ISSUES TO ADDRESS...
• What promotes bonding?
• What types of bonds are there?
• What properties are inferred from bonding?
1

orbital electrons: n = principal quantum number n=3 2
1
Adapted from Fig. 2.1,
Callister 6e.
Nucleus: Z = # protons
= 1 for hydrogen to 94 for plutonium
N = # neutrons
Atomic mass A ≈ Z + N
2

Electrons...
• have discrete energy states
• tend to occupy lowest available energy state.
Adapted from Fig. 2.5,
Callister 6e.
3

Stable electron configurations...
• have complete s and p subshells
• tend to be unreactive .
Adapted from Table 2.2,
Callister 6e.
4

• Most elements: Electron configuration not stable .
Electron configuration
1s 1
1s 2 (stable)
1s 2 2s 1
1s 2 2s 2
1s 2 2s 2 2p 1
1s 2 2s 2 2p 2
...
1s 2 2s 2 2p 6 (stable)
1s 2 2s 2 2p 6 3s 1
1s 2 2s 2 2p 6 3s 2
1s 2 2s 2 2p 6 3s 2 3p 1
...
Adapted from Table 2.2,
Callister 6e.
1s 2 2s 2 2p 6 3s 2 3p 6
...
(stable)
1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4 6 (stable)
• Why? Valence (outer) shell usually not filled completely.
5

• Columns: Similar Valence Structure
Adapted from Fig. 2.6,
Callister 6e.
Electropositive elements:
Readily give up electrons to become + ions.
Electronegative elements:
Readily acquire electrons to become - ions.
6

• Ranges from 0.7
to 4.0
,
• Large values: tendency to acquire electrons.
Smaller electronegativity Larger electronegativity
Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the
Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell
University.
7

• Occurs between + and - ions.
• Requires electron transfer.
• Large difference in electronegativity required.
• Example: NaCl
8

• Predominant bonding in Ceramics
Be
1.5
Mg
1.2
Ca
1.0
Sr
1.0
Ba
0.9
Ra
0.9
H
2.1
Li
1.0
Na
0.9
K
0.8
Rb
0.8
Cs
0.7
Fr
0.7
Ti
1.5
Cr
1.6
Fe
1.8
NaCl
MgO
CaF2
CsCl
Ni
1.8
Zn
1.8
As
2.0
O
3.5
F
4.0
Cl
3.0
Br
2.8
I
2.5
At
2.2
He
-
Ne
-
Ar
-
Kr
-
Xe
-
Rn
-
Give up electrons Acquire electrons
Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the
Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell
University.
9

• Requires shared electrons
• Example: CH
4
C: has 4 valence e, needs 4 more
H: has 1 valence e, needs 1 more
Electronegativities are comparable.
Adapted from Fig. 2.10, Callister 6e.
10

Rb
0.8
Cs
0.7
Fr
0.7
H
2.1
Li
1.0
Na
0.9
K
0.8
Be
1.5
Mg
1.2
Ca
1.0
Sr
1.0
Ba
0.9
Ra
0.9
H2O
H2
C(diamond)
SiC
Ti
1.5
Cr
1.6
Fe
1.8
Ni
1.8
Zn
1.8
Ga
1.6
C
2.5
Si
1.8
Ge
1.8
Sn
1.8
Pb
1.8
As
2.0
GaAs
O
2.0
F
4.0
Cl
3.0
Br
2.8
I
2.5
At
2.2
He
-
Ne
-
Ar
-
Kr
-
Xe
-
Rn
-
F2
Cl2
• Molecules with nonmetals
• Molecules with metals and nonmetals
• Elemental solids (RHS of Periodic Table)
• Compound solids (about column IVA )
11

• Arises from a sea of donated valence electrons
(1, 2, or 3 from each atom).
Adapted from Fig. 2.11, Callister 6e.
• Primary bond for metals and their alloys
12

Arises from interaction between dipoles
• Fluctuating dipoles
Adapted from Fig. 2.13, Callister 6e.
• Permanent dipoles -molecule induced
-general case:
-ex: liquid HCl
-ex: polymer
Adapted from Fig. 2.14,
Callister 6e.
Adapted from Fig. 2.14,
Callister 6e.
13

Type
Ionic
Bond Energy
Large!
Comments
Nondirectional ( ceramics )
Covalent
Metallic
Secondary
Variable large-Diamond small-Bismuth
Directional semiconductors , ceramics polymer chains)
Variable large-Tungsten small-Mercury smallest
Nondirectional ( metals
Directional inter-chain ( polymer ) inter-molecular
)
14

M
• Bond length , r
• Melting Temperature , T m
F r
• Bond energy , E o
F
T m is larger if E o is larger.
15

• Elastic modulus , E
Elastic modulus
F
A o
= E
 L
L o
• E ~ curvature at r o
Energy unstretched length r o r
E is larger if E smaller Elastic Modulus o is larger.
larger Elastic Modulus
16

a
• Coefficient of thermal expansion , a coeff. thermal expansion
 L
Lo
 = a ( T
2
T
1
)
• a ~ symmetry at r o a is larger if E o is smaller.
17

Ceramics
(Ionic & covalent bonding):
Large bond energy large T m large E small a
Metals
(Metallic bonding):
Variable bond energy moderate T m moderate E moderate a
Polymers
(Covalent & Secondary):
Directional Properties
Secondary bonding dominates small T small E large a
18

ISSUES TO ADDRESS...
• How do atoms assemble into solid structures?
• How do the structures of ceramic materials differ from those of metals?
• How does the density of a material depend on its structure?
• When do material properties vary with the sample (i.e., part) orientation?
1

• Non dense, random packing
• Dense, regular packing
Dense, regular-packed structures tend to have lower energy.
2

• tend to be densely packed.
• have several reasons for dense packing:
-Typically, only one element is present, so all atomic radii are the same.
-Metallic bonding is not directional.
-Nearest neighbor distances tend to be small in order to lower bond energy.
• have the simplest crystal structures.
We will look at three such structures...
3

• Rare due to poor packing (only Po has this structure)
• Close-packed directions are cube edges.
• Coordination # = 6
(# nearest neighbors)
Click on image to animate
(Courtesy P.M. Anderson)
4

• APF for a simple cubic structure = 0.52
Adapted from Fig. 3.19,
Callister 6e.
5

• Close packed directions are face diagonals.
--Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing.
• Coordination # = 12
Click on image to animate
(Courtesy P.M. Anderson)
Adapted from Fig. 3.1(a),
Callister 6e.
6

• APF for a body-centered cubic structure = 0.74
Unit cell contains:
6 x 1/2 + 8 x 1/8
= 4 atoms/unit cell a
Adapted from
Fig. 3.1(a),
Callister 6e.
7

• Close packed directions are cube diagonals.
--Note: All atoms are identical; the center atom is shaded differently only for ease of viewing.
• Coordination # = 8
Click on image to animate
(Courtesy P.M. Anderson)
Adapted from Fig. 3.2,
Callister 6e.
8

• APF for a body-centered cubic structure = 0.68
Adapted from
Fig. 3.2,
Callister 6e.
R a
Unit cell contains:
1 + 8 x 1/8
= 2 atoms/unit cell
9

• ABAB... Stacking Sequence
• 3D Projection • 2D Projection
A sites
B sites
A sites
Adapted from Fig. 3.3,
Callister 6e.
• Coordination # = 12
• APF = 0.74
10


Example: Copper
Data from Table inside front cover of Callister (see next slide):
• crystal structure = FCC: 4 atoms/unit cell
• atomic weight = 63.55 g/mol (1 amu = 1 g/mol)
• atomic radius R = 0.128 nm (1 nm = 10 cm)
Result: theoretical 
Cu = 8.89 g/cm3
Compare to actual: 
Cu = 8.94 g/cm3
11

Characteristics of Selected Elements at 20C
Element
Aluminum
Argon
Barium
Beryllium
Boron
Bromine
Cadmium
Calcium
Carbon
Cesium
Chlorine
Chromium
Cobalt
Copper
Flourine
Gallium
Germanium
Gold
Helium
Hydrogen
Cu
F
Ga
Ge
Au
He
H
Br
Cd
Ca
C
Cs
Cl
Cr
Co
Symbol
Al
Ar
Ba
Be
B
At. Weight
(amu)
26.98
39.95
137.33
9.012
10.81
79.90
112.41
40.08
12.011
132.91
35.45
52.00
58.93
63.55
19.00
69.72
72.59
196.97
4.003
1.008
Density
1.87
------
7.19
8.9
8.94
------
5.90
(g/cm3)
2.71
------
3.5
1.85
2.34
------
8.65
1.55
2.25
5.32
19.32
------
------
Atomic radius
(nm)
0.143
------
0.217
0.114
------
------
0.149
0.197
0.071
Adapted from
Table, "Characteristics of
Selected
Elements", inside front cover,
Callister 6e.
0.265
------
0.125
0.125
0.128
------
0.122
0.122
0.144
------
------
12

 metals
•  ceramics
•  polymers
Why?
Metals have...
• close-packing
(metallic bonding)
• large atomic mass
Ceramics have...
• less dense packing
(covalent bonding)
• often lighter elements
Polymers have...
• poor packing
(often amorphous)
• lighter elements (C,H,O)
Composites have...
• intermediate values
Data from Table B1, Callister 6e.
13

• Bonding:
--Mostly ionic, some covalent.
--% ionic character increases with difference in electronegativity.
• Large vs small ionic bond character:
Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the
Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by
Cornell University.
14

• Charge Neutrality :
--Net charge in the structure should be zero.
--General form:
• Stable structures:
--maximize the # of nearest oppositely charged neighbors.
Adapted from Fig. 12.1,
Callister 6e.
15

• Coordination # increases with
Issue: How many anions can you arrange around a cation?
Adapted from Fig. 12.4,
Callister 6e.
Adapted from Table
12.2, Callister 6e.
Adapted from Fig. 12.2,
Callister 6e.
Adapted from Fig. 12.3,
Callister 6e.
16

• On the basis of ionic radii, what crystal structure would you predict for FeO?
Cation
Al3+
Fe2+
Fe3+
Ca2+
Anion
O2-
Cl-
F-
• Answer: r r cation
Data from Table 12.3,
Callister 6e.
anion


0.077
0.140
0.550
based on this ratio,
--coord # = 6
--structure = NaCl
17

m
p
• Consider CaF
2
: r cation r anion

0.100
0.133

0.8
• Based on this ratio, coord # = 8 and structure = CsCl.
• Result: CsCl structure w/only half the cation sites occupied.
• Only half the cation sites are occupied since
#Ca 2+ ions = 1/2 # F ions.
Adapted from Fig. 12.5,
Callister 6e.
18

• Demonstrates " polymorphism "
The same atoms can have more than one crystal structure.
19

• ABCABC... Stacking Sequence
• 2D Projection
A
A
B
C
B
A sites B
C
B
C
B
B sites B B
C sites
• FCC Unit Cell
20

• Compounds: Often have similar close-packed structures.
• Structure of Na Cl • Close-packed directions
--along cube edges.
Click on image to animate
(Courtesy P.M. Anderson)
Click on image to animate
(Courtesy P.M. Anderson)
21

• Some engineering applications require single crystals:
--diamond single --turbine blades crystals for abrasives
(Courtesy Martin Deakins,
GE Superabrasives,
Worthington, OH. Used with permission.)
Fig. 8.30(c), Callister 6e.
(Fig. 8.30(c) courtesy of Pratt and Whitney).
• Crystal properties reveal features of atomic structure.
--Ex: Certain crystal planes in quartz fracture more easily than others.
(Courtesy P.M. Anderson)
22

• Most engineering materials are polycrystals.
Adapted from Fig. K, color inset pages of
Callister 6e.
(Fig. K is courtesy of
Paul E. Danielson,
Teledyne Wah Chang
Albany)
1 mm
• Nb-Hf-W plate with an electron beam weld.
• Each "grain" is a single crystal.
• If crystals are randomly oriented, overall component properties are not directional.
• Crystal sizes typ. range from 1 nm to 2 cm
(i.e., from a few to millions of atomic layers).
23

• Single Crystals
-Properties vary with direction: anisotropic .
-Example: the modulus of elasticity (E) in BCC iron:
Data from Table 3.3,
Callister 6e.
(Source of data is
R.W. Hertzberg,
Deformation and
Fracture Mechanics of
Engineering Materials,
3rd ed., John Wiley and Sons, 1989.)
• Polycrystals
-Properties may/may not vary with direction.
-If grains are randomly oriented: isotropic .
(E poly iron
= 210 GPa)
-If grains are textured , anisotropic.
200 m m
Adapted from Fig.
4.12(b), Callister 6e.
(Fig. 4.12(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].)
24

• Incoming X-rays diffract from crystal planes.
Adapted from Fig.
3.2W, Callister 6e.
• Measurement of:
Critical angles, q c
, for X-rays provide atomic spacing, d.
25

Crystalline materials...
• atoms pack in periodic, 3D arrays
• typical of: -metals
-many ceramics
-some polymers crystalline SiO
2
Adapted from Fig. 3.18(a),
Callister 6e.
Noncrystalline materials...
• atoms have no periodic packing
• occurs for: -complex structures
-rapid cooling
" Amorphous " = Noncrystalline noncrystalline SiO
2
Adapted from Fig. 3.18(b),
Callister 6e.
26

• Basic Unit:
Si4+
O2-
• Glass is amorphous
• Amorphous structure occurs by adding impurities
(Na + ,Mg 2+ ,Ca 2+ , Al 3+ )
• Impurities: interfere with formation of crystalline structure.
• Quartz is crystalline
SiO
2
:
(soda glass)
Adapted from Fig. 12.11,
Callister, 6e.
28

• Atoms may assemble into crystalline or amorphous 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).
• Material properties generally vary with single crystal orientation (i.e., they are anisotropic ), but properties are generally non-directional
(i.e., they are isotropic ) in polycrystals with randomly oriented grains.
27