Conductors and Resistors Chapter 14

MaterialResistivity, Ohm m MaterialResistivity, Ohm m Ag1.6×10 -8 Ni (com)6.8×10 -8 Cu (com)1.7×10 -8 S. Steel7.1×10 -7 Au2.4×10 -8 Nichrome1.08×10 -6 Al (com)2.9×10 -8 Graphite1 ×10 -5 Brass (70-30) 6.2×10 -8 SiC1 ×10 -1

MaterialResistivity, Ohm m MaterialResistivity, Ohm m SiC1 ×10 -1 Bakelite Ge, pure4.5 ×10 -1 Window glass >10 10 Si, pure2.3 ×10 3 Ai 2 O Mica Diamond>10 14 SiO 2 >10 16

Imperfections solutes, vacancies, etc. dislocations grain boundaries act as scattering centres and thereby decrease the mean free path and thus decrease . Of all the imperfections, dissolved impurities (solutes) are more effective than the others as scattering centres.

Phonons:elastic waves produced by the random vibrations of atoms Random nature destroys the ideal periodicity and interferes with the electron motion. Conductivity thus decreases with increasing temperature.

Cu-3%Ni Cu-2%Ni Pure Cu Fig  T Experiment 9 Dependence of resistivity on temperature and composition  =  T +  r  = resitivity  T = thermal part of the resitivity  r =residual resitivity due to impurity and imperfections Mattheissen’s Rule :  T and  r are independent of each other; i.e.,  T depends only on tempearture and  r depends only on compositon

Applications Conductors:Requirements 1. Low I 2 R loss (High Conductivity) 2. Fabricability 3. Cost 4. Strength

Candidate Materials Long distance transmission lines - Al - ACSR: Al conductor steel reinforced

(Cu is more expensive) Distribution lines, Bus bars, Energy Conversion Applications - OFHC copper Use of Cd as solute in improving the strength

Electrical Requirements Contacts:1. High  switches2. High Thermal brushesConductivity relays3. High m.p. 4. Good Oxidation Resistance

Candidate Materials - Cu and Ag Cu is cheaper Ag, which is expensive, is preferred for critical contacts. Strength of Ag is increased by dispersed CdO (Dispersion Strengthening) Absorbs heat by decomposing

Resistors:Requirements 1. Uniform resistivity 2. Stable resistance 3. Small temp. Coefficient of resistivity 4. Low thermoelectric pot. w.r.t. copper 5. Good resistance to atmospheric corrosion

Candidates: Manganin (87% Cu, 13% Mn)  = 20 × K -1 low as compare to that for Cu, which is 4000 × K -1. Constantan (60% Cu, 40% Ni) Ballast Resistors are used in circuits to maintain constant current – these must have high . 71% Fe, 29% Ni alloy is used  = 4500 × K -1

Heating Requirements Elements:1. High m.p. 2. High resistivity 3. Good Oxidation Resistance 4. Good Creep Strength 5. Resistance to thermal fatigue - low elastic modulus - low therm. expansion

Candidates Nichrome (80% Ni, 20% Cr) Kanthal (69% Fe, 23% Cr, 6% Al, 2% Co) SiC MoSi 2 Graphite in inert atmosphere Mo, Ta Poor oxidation resistance W (filaments) – ThO 2 dispersion to improve creep resistance

Resistance Thermometers: Requirement - High  Candidate -Platinum (pure metal)

Superconductors Section 14.5

1. Phenomenon Resistivity of silver  ( ohm m) T, K Fig a

Resistivity of tin Can be used for producing large permanent magnetic field  ( ohm m) T, K Fig b

Loss of superconductivity  0 H c, Wb m -2 T, K TcTc Superconductor Normal Fig. 14.8

The maximum current that a superconductor carries at a given temperature below T c is limited by the magnetic field it produces at the surface of the superconductor J c, A m -2 T, K TcTc Superconductor Normal Fig not in book

Meissner Effect Normal Superconductor Fig T>T c T<T c

BCS Theory (Bardeen, Cooper, Schreiffer) Three way interaction between two electrons and a phonon Electron pair (cooper pair): The attractive interaction energy The repulsive energy Attraction is disrupted at T  T c

2. Two types I and II of superconductors -M Type IType II HcHc H H H c1 H c2

Type II Great practical interest because of high J c. This state is determined by the microstructural conditions of the material

Heavily cold worked & recovery annealed Cell walls of high dislocation density Magnetic flux lines are pinned effectively Fine grain sizeGrain boundaries Pinning action Dispersed fine precipitate Interparticle spacing of about 300 Å Pinning action

Nb-40% Ti at 4.2 K, 0.9 H c2 MicrostructureJ c, A m -2 Recrystallised10 5 Cold worked and recovery annealed 10 7 Cold worked and precipitation hardened 10 8

3. Potential Applications Strong Magnets (50 Tesla) MHD power generation Logic and Storage functions in computers switching times  10 ps Levitation transportation

Transmission No I 2 R loss

Yamanashi Maglev Test Line Magnetic Levitation (Maglev) is a system in which the vehicle runs levitated from the tracks by using electromagnetic forces between superconducting magnets on board the vehicle and coils on the ground. December 2, 2003, maximum speed 581 km/h (manned run). Max speed of Rajdhani Express 140 km/h

Magnetic Resonance Imaging

4. New Developments Nb 3 Ge 23 K1976 La-Ba-Cu-O 34 K1986, Bednorz and Muller YBa 2 Cu 3 O 7-x 90 K1988

Recipe: Y 2 O 3, BaCO 3, CuO compacted powder in right proportion is heated ( °C) BaCO 3 BaO + CO 2 Annealing at 800 °C in O 2 atmosphere The super conducting properties appear to be sensitive function of the oxygen content and, therefore, of the partial pressure of oxygen during heat treatment

YBa2Cu3O7-x Ba Y Cu O

Engineering aspects remain Elusive Reactive and Brittle Unable to support any significant stress Cannot be easily formed or joined Superconducting properties deteriorate during heating for forming purposes Or even in humid room Attempts Explosive forming atm (100°C) Isostatic Pressing