Types of Primary Chemical Bonds
Isotropic, filled outer shells
• Metallic
– Electropositive: give up electrons
• Ionic
– Electronegative/Electropositive
• Colavent
– Electronegative: want electrons
+
+
e-
e+
+
+
+
+
+
+
+
-
+
-
+
-
+
-
+
e-
– Shared electrons along
bond direction
Close-packed
structures
Metals
• single element, fairly electropositive
• elements similar in electronegativity
Ionic Compounds
• elements differing
in electronegativity
cation
anion
Covalent Compounds
sp3
s2p1 s2p2 s2p3 s2p4
s2
Hybridized Bonds
• Elemental carbon (no other elements)
sp3 hybridization
diamond

 









also methane: CH4
one s + three p orbitals  4 (x 2) electron states
(resulting orbital is a combination)
Covalent Structures
Recall: zinc blende  both species tetrahedral
ZnS: +2 -2
or sp3
GaAs: +3 -3
single element: C or Si or Sn
S
Zn
diamond
Another way to hybridize
• Elemental carbon (no other elements)
sp2 hybridization
graphite








one s + two p orbitals  3 (x 2) electron states
(resulting orbital is a combination)
one unchanged p orbital




















trigonal symmetry
Forms of carbon with sp2 bonds
Graphite*
Nobel Prize Chemistry, 1996
Fullerene
Nobel Prize Physics, 2010
Graphene
Nanotube
* http://www.electronics-cooling.com/assets/images/2001_August_techbrief_f1.jpg
source: Wikipedia
Structural Characteristics
• Metals
– Close-packed structures (CN = 12)
– Slightly less close-packed (CN = 8)
• Ionic structures
– Close-packed with constraints
– CN = 4 to 8, sometimes 12
• Covalent structures
– Not close-packed, bonding is directional
• Any can be strongly or weakly bonded (Tm)
Diamond vs. CCP
8 atoms/cell, CN = 4
4 atoms/cell, CN = 12
½ tetrahedral
sites filled
3a  8R
3
 8  3
3
V a 
R

98.5
R

3


3
V / atom  12.3R3
2a  4R
3
 4  3
3
3
V a 
R

22.6
R

2


V / atom  5.7R3
Computing density
• Establish unit cell contents
• Compute unit cell mass
• Compute unit cell volume
– Unit cell constant, a, given (or a and c, etc.)
– Or estimate based on atomic/ionic radii
• Compute mass/volume, g/cc
• Example: NaCl
–
–
–
–
Contents = 4 Na + 4 Cl
Mass = 4(atom mass Na + atomic mass Cl)/No
Vol = a3
Avogardo’s #
g / mol
3
Units = cm3  #/ mol  g / cm
Cl
Na
Single Crystal vs. Polycrystalline
Rb3H(SO4)2
Diamond
Quartz (SiO2)
Ba(Zr,Y)O3-d
Periodicity extends uninterrupted
throughout entirety of the sample
External habit often reflects
internal symmetry
Regions of uninterrupted periodicity
amalgamated into a larger compact
= grains
delineated by grain boundaries
Isotropic vs. Anisotropic
graphite*
polycrystalline averaging
* http://www.electronics-cooling.com/assets/images/2001_August_techbrief_f1.jpg
diamond
Types of Bonds  Types of Materials
• Metallic
Isotropic, filled outer shells
– Electropositive: give up electrons
+
+
e-
e+
+
+
+
+
+
+
+
-
+
-
+
-
+
-
+
e-
• Ionic
– Electronegative/Electropositive
• Colavent
– Electronegative: want electrons
– Shared electrons along
bond direction
Close-packed
structures
What’s Missing?
units
many
methane
H
Long chain molecules with repeated units
Molecules formed by covalent bonds
Secondary bonds link molecules into solids
H H
H
C
C
C
H
H H
H
C
C
H
H H
H
H
H
H
C
C
H
H
H
C
C
C
C
H
H
http://en.wikipedia.org/wiki/File:Polyethylene-repeat-2D.png
Polymer Synthesis
• Traditional synthesis
H H
C=C
H H
– Initiation, using a catalyst that creates a free
radical
unpaired electron
R  + C=C  R – C – C 
– Propagation
R…… C – C  + C=C  R……C – C – C – C 
– Termination
R…… C – C  +  C – C……R  R –(C-C)n– R
Polydispersity
• Traditional synthesis  large variation in chain length
# of polymer chains
Average chain molecular weight
Mn
width is a measure
of polydispersity
molecular weight
number average M n  xi M i
Mw
# of polymer chains of Mi
total number of chains
weight average
M w  wi M i
weight of polymer chains of Mi = weight
fraction
total weight of all chains
molecular weight
• Degree of polymerization
– Average # of mer units/chain
Mn
nn 
m
Mw
nw 
m
by number
mer molecular weight
by weight
Polydispersity
• Traditional synthesis  large variation in chain length
# of polymer chains
Average chain molecular weight
Mn
width is a measure
of polydispersity
molecular weight
number average M n  xi M i
Mw
# of polymer chains of Mi
total number of chains
weight average
M w  wi M i
weight of polymer chains of Mi = weight
fraction
total weight of all chains
molecular weight
• Degree of polymerization
– Average # of mer units/chain
Mn
nn 
m
Mw
nw 
m
by number
mer molecular weight
by weight
New modes of synthesis
• “Living polymerization”
–
–
–
–
Initiation occurs instantaneously
Chemically eliminate possibility of random termination
Polymer chains grow until monomer is consumed
Each grows for a fixed (identical) period
Polymers
• Homopolymer
– Only one type of ‘mer’
• Copolymer
– Two or more types of ‘mers’
• Block copolymer
– Long regions of each type of ‘mer’
• Bifunctional mer
– Can make two bonds, e.g. ethylene  linear polymer
• Trifunctional mer
– Can make three bonds  branched polymer
Polymer Configurations
• Linear
H
H
C=C
C
C
C
C
• Branched
• Cross-linked
C
C
C
C
H
C
H
Polymers
H
H out
C=C
H in
H
C
C
C
H
C
C
109.5°
C
H
C
C
C
R
Placement of side groups is fixed once polymer is formed
Example side group: styrene
R=
Cl
Isotactic
C=C
H
C
R R
R
C
C
C
R
C
C
H
C
R
R
H
C
R
C
C
C
C
C
R
C
C

C
C
Syndiotactic

C
R
R
C
Atactic
C
R
C
C
R
C
C
C
C
C
• Thermal Properties
– Thermoplastics
• Melt (on heating) and resolidify (on cooling)
• Linear polymers
– Thermosets
• Soften, decompose irreversibly on heating
• Crosslinked
• Crystallinity
• Linear: more crystalline
than branched or crosslinked
• Crystalline has higher
density than amorphous
Formal Crystallography
• Crystalline
– Periodic arrangement of atoms
– Pattern is repeated by translation
c
• Three translation vectors define:
– Coordinate system
– Crystal system
– Unit cell shape
• Lattice points
b
a
g
b
a
– Points of identical environment
– Related by translational symmetry
– Lattice = array of lattice points
•
•
•
•
•
space filling
defined by 3 vectors
parallelipiped
arbitrary coord system
lattice pts at corners +
hcp
ccp (fcc)
c
b
a
g
a
bcc
Hexagonal unit cell
Specify: a, c
Hexagonal implies:
|a1| = |a2| = a
g = 120°
a = b = 90°
Cubic unit cells
Specify: a
Cubic implies:
|a1| = |a2| = |a3| = a
a = b = g = 90°
But the two types of cubic unit cells are different!
b
Crystal system
Lattices
a, b, c, a, b, g – all arbitrary
triclinic
simple
base-centered
monoclinic
C or A centered
for b = arbitrary
Convention:
a, b,= 90°
c – arbitrary
b
instead
= of=a 90
a = 90°
a
simple
g
base-centered body-centered face-centered
orthorhombic
a = b = g = 90°
a, b, c – arbitrary
6 or 7
crystal
systems
hexagonal
g = 120°
c
a
a
a = b = ga
simple
tetragonal
body-centered
a, c – arbitrary
a = b = g = 90°
a=b
simple
a = b = g = 90°
a=b=c
14 lattices
a – arbitrary; a = b = c
a – arbitrary; a = b = g
rhombohedral
(trigonal)
cubic
(isometric)
a, c – arbitrary
b=a
a = b = 90
body-centered face-centered
a – arbitrary
Centered Lattices
unconventional
choice
conventional
choice
b
a
b
a
b
b
a
unconventional
choice
both are primitive cells
a
conventional
choice
unconventional is primitive
conventional is centered
More on Lattices
X
More on Lattices
X
Lattice types of some structures
Lattice types?
BCC Metal
CsCl Structure
How many lattice points per unit cell?
Lattice types?
Zinc blende (sphaelerite)
Fluorite
Lattice types?
A
M
Diamond
Perovskite: AMO3
O