MSE 528
Fall 2010
ISSUES TO ADDRESS...
• What promotes bonding?
• What types of bonds are there?
• What properties are inferred from bonding?
1
Atomic Structure and Interatomic Bonding
Nucleus: Z = # protons
2
orbital electrons: n = principal quantum number
n=3 2 1
= 1 for hydrogen to 94 for plutoniumN = # neutrons
Atomic mass A ≈ Z + N
Adapted from Fig. 2.1, Callister 6e.
BOHR ATOM
• have discrete energy states• tend to occupy lowest available energy state.
3
Incr
easi
ng e
nerg
y
n=1
n=2
n=3
n=4
1s2s
3s2p
3p
4s4p
3d
Electrons...
Adapted from Fig. 2.5, Callister 6e.
ELECTRON ENERGY STATES
4
• have complete s and p subshells• tend to be unreactive.
Stable electron configurations...
Z Element Configuration
2 He 1s2
10 Ne 1s22s22p6
18 Ar 1s22s22p63s23p6
36 Kr 1s22s22p63s23p63d104s24p6
Adapted from Table 2.2, Callister 6e.
STABLE ELECTRON CONFIGURATIONS
5
• Why? Valence (outer) shell usually not filled completely.
• Most elements: Electron configuration not stable.Element Hydrogen Helium Lithium Beryllium Boron Carbon ... Neon Sodium Magnesium Aluminum ... Argon ... Krypton
Atomic # 1 2 3 4 5 6
10 11 12 13
18 ... 36
Electron configuration 1s1 1s2 (stable) 1s22s1 1s22s2 1s22s22p1 1s22s22p2 ... 1s22s22p6 (stable) 1s22s22p63s1 1s22s22p63s2 1s22s22p63s23p1 ... 1s22s22p63s23p6 (stable) ... 1s22s22p63s23p63d104s246 (stable)
Adapted from Table 2.2, Callister 6e.
SURVEY OF ELEMENTS
6
• Columns: Similar Valence Structure
Electropositive elements:Readily give up electronsto become + ions.
Electronegative elements:Readily acquire electronsto become - ions.
He
Ne
Ar
Kr
Xe
Rn
inert
gase
s acc
ept
1e
acc
ept
2e
giv
e u
p 1e
giv
e u
p 2e
giv
e u
p 3e
F Li Be
Metal
Nonmetal
Intermediate
H
Na Cl
Br
I
At
O
S Mg
Ca
Sr
Ba
Ra
K
Rb
Cs
Fr
Sc
Y
Se
Te
Po
Adapted from Fig. 2.6, Callister 6e.
THE PERIODIC TABLE
7
• Ranges from 0.7 to 4.0,
Smaller electronegativity Larger electronegativity
He -
Ne -
Ar -
Kr -
Xe -
Rn -
F 4.0
Cl 3.0
Br 2.8
I 2.5
At 2.2
Li 1.0
Na 0.9
K 0.8
Rb 0.8
Cs 0.7
Fr 0.7
H 2.1
Be 1.5
Mg 1.2
Ca 1.0
Sr 1.0
Ba 0.9
Ra 0.9
Ti 1.5
Cr 1.6
Fe 1.8
Ni 1.8
Zn 1.8
As 2.0
• Large values: tendency to 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 CornellUniversity.
ELECTRONEGATIVITY
Na (metal) unstable
Cl (nonmetal) unstable
electron
+ - Coulombic Attraction
Na (cation) stable
Cl (anion) stable
8
• Occurs between + and - ions.• Requires electron transfer.• Large difference in electronegativity required.• Example: NaCl
IONIC BONDING
9
• Predominant bonding in Ceramics
Give up electrons Acquire electrons
He -
Ne -
Ar -
Kr -
Xe -
Rn -
F 4.0
Cl 3.0
Br 2.8
I 2.5
At 2.2
Li 1.0
Na 0.9
K 0.8
Rb 0.8
Cs 0.7
Fr 0.7
H 2.1
Be 1.5
Mg 1.2
Ca 1.0
Sr 1.0
Ba 0.9
Ra 0.9
Ti 1.5
Cr 1.6
Fe 1.8
Ni 1.8
Zn 1.8
As 2.0
CsCl
MgO
CaF2
NaCl
O 3.5
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 CornellUniversity.
EXAMPLES: IONIC BONDING
10
• Requires shared electrons• Example: CH4
C: has 4 valence e, needs 4 more
H: has 1 valence e, needs 1 more
Electronegativities are comparable.
shared electrons from carbon atom
shared electrons from hydrogen atoms
H
H
H
H
C
CH4
Adapted from Fig. 2.10, Callister 6e.
COVALENT BONDING
11
• Molecules with nonmetals• Molecules with metals and nonmetals• Elemental solids (RHS of Periodic Table)• Compound solids (about column IVA)
He -
Ne -
Ar -
Kr -
Xe -
Rn -
F 4.0
Cl 3.0
Br 2.8
I 2.5
At 2.2
Li 1.0
Na 0.9
K 0.8
Rb 0.8
Cs 0.7
Fr 0.7
H 2.1
Be 1.5
Mg 1.2
Ca 1.0
Sr 1.0
Ba 0.9
Ra 0.9
Ti 1.5
Cr 1.6
Fe 1.8
Ni 1.8
Zn 1.8
As 2.0
SiC
C(diamond)
H2O
C 2.5
H2
Cl2
F2
Si 1.8
Ga 1.6
GaAs
Ge 1.8
O 2.0
colu
mn IVA
Sn 1.8Pb 1.8
EXAMPLES: COVALENT BONDING
12
• Arises from a sea of donated valence electrons (1, 2, or 3 from each atom).
• Primary bond for metals and their alloys
+ + +
+ + +
+ + +Adapted from Fig. 2.11, Callister 6e.
METALLIC BONDING
13
Arises from interaction between dipoles
• Permanent dipoles-molecule induced
• Fluctuating dipoles
+ - secondary bonding + -
H Cl H Clsecondary bonding
secondary bonding
HH HH
H2 H2
secondary bonding
ex: liquid H2asymmetric electron clouds
+ - + -secondary bonding
-general case:
-ex: liquid HCl
-ex: polymer
Adapted from Fig. 2.13, Callister 6e.
Adapted from Fig. 2.14, Callister 6e.
Adapted from Fig. 2.14, Callister 6e.
SECONDARY BONDING
14
Type
Ionic
Covalent
Metallic
Secondary
Bond Energy
Large!
Variablelarge-Diamondsmall-Bismuth
Variablelarge-Tungstensmall-Mercury
smallest
Comments
Nondirectional (ceramics)
Directionalsemiconductors, ceramics
polymer chains)
Nondirectional (metals)
Directionalinter-chain (polymer)
inter-molecular
SUMMARY: BONDING
15
• Bond length, r
• Bond energy, Eo
F F
r
• Melting Temperature, Tm
Eo=
“bond energy”
Energy (r)
ro r
unstretched length
r
larger Tm
smaller Tm
Energy (r)
ro
Tm is larger if Eo is larger.
PROPERTIES FROM BONDING: TM
16
• Elastic modulus, E
• E ~ curvature at ro
cross sectional area Ao
L
length, Lo
F
undeformed
deformed
L F Ao
= E Lo
Elastic modulus
r
larger Elastic Modulus
smaller Elastic Modulus
Energy
ro unstretched length
E is larger if Eo is larger.
PROPERTIES FROM BONDING: E
17
• Coefficient of thermal expansion,
• ~ symmetry at ro
is larger if Eo is smaller.
L
length, Lo
unheated, T1
heated, T2
= (T2-T1) L Lo
coeff. thermal expansion
r
smaller
larger
Energy
ro
PROPERTIES FROM BONDING:
18
Ceramics(Ionic & covalent bonding):
Metals(Metallic bonding):
Polymers(Covalent & Secondary):
secondary bonding
Large bond energylarge Tm
large Esmall
Variable bond energymoderate Tm
moderate Emoderate
Directional PropertiesSecondary bonding dominates
small Tsmall Elarge
SUMMARY: PRIMARY BONDS
ISSUES TO ADDRESS...• 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?
1
Structures of Metals and Ceramics
•How do the structures of ceramic materials differ from those of metals?
2
• Non dense, random packing
• Dense, regular packing
Dense, regular-packed structures tend to have lower energy.
Energy
r
typical neighbor bond length
typical neighbor bond energy
Energy
r
typical neighbor bond length
typical neighbor bond energy
ENERGY AND PACKING
3
• 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...
METALLIC CRYSTALS
4
• Rare due to poor packing (only Po has this structure)• Close-packed directions are cube edges.
• Coordination # = 6 (# nearest neighbors)
(Courtesy P.M. Anderson)
SIMPLE CUBIC STRUCTURE (SC)
Click on image to animate
5
APF = Volume of atoms in unit cell*
Volume of unit cell
*assume hard spheres
• APF for a simple cubic structure = 0.52
APF = a3
4
3(0.5a)31
atoms
unit cellatom
volume
unit cellvolume
close-packed directions
a
R=0.5a
contains 8 x 1/8 = 1 atom/unit cell
Adapted from Fig. 3.19, Callister 6e.
ATOMIC PACKING FACTOR
6
• Coordination # = 12
Adapted from Fig. 3.1(a), Callister 6e.
(Courtesy P.M. Anderson)
• Close packed directions are face diagonals.--Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing.
FACE CENTERED CUBIC STRUCTURE (FCC)
Click on image to animate
APF = a3
4
3( 2a/4)34
atoms
unit cell atomvolume
unit cell
volume
Unit cell contains: 6 x 1/2 + 8 x 1/8 = 4 atoms/unit cell
a
7
• APF for a body-centered cubic structure = 0.74
Close-packed directions: length = 4R
= 2 a
Adapted fromFig. 3.1(a),Callister 6e.
ATOMIC PACKING FACTOR: FCC
• Coordination # = 8
8
Adapted from Fig. 3.2, Callister 6e.
(Courtesy P.M. Anderson)
• Close packed directions are cube diagonals.--Note: All atoms are identical; the center atom is shaded differently only for ease of viewing.
BODY CENTERED CUBIC STRUCTURE (BCC)
Click on image to animate
aR
9
• APF for a body-centered cubic structure = 0.68
Close-packed directions: length = 4R
= 3 a
Unit cell contains: 1 + 8 x 1/8 = 2 atoms/unit cell
Adapted fromFig. 3.2,Callister 6e.
ATOMIC PACKING FACTOR: BCC
APF = a3
4
3( 3a/4)32
atoms
unit cell atomvolume
unit cell
volume
10
• Coordination # = 12
• ABAB... Stacking Sequence
• APF = 0.74
• 3D Projection • 2D Projection
A sites
B sites
A sites Bottom layer
Middle layer
Top layer
Adapted from Fig. 3.3, Callister 6e.
HEXAGONAL CLOSE-PACKED STRUCTURE (HCP)
11
Example: Copper
n AVcNA
# atoms/unit cell Atomic weight (g/mol)
Volume/unit cell
(cm3/unit cell)Avogadro's number (6.023 x 1023 atoms/mol)
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)-7
Vc = a3 ; For FCC, a = 4R/ 2 ; Vc = 4.75 x 10-23cm3
Compare to actual: Cu = 8.94 g/cm3Result: theoretical Cu = 8.89 g/cm3
THEORETICAL DENSITY,
12
Element Aluminum Argon Barium Beryllium Boron Bromine Cadmium Calcium Carbon Cesium Chlorine Chromium Cobalt Copper Flourine Gallium Germanium Gold Helium Hydrogen
Symbol Al Ar Ba Be B Br Cd Ca C Cs Cl Cr Co Cu F Ga Ge Au He H
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
Atomic radius (nm) 0.143 ------ 0.217 0.114 ------ ------ 0.149 0.197 0.071 0.265 ------ 0.125 0.125 0.128 ------ 0.122 0.122 0.144 ------ ------
Density (g/cm3) 2.71 ------ 3.5 1.85 2.34 ------ 8.65 1.55 2.25 1.87 ------ 7.19 8.9 8.94 ------ 5.90 5.32 19.32 ------ ------
Crystal Structure FCC ------ BCC HCP Rhomb ------ HCP FCC Hex BCC ------ BCC HCP FCC ------ Ortho. Dia. cubic FCC ------ ------
Adapted fromTable, "Charac-teristics ofSelectedElements",inside frontcover,Callister 6e.
Characteristics of Selected Elements at 20C
metals ceramics polymers
13
(g
/cm
3)
Graphite/ Ceramics/ Semicond
Metals/ Alloys
Composites/ fibersPolymers
1
2
20
30Based 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). 10
3 4 5
0.3 0.4 0.5
Magnesium
Aluminum
Steels
Titanium
Cu,Ni
Tin, Zinc
Silver, Mo
Tantalum Gold, W Platinum
Graphite Silicon
Glass -soda Concrete
Si nitride Diamond Al oxide
Zirconia
HDPE, PS PP, LDPE
PC
PTFE
PET PVC Silicone
Wood
AFRE *
CFRE *
GFRE*
Glass fibers
Carbon fibers
Aramid fibers
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.
DENSITIES OF MATERIAL CLASSES
14
• Bonding: --Mostly ionic, some covalent. --% ionic character increases with difference in electronegativity.
He -
Ne -
Ar -
Kr -
Xe -
Rn -
Cl 3.0
Br 2.8
I 2.5
At 2.2
Li 1.0
Na 0.9
K 0.8
Rb 0.8
Cs 0.7
Fr 0.7
H 2.1
Be 1.5
Mg 1.2
Sr 1.0
Ba 0.9
Ra 0.9
Ti 1.5
Cr 1.6
Fe 1.8
Ni 1.8
Zn 1.8
As 2.0
C 2.5Si 1.8
F 4.0
Ca 1.0
Table of Electronegativities
CaF2: large
SiC: small
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 byCornell University.
• Large vs small ionic bond character:
CERAMIC BONDING
15
• Charge Neutrality: --Net charge in the structure should be zero.
--General form: AmXp
m, p determined by charge neutrality• Stable structures: --maximize the # of nearest oppositely charged neighbors.
Adapted from Fig. 12.1, Callister 6e.
- -
- -+
unstable
- -
- -+
stable
- -
- -+
stable
CaF2: Ca2+cation
F-
F-
anions+
IONIC BONDING & STRUCTURE
16
• Coordination # increases with Issue: How many anions can you arrange around a cation?
rcationranion
rcationranion
Coord #
< .155 .155-.225 .225-.414 .414-.732 .732-1.0
ZnS (zincblende)
NaCl (sodium chloride)
CsCl (cesium chloride)
2 3 4 6 8
Adapted from Table 12.2, Callister 6e.
Adapted from Fig. 12.2, Callister 6e.
Adapted from Fig. 12.3, Callister 6e.
Adapted from Fig. 12.4, Callister 6e.
COORDINATION # AND IONIC RADII
17
• On the basis of ionic radii, what crystal structure would you predict for FeO?
Cation
Al3+
Fe2+
Fe3+
Ca2+ Anion
O2-
Cl-
F-
Ionic radius (nm)
0.053
0.077
0.069
0.100
0.140
0.181
0.133
• Answer:
rcationranion
0.0770.140
0.550
based on this ratio,--coord # = 6--structure = NaCl
Data from Table 12.3, Callister 6e.
EX: PREDICTING STRUCTURE OF FeO
18
• Consider CaF2 :
rcationranion
0.1000.133
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 #Ca2+ ions = 1/2 # F- ions.
Adapted from Fig. 12.5, Callister 6e.
AmXp STRUCTURES
19
• Demonstrates "polymorphism" The same atoms can have more than one crystal structure.
DEMO: HEATING ANDCOOLING OF AN IRON WIRE
Temperature, C
BCC Stable
FCC Stable
914
1391
1536
shorter
longer!shorter!
longer
Tc 768 magnet falls off
BCC Stable
Liquid
heat up
cool down
20
• ABCABC... Stacking Sequence• 2D Projection
A sites
B sites
C sitesB B
B
BB
B BC C
CA
A
• FCC Unit CellA
BC
FCC STACKING SEQUENCE
21
• Compounds: Often have similar close-packed structures.
• Close-packed directions --along cube edges.
• Structure of NaCl
(Courtesy P.M. Anderson) (Courtesy P.M. Anderson)
STRUCTURE OF COMPOUNDS: NaCl
Click on image to animate Click on image to animate
22
• Some engineering applications require single crystals:
• Crystal properties reveal features of atomic structure.
(Courtesy P.M. Anderson)
--Ex: Certain crystal planes in quartz fracture more easily than others.
--diamond single crystals for abrasives
--turbine bladesFig. 8.30(c), Callister 6e.(Fig. 8.30(c) courtesyof Pratt and Whitney).(Courtesy Martin
Deakins,GE Superabrasives, Worthington, OH. Used with permission.)
CRYSTALS AS BUILDING BLOCKS
23
• Most engineering materials are polycrystals.
• 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).
Adapted from Fig. K, color inset pages of Callister 6e.(Fig. K is courtesy of Paul E. Danielson, Teledyne Wah Chang Albany)
1 mm
POLYCRYSTALS
24
• Single Crystals-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 (diagonal) = 273 GPa
E (edge) = 125 GPa
200 m
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.)
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].)
SINGLE VS POLYCRYSTALS
d=n/2sinc
x-ray intensity (from detector)
c25
• Incoming X-rays diffract from crystal planes.
• Measurement of: Critical angles, c, for X-rays provide atomic spacing, d.
Adapted from Fig. 3.2W, Callister 6e.
X-RAYS TO CONFIRM CRYSTAL STRUCTURE
reflections must be in phase to detect signal
spacing between planes
d
incoming
X-rays
outg
oing
X-ra
ys
detector
extra distance travelled by wave “2”
“1”
“2”
“1”
“2”
• atoms pack in periodic, 3D arrays• typical of:
26
Crystalline materials...
-metals-many ceramics-some polymers
• atoms have no periodic packing• occurs for:
Noncrystalline materials...
-complex structures-rapid cooling
Si Oxygen
crystalline SiO2
noncrystalline SiO2"Amorphous" = NoncrystallineAdapted from Fig. 3.18(b), Callister 6e.
Adapted from Fig. 3.18(a), Callister 6e.
MATERIALS AND PACKING
28
• Quartz is crystalline SiO2: Si4+
Na+
O2-
• Basic Unit:
Si04 tetrahedron4-
Si4+
O2-
• Glass is amorphous• Amorphous structure occurs by adding impurities
(Na+,Mg2+,Ca2+, Al3+)• Impurities: interfere with formation of crystalline structure.
(soda glass)Adapted from Fig. 12.11, Callister, 6e.
GLASS STRUCTURE
• 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
SUMMARY