonal) = 273 GPa
Data from Table 3.3,
Callister & Rethwisch
8e. (Source of data is
R.W. Hertzberg,
Deformation and
Fracture Mechanics of
Engineering Materials,
3rd ed., John Wiley and
Sons, 1989.)
-Properties vary with
direction: anisotropic.
-Example: the modulus
of elasticity (E) in BCC iron:
• Polycrystals
-Properties may/may not
vary with direction.
-If grains are randomly
oriented: isotropic.
(Epoly iron = 210 GPa)
-If grains are textured,
anisotropic.
E (edge) = 125 GPa
200 mm
Adapted from Fig.
4.14(b), Callister &
Rethwisch 8e.
(Fig. 4.14(b) is courtesy
of L.C. Smith and C.
Brady, the National
Bureau of Standards,
Washington, DC [now
the National Institute of
Standards and
Technology,
Gaithersburg, MD].)
Chapter 3 -
32
Polymorphism
• Two or more distinct crystal structures for the same
material (allotropy/polymorphism)
iron system
titanium
liquid
, -Ti
1538ºC
-Fe
BCC
carbon
1394ºC
diamond, graphite
-Fe
FCC
912ºC
BCC
-Fe
Chapter 3 -
33
Crystal Systems
Unit cell: smallest repetitive volume which
contains the complete lattice pattern of a crystal.
7 crystal systems
14 crystal lattices
a, b, and c are the lattice constants
Fig. 3.4, Callister & Rethwisch 8e.
Chapter 3 -
34
Point Coordinates
z
Point coordinates for unit cell
center are
111
c
a/2, b/2, c/2
y
000
a
x
½½½
b
Point coordinates for unit cell
corner are 111

z
2c



b
y
Translation: integer multiple of
lattice constants  identical
position in another unit cell
b
Chapter 3 -
35
Crystallographic Directions
z
pt. 2
head
Example 2:
pt. 1 x1 = a, y1 = b/2, z1 = 0
pt. 2 x2 = -a, y2 = b, z2 = c
y
x
pt. 1:
tail
=> -2, 1/2, 1
Multiplying by 2 to eliminate the fraction
-4, 1, 2 => [ 412 ]
where the overbar represents a
negative index
families of directions <uvw>
Chapter 3 -
36
Crystallographic Directions
z
Algorithm
1. Vector repositioned (if necessary) to pass
through origin.
2. Read off projections in terms of
unit cell dimensions a, b, and c
y 3. Adjust to smallest integer values
4. Enclose in square brackets, no commas
[uvw]
x
ex: 1, 0, ½ => 2, 0, 1 => [ 201 ]
-1, 1, 1 => [ 111 ]
where overbar represents a
negative index
families of directions <uvw>
Chapter 3 -
37
Linear Density
• Linear Density of Atoms  LD =
Number of atoms
Unit length of direction vector
[110]
ex: linear density of Al in [110]
direction
a = 0.405 nm
# atoms
a
Adapted from
Fig. 3.1(a),
Callister &
Rethwisch 8e.
LD =
length
2
= 3.5 nm-1
2a
Chapter 3 -
38
HCP Crystallographic Directions
z
Algorithm
a2
-
a3
a1
1. Vector repositioned (if necessary) to pass
through origin.
2. Read off projections in terms of unit
cell dimensions a1, a2, a3, or c
3. Adjust to smallest integer values
4. Enclose in square brackets, no commas
[uvtw]
a
2
Adapted from Fig. 3.8(a),
Callister & Rethwisch 8e.
ex:
½, ½, -1, 0
-a3
a2
2
=>
[ 1120 ]
a3
dashed red lines indicate
projections onto a1 and a2 axes
a1
2
a1
Chapter 3 -
39
HCP Crystallographic Directions
• Hexagonal Crystals
– 4 parameter Miller-Bravais lattice coordinates are
related to the direction indices (i.e., u'v'w') as
follows.
z
[ u 'v 'w ' ]  [ uvtw ]
a2
-
a3
a1
1
u = (2 u ' - v ')
3
1
v = (2 v ' - u ')
3
t = - (u +v )
w = w'
Fig. 3.8(a), Callister & Rethwisch 8e.
Chapter 3 -
40
Crystallographic Planes
Adapted from Fig. 3.10,
Callister & Rethwisch 8e.
Chapter 3 -
41
Crystallographic Planes
• Miller Indices: Reciprocals of the (three) axial
intercepts for a plane, cleared of fractions &
common multiples. All parallel planes have
same Miller indices.
• Algorithm
1. Read off intercepts of plane with axes in
terms of a, b, c
2. Take reciprocals of intercepts
3. Reduce to smallest integer values
4. Enclose in parentheses, no
commas i.e., (hkl)
Chapter 3 -
42
Crystallographic Planes
z
example
1. Intercepts
2. Reciprocals
3.
Reduction
a
1
1/1
1
1
4.
Miller Indices
(110)
example
1. Intercepts
2. Reciprocals
3.
Reduction
a
1/2
1/½
2
2
4.
Miller Indices
(100)
b
1
1/1
1
1
c

1/
0
0
c
y
b
a
x
b

1/
0
0
c

1/
0
0
z
c
y
a
b
x
Chapter 3 -
43
Crystallographic Planes
z
example
1. Intercepts
2. Reciprocals
3.
Reduction
4.
Miller Indices
a
1/2
1/½
2
6
b
1
1/1
1
3
(634)
c
c
3/4
1/¾
4/3

4 a
x


y
b
Family of Planes {hkl}
Ex: {100} = (100), (010), (001), (100), (010), (001)
Chapter 3 -
44
Crystallographic Planes (HCP)
• In hexagonal unit cells the same idea is used
z
example
1. Intercepts
2. Reciprocals
3.
Reduction
a1
1
1
1
1
a2

1/
0
0
a3
-1
-1
-1
-1
c
1
1
1
1
a2
a3
4.
Miller-Bravais Indices
(1011)
a1
Adapted from Fig. 3.8(b),
Callister & Rethwisch 8e.
Chapter 3 -
45
Crystallographic Planes
•
•
We want to examine the atomic packing of
crystallographic planes
Iron foil can be used as a catalyst. The
atomic packing of the exposed planes is
important.
a) Draw (100) and (111) crystallographic planes
for Fe.
b) Calculate the planar density for each of these
planes.
Chapter 3 -
46
Virtual Materials Science & Engineering (VMSE)
• VMSE is a tool to visualize materials science topics such as
crystallography and polymer structures in three dimensions
• Available in Student Companion Site at www.wiley.com/college/callister
and in WileyPLUS
Chapter 3 -
47
VMSE: Metallic Crystal Structures &
Crystallography Module
• VMSE allows you to view crystal structures, directions, planes,
etc. and manipulate them in three dimensions
Chapter 3 -
48
Unit Cells for Metals
• VMSE allows you to view the unit cells and manipulate
them in three dimensions
• Below are examples of actual VMSE screen shots
FCC Structure
HCP Structure
Chapter 3 -
49
VMSE: Crystallographic Planes Exercises
Additional practice on indexing crystallographic planes
Chapter 3 -
50
Planar Density of (100) Iron
Solution: At T < 912ºC iron has the BCC structure.
2D repeat unit
(100)
Planar Density =
area
2D repeat unit
1
a2
=
4 3
R
3
Radius of iron R = 0.1241 nm
Adapted from Fig. 3.2(c), Callister & Rethwisch 8e.
atoms
2D repeat unit
a=
1
4 3
R
3
atoms
atoms
19
= 1.2 x 10
2 = 12.1
2
nm
m2
Chapter 3 -
51
Planar Density of (111) Iron
Solution (cont): (111) plane
1 atom in plane/ unit surface cell
2a
atoms in plane
atoms above plane
atoms below plane
h=
3
a
2
2
atoms
2D repeat unit
 4 3  16 3 2
2
area = 2 ah = 3 a = 3 
R  =
R
3
 3

1
atoms =
= 7.0
2
Planar Density =
area
2D repeat unit
16 3
3
R
2
nm
0.70 x 1019
atoms
m2
Chapter 3 -
52
VMSE Planar Atomic Arrangements
• VMSE allows you to view planar arrangements and rotate
them in 3 dimensions
BCC (110) Plane
Chapter 3 -
53
X-Ray Diffraction
• Diffraction gratings must have spacings comparable to
the wavelength of diffracted radiation.
• Can’t resolve spacings  
• Spacing is the distance between parallel planes of
atoms.
Chapter 3 -
54
X-Rays to Determine Crystal Structure
• Incoming X-rays diffract from crystal planes.
extra
distance
travelled
by wave “2”
q
q

d
Measurement of
critical angle, qc,
allows computation of
planar spacing, d.
reflections must
be in phase for
a detectable signal
Adapted from Fig. 3.20,
Callister & Rethwisch 8e.
spacing
between
planes
X-ray
intensity
(from
detector)
n
d=
2 sin qc
q
qc
Chapter 3 -
55
X-Ray Diffraction Pattern
z
z
Intensity (relative)
c
a
x
z
c
b
y (110)
a
x
c
b
y
a
x (211)
b
y
(200)
Diffraction angle 2q
Diffraction pattern for polycrystalline -iron (BCC)
Adapted from Fig. 3.22, Callister 8e.
Chapter 3 -
56
SUMMARY
• Atoms may assemble into crystalline or
amorphous structures.
• Common metallic crystal structures are FCC, BCC, and
HCP. Coordination number and atomic packing factor
are the same for both FCC and HCP crystal structures.
• We can predict the density of a material, provided we
know the atomic weight, atomic radius, and crystal
geometry (e.g., FCC, BCC, HCP).
• Crystallographic points, directions and planes are
specified in terms of indexing schemes.
Crystallographic directions and planes are related
to atomic linear densities and planar densities.
Chapter 3 -
57
SUMMARY
• Materials can be single crystals or polycrystalline.
Material properties generally vary with single crystal
orientation (i.e., they are anisotropic), but are generally
non-directional (i.e., they are isotropic) in polycrystals
with randomly oriented grains.
• Some materials can have more than one crystal
structure. This is referred to as polymorphism (or
allotropy).
• X-ray diffraction is used for crystal structure and
interplanar spacing determinations.
Chapter 3 -
58
ASSIGNMENT (by-group)
Make a power point presentation
and report on the following topics:
1.
Metals
A. Iron (group1)
B. Steel (2)
C. Aluminum (3)
D. Copper (4)
2. Polymers
A. PVC (5)
B. Rubber (6)
C. Kevlar (7)
3. Ceramics
A. Glass (8)
B. Cement (9)
4. Semiconductor (10)
The presentation outline the
discussion on the materials:
1. Discovery
2. Properties (physical and
chemical)
3. Manufacturing processes
4. Uses
NOTE: Everyone must take part in
the report.
Chapter 3 -
59