Transition Metal Oxide Perovskites: Band Structure, Electrical and Magnetic Properties

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Transition Metal Oxide PerovskitesBand
Structure, Electrical and Magnetic Properties
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Transition Metal Oxides

• To illustrate the relationship between crystal
  structure, bonding, band structure, electrical
  and magnetic properties we are going to consider
  transition metal oxides of three structure types.
• Perovskite (AMO3)/ReO3
• Rock Salt (MO)
• Rutile (MO2)
• For all three structures M-O interactions will
  dictate the properties. In the latter two
  structure types we also need to consider M-M
  bonding.

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NiO

• Nickel oxide is a classic example of one of the
  class of materials which have excited and
  perplexed over the past 70 years, first-row
  transition metal monoxides. In a purely ionic
  picture of NiO the Ni ions have a partially
  filled shell in a ground-state configuration.
  According to conventional band-theory this should
  result in metallic behaviour, yet NiO is an
  insulator with a bulk band gap of 4.3 eV. It
  crystallizes in the rock-salt structure (as MgO)
  with a lattice constant of 0.417 nm and a
  high-spin anti-ferromagnetic spin structure at
  low temperatures. Its Néel temperature ( ) is 523
  K

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?The Sodium chloride (or rock salt) structure
?The unit cell is cubic, the structure
consists of two interpenetrating
faced-centered (F) array, one of Na and
the other of Cl- ions. ?C. N. for Na 6
a 5.6402 Å
Figure The crystal structure of sodium chloride
(NaCl)
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B
A
C
?c. c. p. (cubic close-packed) array of Cl-
ions with Na ion filling all the octahedral
holes.
Figure A unit cell of sodium chloride showing
the position of the close-packed layers.
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Figure (a) An MX6 octahedron. (b) The solid
octahedron. (c) Plan of an octahedron
with contours.
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Edge-shared
Corner-shared
Edge-shared
Face-shared
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NaCl6 Sharing edges
T-site
Figure NaCl structure showing edge sharing of
octahedra. (A tetrahedral space is
also shown shared in colour. )
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Ordering of the magnetic dipoles in magnetic
materials
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A Mott Insulator

• Understanding the electronic structure of NiO,
  and other transition metal monoxides, has been a
  topic of great interest for many theorists. Mott
  proposed that the band gaps in these materials
  were due to strong on-site repulsion between the
  -electrons of the metal ions

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Generic Octahedral MO Diagram
t1u (s p)
a1g (s)
(n1)p
Oxygen
(n1)s
eg (s)
nd eg (dx2-y2, dz2)
t2g (p)
O 2p p (6) - t2g, t1u O 2p NB (6)-t1g, t2u
(n1)d t2g (dxy, dxz, dyz)
t1g t2u
O 2p s (6) a1g, t1u, eg
t2g (p)
Transition Metal
eg (s)
t1u (s p)
a1g (s)
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Simplified Band Structure
Bands of interest
s 4
(n1)p
Oxygen
(n1)s
M-O s 2
nd eg (dx2-y2, dz2)
M-O p 3
(n1)d t2g (dxy, dxz, dyz)
O 2p p (12)
O 2p NB
O 2p s (6) a1g, t1u, eg
M-O p
Transition Metal
M-O s
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Orbital Overlap s and p Bands
p Overlap (M d t2g O 2p p) G ? M Band Runs
Uphill
Greater Spatial Overlap W(s) gt W(p)
M point (kxkyp/a) antibonding
G point (kxky0) non-bonding
s Overlap (M d eg O 2p s) G ? M Band Runs
Uphill
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Overlap in 3D
So far we have been working mostly in 1D and 2D.
In 3D keep the following overlap considerations
in mind X Point (kxp/a, kykz0) dxy, dxz ?
1/2 antibonding dyz ? nonbonding 2 degenerate
bands M Point (kxkyp/a, kz0) dxy, ?
antibonding dyz, dxz ? 1/2 antibonding 2
degenerate bands R Point (kxkykz p/a) dxy,
dyz, dxz ? antibonding 3 degenerate bands
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Ferromagnetic Materials
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Hysteresis loop for a ferro- or ferrimagnet.
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Curie-Weiss law
the magnetic susceptibility
Weiss postulated that an internal molecular
field acts in ferromagnetic materials to align
the magnetic moments parallel to each other. We
now understand the origin of this molecular field
to be the quantum mechanical exchange energy,
which causes electrons with parallel spins (and
therefore parallel magnetic moments) to have a
lower energy than electrons with antiparallel
spins.
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Schematic 3d and 4s densities of states, D(E), in
first-row transition metals.
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3d and 4s up- and down-spin densities of states
in first-row transition metals, with exchange
interaction included
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Ferromagnetic Curie Temperatures

• Material Curie
  temperature(K)
• Fe
  1043
• Co
  1388
• Ni
  627
• Gd
  293
• Dy
  85
• Au2MnAl 200
• EuO 77
• GdCl3 2.2

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Magnetic Domains

• The microscopic ordering of electron spins
  characteristic of ferromagnetic materials leads
  to the formation of regions of magnetic alignment
  called domains.
• The main implication of the domains is that there
  is already a high degree of magnetization in
  ferromagnetic materials within individual
  domains, but that in the absence of external
  magnetic fields those domains are randomly
  oriented. A modest applied magnetic field can
  cause a larger degree of alignment of the
  magnetic moments with the external field, giving
  a large multiplication of the applied field.

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Domains may be made visible with the use of
magnetic colloidal suspensions which concentrate
along the domain boundaries.
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Rutile TiO2

• oxides MO2 (e.g. Ti, Nb, Cr, Mo, Ge, Pb, Sn)
• fluorides MF2 (e.g. Mn, Fe, Co, Ni, Cu, Zn, Pd)

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?The rutile structure
(???) ?TiO2 ?Tetragonal unit cell ?not based on
close-packing (each titanium atom is coordinated
by six oxygens at the corners of a slightly
distorted octahedron.)
(2.9581Å) c ?
? a (4.5937Å)
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Side way Top down
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• Rutile is an interesting, varied and important
  mineral. Rutile is a major ore of titanium, a
  metal used for high tech alloys because of its
  light weight, high strength and resistance to
  corrosion. Rutile is also unwittingly of major
  importance to the gemstone markets. It also forms
  its own interesting and beautiful mineral
  specimens.

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?The zinc blende and wurtzite structures
?(c. c. p.) array of sulphide ions with
zinc ions occupying every other
tetradral hole ?Each zinc ion is
tetrahedrally coordinated by four
sulphides ?eg. copper halides Zn, Cd,
Hg sulphides
Figure The crystal structure of zinc blende
(ZnS)
??? (sphalerite)
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Cubic Peroskite ABO3
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Perovskite Crystal Structure
M
O
A
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Perovskites and Band Structure

• Octahedral Molecular Orbital Diagram
• p(t2g) and s(eg) Bands
• Orbital Overlap and Bandwidth (ReO3 vs. MnO32-)
• Structural Distortions (Octahedral Tilting)
• Exchange Splitting (Spin Pairing Energy)
• The d-electron count (SrTiO3 to SrFeO3)
• Instabilities and the d4 electron count
• SrFeO3
• LaMnO3
• CaFeO3

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?The perovskite structure CaTiO3
(ABX3)
eg. Table SrTiO3 SrThO3 SrZnO3
CsCaF3 SrHfO3 CsCdBr3 SrSnO3
CsHgBr3 BaSnO3 CsHgCl3 KNbO3 KTaO3
KIO3 NaNbO3 LaCoO3 LaCrO3 LaFeO3
LaGaO3 LaVO3
a 3.9051 Å
?c. c. p. array of A and X atoms with the B
atoms occupying the octahedral holes
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The perovskite type structure (ABO3)
rA r0 v2 t (rB r0)
rA radius of A cation rB radius of B
cation rO radius of O cation
Perovskite 0.8lttlt1

• 0.9 lttlt1 Ideal or cubic structure
• e.g. BaCeO3, BaSnO3
• (2)0.8 lttlt0.9Distorted structure (with different
  symmetry group)
• (tilted BO6, Oh)
• e.g. NaNbO3, CaTiO3,
  PrAlO3)

unstable
tlt0.8
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Structural Distortions CaMnO3
Cubic (Pm3m) Linear Mn-O-Mn
Orthorhombic (Pnma) Bent Mn-O-Mn
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???(Perovskite)?? ??ABO3 ??CaTiO3
YBa2Cu3O7 (?3?Perovskite????)
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3d TM Oxide Perovskites
p, s implies delocalized electrons t2g, eg
implies localized electrons
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SrFeO3-The Edge of Instability
Cubic Structure No Jahn-Teller Distortion All Fe
atoms equivalent Localized t2g electrons Delocaliz
ed eg electrons Metallic to at least 4 K
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LaMnO3-Cooperative Jahn Teller Dist.
Fe(Mn)-O Distances LaMnO3 2 ? 1.907(1) Å 2 ?
2.178(1) Å 2 ? 1.968(1) Å SrFeO3 ? 6 ? 1.92
Å Fe(Mn)-O-Fe(Mn) Angles CaFeO3 155.48(5)? 155.11
(5)? SrFeO3 ? 180?
Octahedral tilting and decreased covalency both
narrow the s (eg) band. This leads to electron
localization and a cooperative Jahn-Teller
Distortion
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LaMnO3-Cooperative Jahn Teller Dist.
Symmetric MnO6
Jahn-Teller Distortion
Orthorhombic Structure Pronounced Jahn-Teller
Distortion All Mn atoms equivalent Localized t2g
eg electrons Semiconductor
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CaFeO3-Charge Disproportionation
Fe-O Distances CaFeO3 2 ? 1.919(2) Å 2 ? 1.927(2)
Å 2 ? 1.919(1) Å SrFeO3 ? 6 ? 1.92 Å Fe-O-Fe
Angles CaFeO3 158.1(1)? 158.4(2)? SrFeO3 ? 180?
Octahedral tilting narrows s (eg) band, leads to
electron localization!
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Soft Mode Condensation (290 K)
Oxygen shift alters crystal field
splitting Localizes the eg electrons Drives Metal
to Semiconductor Transition
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Colossal Magnetoresistance Compounds

• The typical CMR material is
• derived by substitutional doping
• of LaMnO3, which has a modified
• perovskite crystal structure. The
• doping is usually achieved by
• replacement of La by e.g. Ca,
• Sr or Pb

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Consider an electric current running in a
material like iron. Placed in a strong
magnetic field, its resistance drops or increases
by several percent, depending on
orientation -- hence magnetoresistance, or MR

• In 1988, thinly layered materials were found that
  increased or decreased their resistivity by 20
  percent or more in relatively weak magnetic
  fields -- hence "giant" magnetoresistance, or
  GMR. While not completely understood, the basic
  effect depends on the alignment of electron spins
  at the interface of different kinds of magnetic
  materials
• Then in 1993, materials were found that could
  increase or decrease resistance not by a few
  percent but by orders of magnitude. Hence
  "colossal" magnetoresistance -- an effect no
  existing theory can explain---CMR

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LANTHANUM STRONTIUM MANGANESE OXIDE IS A
PEROVSKITE WITH DOUBLE LAYERS OF MANGANESE OXIDE
(OCTAHEDRONS), PLUS LANTHANUM AND STRONTIUM,
SEPARATED BY LAYERS OF LANTHANUM, STRONTIUM, AND
OXYGEN

• CMR is found in materials with the crystalline
  structure called perovskite, whose atoms are
  arranged in discrete layers of differing
  composition.

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CMR
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• The large drop of resistivity with applied
  magnetic field in these oxides is accompanied by
  a paramagnetic-to-ferromagnetic transition, and
  it is quite clear that the CMR is a result of a
  unique type of metal-insulator transition

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Cubic Peroskite ABO3
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Characteristic double-well potential energy as a
function ofthe position of the B cation between
the oxygen anions in perovskite
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The spontaneous Jahn-Teller effect

• The static Jahn-Teller effect occurs if the
  lowest energy level of a molecule is degenerate,
  in which case it will distort spontaneously so as
  to remove the degeneracy and make one energy
  level more stable. The proof is technical and
  difficult, and requires a rather sophisticated
  application of group theory to quantum
  mechanics. For octahedral coordination,
  susceptible species are d4 , d9 , and low spin
  d7 in which 1 or 3 electrons occupy eg . The
  effect is small when the degeneracy is in the
  group t2g

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The effect of Jahn-Teller distortions is best
documented for Cu(II) complexes (with 3 electrons
in the eg level) where the result is that many
complexes are found to have either elongation or
contraction along the z-axis.
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An Example of Jahn-Teller Distortion
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Ferroelectric Materials

• Applications
• transducers and actuators piezoelectricity
• Capacitors high dielectric permittivity
• memory applications hysteresis properties
• result in two stable states of opposite
  
• polarization

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BaTiO3 Info
BaO TiO2
BaTiO3
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• BaTiO3 Properties
• Perovskite Structure
• Piezoelectricity
• Density 5.85 g/cm3
• High Dielectric constant

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Uses for BaTiO3

• Underwater Sonar
• Guided Missiles
• Acoustic Mines
• Sound Reproduction

• Ultrasonic Therapy
• Electronic Materials
• Ultrasonic Cleaning
• Filters

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Ceramic Capacitors

• Multilayer Ceramic Capacitors (MLCC)

Barium titanate powder, Made into capacitors
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Lets build up the phase diagram.
BaTiO3
Liquid
Label important phase fields
Ba2TiO4Liq
TiO2 Liq
Ba2TiO4 Hex BaTiO3
BaOBa2TiO4
Cubic BaTiO3 Liq
Ba2TiO4 Cubic BaTiO3
BaTi4O9 TiO2
Cubic BaTiO3BaTi2O5
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Lets build up the phase diagram.
BaTiO3
Liquid
Label important phase fields
Ba2TiO4Liq
TiO2 Liq
Ba2TiO4 Hex BaTiO3
BaOBa2TiO4
Cubic BaTiO3 Liq
Ba2TiO4 Cubic BaTiO3
BaTi4O9 TiO2
Cubic BaTiO3BaTi2O5
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Some finishing touches
Eutectic Points
Congruent Melting Pts
Peritectic Points
Some important points
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?Other important crystal structures
eg. The rhenium trioxide structure, ReO3
Table ReO3 a 3.734 Å UO3 MoO3 NbO3 TaF3 Cu3N

?The structure consists of ReO6 octahedra
linked together through each corner to give
a highly symmetrical three-dimensional
network with cubic symmetry. ?eg. WO3 (at high
temperature)
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Examples WO3 , AlF3 , ScF3 , FeF3 , CoF3 ,
Sc(OH)3 (distorted)
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Metallic for single crystal ReO3The other curves
are for thin film formation of Re(V)
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?Mixed oxide structures ?Spinel
AB2O4 A2 , B3 ?
A2tet B32oct O4 (MgAl2O4) c. c. p.
array of oxide ions with A2 ions occupying
tetrahedral holes and B3
ions occupying octahedral
holes.
A
B
Table MgAl2O4 a 8.08 Å CoAl2O4 CuCr2S4
CuCr2Se4 CuCr2Te4 MgTi2O4 Co2GeO4 Re2GeO4
eg. MAl2O4 M Mg, Fe, Co, Ni, Mn, Zn
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Secondary Lithium Batteries
Oxygen ions
Transition metal (Co, Ni, Mn)
graphite
Lithium ions
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I. S-shapeMn2O4(?-MnO2)----gtLixMn2O4(x00.5) I
I. L-shapeLi0.5Mn2O4 ----gt LixMn2O4(x0.51) III
. LiMn2O4----gt LixMn2O4(x12)
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?Inverse - Spinel
AB2O4 B (AB) O4 ? B3tet A2, B3oct -half
of the B3 ions now occupy tetrahedral sites, and
the remaining half together with the A2
ions, occupy the octahedral sites. -eg.
Fe3O4, Fe(MgFe)O4, Fe(ZnFe)O4
Table MgFe2O4 a 8.389 Å NiFe2O4
MgIn2O4 MgIn2S4 Mg2TiO4 Zn2SnO4 Zn2TiO4
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Metal Oxide Gas Sensor

• Metal oxides based chemical sensors are devices
  that translate the changes in the concentration
  of gaseous chemical species into electrical
  signals, generally changes of resistance/conductan
  ce. A sensor element normally comprises the
  following parts a) Sensitive layer deposited
  over a b) Substrate provided with c) Electrodes
  for the measurement of the electrical
  characteristics. The device is generally heated
  by its own d) Heater this one is separated from
  the sensing layer and the electrodes by an
  electrical insulating layer. The base of the gas
  detection is the interaction of the gaseous
  species at the surface of the semiconducting
  sensitive metal oxide layer.

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Principle of operation

• A solid state sensor consists of one or more
  metal oxides such as tin oxide or aluminum oxide.
  These metals are prepared and processed into a
  paste which is used to form a bead type sensor. A
  heating element is used to regulate the sensor
  temperature, since the finished sensors exhibit
  different gas response characteristics at
  different temperature ranges.
• The sensor is then processed at a specific high
  temperature which determines the specific
  characteristics of the finished sensor.  In the
  presence of gas, the metal oxide causes the gas
  to dissociate into charged ions  which result in
  the transfer of electrons.

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Sol-gel process for making mixed oxide
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Sol-gel

• Mo(OC3H7) 5 W(OC2H5)6

Butanol
MoO3 WO3
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The technical dehydrogenation of ethylbenzene to
styrene is performed over potassium-promoted iron
oxide catalysts in the presence of steam
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????????? ?,???????????,??????????????????????
???????????     ??????????????(???)
????,?????(e)??????? ??????????,??(h)??,
??(h)??????(O 2)??(H O) ????,??????????????
(OH.)??????????????? ????????,??????????
?????????,???(e)????????,????????????
??????,???????????? ???????? ? ??????????
    1.????????????????????????????????????????
?????????    2.?????????????????????????????????
??????? ????????     3.?????????????????????????
?     4.???????????????????????????????????????
???????????????     5.????????????????????????,?
????????,????? ????? ?????????????????,?????????
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Photocatalyzed Decomposition of Organic Compounds
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Sol-gel process making SiO2-ZrO2 Aerogel

• The metal alkoxides were stored in an inert
  atmosphere (N2), moisture-free glove box.
• 5.04 g of zirconium n-propoxide were mixed
• with 25 g of TMOS at room temperature in a dry,
• inert glove box. This colorless solution was
  sealed
• with a septum and removed from the glove box.
• To this solution was added a mixture of 84 ml of
• CH3OH and 1.8 ml of concentrated NH4OH, and
• then 12 g of DI H2O.

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Catalysis of Oxidation of Organics
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YBa2Cu3O7 (Tc 90K)???? ????(Perovskite)??
????
???????
O Cu Y Ba
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High Tc Superconductors

• The first High Tc Cuprate Superconductors was
  found in 1986 by J. Georg Bednorz and K.
  Alexander M?ler working at an IBM lab in Zurich.
  they found that lanthanum copper oxide doped with
  barium or strontium would superconduct up to 38K.
  This added around 10 degrees kelvin to the
  highest known critical temperature (Tc), which
  had remained constant for twenty years, and broke
  the theoretical limit for Tc, whih was 30K. Their
  discovery caused a great amount of research into
  these new superconductors, and the current record
  for Tc now stands at 160K for a mercury based
  cuprate, as well as earning Bednorz and M?ler the
  Nobel Prize in 1987, the shortest amount of time
  between a discovery and the awarding of a Nobel
  Prize for physics

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Meissner Effect
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Cooper pair
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Cooper pair
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