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Chapter 10 & 11 Molecular Bonds & Band Structure Semiconductors Superconductivity Lasers Harris, “Modern Physics” Eisberg & Resnick, “Quantum Physics of.

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Presentation on theme: "Chapter 10 & 11 Molecular Bonds & Band Structure Semiconductors Superconductivity Lasers Harris, “Modern Physics” Eisberg & Resnick, “Quantum Physics of."— Presentation transcript:

1 Chapter 10 & 11 Molecular Bonds & Band Structure Semiconductors Superconductivity Lasers Harris, “Modern Physics” Eisberg & Resnick, “Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles”

2 Outline 10.1 Molecular Bonding (~2 atoms together) – pages Band Theory (~10 23 atoms together) – pages Semiconductor Theory –mainly pages Superconductivity – pages Stimulated Emission & Lasers – mainly pages

3 MOLECULES (~2 atoms together) Ionic & Covalent Bonds Molecular Excitations Rotation, Vibration, Electric

4 Ionic Bonds RNave, GSU at ENERGY BALANCE= Ionization +Electron + Affinity Attraction of + Cores Pauli Repulsion of Electrons

5 Ionic Bond Energy Balance IonizElectron Affinity Coul Attraction Pauli Repulsion Energy Balance NaCl NaF KCl HH

6 Covalent Bonds RNave, GSU at

7 Covalent Bonding SYM ASYM spatial spin ASYM SYM spatial spin space-symmetric tend to be closer Ref: Harris

8 Ionic vs Covalent Bond Properties Ionic Characteristics –Crystalline solids –High melting & boiling point –Conduct electricity when melted –Many soluble in water, but not in non-polar liquids Covalent Characteristics –Gases, liquids, non- crystalline solids –Low melting & boiling point –Poor conductors in all phases –Many soluble in non-polar liquids but not water

9 Molecular Excitations Rotational Spectra  rotational A.M. moment of inertia

10 Rotational Spectra Ref: Harris

11 Molecular Excitations Vibration Molecule “Spring Const” ( N/m ) HF970 HCl480 HBr410 Hi320 CO1860 NO1530

12 Vibration (in an Electronic state)

13 Ocean Optics: Nitrogen N 2 ~ 0.3 eV ~ 0.4 eV

14 Electronic + Vibration Ref: Harris

15 Electronic + Vibration + Rotation eV eV electronic excitation gap vibrational excitation gaps Ref: Eisberg&Resnick

16 Electronic + Vibration + Rotation eV electronic excitation gap vibrational excitation gaps Vibrational Well depth ~ eV Ref: Eisberg&Resnick

17 Electronic, Vibration, Rotation Electronic ~ optical & UV ~ 1 – 3 eV Vibration ~ IR ~ 10ths of eV Rotation ~ microwave ~ 1000ths of eV Harris 9.24

18 Some Molecular Constants MoleculeEquilibrium Distance R o (Å) Dissociation NRG D o (eV) Vibrational freq v a (cm -1 ) Moment of Inertia B b (cm -1 ) H2+H H2H O2O N2N CO NO HCl NaCl Notes: a) vibrational frequency in table is given as f / c b) moment of inertia in table is given as hbar 2 /(2I) / hc

19 SOLIDS (~10 x atoms together)

20 Isolated Atoms

21 Diatomic Molecule

22 Four Closely Spaced Atoms valence band conduction band

23 Solid of N atomsTwo atomsSix atoms ref: A.Baski, VCU 01SolidState041.ppt

24 Sodium Bands vs Separation Rohlf Fig 14-4 and Slater Phys Rev 45, 794 (1934)

25 Copper Bands vs Separation Rohlf Fig 14-6 and Kutter Phys Rev 48, 664 (1935)

26 Differences down a column in the Periodic Table: IV-A Elements Sandin same valence config

27 Conductors vs insulators vs semiconductors

28 Conductors & Insulators at T=0 Harris9.35a

29 Conductors & Insulators at T>0 Harris9.35b


31 Semiconductors & Superconductors Rex Thorton p p

32 Solid of N atomsTwo atomsSix atoms ref: A.Baski, VCU 01SolidState041.ppt

33 Temperature Dependence of Resistivity Ag    m Cu   C amorphous   Rubber   Air  

34 Conductors & Insulators at T=0 Harris9.35a

35 Conductors & Insulators at T>0 Harris9.35b

36 Conductors –Resistivity  increases with increasing Temp –  Temp   but same # conduction e-’s   Semiconductors & Insulators –Resistivity  decreases with increasing Temp –  Temp   but more conduction e-’s  

37 Semiconductors 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 ~1/40 eV gap ~0.01 eV gap with adjustable charge carrier density ~1 eV gap

38 Intrinsic Semiconductors Silicon Germanium RNave:

39 Doped Semiconductors lattice p-type dopants n-type dopants

40 5A in 4A lattice 3A in 4A lattice 5A doping in a 4A lattice Sandin, “Modern Physics” Almost free, but not quite

41 Bands in n-doped Semiconductor 9.44

42 Bands in p-doped Semiconductor 9.45


44 First observed Kamerlingh Onnes 1911 Superconductivity

45 Only in nanotubes Note: The best conductors & magnetic materials tend not to be superconductors (so far)

46 Discovery of “Type II” --- Cu x O y

47 Superconductor Classifications Type I – tend to be pure elements or simple alloys –  = 0 at T < T crit –Internal B = 0 (Meissner Effect) –At j internal > j crit, no superconductivity –At B ext > B crit, no superconductivity –Well explained by BCS theory Type II –tend to be ceramic compounds –Can carry higher current densities ~ A/m 2 –Mechanically harder compounds –Higher B crit critical fields –Above B ext > B crit-1, some superconductivity

48 Superconductor Classifications

49 Type I Bardeen, Cooper, Schrieffer 1957, 1972 “Cooper Pairs” Symmetry energy ~  0.01 eV Q: S tot =0 or 1? L? J? e 

50 Sn 230 nm Al 1600 Pb 83 Nb 38 Best conductors  best ‘free-electrons’  no e  – lattice interaction  not superconducting Popular Bad Visualizations: Pairs are related by momentum ±p, NOT position. correlation lengths

51 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

52 Experimental Support of BCS Theory –Isotope Effects –Measured Band Gaps corresponding to T crit predictions –Energy Gap decreases as Temp  T crit –Heat Capacity Behavior

53 Normal Conductor Semiconductor or Superconductor

54 Superconductors and Semiconductors are the same animal from a band model viewpoint

55 Another fact about Type I: -- Interrelationship of B crit and T crit

56 Type II Q: does BCS apply ? YrComposition TcTc Mar 2011 (Tl 5 Pb 2 )Ba 2 MgCu 10 O C 293 K Oct 2010 (Tl 4 Pb)Ba 2 MgCu 8 O 13+ 3C 276K May 2006 InSnBa 4 Tm 4 Cu 6 O Hg 0.8 Tl 0.2 Ba 2 Ca 2 Cu 3 O YBa 2 Cu 3 O (La 1.85 Ba.15 )CuO 4 30


58 actual ~ 8  m Sandin

59 Type II – mixed phases Q: does BCS apply ? fluxon

60 Y Ba 2 Cu 3 O 7 crystalline La 2-x Ba x Cu O 2 solid solution may control the electronic config of the conducting layer

61 Applications OR Other Features of Superconductors

62 Meissner Effect

63 Magnetic Levitation – Meissner Effect Q: Why ? Kittel states this explusion effect is not clearly directly connected to the  = 0 effects

64 Magnetic Levitation – Meissner Effect MLX01 Test Vehicle km/h 361 mph ,000+ riders 2005 tested passing trains at relative 1026 km/h

65 MagLev in Shanghai

66 Maglev in Germany 32 km track 550,000 km since 1984 Design speed 550 km/h Regularly operated at 420 km/h 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.

67 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.

68 Josephson Junction ~ 2 nm

69 SQUID superconducting quantum interference device The phase of the wfn in left and right branches is different because of the penetrating flux.

70 Typical B fields (Tesla)(# flux quanta)

71 MAGSAFE will be able to locate targets without flying close to the surface. Image courtesy Department of Defence. 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 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.

72 Phillip Schmidt etal. Exploration Geophysics 35, 297 (2004).


74 SQUID 2 nm 10  14 T SQUID threshold Heart signals 10  10 T Brain signals 10  13 T

75 Fundamentals of superconductors: – Basic Introduction to SQUIDs: – Detection of Submarines – Fancy cross-referenced site for Josephson Junctions/Josephson: – – SQUID sensitivity and other ramifications of Josephson’s work: – Understanding a SQUID magnetometer: – Some exciting applications of SQUIDs: –

76 Relative strengths of pertinent magnetic fields – The 1973 Nobel Prize in physics – Critical overview of SQUIDs – Research Applications – Technical overview of SQUIDs: – –


78 Lasing Systems RexThorton p

79 Stimulated Emission Energy Level Diagrams Ruby Laser He-Ne Laser Diode Lasers Green Laser Pointers Free Electron Lasers National Ignition Facility

80 Parts of a Laser Principal components: 1. Gain medium 2. Laser pumping energy 3. High reflector 4. Output coupler 5. Laser beamOutput coupler

81 Spontaneous Emission Stimulated Emission Population Inversion PUMP

82 Energy Level Diagram Three Level System PUMPING Light Absorption Electrical discharge Molecular collisions

83 Ruby Laser

84 Ruby Laser Rami Arieli: "The Laser Adventure" Section page 2

85 Energy Level Diagram Four Level System PUMPING Light Absorption Electrical discharge Molecular collisions

86 He-Ne Laser

87 He-Ne Laser #1 #4 #3 #2’s Electric Discharge

88 He-Ne Laser #4’s #2’s #3’s #1

89 He-Ne Laser #4’s #2’s #3’s #1

90 Diode Laser

91 Laser Diode

92 Laser Diode

93 Green Laser Pointer

94 CO 2 Lasers


96 CO 2 Lasers

97 CO 2 Lasers

98 Free Electron Lasers

99 Boeing YAL-1 Airborne Laser (ABL) anti-ballistic missile weapons system anti-ballistic missile Developed fromBoeing FBoeing F megawatt-class chemical oxygen iodine laser (COIL)

100 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 µm, the wavelength of transition of atomic iodine.infraredchemical lasercitation needed wavelengthwavelength of transition 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 µm in the optical resonator region of the laser.chlorineiodinehydrogen peroxidepotassium hydroxidechemical reactionpotassium chloridesinglet delta oxygeniodinestimulated emissionoptical resonator


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