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%


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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♦ Metallic Structures,

♦ Structures of Binary and More Complex Compounds

& Unit Cell Info

4



♦ Structures of Binary... ...and More Complex Compounds



♦ 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

8


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


9

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


Valence Band

Conduction B

doped semi-conductors

n - type

Valence Band

Conduction B

p - type

n-type

p-type


0.66

10

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)


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


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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


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.


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p-n junctions & diodes:

(b) Forward-Bias (c) Reverse-Bias(a) Equilibrium


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


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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


back contact

front contact

anti-reflectivecoating

semiconductormaterial

Efficiency-ProblemBell’s 1954 PV cell: 4.5%

Problem:one cell - one material – one wavelength!


14

Specific wave lengthsfor PV materials withdifferent band gapenergies Eg



NREL’s Multi-junction (cascade or tandem ) cell efficiency: 34% !


15



16

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)


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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


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


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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)


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:


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b) Perovskite Structure CaTiO3

Unit-Cells of a) Defect-PerovskiteYBa2Cu3O~7

What is a “unit-cell”? How do we get from Ca8TiO6 to CaTiO3?



PerovskiteStructureCaTiO3

Shift of OriginYBa2Cu3O9

Oxygen-Deficient (defect)Perovskite YBa2Cu3O7


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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.


Zero (!) Resistance!


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Resistance & Susceptibility


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


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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


Selected Densities (g/cm

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