Conductors and Resistors

Chapter 14

Material Resistivity, Ohm m

Material Resistivity, Ohm m

Ag 1.6×10-8 Ni (com) 6.8×10-8

Cu (com) 1.7×10-8 S. Steel 7.1×10-7

Au 2.4×10-8 Nichrome 1.08×10-6

Al (com) 2.9×10-8 Graphite 1 ×10-5

Brass (70-30)

6.2×10-8 SiC 1 ×10-1

Material Resistivity, Ohm m

Material Resistivity, Ohm m

SiC 1 ×10-1 Bakelite 107 - 1011

Ge, pure 4.5 ×10-1 Window glass

>1010

Si, pure 2.3 ×103 Ai2O3 1010-1012

Mica 1011-1015

Diamond >1014

SiO2 >1016

Imperfections solutes, vacancies, etc.dislocationsgrain 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

Pur

e Cu

Fig. 14.6

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 I2R loss

(High Conductivity)

2. Fabricability

3. Cost

4. Strength

Candidate MaterialsLong 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 switches 2. High Thermal brushes

Conductivity

relays 3. 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 × 10-6 K-1 low as compare to that for Cu, which is 4000 × 10-6 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 × 10-6 K-1

Heating RequirementsElements:1. High m.p.

2. High resistivity3. Good Oxidation Resistance4. Good Creep Strength5. Resistance to thermal fatigue

- low elastic modulus- low therm.

expansion

CandidatesNichrome (80% Ni, 20% Cr)Kanthal (69% Fe, 23% Cr, 6% Al, 2% Co)

SiC

MoSi2Graphite in inert atmosphereMo, Ta Poor oxidation resistance

W (filaments) – ThO2 dispersion to improve creep resistance

Resistance Thermometers:

Requirement - High Candidate - Platinum (pure metal)

Superconductors

Section 14.5

1. Phenomenon

Resistivity of silver

(1

0-11 o

hm m

)

T, K

Fig. 14.7 a

Resistivity of tin

Can be used for producing large permanent magnetic field

(1

0-11 o

hm m

)

T, K

Fig. 14.7 b

Loss of superconductivity

0 H

c, W

b m

-2

T, K Tc

Superconductor

Normal

Fig. 14.8

The maximum current that a superconductor carries at a given temperature below Tc is limited by the magnetic field it produces at the surface of the superconductor

J c,

A m

-2

T, KTc

Superconductor

Normal

Fig not in book

Meissner Effect

NormalSuperconductor

Fig. 14.9

T>Tc T<Tc

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 Tc

2. Two types I and II of superconductors

-M -M

Type I Type II

Hc

HH

Hc1 Hc2

Type II

Great practical interest because of high Jc.

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 size Grain boundaries

Pinning action

Dispersed fine precipitate

Interparticle spacing of about 300 Å

Pinning action

Nb-40% Ti at 4.2 K, 0.9 Hc2

Microstructure Jc, A m-2

Recrystallised 105

Cold worked and recovery annealed

107

Cold worked and precipitation hardened

108

3. Potential Applications

• Strong Magnets (50 Tesla)

MHD power generation

• Logic and Storage functions in computers

switching times 10 ps

• Levitation

transportation

• Transmission

No I2R 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

Nb3Ge 23 K 1976

La-Ba-Cu-O 34 K 1986,

Bednorz and

Muller

YBa2Cu3O7-x 90 K 1988

Recipe: Y2O3, BaCO3, CuO

compacted powder in right proportion

is heated (900 - 1100°C)

BaCO3 BaO + CO2

Annealing at 800 °C in O2 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 ElusiveReactive 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 50 000 atm (100°C)

Isostatic Pressing