Selected Densities (g/cm 3 )

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1 Selected Densities (g/cm 3 ) Mg 1.74 Be 1.85 Al 2.70 Ti 4.54 Pb 11.3 Hg 13.5 Uranium Plutonium Au 19.3 Pt 21.4 Ir 22.4 Os 22.5 Crystal Classes Bravais Lattices Closed-Packed Structures: hexagonal close (hcp) cubic close packing (ccp) = face-centered cubic CON = 12; Vol.: 74.1% 1

2 Closed-Packed Structures: hexagonal close ~ (hcp) cubic close packing (ccp) = face-centered cubic (fcc) CON = 12 Vol. = 74.1% Closed-Packed Structures: The diamond structure: cubic close packing (ccp) = face-centered cubic (fcc) C dia : d = nm and Si: d = nm "two interpenetrating face-centered cubic" lattices 2

3 Closed-Packed Structures: Closed-Packed Structures: Metallic Structures, Structures of Binary and More Complex Compounds & Unit Cell Info 3

4 Closed-Packed Structures: Metallic Structures, Structures of Binary......and More Complex Compounds Closed-Packed Structures: Metallic Structures, Structures of Binary......and More Complex Compounds 4

Radius Ratios & Coordination Numbers Radius Ratio Limiting Values* Coordination Number Geometry Ionic Compounds 0.414 0.

00 12 Cubooctaedron NO ionic examples but many 12-coord. metals! * ) usually r + /r, on rare occasions (e.g.

5 Radius Ratios & Coordination Numbers Radius Ratio Limiting Values* Coordination Number Geometry Ionic Compounds Tetrahedral Square Planar Octahedral Cubic ZnS None NaCl, TiO 2 (rutile) CsCl, CaF 2 (fluorite) Cubooctaedron NO ionic examples but many 12-coord. metals! * ) usually r + /r, on rare occasions (e.g. CsF: r + > r ) r /r + = 119/181 = => NaCl Structure Superconductor: YBa 2 O 7 δ perovskite unit cell stacked perovskite YBa 2 O 9 oxygen-deficient perovskite YBa 2 O 7 YBa 2 O 7 Y 5

6 1-2-3 Superconductor: YBa 2 O 7 δ perovskite unit cell stacked perovskite YBa 2 O 9 oxygen-deficient perovskite YBa 2 O 7 The Crystalline Solid Bonding in Metals Molecular Orbitals the Photovoltaic Effect, Solar-Cells, and (Light-Emitting) Diodes Low- and High-Temperature Superconducting 6

The Crystalline Solid Formation of Molecular Orbitals (MO s) from Atomic Orbitals (AO s) Ψ = c a Ψ a + c b Ψ b Ψ = molecular wave function Ψ a and Ψ b = atomic wave functions c a and c b = adjustable

7 The Crystalline Solid Formation of Molecular Orbitals (MO s) from Atomic Orbitals (AO s) Ψ = c a Ψ a + c b Ψ b Ψ = molecular wave function Ψ a and Ψ b = atomic wave functions c a and c b = adjustable coefficients for H 2 H a + H b H a -H b Ψ(σ) = Ν [c a Ψ(1s a ) + c b Ψ(1s b )] = 1/ 2 [Ψ(1s a ) + Ψ(1s b )] Ψ(σ ) = Ν [c a Ψ(1s a ) c b Ψ(1s b )] = 1/ 2 [Ψ(1s a ) Ψ(1s b )] c a = c b = 1 and N = 1/ 2 for σ and σ* Approximation! Remember, an anti-bonding MO is more anti-bonding then a bonding is bonding Molecular Orbitals 7

8 Molecular Orbitals 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 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. Molecular Orbitals Band Structures of Insulators & Conductors conduction band (empty) bands of orbitals band gapprevents motion of electrons filled valence band e excited to higher energy levels within valence band an Insulator Conductors of Electricity & Heat Metal with NO voltage applied Metal WITH voltage applied 8

9 Molecular Orbitals Energy Conduction B Large energy gap between valence and conduction bands Valence Band Si and Ge are intrinsic semiconductors Conduction B Valence Band Fermi Level Conduction B Valence Band Insulator Semiconductor Conductor Molecular Orbitals doped semiconductors 0.66 Conduction B n - type Valence Band n-type Conduction B p - type Valence Band p-type 9

10 Molecular Orbitals n-type semiconductors Conduction B E F 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. extra electron energy levels Valence Band Conduction B Valence Band E.g. Si (group 14) doped with P, As, Sb (group 15) 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. Molecular Orbitals p-type semiconductors Conduction B Valence Band E F 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) Conduction B Valence Band E F 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. 10

Molecular Orbitals p-type semiconductors Conduction B Valence Band E F Addition of acceptor impurities contributes hole levels low in the semiconductor band gap so that electrons can be easily

11 Molecular Orbitals p-type semiconductors Conduction B Valence Band E F 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. Conduction B Valence Band E F 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. Molecular Orbitals p-n junctions & diodes: conductive conductive junction: non-conductive electron/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. 11

Molecular Orbitals p-n junctions & diodes: (a) Equilibrium (b) Forward-Bias (c) Reverse-Bias Molecular Orbitals Photovoltaic Effect: Photovoltaics is the direct conversion of light into electricity

12 Molecular Orbitals p-n junctions & diodes: (a) Equilibrium (b) Forward-Bias (c) Reverse-Bias Molecular Orbitals 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 light 1905: Einstein explains the Photoelectric Effect photonenergy photonelectron Remember wave-particle duality? 12

Molecular Orbitals Photovoltaic Effect: Photovoltaics is the direct conversion of light into

Timeline: 1839: Becquerel discovers that certain materials produce electric current when

develop the first module http://science.nasa.gov/headlines/y2002/solarcells.

13 Molecular Orbitals 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 light 1905: Einstein explains the Photoelectric Effect 1954: Bell Laboratories develop the first module Molecular Orbitals Efficiency-Problem Bell s 1954 PV cell: 4.5% antireflective coating front contact semiconductor material back contact Problem: one cell - one material one wavelength! 13

14 Molecular Orbitals Specific wave lengths for PV materials with different band gap energies E g Molecular Orbitals NREL s Multi-junction (cascade or tandem ) cell efficiency: 34%! 14

15 Molecular Orbitals Molecular Orbitals 15

Superconducting Superconductor: Elements conduct electricity without resistance below a certain temperature (T c ) Electrical current will flow forever in a closed

Bardeen, L. Cooper & R. Schriefer (Theory) 1973: Brian Josephson (SQUID Application) 1987: Bednarz & Mueller ( Milestone Discovery) So what are we waiting for?

16 Superconducting Superconductor: Elements conduct electricity without resistance below a certain temperature (T c ) Electrical current will flow forever in a closed loop of superconducting material! Superconduction must be important : so far four (4) Nobel Prizes in Physics 1913: Heike Kamerlingh-Onnes (Phenomenon) 1972: J. Bardeen, L. Cooper & R. Schriefer (Theory) 1973: Brian Josephson (SQUID Application) 1987: Bednarz & Mueller ( Milestone Discovery) So what are we waiting for??? Superconducting The coldest places on Earth: 1908 Helium Liquefaction in Leyden (Netherlands) Kamerlingh-Onnes & van der Waals Ehrenfest, Lorentz, Bohr & Onnes (left to right) 16

17 Superconducting 1911: H. Kamerlingh-Onnes Discovers Superconductivity Type I SC: boiling point of liquid He T = 4.2 K lambda point of liquid He T = 2.17 K pumping on liquid He T ~ 0.9 K 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) K 4.88 K 4.47 K 4.15 K 3.72 K 3.41 K 3.3 K 3 K 2.38 K K 1.40 K 1.38 K K K 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) K 0.85 K 0.66 K 0.61 K 0.60 K K 0.49 K 0.40 K 0.20 K K K K K K K μk: 3 He b.p. = 3.2 K, I = ½ fermion, no λ-point Superconducting 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. Cooper-pair * ) London Theory: (macroscopic) F = Ee = mdv/dt E = E 0 + E kin + E mag Sudden-Polarization Theory (high T) F. Matsen J. Chem. Ed. (1987) p

18 Superconducting Type II Superconductor: NdBa 2 O 7 Y 2 Ba 4 Cu 7 O 15 GdBa 2 O 7 YBa 2 O 7 TmBa 2 O 7 YbBa 2 O 7 96 K 95 K 94 K 92 K 90 K 89 K boiling point of liquid N 2 T = 77 K Chem 123, Exp. #2 (Spring 06): Synthesis & Characterization of the Superconductor YBa 2 O 7 current world-record (@ 1 atm) (Hg 0.8 Tl 0.2 )Ba 2 Ca 2 O 8.33 HgBa 2 Ca 2 O HgBa 2 Ca 3 Cu 4 O 10+ HgBa 2 (Ca 1-x Sr x )Cu 2 O 6+ HgBa 2 CuO K K K K K Superconducting The Superconductor YBa 2 O 7 Georg Bednorz & Alex Mueller (1986, IBM labs Zuerich, CH) Superconductivity in Ceramics (Type II): Cooking Recipe: Y(NO 3 ) 3 5H 2 O + Cu(NO 3 ) 2 2.5H 2 O + Ba(NO 3 ) 2 in aqueous urea/oxalic 100 o C N 2 /O 2 baking between o C 18

Superconducting The 1-2-3 Superconductor YBa 2 O 7 (Type II): Unit-Cells of a) Defect-Perovskite YBa 2 O ~7 b) Perovskite Structure CaTiO 3 What is a unit-cell?

19 Superconducting The Superconductor YBa 2 O 7 (Type II): Unit-Cells of a) Defect-Perovskite YBa 2 O ~7 b) Perovskite Structure CaTiO 3 What is a unit-cell? How do we get from Ca 8 TiO 6 to CaTiO 3? Superconducting The Superconductor YBa 2 O 7 (Type II): Perovskite Structure CaTiO 3 Shift of Origin YBa 2 O 9 Oxygen-Deficient (defect) Perovskite YBa 2 O 7 19

20 Superconducting Remember: Superconductors have two outstanding features (below T c ): 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 Zero (!) Resistance! 20

disk When a material makes the transition from the normal to superconducting state,

21 Superconducting Resistance & Susceptibility Superconducting Meissner Effect: note, magnet is moved towards supercond. disk When a material makes the transition from the normal to superconducting state, it actively excludes magnetic fields from its interior; this is called the Meissner effect. 21

Superconducting Meissner Effect: proof of perfect diamagnetism current in outer skin generates magnetic field opposite to external magnetic field (strength & direction); penetration depth: 10 100 nm

22 Superconducting Meissner Effect: proof of perfect diamagnetism current in outer skin generates magnetic field opposite to external magnetic field (strength & direction); penetration depth: nm When a material makes the transition from the normal to superconducting state, it actively excludes magnetic fields from its interior; this is called the Meissner Effect. 22

Energy Levels Zero energy. From Last Time Molecules. Today. n- and p-type semiconductors. Energy Levels in a Metal. Junctions

Energy Levels Zero energy. From Last Time Molecules. Today. n- and p-type semiconductors. Energy Levels in a Metal. Junctions Today From Last Time Molecules Symmetric and anti-symmetric wave functions Lightly higher and lower energy levels More atoms more energy levels Conductors, insulators and semiconductors Conductors and