Chapter 10 & 11 Molecular Bonds & Band Structure Semiconductors Superconductivity
Chapter 10 & 11 Molecular Bonds & Band Structure Semiconductors Superconductivity Lasers Harris, “Modern Physics” Eisberg & Resnick, “Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles” Outline • 10.1 Molecular Bonding (~2 atoms together) – pages 334-342 • 11.1 Band Theory (~1023 atoms together) – pages 387-392 • 11.2 Semiconductor Theory – mainly pages 395-398 • 10.5 Superconductivity – pages 362-381 • 10.2 Stimulated Emission & Lasers – mainly pages 342-347 MOLECULES (~2 atoms together) Ionic & Covalent Bonds Molecular Excitations Rotation, Vibration, Electric Ionic Bonds ENERGY BALANCE= Ionization + Electron + Affinity Attraction of + Pauli Repulsion of Cores Electrons RNave, GSU at http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html#c4 Ionic Bond Energy Balance Ioniz Electron Affinity Coul Attraction Pauli Repulsion Energy Balance NaCl 5.14 -3.62 -6.10 0.31 -4.27 NaF 5.14 -3.41 -7.46 0.35 -5.34 KCl 4.34 -3.62 -5.39 0.19 -4.49 HH 13.6 -0.76 Covalent Bonds RNave, GSU at http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/bond.html#c4 Covalent Bonding SYM spatial ASYM spin ASYM spatial SYM spin space-symmetric tend to be closer Ref: Harris Ionic vs Covalent Bond Properties • Ionic Characteristics – Crystalline solids • Covalent Characteristics – High melting & boiling point – Gases, liquids, noncrystalline solids – Low melting & boiling point – Conduct electricity when melted – Poor conductors in all phases – Many soluble in water, but not in non-polar liquids – Many soluble in non-polar liquids but not water Molecular Excitations Rotational Spectra rot KE ~ 1 I 2 2 1 2 Lop 2I 2 ( 1) 2I moment of inertia rotational A.M. Rotational Spectra Photon Energy hf Ref: Harris Molecular Excitations Vibration Molecule “Spring Const” ( N/m ) HF 970 HCl 480 HBr 410 Hi 320 CO 1860 NO 1530 Vibration (in an Electronic state) Ocean Optics: Nitrogen N2 ~ 0.3 eV ~ 0.4 eV http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/atspect.html Electronic + Vibration Ref: Harris Electronic + Vibration + Rotation 2.550 eV 2.656 eV electronic excitation gap vibrational excitation gaps Ref: Eisberg&Resnick Electronic + Vibration + Rotation Vibrational Well 2.656 eV Vibrational Well depth ~ 0.063 eV electronic excitation gap vibrational excitation gaps Ref: Eisberg&Resnick Electronic, Vibration, Rotation Electronic ~ optical & UV ~ 1 – 3 eV Vibration ~ IR ~ 10ths of eV Rotation ~ microwave ~ 1000ths of eV Harris 9.24 Some Molecular Constants Molecule Equilibrium Distance Ro (Å) Dissociation NRG Do (eV) Vibrational freq v a (cm-1) Moment of Inertia Bb (cm-1) H2+ 1.06 2.65 2297 29.8 H2 0.742 4.48 4395 60.8 O2 1.21 5.08 1580 1.45 N2 1.09 9.75 2360 2.01 CO 1.13 9.60 2170 1.93 NO 1.15 5.3 1904 1.70 HCl 1.28 4.43 2990 10.6 NaCl 2.36 4.22 365 0.190 Notes: a) vibrational frequency in table is given as f / c b) moment of inertia in table is given as hbar2/(2I) / hc SOLIDS x (~10 atoms together) Isolated Atoms Diatomic Molecule Four Closely Spaced Atoms conduction band valence band Two atoms Six atoms Solid of N atoms ref: A.Baski, VCU 01SolidState041.ppt www.courses.vcu.edu/PHYS661/pdf/01SolidState041.ppt Sodium Bands vs Separation Rohlf Fig 14-4 and Slater Phys Rev 45, 794 (1934) Copper Bands vs Separation Rohlf Fig 14-6 and Kutter Phys Rev 48, 664 (1935) Differences down a column in the Periodic Table: IV-A Elements same valence config Sandin Conductors vs insulators vs semiconductors Conductors & Insulators at T=0 Harris9.35a Conductors & Insulators at T>0 Harris9.35b Semiconductors & Superconductors Rex Thorton p 395-398 p 362-381 Two atoms Six atoms Solid of N atoms ref: A.Baski, VCU 01SolidState041.ppt www.courses.vcu.edu/PHYS661/pdf/01SolidState041.ppt Temperature Dependence of Resistivity R L A Ag 1.5*10-8 Wm Cu 1.7*10-8 C amorphous 10-4 Rubber 1013 Air 1016 Conductors & Insulators at T=0 Harris9.35a Conductors & Insulators at T>0 Harris9.35b • Conductors – Resistivity increases with increasing Temp – Temp t but same # conduction e-’s • Semiconductors & Insulators – Resistivity decreases with increasing Temp – Temp t but more conduction e-’s Semiconductors ~1/40 eV gap ~1 eV gap • Types – Intrinsic – by thermal excitation or high nrg photon – Photoconductive – excitation by VIS-red or IR – Extrinsic / Doped • n-type • p-type • ~1-4 eV gap ~0.01 eV gap with adjustable charge carrier density Intrinsic Semiconductors Silicon Germanium RNave: http://hyperphysics.phy-astr.gsu.edu/hbase/solcon.html#solcon Doped Semiconductors lattice p-type dopants n-type dopants 5A doping in a 4A lattice Almost free, but not quite Sandin, “Modern Physics” 5A in 4A lattice 3A in 4A lattice Bands in n-doped Semiconductor 9.44 Bands in p-doped Semiconductor 9.45 Superconductivity First observed Kamerlingh Onnes 1911 Note: The best conductors & magnetic materials tend not to be superconductors (so far) Superconductors.org Only in nanotubes Discovery of “Type II” --- CuxOy Superconductor Classifications • Type I – tend to be pure elements or simple alloys – = 0 at T < Tcrit – Internal B = 0 (Meissner Effect) – At jinternal > jcrit, no superconductivity – At Bext > Bcrit, no superconductivity – Well explained by BCS theory • Type II – tend to be ceramic compounds – Can carry higher current densities ~ 1010 A/m2 – Mechanically harder compounds – Higher Bcrit critical fields – Above Bext > Bcrit-1, some superconductivity Superconductor Classifications Type I Bardeen, Cooper, Schrieffer 1957, 1972 “Cooper Pairs” e- Q: Stot=0 or 1? L? J? eSymmetry energy ~ -0.01 eV Popular Bad Visualizations: correlation lengths Pairs are related by momentum ±p, NOT position. Sn 230 nm Al 1600 Pb 83 Nb 38 Best conductors best ‘free-electrons’ no e- – lattice interaction not superconducting More realistic 1-D billiard ball picture: Cooper Pairs are ±k sets Furthermore: “Pairs should not be thought of as independent particles” -- Ashcroft & Mermin Ch 34 • Experimental Support of BCS Theory – Isotope Effects – Measured Band Gaps corresponding to Tcrit predictions – Energy Gap decreases as Temp Tcrit – Heat Capacity Behavior Normal Conductor Semiconductor or Superconductor Superconductors and Semiconductors are the same animal from a band model viewpoint Another fact about Type I: -- Interrelationship of Bcrit and Tcrit Type II Yr Mar 2011 Oct 2010 Q: does BCS apply ? Composition (Tl5Pb2)Ba2MgCu10O17+ (Tl4Pb)Ba2MgCu8O13+ Tc 20 C 293 K 3C 276K May 2006 InSnBa4Tm4Cu6O18+ 150 2004 Hg0.8Tl0.2Ba2Ca2Cu3O8.33 138 1987 YBa2Cu3O7 93 1986 (La1.85Ba.15)CuO4 30 actual ~ 8 mm Sandin Type II – mixed phases fluxon Q: does BCS apply ? Y Ba2 Cu3 O7 crystalline may control the electronic config of the conducting layer La2-x Bax Cu O2 solid solution Applications OR Other Features of Superconductors http://superconductors.org/Uses.htm Meissner Effect Magnetic Levitation – Meissner Effect Kittel states this explusion effect is not clearly directly connected to the = 0 effects Q: Why ? Magnetic Levitation – Meissner Effect MLX01 Test Vehicle 2003 581 km/h 361 mph 2005 80,000+ riders 2005 tested passing trains at relative 1026 km/h http://www.rtri.or.jp/rd/maglev/html/english/maglev_frame_E.html MagLev in Shanghai Maglev in Germany 32 km track 550,000 km since 1984 Design speed 550 km/h Regularly operated at 420 km/h http://en.wikipedia.org/wiki/2006_Lathen_maglev_train_accident NOTE(061204): I’m not so sure this track is superconducting. The MagLev planned for the Munich area will be. France is also thinking about a sc maglev. Maglev Frog A live frog levitates inside a 32 mm diameter vertical bore of a Bitter solenoid in a magnetic field of about 16 Tesla at the Nijmegen High Field Magnet Laboratory. http://www.hfml.ru.nl/pics/Movies/frog.mpg Josephson Junction ~ 2 nm SQUID superconducting quantum interference device o ~ oe ileft ~ o e The phase of the wfn in left and right branches is different because of the penetrating flux. i right Typical B fields (Tesla) (# flux quanta) http://www.csiro.au/science/magsafe.html Finding 'objects of interest' at sea with MAGSAFE MAGSAFE is a new system for locating and identifying submarines. Operators of MAGSAFE should be able to tell the range, depth and bearing of a target, as well as where it’s heading, how fast it’s going and if it’s diving. Building on our extensive experience using highly sensitive magnetic sensors known as Superconducting QUantum Interference Devices (SQUIDs) for minerals exploration, MAGSAFE harnesses the power of three SQUIDs to measure slight variations in the local magnetic field. MAGSAFE will be able to locate targets without flying close to the surface. Image courtesy Department of Defence. MAGSAFE has higher sensitivity and greater immunity to external noise than conventional Magnetic Anomaly Detector (MAD) systems. This is especially relevant to operation over shallow seawater where the background noise may 100 times greater than the noise floor of a MAD instrument. http://www.csiro.au/science/magsafe.html Phillip Schmidt etal. Exploration Geophysics 35, 297 (2004). http://nextbigfuture.com/2007_10_28_archive.html http://en.wikipedia.org/wiki/Magnetoencephalography http://www.neurevolution.net/2007/08/20/magnetoencephalography/ http://www2.fz-juelich.de/nic/Publikationen/Broschuere/sonstiges-e.html SQUID 2 nm 10-14 T SQUID threshold Heart signals 10 -10 T Brain signals 10 -13 T • • • • • • • Fundamentals of superconductors: – http://www.physnet.uni-hamburg.de/home/vms/reimer/htc/pt3.html Basic Introduction to SQUIDs: – http://www.abdn.ac.uk/physics/case/squids.html Detection of Submarines – http://www.csiro.au/science/magsafe.html Fancy cross-referenced site for Josephson Junctions/Josephson: – http://en.wikipedia.org/wiki/Josephson_junction – http://en.wikipedia.org/wiki/B._D._Josephson SQUID sensitivity and other ramifications of Josephson’s work: – http://hyperphysics.phy-astr.gsu.edu/hbase/solids/squid2.html Understanding a SQUID magnetometer: – http://hyperphysics.phy-astr.gsu.edu/hbase/solids/squid.html#c1 Some exciting applications of SQUIDs: – http://www.lanl.gov/quarterly/q_spring03/squid_text.shtml • • • • • Relative strengths of pertinent magnetic fields – http://www.physics.union.edu/newmanj/2000/SQUIDs.htm The 1973 Nobel Prize in physics – http://nobelprize.org/physics/laureates/1973/ Critical overview of SQUIDs – http://homepages.nildram.co.uk/~phekda/richdawe/squid/popular/ Research Applications – http://boojum.hut.fi/triennial/neuromagnetic.html Technical overview of SQUIDs: – http://www.finoag.com/fitm/squid.html – http://www.cmp.liv.ac.uk/frink/thesis/thesis/node47.html Lasing Systems RexThorton p 342-351 • • • • • • • • Stimulated Emission Energy Level Diagrams Ruby Laser He-Ne Laser Diode Lasers Green Laser Pointers Free Electron Lasers National Ignition Facility Parts of a Laser Principal components: 1. Gain medium 2. Laser pumping energy 3. High reflector 4. Output coupler 5. Laser beam http://en.wikipedia.org/wiki/Laser Spontaneous Emission Stimulated Emission Population Inversion PUMP Energy Level Diagram Three Level System PUMPING Light Absorption Electrical discharge Molecular collisions Ruby Laser http://en.wikipedia.org/wiki/Theodore_Maiman Ruby Laser http://www.olympusmicro.com/primer/anatomy/sources.html http://web.phys.ksu.edu/vqm/laserweb/Ch-6/C6s2t1p2.htm Rami Arieli: "The Laser Adventure" Section 6.2.1 page 2 Energy Level Diagram Four Level System PUMPING Light Absorption Electrical discharge Molecular collisions http://www.i-fiberoptics.com/lasers.php?cat=helium-neon-lasers&sum=1630 He-Ne Laser http://en.wikipedia.org/wiki/Helium%E2%80%93neon_laser http://www.mi-lasers.com/hene-lasers-c-17 He-Ne Laser #4 #3 #2’s Electric Discharge #1 He-Ne Laser #3’s #4’s #2’s #1 He-Ne Laser #3’s #4’s #2’s #1 http://web.phys.ksu.edu/vqm/laserweb/Ch-6/F6s1t1p1.htm http://www.intenseco.com/news/detail.asp?RecordID=122 Diode Laser http://britneyspears.ac/physics/fplasers/fplasers.htm http://www.instructables.com/id/Laser-Flashlight-Hack!!/step3/Extract-the-DVD-Laser-Diode/ Laser Diode http://www.rp-photonics.com/laser_pointers.html http://donklipstein.com/lds.gif Laser Diode http://zone.ni.com/devzone/cda/ph/p/id/249 http://www.dragonlasers.com/catalog/Green-Laser-Pointer-532nm-Laser-Viper-Series-Lasers-price0-p-1-c-262.html Green Laser Pointer http://en.wikipedia.org/wiki/Laser CO2 Lasers CO2 Lasers http://laserstars.org/history/mars.html CO2 Lasers http://what-when-how.com/electronic-properties-of-materials/applications-optical-properties-of-materials-part-5/ CO2 Lasers http://chemwiki.ucdavis.edu/Wikitexts/UCD_Chem_205%3A_Larsen/ChemWiki_Module_Topics/How_a_Laser_operates Free Electron Lasers Boeing YAL-1 Airborne Laser (ABL) anti-ballistic missile weapons system Developed fromBoeing 747-400F megawatt-class chemical oxygen iodine laser (COIL) http://en.wikipedia.org/wiki/Boeing_YAL-1 http://en.wikipedia.org/wiki/Chemical_oxygen_iodine_laser Chemical oxygen iodine laser, or COIL, is an infrared chemical laser. As the beam is infrared, it cannot be seen with the naked eye. It is capable of output power scaling up to megawatts in continuous mode[citation needed]. Its output wavelength is 1.315 µm, the wavelength of transition of atomic iodine. The laser is fed with gaseous chlorine, molecular iodine, and an aqueous mixture of hydrogen peroxide and potassium hydroxide. The aqueous peroxide solution undergoes chemical reaction with chlorine, producing heat, potassium chloride, and oxygen in excited state, singlet delta oxygen. Spontaneous transition of excited oxygen to the triplet sigma ground state is forbidden giving the excited oxygen a spontaneous lifetime of about 45 minutes. This allows the singlet delta oxygen to transfer its energy to the iodine molecules injected to the gas stream; they are nearly resonant with the singlet oxygen, so the energy transfer during the collision of the particles is rapid. The excited iodine then undergoes stimulated emission and lases at 1.315 µm in the optical resonator region of the laser.
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