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Investigations in Superconductivity

Investigations in Superconductivity. Lulu Liu Partner: Chris Chronopoulos. 8.14 Experiment 4 May 12, 2008. Theory of Superconductivity. Electron-phonon interactions  Electron-Electron Attraction. At Low T, overcomes Coulomb Repulsion  Coupling of remote electron pairs  Boson pairs.

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Investigations in Superconductivity

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  1. Investigations in Superconductivity Lulu Liu Partner: Chris Chronopoulos 8.14 Experiment 4 May 12, 2008

  2. Theory of Superconductivity • Electron-phonon interactions  Electron-Electron Attraction • At Low T, overcomes Coulomb Repulsion  Coupling of remote electron pairs  Boson pairs • Binding Energy ~ kTc • Bosons tend to occupy same state: at T < Tc all Cooper pairs condense into single state Crux of BCS Theory

  3. Consequences • Zero resistivity: • Resistance: loss of momentum from interactions of charge carriers w/ environment • Superconductor – presence of large energy gap, boson pairs cannot be excited into higher state  flow together • Meisner Effect • instead of as perfect conductor • Beyond L, excludes all magnetic field from interior F. & H. London Theory • Combined Effect: • Persistent Currents in superconducting state

  4. Critical Temperature and Field • Tc measure of binding energy, T > Tc breaking of Cooper Pairs, return to normal conductivity • External magnetic field B similar energetic effect: • Critical Field Bc, NC transition for B > Bc • Strongly correlated w/ Tc and Band Gap

  5. Outline • Equipment & Calibration (Probes) • Meisner & Hysteresis Effect (Tc of Vanadium) • Persistent Current (Tc of Lead) • Critical Field Curve (Bc of Lead) • High Tc (YBCo) Superconductor Properties: • Evidence of Superconducting Behavior (DC) • Non-Zero AC Impedance at high frequency • Errors • Conclusions

  6. Equipment (Probe 1) • Mutual Inductance of Nested Solenoids  pass current through one, measure EMF in other • Superconductor (Vanadium) in center • Voltage drop across Silicon Diode  Temperature • Helium (4.2K) Cooled: Oscilloscope shows change in EMF over Tc transition • Broke on Day 2

  7. Probe 1 Method • Perfect Conductor Vs. Superconductor Marten Sjostrom

  8. Probe 1 Calibration • 10  A current through Diode/ ~30mV AC through outer Solenoid EMF = - N d/dt reduced when material goes SC  EMF drop  0 imperfect filling Vanadium 27.1 19.3 mV from Lakeshore Spec Sheets

  9. Vanadium Data (Probe 1) • Hysteresis Effect evident Data points used in average Tc = 5.42 § 0.06 K Established: Tc = 5.4 K azom.com

  10. Probe 2 Equipment & Setup • Hollow Lead Tube – persistent current measures B-field CRT calibration for T(Resistance) -- imprecise

  11. Carbon Resistance Thermometer Calibration (X-axis) Empirically determined: R.E. Bedford “Techniques...” Three points: LN2 – 77K LH (?) – 4.2K RT – 24.6K

  12. Hall Probe Calibration (Y-axis)

  13. Generating a Persistent Current • Phenomenon peculiar to Superconductors • SC transition excludes field (B < Bc) from interior  current on outer and inner surface • B-field switched OFF: Outer current disappears, inner persists  detected via Hall Probe (mV) • Bring out of SC phase  persistent current dissipates (heat) from Feynman

  14. Results (Lead – Probe 2) Imperfect Geometry – marks Tc

  15. Critical Field Measurements • Hold Temperature Constant - increase/decrease external field Enter SC state w/ zero field increasing external field from zero

  16. Conclusions • Existence of Superconductors distinct from perfect conductors

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