Selected Densities (g/cm
Transcript of Selected Densities (g/cm
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Selected Densities (g/cm3)
Mg1.74
Be1.85
Al2.70
Ti4.54
Pb11.3
Hg13.5
Au19.3
Pt21.4
Ir22.4
Os22.5
Uranium18.95
Plutonium19.84
Crystal ClassesBravais Lattices
Closed-PackedStructures:
hexagonal close (hcp)
cubic close packing (ccp)= face-centered cubic
CON = 12; Vol.: 74.1%
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Closed-Packed Structures:
hexagonal close ~ (hcp) cubic close packing (ccp)= face-centered cubic (fcc)
CON = 12Vol. = 74.1%
Closed-Packed Structures:
cubic close packing (ccp)= face-centered cubic (fcc)
"two interpenetrating face-centered cubic" lattices
The diamond structure:
Cdia: d = 0.543 nm and Si: d = 0.566 nm
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Closed-Packed Structures:
Closed-Packed Structures:
♦ Metallic Structures,
♦ Structures of Binary and More Complex Compounds
& Unit Cell Info
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Closed-Packed Structures:
♦ Metallic Structures,
♦ Structures of Binary... ...and More Complex Compounds
Closed-Packed Structures:
♦ Metallic Structures,
♦ Structures of Binary... ...and More Complex Compounds
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Radius Ratios & Coordination Numbers
NO ionic examplesNO ionic examplesbut many 12but many 12--coord.coord.metals!metals!
CubooctaedronCubooctaedron1212
CsCl, CaFCsCl, CaF2 2 (fluorite)(fluorite)CubicCubic88
NoneNoneNaCl, TiONaCl, TiO22 (rutile) (rutile)
Square PlanarSquare PlanarOctahedralOctahedral
4466
ZnSZnSTetrahedralTetrahedral440.4140.414
0.7320.732
1.001.00
Ionic Ionic CompoundsCompounds
GeometryGeometryCoordination Coordination NumberNumber
Radius Ratio Radius Ratio Limiting Values*Limiting Values*
*) usually r+/r−, on rare occasions (e.g. CsF: r+ > r−) r−/r+ = 119/181 = 0.657 => NaCl Structure
perovskite unit cell stacked perovskite YBa2Cu3O9
oxygen-deficient perovskite YBa2Cu3O7
Y
YBa2Cu3O7
1-2-3 Superconductor: YBa2Cu3O7−δ
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perovskite unit cell stacked perovskite YBa2Cu3O9
oxygen-deficient perovskite YBa2Cu3O7
1-2-3 Superconductor: YBa2Cu3O7−δ
The Crystalline Solid
Bonding in Metals
Molecular Orbitals & Band Structure
the Photovoltaic Effect, Solar-Cells, and (Light-Emitting) Diodes
Low- and High-Temperature Superconducting Materials
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Formation of Molecular Orbitals (MO’s)from Atomic Orbitals (AO’s)
Ψ = caΨa + cbΨb
Ψ = molecular wave functionΨa and Ψb = atomic wave functionsca and cb = adjustable coefficients
Ψ(σ) = Ν [caΨ(1sa) + cbΨ(1sb)] = 1/√2 [Ψ(1sa) + Ψ(1sb)]
Ψ(σ∗) = Ν [caΨ(1sa) − cbΨ(1sb)] = 1/√2 [Ψ(1sa) − Ψ(1sb)]
for H2
Ha + Hb
Ha - Hb
ca = cb = 1 and N = 1/√2 for σ and σ*Approximation! Remember, an anti-bonding MOis more anti-bonding then a bonding is bonding
The Crystalline Solid
Molecular Orbitals& Band Structure
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Molecular Orbitals& Band Structure
According to molecular orbital theory, if several atoms are brought together into a molecule, their atomic orbitals split, producing a number of molecular orbitals proportional to the number of atoms.
When a large number of atoms (of order 1020 or more) are brought together to form a solid, the number of orbitals becomes exceedingly large, and the difference in energy between them becomes very small.
Band theory makes the assumption that these energy levels are so numerous as to be indistinct.
Band Structures of Insulators & Conductors
an Insulator
Metal with NOvoltage applied
Metal WITHvoltage applied
“bands” oforbitals
valenceband
conductionband (empty)
band gap-prevents motion
of electrons
filled
Conductors of Electricity & Heat
e − excited to higher energylevels withinvalence band
Molecular Orbitals& Band Structure
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Ene
rgy
Valence Band
Conduction B
Large energygap between valence andconduction bands
Insulator Semiconductor
Valence Band
Conduction B
Valence Band
Conduction BFermiLevel
Conductor
Si and Ge are intrinsic semi-
conductors
Molecular Orbitals& Band Structure
Valence Band
Conduction B
doped semi-conductors
n - type
Valence Band
Conduction B
p - type
n-type
p-type
Molecular Orbitals& Band Structure
0.66
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Valence Band
Conduction B
n-type semi-conductors
Addition of donor impurities contributes electron energy levels high in the semi-conductor band gap so that electrons can be easily excited into the conduction band. This shifts the effective Fermi level to a point about halfway between the donor levels and the conduction band.
Electrons can be elevated to the conduction band with the energy provided by an applied voltage and move through the material. The electrons are said to be the "majority carriers" for current flow in an n-type semiconductor.
extra electron energy levels
EF
Valence Band
Conduction B
E.g. Si (group 14) doped with P, As, Sb(group 15)
Molecular Orbitals& Band Structure
Valence Band
Conduction B
p-type semi-conductors
EF
Addition of acceptor impurities contributes hole levels low in the semiconductor band gap so that electrons can be easily excited from the valence band into these levels, leaving mobile holes in the valence band. This shifts the effective Fermi level to a point about halfway between the acceptor levels and the valence band.
E.g.: Blue diamonds, which contain boron (B) impurities (naturally occurring p-type SC)
Electrons can be elevated from the valence band to the holes in the band gap with the energy provided by an applied voltage. Since electrons can be exchanged between the holes, the holes are said to be mobile. The holes are said to be the "majority carriers" for current flow in a p-type semiconductor.
Valence Band
Conduction B
EF
Molecular Orbitals& Band Structure
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Valence Band
Conduction B
p-type semi-conductors
EF
Addition of acceptor impurities contributes hole levels low in the semiconductor band gap so that electrons can be easily excited from the valence band into these levels, leaving mobile holes in the valence band. This shifts the effective Fermi level to a point about halfway between the acceptor levels and the valence band.
Electrons can be elevated from the valence band to the holes in the band gap with the energy provided by an applied voltage. Since electrons can be exchanged between the holes, the holes are said to be mobile. The holes are said to be the "majority carriers" for current flow in a p-type semiconductor.
Valence Band
Conduction B
EF
Molecular Orbitals& Band Structure
p-n junctions& diodes:
conductive conductive
junction: non-conductiveelectron/hole recombination
in “depletion zone”
By manipulating this nonconductive layer, p-n junctions are commonly used as diodes: electrical switches that allow a flow of electricity in one direction but not in the other (opposite) direction. This property is explained in terms of the forward-bias and reverse-bias effects, where the term bias refers to an application of electric voltage to the p-n junction.
Molecular Orbitals& Band Structure
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p-n junctions & diodes:
(b) Forward-Bias (c) Reverse-Bias(a) Equilibrium
Molecular Orbitals& Band Structure
http://science.nasa.gov/headlines/y2002/solarcells.htm
Photovoltaic Effect: Photovoltaics is the direct conversion of light into electricity at the atomic levelTimeline:1839: Becquerel discovers that certain materials produce
electric current when exposed to light1905: Einstein explains the Photoelectric Effect
Rememberwave-particle
duality?
photon-energy
photon-electron
Molecular Orbitals& Band Structure
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http://science.nasa.gov/headlines/y2002/solarcells.htm
Photovoltaic Effect: Photovoltaics is the direct conversion of light into electricity at the atomic level.Timeline:1839: Becquerel discovers that certain materials produce
electric current when exposed to light1905: Einstein explains the Photoelectric Effect1954: Bell Laboratories develop the first module
Molecular Orbitals& Band Structure
back contact
front contact
anti-reflectivecoating
semiconductormaterial
Efficiency-ProblemBell’s 1954 PV cell: 4.5%
Problem:one cell - one material – one wavelength!
Molecular Orbitals& Band Structure
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Specific wave lengthsfor PV materials withdifferent band gapenergies Eg
Molecular Orbitals& Band Structure
http://science.nasa.gov/headlines/y2002/solarcells.htm
NREL’s Multi-junction (cascade or tandem ) cell efficiency: 34% !
Molecular Orbitals& Band Structure
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Molecular Orbitals& Band Structure
Molecular Orbitals& Band Structure
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Superconducting Materials
Superconductor:Elements conduct electricity without resistance below a certain temperature (Tc)
Electrical current will flow forever in a closed loop of superconducting material!
“Superconduction” must be important :so far four (4) 1913: Heike Kamerlingh-Onnes (Phenomenon)Nobel Prizes 1972: J. Bardeen, L. Cooper & R. Schriefer (Theory)in Physics 1973: Brian Josephson (SQUID Application)
1987: Bednarz & Mueller (“Milestone” Discovery)
So what are we waiting for???
Kamerlingh-Onnes & van der Waals
Ehrenfest, Lorentz, Bohr & Onnes(left to right)
The coldest places on Earth: 1908 Helium Liquefaction in Leyden (Netherlands)
Superconducting Materials
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Lead (Pb) Lanthanum (La) Tantalum (Ta) Mercury (Hg)Tin (Sn) Indium (In) Palladium (Pd)* Chromium (Cr)* Thallium (Tl) Rhenium (Re) Protactinium (Pa) Thorium (Th) Aluminum (Al) Gallium (Ga)
Molybdenum (Mo)Zinc (Zn) Osmium (Os) Zirconium (Zr) Americium (Am) Cadmium (Cd) Ruthenium (Ru) Titanium (Ti) Uranium (U) Hafnium (Hf) Iridium (Ir) Beryllium (Be) Tungsten (W) Platinum (Pt)Rhodium (Rh)
0.915 K 0.85 K 0.66 K 0.61 K 0.60 K 0.517 K 0.49 K 0.40 K 0.20 K 0.128 K 0.1125 K 0.023 K 0.0154 K 0.0019 K 0.000325 K
7.196 K 4.88 K 4.47 K 4.15 K3.72 K 3.41 K 3.3 K 3 K 2.38 K 1.697 K 1.40 K 1.38 K 1.175 K 1.083 K
boiling pointof liquid HeT = 4.2 K
lambda pointof liquid HeT = 2.17 K
pumping onliquid HeT ~ 0.9 K
1911: H. Kamerlingh-Onnes Discovers Superconductivity
Type I SC:
μK: 3He b.p. = 3.2 K, I = ½fermion, no λ-point
Superconducting Materials
Theory of Superconductivity (SC Type I):
Bardeen - Cooper – Schrieffer (BCS Theory)
Two electrons that appear to "team up" in accordance with theory - BCS or other - despite the fact that they both have a negative charge and normally repel each other.
Below the superconducting transition temperature, paired electrons form a condensate - a macroscopically occupied single quantum state - which flows without resistance.
*) London Theory:(macroscopic)F = Ee = mdv/dtE = E0 + Ekin + Emag
Sudden-PolarizationTheory (high T)
F. Matsen J. Chem. Ed. (1987) p.842
+ + + +
+ + + +
Coop
er-p
air
Superconducting Materials
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Type II Superconductor:96 K 95 K94 K92 K90 K89 K
NdBa2Cu3O7Y2Ba4Cu7O15GdBa2Cu3O7YBa2Cu3O7TmBa2Cu3O7YbBa2Cu3O7
Chem 123, Exp. #2 (Spring ’06):Synthesis & Characterization of the 1-2-3 Superconductor YBa2Cu3O7
boiling pointof liquid N2T = 77 K
138 K133-135 K125-126 K 123-125 K 94-98 K
(Hg0.8Tl0.2)Ba2Ca2Cu3O8.33HgBa2Ca2Cu3OHgBa2Ca3Cu4O10+HgBa2(Ca1-xSrx)Cu2O6+HgBa2CuO4+
current world-record(@ 1 atm)
Superconducting Materials
The 1-2-3 Superconductor YBa2Cu3O7 (Type II):
Georg Bednorz & Alex Mueller(1986, IBM labs Zuerich, CH)
Superconductivity in Ceramics
Y(NO3)3 5H2O + Cu(NO3)2 2.5H2O +Ba(NO3)2
in aqueous urea/oxalic acid@ 100oC
N2/O2 baking between 500 – 900oC
CookingRecipe:
Superconducting Materials
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The 1-2-3 Superconductor YBa2Cu3O7 (Type II):
b) Perovskite Structure CaTiO3
Unit-Cells of a) Defect-PerovskiteYBa2Cu3O~7
What is a “unit-cell”? How do we get from Ca8TiO6 to CaTiO3?
Superconducting Materials
The 1-2-3 Superconductor YBa2Cu3O7 (Type II):
PerovskiteStructureCaTiO3
Shift of OriginYBa2Cu3O9
Oxygen-Deficient (defect)Perovskite YBa2Cu3O7
Superconducting Materials
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Remember: Superconductors
have two outstanding features (below Tc):
Zero electrical resistivity (resistance). This means that an electrical current in a superconducting ring continues indefinitely until a force is applied to oppose the current.
The magnetic field inside a bulk sample is zero (the Meissner Effect). When a magnetic field is applied current flows in the outer skin of the material leading to an induced magnetic field that exactly opposes the applied field. The material is strongly diamagnetic as a result.
Superconducting Materials
Zero (!) Resistance!
Superconducting Materials
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Resistance & Susceptibility
Superconducting Materials
Meissner Effect:
When a material makes the transition from the normal to superconductingstate, it actively excludes magnetic fields from its interior; this is called the Meissner effect.
note, magnet is
moved towards
supercond. d
isk
http://www.hfml.science.ru.nl/levitate.html
Superconducting Materials
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Meissner Effect:
When a material makes the transition from the normal to superconductingstate, it actively excludes magnetic fields from its interior; this is called the Meissner Effect.
proof of perfe
ct
diamagnetism
http://www.hfml.science.ru.nl/levitate.html
current in outer “skin” generates magnetic field opposite to external magnetic field (strength & direction);
penetration depth:
10 – 100 nm
Superconducting Materials