investigations in superconductivity lulu liu partner: chris chronopoulos 8.14 experiment 4 may 12,...
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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
Binding Energy ~ kTc Bosons tend to occupy same state: at T < Tc all Cooper pairs condense into single state
Crux of BCS Theory
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
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
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
Equipment (Probe 1)
Mutual Inductance of Nested Solenoids pass current through one, measure EMF in other
Superconductor (Vanadium) in center
Helium (4.2K) Cooled: Oscilloscope shows change in EMF over Tc transition
Voltage drop across Silicon Diode Temperature
Broke on Day 2
Probe 1 Method
Perfect Conductor Vs. Superconductor
Marten Sjostrom
Probe 1 Calibration 10 A current through Diode/ ~30mV AC through
outer Solenoid
from Lakeshore Spec Sheets
EMF = - N d/dt
reduced when material goes SC EMF drop
0 imperfect filling
Vanadium
27.1 19.3 mV
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
Probe 2 Equipment & Setup
Hollow Lead Tube – persistent current
CRT calibration for
T(Resistance) -- imprecise
measures B-field
Carbon Resistance Thermometer Calibration (X-axis)
Empirically determined:
R.E. Bedford “Techniques...”
Three points:
LN2 – 77K
LH (?) – 4.2K
RT – 24.6K
Hall Probe Calibration (Y-axis)
Generating a Persistent Current
Phenomenon peculiar to Superconductors
from Feynman
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)
Results (Lead – Probe 2)
Imperfect Geometry –
marks Tc
Critical Field Measurements Hold Temperature Constant -
increase/decrease external field
increasing external field from zero
Enter SC state w/ zero field
Conclusions
Existence of Superconductors distinct from perfect conductors