1Wed. Apr. 5, 2006 Phy107 Lecture 291Due today: Essay outline & HW 9HW10: Two ‘web qestions’ + G Chap 19: Q4, Q6, E2, E4, E10• Solids are large numbers of atoms arranged in a regularcrystal structure.• Each type of atomic electron state (e.g. 1s) correspondsto a broadened ‘band’ of energy levels• Energy band is a range of closely-spaced electron states.• Band filling determines electrical properties– Partially full bands = metal– Bands completely full or empty = insulator / semiconductor• Substitutional doping of a semiconductor leads to amaterial useful in electronic devices.From last time…Wed. Apr. 5, 2006 Phy107 Lecture 292Electrical resistance• Last time we said that a metalcan conduct electricity.• Electrons can flow through thewire when pushed by abattery.• But remember that the wire ismade of atoms.• Electrons as waves driftthrough the atomic lattice.Wed. Apr. 5, 2006 Phy107 Lecture 293Resistance questionSuppose we have a perfect crystal ofmetal in which we produce anelectric current. The electrons inthe metalA. Collide with the atoms, causingelectrical resistanceB. Twist between atoms, causingelectrical resistanceC. Propagate through the crystalwithout any electrical resistanceIf all atoms are perfectly in place, the electronmoves though the without any resistance!Wed. Apr. 5, 2006 Phy107 Lecture 294Life is tough• In the real world, electronsdon’t have it so easySome missing atoms (defects)Vibrating atoms!Electron scatters from theseirregularities, -> resistanceWed. Apr. 5, 2006 Phy107 Lecture 295Temperature-dependent resistanceSuppose we cool down thewire that carries electricalcurrent to light bulb. Thelight willA. Get brighterB. Get dimmerC. Stay sameWed. Apr. 5, 2006 Phy107 Lecture 296Resistance• As elecron wave propagatesthrough lattice, it facesresistance• Resistance: Bumps from vibrating atoms Collisions with impurities Repulsion from other electrons• Electrons ‘scatter’ from theseatomic vibrations and defects.• Vibrations are less at lowtemperature, so resistancedecreases.• More current flows through wire• Life is tough for electrons,especially on hot dayshttp://regentsprep.org/Regents/physics/phys03/bresist/default.htm2Wed. Apr. 5, 2006 Phy107 Lecture 297Why does temperature matter?Temperature is related to the energy of amacroscopic object.• The energy usually shows up as energy ofrandom motion.• There really is a coldest temperature,corresponding to zero motional energy!• The Kelvin scale has the same size degreeas the Celsius (˚C) scale. But 0 K means nointernal kinetic energy.• 0 degrees Kelvin (Absolute Zero) is thecoldest temperature possible– This is -459.67 ˚FWed. Apr. 5, 2006 Phy107 Lecture 298Temperature scales• Kelvin (K):– K = C + 273.15– K = 5/9 F + 255.37absolute zero0-273.15-459.67liquid helium boils4.2-268.95-452.11liquid nitrogen boils77.36-195.79-300.42water freezes273.15032water boils373.15100212commentsKelvinCelsiusFahrenheitWed. Apr. 5, 2006 Phy107 Lecture 299Reaching low temperature• Low temperatures obtained with liquid gases.• To turn a liquid into a gas at fixed temperaturerequires a certain amount of heat (latent heat)• So the liquid warms up to its boiling point, thenturns into vapor a little at a time.• A liquid gas will remain at its boiling point.– Liquid Oxygen: 90.2 K (-297.4 F)– Liquid Nitrogen: 77 K (-320.4 F)– Liquid Hydrogen: 20.4 K (-423.2 F)– Liquid Helium: 4.2 K (-452.1 F)Wed. Apr. 5, 2006 Phy107 Lecture 2910Low temperature properties• Superconductors become superconducting atlow temperature• But also, many mechanical propertieschange at low temperature.• Many materials lose their elasticity.• More subject to fracture.Wed. Apr. 5, 2006 Phy107 Lecture 2911What happens at the lowesttemperature?Kelvin (1824-1907): electrons freeze and resistance increases Onnes (1853-1926):Resistance continues drop,finally reaching zero at zerotemperatureWed. Apr. 5, 2006 Phy107 Lecture 2912Heike Kamerlingh Onnes• 1908 - liquefied helium(~4 K = - 452°F )• 1911- investigated lowtemperature resistance ofmercury• Found resistance droppedabruptly to zero at 4.2 K• 1913 - Nobel Prize in physicsSometimes,something else!3Wed. Apr. 5, 2006 Phy107 Lecture 2913OnnesOnnes published thefinding in November1911 as“On the SuddenChange in the Rateat Which theResistance ofMercury Disappears.”Wed. Apr. 5, 2006 Phy107 Lecture 2914Superconductivity• Superconductors are materialsthat have exactly zeroelectrical resistance.• But this only occurs attemperatures below acritical temperature, Tc• In most cases thistemperature is far belowroom temperature.Hg (mercury)Not superconducting (normal)SuperconductingCriticalTemperatureWed. Apr. 5, 2006 Phy107 Lecture 2915Persistent currents• How zero is zero?• EXACTLY!• Can set up a persistent current ina ring.• The magnitude of the currentmeasured by the magnetic fieldgenerated.• No current decay detected overmany years!PersistentsupercurrentMagneticfieldWed. Apr. 5, 2006 Phy107 Lecture 2916Critical current• If the current is too big,superconductivity isdestroyed.• Maximum current forzero resistance is calledthe critical current.• For larger currents, thevoltage is no longer zero,and power is dissipated.CurrentVoltageCriticalcurrentNot superconducting (normal)SuperconductingCriticalCurrentWed. Apr. 5, 2006 Phy107 Lecture 2917Superconducting elements• Many elements are in fact superconducting• In fact, most of them are!Wed. Apr. 5, 2006 Phy107 Lecture 2918Critical temperaturesIf superconductivity is so common, why don’t wehave superconducting cars, trains, toothbrushes?Many superconducting critical temperatures are low.-443-2649.25Niobium-453-2693.72Tin-447-2667.2Lead-452-2694.15Mercury-457-2711.75Aluminum(˚F)(˚C)Critical T. (K)Element4Wed. Apr. 5, 2006 Phy107 Lecture 2919Higher transition temperatures• Much higher critical temperature alloys havebeen discovered• NbTi 10 K• Nb3Sn 19 K• YBa2Cu3O7, 92 K• BiSrCaCuO, 120 KHigh-temperaturesuperconductorsWed. Apr. 5, 2006 Phy107 Lecture 2920A century of superconductivity1957: BCSmicroscopic theory1986:high tempsuperconductivity1933:Meissner effect1911:superconductivitydiscovered:Hg at 4K1954: Type IIsuperconductors1962: Josephson effect1950: Landau-Ginzburg theory2011Wed. Apr. 5, 2006 Phy107 Lecture 2921Meissner effect• Response to magnetic field• For small magnetic fields asuperconductor
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