Defects
The Beauty of Imperfection
Corundum
Corundum
The funny thing about corundum is, when you have it in a clean single
crystal, you get something much different.
Sapphire is Gem-quality corundum
with Ti(4+) & Fe(2+) replacing Al(3+)
Ruby
Gem-quality corundum
with ~3% Cr(3+) replacing Al(3+)
Energy
Born Haber Cycles
Relate Lattice Enthalpy and Heat of Formation
Elements in
Standard
States:
M(s) , X2(g)
DHf Must be (-) for a stable solid
ionic solid
Born Haber Cycles
M+(g)
Energy
X (g)
DHEA
M+(g) , X- (g)
DHI.E.
X- (g)
M(g)
DHBD
DHsub
DHlattice
M(s) , X2(g)
Elements in
Standard States
ionic solid, MX
DHf must be (-) for a stable solid
Born Haber Cycles
M+(g)
Energy
X (g)
DHEA
M+(g) , X- (g)
DHI.E.
X- (g)
M(g)
DHBD
DHsub
DHlattice
M(s) , X2(g)
DHf
ionic solid, MX
DHf = DHsub + DHI.E + DHBD + DHEA + DHlattice
Born Haber Cycles
M+(g)
Energy
X (g)
DHEA
M+(g) , X- (g)
DHI.E.
X- (g)
M(g)
DHBD
DHsub
DHlattice
M(s) , X2(g)
DHf
ionic solid, MX
DHf = DHsub + DHI.E + DHBD + DHEA +
lattice = +108 + 496 + 121
For NaCl: DH-381
– 349
- 75
DHf = D Hsub+ DHI.E + DHBD + DHEA + DHlattice
For NaCl:
-381 = +108 +
496
+ 121
– 349
- 757
For Al2O3:
-2365 = 2(+150 + 5139) + 3/2 (493) + 3 (639) - 15,600
For NaO:
+600 = +108 + 5058
+ ½ (493)
+ 639 - 3820
Positive DHf: NaO does not (can not) exist!
Compare these DHlattice values:
why is NaCl so small? Al2O3 so large?
For NaCl:
-381 = +108 +
496
+ 121
– 349
- 757
For Al2O3:
-2365 = 2(+150 + 5139) + 3/2 (493) + 3 (639) - 15,600
Lattice Enthalpy DHlattice ~ Lattice Energy, U
Born equation for Lattice energy, U
U=
N Z+ Z- A e2
4 p eo d
(1 - n)
Where:
N is Avogadro’s # 6.022 x 1023 ion pairs/mol
Z+ Z- is the charge product
A is the Madelung constant
e2 and eo are charge on e- and permittivity constants
d is the distance (cm) between r+ and rn is a number, Born constant
A is the Madelung constant:
It expresses the geometry of charge arrangement in
a particular lattice
1/4 NaCl unit cell
+
+
√2d√2d-
-
√5d+
+
√6d-
√3d+
d+
d+
√2d-
+
-
+
√5d+
-
-
+
d+
2d-
Madelung Constant, A = S [ + 6 -12/√2 + 8/√3 - 6/2 + 24/√5 ….]
A converges to: 1.74756 (NaCl)
2.51938 (CaF2)
Lattice Enthalpy DHlattice ~ Lattice Energy, U
Born Lattice energy, U
U=
N Z+ Z- A e2
4 p eo d
(1 - n)
Where:
N is Avogadro’s # 6.022 x 1023 ion pairs/mol
Z+ Z- is the charge product
A is the Madelung constant
e2 and eo are charge on e- and permittivity constants
d is the distance (cm) between r+ and rn is a number, Born constant
n is a number, Born constant
n is a number related to the electronic configurations of
the ions involved. The n values and the electronic
configurations (e.c.) of the corresponding inert gases are
given below:
n=
e.c.
5
He
7
Ne
9
Ar
10
Kr
12
Xe
The following values of n have been suggested for some
common solids:
n=
e.c.
5.9
LiF
8.0
LiCl
8.7
LiBr
9.1
9.5
NaCl NaBr
U=
N Z+ Z- A e2
4 p eo d
(1 - n)
For NaCl:
6.022x1023 /mol * (1+1-) * 1.747558 * (1.6022 E-19)2
U = - ---------------------------------------- ( 1 - 1/9.1)
4p * 8.854x10-12 C2/m * 282x10-12 m
= - 766376 J/mol
= - 766 kJ/mol
U=
N Z+ Z- A e2
4 p eo d
(1 – 1/n)
For NaCl:
6.022x1023 /mol * (1+1-) * 1.747558 * (1.6022 E-19)2
U = - --------------------------------------- ( 1 - 1/9.1)
4p * 8.854x10-12 C2/m * 282x10-12 m
 U = - 766 kJ/mol
For Al2O3 as corundum:
6.022x1023 /mol * (3+2-) * 4.1719 * (1.6022 E-19)2
U = - ---------------------------------------- ( 1 - 1/7)
4p * 8.854x10-12 C2/m * 191x10-12 m
 U = - 15,600 kJ/mol
2Al(s) + 3/2 O2(g)  Al2O3(s)
The same reaction occurs in the
commercial drain cleaner Drano.
This consists of sodium hydroxide,
blue dye, and aluminum turnings.
When placed in water, the lye
removes the oxide coating from the
aluminum pieces causing them to
fizz as they displace hydrogen from
water. This makes it sound like
the Drano is really working
effectively, even though it's the lye
that actually cleans out the drain
clog.
What is the parallel with metals?
Metals have Bonding “Bands”
How Band Theory Evolves from Molecular Orbital Theory
Recall the most basic view of MOT
Energy
antibonding orbital
atomic orbital,
Like 1s
atomic orbital,
Like 1s
bonding orbital
Make a little more complex:
Energy
2 antibonding MO’s
2 a.o.’s
2 a.o.’s
2 bonding MO’s
Make a lot more complex:
Energy
20 antibonding MO’s
20 a.o.’s
20 a.o.’s
20 bonding MO’s
Make a mole of a metal M:
Energy
6.022 x 1023 MO.’s:
a Band of
AntiBonding MO’s
6.022 x 1023 M a.o.’s:
make a Band
of many, many
closely spaced
Atomic orbitals
6.022 x 1023 a.o.’s
6.022 x 1023 MO.’s:
a Band of Bonding MO’s
The Type of Element Determines Band Gap,
Energy
Band Gap = the energy separation between Bonding
and Anti-bonding Bands
AntiBonding
Band
Of a
Metal
Band Gap ~ 0 eV
Bonding
Band
Of a
Metal
The Type of Element Determines Band Gap
Energy
AntiBonding
Band
Of a
Network Solid
AntiBonding
Band
Of a
Metal
Band Gap is Large
Band Gap ~ 0 eV
Bonding
Band
Of a
Network Solid
Bonding
Band
Of a
Metal
~0 Band Gap Allows Electronic Movement
 makes Metal a Conductor
Energy
AntiBonding
Band
of a
Metal
is Empty
Band Gap ~ 0 eV
Bonding
Band
of a
Metal
is e- filled
Conduction
Band
e- ee- e-
e- ee- e-
Valence
Band
Large Band Gap Prevents Electronic Movement
 makes Metal an Insulator
Energy
Conduction Band
at High Energy
Band Gap is Too Large
for Electrons to “jump”
Valence
Band
At Low Energy
~Small Band Gap Allows Electronic Movement if
Energy added  makes a Semiconductor
Energy
Conduction
Band
by E = Light: Solar Cells
e-
e-
Band Gap overcome
by E = Heat: Thermisters
(heat regulators)
Valence
Band
Tuesday, February 22, 2011
New transistors: An alternative to silicon and better than graphene
Smaller and more energy-efficient electronic chips could be made using molybdenite. In an
article appearing online January 30 in the journal Nature Nanotechnology, EPFL's Laboratory of
Nanoscale Electronics and Structures (LANES) publishes a study showing that this material has distinct
advantages over traditional silicon or graphene for use in electronics applications.
One of molybdenite's advantages is
that it is less voluminous than
silicon, which is a three-dimensional
material. "In a 0.65-nanometer-thick sheet of
MoS2, the electrons can move around as
easily as in a 2-nanometer-thick sheet of
silicon," explains Kis. "But it's not currently
possible to fabricate a sheet of silicon as thin
as a monolayer sheet of MoS2." Another
advantage of molybdenite is that it
can be used to make transistors that
consume 100,000 times less energy
in standby state than traditional silicon
transistors. A semi-conductor with a "gap"
must be used to turn a transistor on and off,
and molybdenite's 1.8 electron-volt gap is ideal
for this purpose.
Caption: This is a digital model showing how molybdenite can be integrated into a transistor.
http://nanotechnologytoday.blogspot.com/2011/02/new-transistors-alternative-to-silicon.html
Defects:
Impurities Create New Possibilities
~Impurities Decrease Band Gap
 makes a Better Semiconductor
Energy
Conduction
Band
Ge
e-
Ga orbitals (empty)
eValence
Band
Ge
Ge
Ga doped Ge –is
a p-type semiconductor
~Impurities Decrease Band Gap
 makes a Better Semiconductor
Energy
Conduction
Band
Ge
e-
Valence
Band
Ge
e-
As doped–Ge
is an n-type
semiconductor
Ge
Combining a P-type and N-type Semiconductors
Makes a Diode
N-type
P-type
e-
ee-
e-
Current  this way only
A Diode made of the right materials causes DE loss to
be converted to Light: Light Emitting Diode (LED)
N-type
P-type
e-
e-
e-
e-
Semiconductors: where do they come from?
Semiconductors: where do they come from?
Semiconductors: where do they come from?
Schematic of a junction between two
organic semiconductors, an anthracene
derivative containing free positive ions and
a ruthenium, complex containing negative
ions. When the two are joined, ions diffuse
across the junction creating a difference in
energy levels that facilitates rectification,
electroluminiscence and photovoltaic
response. For experimental purposes the
materials were sandwiched between
electrodes made of gold and indium tin
oxide.
Thedesigned
latter is transparent.
Can be
to be ‘organic’
Malliaras lab/Cornell University
Can mix‘organic’ and
coordination complexes
Semi-conductor humor:
The Xerox
Process for
Photocopying
2. Blue dots are the “picture”/text
1. Induces charge on surface
Based on
semi-conductor
properties of a
photo-reactive
material: Se
3. Light reflection off white
surfaces induces charge
separation, Se surface now has +
charges.
4. “toner” sticks to positive surface
areas
5. “toner” transfers to paper
Ceramics go beyond Dirt
Ceramics: can
The mean
Traditional
many View
things
Make from pulverized rocks (“dirt”)
Composition: MAlxSiyOz.H2O
from silicate and aluminosilicate minerals
Begin “Plastic” (workable, malleable) when mixed with water then
HEAT causes vitrification (“glassification”)
Structure:
Amorphous with polycrystallites
or
vitreous (glass)
Properties:
very high melting points—refractories (furnace linings)
brittle (not malleable)
high mechanical strength and stability
chemically inert
Common examples and how they differ:
Terra cotta -
From “common” clay; red color from
FeO iron oxides in “dirt”
Fired at lowest temp; not glassy
Stoneware-
From “common” clay;
Fired at higher temp
Porcelain -
From flint + feldspar clays;
Fired at highest temp; more vitreous
Most translucent, most vitreous, most white, most pure
China – Clay (kaolin) from China: Al O .2SiO .2H O .
2 3
2
2
“Bone China” originally made from calcined bone, CaO
The ‘ring’ test…
Firing process: evaporates remaining water away
and initiates vitrification
What goes on top of Ceramics is ceramic too —
Glazes
Composition similar: silicates + flint + feldspar + “flux”
(SiO2 + SiAlO3)
(K2O, ZnO, BaCO3)
Structure: vitreous
Color from Transition Metal minerals/salts added
Fe(3+) – red-brown
Cu(2+) – turquoise blue and green
Co(2+) – “cobalt” blue
Ni(2+) – green, brown
Mn(2+) –purple, brown
Ceramics: the Modern View
Advanced Ceramics or Materials:
•
silicon carbides SiC and nitrides Si3N
• composites: SiC/Al2O3 “whiskers”
Improved Properties:
• tougher, higher temperatures, fewer defects
Examples from Dr. Lukacs
• golf heads
• Machine parts
• tiles
All common stuff
New Materials are Hot
diamond
graphite
lonsdaleite
Snazzy
graphite
relatives:
fullerenes,
carbon
nanotubes
C-60 fullerene
fullerenes
C-70 fullerene
nanotube
amorphous carbon
New Materials are Hot
diamond
graphite
Snazzy graphite relatives: fullerenes,
carbon nanotubes
lonsdaleite
For:
drug delivery??
gene therapy?
electronics?
solar cells?
New Materials are Hot
Biomineralization: how does it grow like that?
SiO2
Ca3(PO4)2
Knowledge for making
Artificial bone?
New Materials are Hot
Snazzy graphite relatives: fullerenes, carbon nantubes
drug delivery??
electronics?
Better materials for Solar cells
Biomineralization: how does it grow like that?
Artificial bone?
Superconducting Solids
And Molecular Magnets
http://superconductors.org/
Get to know the perovskite unit cell
Empirical formula:
ABX3
Prototype CaTiO3
Introducing the
1-2-3 Superconductor
Rare earth doped material
YBa2Cu3O7 :
“1-2-3 type” superconductor:
mixed valence Cu oxide
Y3+(Ba2+)2(Cu2+)2(Cu3+)(O2-)7
3 perovskite
unit cells
O vacancies
 Square planar (CuO4)
and
 Square Pyramidal (CuO5)
Cu Sites
CuOx planes carry e-
Square planar Cu(2+) is
d9, with one e- in the
high E dx2-y2 orbital
Housecroft:
“A superconductor is a material whose electrical resistance drops
to zero when cooled below its critical temperature, Tc”
The Meissner effect
The Meissner effect in superconductors like this black ceramic yttrium based superconductor acts to exclude magnetic
fields from the material. Since the electrical resistance is zero, supercurrents are generated in the material to exclude
the magnetic fields from a magnet brought near it. The currents which cancel the external field produce magnetic poles
which mirror the poles of the permanent magnet, repelling them to provide the lift to levitate the magnet.
The levitation process is quite remarkable. Since the levitating currents in the superconductor meet no resistance, they
can adjust almost instantly to maintain the levitation. The suspended magnet can be moved, put into oscillation, or even
spun rapidly and the levitation currents will adjust to keep it in suspension.