1 / 36

CONDUCTIVITY

CONDUCTIVITY. Conductivity Superconductivity. Electronic Properties Robert M Rose, Lawrence A Shepart, John Wulff Wiley Eastern Limited, New Delhi (1987). Resistivity range in Ohm m  25 orders of magnitude. Semi-conductors. Metallic materials. Insulators. Metals. Semi-metals.

sakura
Télécharger la présentation

CONDUCTIVITY

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CONDUCTIVITY • Conductivity • Superconductivity Electronic Properties Robert M Rose, Lawrence A Shepart, John Wulff Wiley Eastern Limited, New Delhi (1987)

  2. Resistivity range in Ohm m  25 orders of magnitude Semi-conductors Metallic materials Insulators

  3. Metals Semi-metals Classificationbased on Conductivity Semi-conductors Insulators

  4. Free Electron Theory • Outermost electrons of the atoms take part in conduction • These electrons are assumed to be free to move through the whole solid Free electron cloud / gas, Fermi gas • Potential field due to ion-cores is assumed constant  potential energy of electrons is not a function of the position(constant negative potential) • The kinetic energy of the electron is much lower than that of bound electrons in an isolated atom

  5. Wave particle duality of electrons •  → de Broglie wavelength • v → velocity of the electrons • h → Planck’s constant Wave number vector (k) Non relativistic

  6.  ↑ → k ↓ → E ↓ E → Discrete energy levels (Pauli’s exclusion principle) k→

  7. Electron in an 1D box L If the length of the box is L n → integer (quantum number) Quantization of Energylevels Number of electrons moving from left to right equals the number in the opposite direction

  8. In 3D • Each combination of the quantum numbers nx , ny , nz corresponds to to a distinct quantum state • Many such quantum states have the same energy and said to be degenerate • The probability of finding an electron at any point in box is proportional to the square of the amplitude  there are peaks and valleys within L • If the electron wave is considered as a travelling wave the amplitude will be constant

  9. Fermi level • At zero K the highest filled energy level (EF) is called the Fermi level • If EF is independent of temperature (valid for usual temperatures) ► Fermi level is that level which has 50% probability of occupation by an electron

  10. T > 0 K 0K P(E) → Increasing T E →

  11. Conduction by free electrons • If there are empty energy states above the Fermi level then in the presence of an electric field there is a redistribution of the electron occupation of the energy levels ElectricField EF EF E → k→ k→

  12. Force experienced by an electron • m → mass of an electron • E → applied electric field

  13. Collisions vd Velocity →  time → • In the presence of the field the electron velocity increases by an amount (above its usual velocity) by an amount called the drift velocity • The velocity is lost on collision with obstacles • vd → Drift velocity •  → Average collision time

  14. The flux due to flow of electrons → Current density (Je) • n → number of free electrons ~ Ohm’s law

  15. Mean free path (MFP) (l) of an electron • l = vd • The mean distance travelled by an electron between successive collisions • For an ideal crystal with no imperfections (or impurities) the MFP at 0 K is  • Ideal crystal  there are no collisions and the conductivity is  • Scattering centres → MFP↓ , ↓  ↓ , ↑ Scattering centres Thermal vibration → Phonons Sources ofElectron Scattering Solute / impurity atoms Defects Dislocations Grain boundaries Etc.

  16. Thermal scattering • At T > 0K → atomic vibration scatters electrons → Phonon scattering •  T ↑ →  ↓ →  ↑ • Low T MFP  1 / T3  1 / T3 • High T MFP  1 / T  1 / T Impurity scattering • Resistivity of the alloy is higher than that of the pure metal at all T • The increase in resistivity is  the amount of alloying element added !

  17. Cu-Ni alloy Increased phonon scattering 5 Cu-3%Ni 4 Cu-2%Ni Resistivity () [x 10-8 Ohm m] → 3 Impurity scattering (r) 2 1 Pure Cu With low density ofimperfections 100 200 300 T (K) → → 0 as T→ 0K

  18. Mattheissen rule  = T + r Net resistivity = Thermal resistivity + Resistivity due to impurity scattering

  19. Applications Conductors • Power transmission lines → low I2R loss → large cross sectional area • Al used for long distance distribution lines (Elastic ModulusAl increased by steel reinforcement) • OFHC (Oxygen Free High Conductivity) Cu (more expensive) is used for distribution lines and busbars. ► Fe, P, As in Cu degrade conductivity drastically

  20. Electrical contacts • Electrical contacts in switches, brushes and relays • Properties:► High electrical conductivity► High thermal conductivity → heat dissipation ►High melting point → accidental overheating► Good oxidation resistance • Cuand Ag used • Ag strengthened by dispersion strengthening by CdO■ CdO ► Strengthens Ag ► Improves wear resistance ► If arcing occurs → decomposes (At MP of Ag) to absorb the heat

  21. Resistor • Properties:► Uniform resistivity → homogenous alloy► Stable resistance → Avoid aging / stress relaxation / phase change► Small T coefficient of resistance (R)→minimizes error in measurement► Low thermoelectric potential wrt Cu ►Good corrosion resistance • Manganin (87% Cu, 13% Mn, R = 20 x 106 / K) and Constantan (60% Cu, 40% Ni) are good as resistor materials [R (Cu) = 4000 x 106 / K] • Low thermoelectric potential wrt to contact material (usually Cu) reduces error due to temperature difference between junctions. For high precision dissimilar junctions should be maintained at same temperature • Ballast resistors are used in maintaining constant current →I ↑ → T ↑ → R ↑I ↓ Requriement: high R (71% Fe, 29% Ni → R = 4500 x 106 / K)

  22. Heating elements • Properties:► High melting point ► High resistivity ► Good oxidation resistance► Good creep strength ►Resistance to thermal fatigue low elastic modulus  low coefficient of thermal expansion • ■ Upto 1300oC Nichrome (80% Ni, 20% Cr), Kanthal (69% Fe, 23% Cr, 6% Al, 2% Co)■ Upto 1700oC: SiC & MoSi2■ Upto 1800oC: Graphite • Mo and Ta need protective atmosphere at high T • W (MP = 3410oC) is used is used as filament in light bulbs → creep resistance above 1500oC improved by dispersion hardening with ThO2 • Resistance thermometers: ► High temperature coefficient of resistivity ► Pure Pt

  23. SUPERCONDUCTIVITY

  24. Superconducting transition 20 10 Sn Ag Resistivity () [x 10-11 Ohm m] → Resistivity () [x 10-11 Ohm m] → 10 5 ? 5 0 10 0 Tc 10 20 T (K) → T (K) → Superconducting transition temperature

  25. Current carrying capacity • The maximum current a superconductor can carry is limited by the magnetic field that it produces at the surface of the superconductor Hc / Jc Normal Jc [Amp / m2] → 0 Hc [Wb / m2] → Superconducting T (K) → Tc

  26. Meissner effect • A superconductor is a perfect diamagnet (magnetic suceptibility  = 1) • Flux lines of the magnetic field are excluded out of the superconductor Meissner effect Superconducting Normal

  27. Theory of low temperature superconductivity- Bardeen-Cooper-Schreiffer (BCS) theory • Three way interaction between an two electron and a phonon • Phonon scattering due to lattice vibrations felt by one electron in the Cooper pair is nullified by the other electron in the pair  the electron pair moves through the lattice without getting scattered by the lattice vibrations • The force of attraction between the electrons in the Cooper pair is stronger than the repulsive force between the electrons when T < Tc

  28. Type I and Type II superconductors

  29. Type I (Ideal) superconductors • Type I SC placed in a magnetic field totally repels the flux lines till the magnetic field attains the critical value Hc Type I M→ Normal Superconducting H → Hc

  30. Type II (Hard) superconductors • Type II SC has three regions Vortex Region Gradual penetration of the magnetic flux lines Type I M→ Superconducting Vortex Normal H → Hc1 Hc Hc2

  31. As type II SC can carry high current densities (Jc) they are of great practical importance • The penetration characteristics of the magnetic flux lines (between Hc1 and Hc2) is a function of the microstructure of the material  presence of pinning centres in the material • Pinning centres: Cell walls of high dislocation density (cold worked/recovery annealed) Grain boundaries (Fine grained material) Precipitates (Dispersion of very fine precipitates with interparticle spacing ~ 300 Å) • Jc↑ as Hc2↑

  32. Potential Applications • Strong magnetic fields → 50 Tesla (without heating, without large power input) • Logic and storage functions in computers Josephson junction → fast switching times (~ 10 ps) • Magnetic levitation (arising from Meissner effect) • Power transmission

  33. High Tc superconductivity

  34. Manufacture of YBa2Cu3O7-x Please read from text book

  35. Crystal structure of YBa2Cu3O7x Y Cu O Ba

More Related