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electrical resistivity of ferromagnetic nickel

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- 1. Electrical Resistivity of Ferromagnetic Nickel RESISTIVITY ( ) is a material property, independent of size of the sample DEPENDS ON TEMPERATURE CONDUCTIVITY( ) : = 1/ = n e , = v / E = RA / l = VA / I l I Methods of Measurement: 1. Two probe method : for Insulators 2. Four Probe method : for semiconductors and metals l A
- 2. = 1/ = n e = n e 2 / m , is mobility of the charge carriers and n is the charge density = v / E = e / m , v is velocity of the carriers is relaxation time or time interval between collisions decreases with increase in T , the temperature and depend on and follow the variation in (T) 1. In metals : T dependence of is vital hence plays an important role. and hence and decrease with rise in T 2. In semiconductors : T dependence of n is vital n = n 0 exp( - E g / K B T) , = n e = 0 exp(- E g / K B T) 3. In insulators, E g is large and hence n is small Formulae
- 3. Band Picture of Solids Band gap E g is ~ 7 eV in Diamond ( Insulator ) ~ 1 ev in Semiconductors Zero in conductors Lennard-Jones potential E(R) = -(A/R m ) +(B/R n ) At R = R 0 , d E/dR = 0
- 4. <ul><li>Fermi function - Metals </li></ul><ul><li>Highest filled energy level is E F </li></ul><ul><li>Only the electrons in the range K B T near E F participate in conduction. </li></ul>N(E) = No. of states between E and E+dE F(E) = Probability that the state at E is occupied. N= ∑ N(E) F(E) dE K B T
- 5. T Semiconductors Metals --- Phonon contribution is linear in T at high T Semiconductors Slope = E g / K B <ul><li> = n e = 0 exp(- E g / K B T) </li></ul><ul><li>= 0 exp(E g / K B T) </li></ul><ul><li>log =log 0 +(E g / K B )(1/T) </li></ul>
- 6. Four Probe Measurement Insulators – Two Probe Measurement Metals & Semiconductors Four Probe Measurement Block diagram for four-probe conductivity measurement An equivalent circuit for four-probe method
- 7. Pressure contacts for four-probe technique. Four Probe Arrangement Four probe method is used to minimize contribution from contact resistances. V s + = + IR S + V Th V s - = - IR S + V Th V s + - V s - = 2 IR S I = (V R + - V R - ) /R V s + + V s - = 2 V Th V Th is independent of the current direction Any local temperature gradients between points 3 and 4 will generate V Th
- 8. Heating the Sample : The sample is heated using a furnace. The furnace is made by winding a high resistive wire ( Nichrome ) on a muffle which gives out heat ( Joule heating ) as i 2 r when a current i is sent through the furnace wire whose resistance is r. Thermal sensors/ Thermocouples : 1. Commonly used are Pt 100 Ω resistor, or thermocouples There are different types of thermocouples appropriate to sense the temperature at different temperature ranges 2. Chromel- Alumel is the thermocouple used for temps above RT up to 1200 0 C 3. Works on the principle of Seebeck effect. 4. Two junctions , one at O 0 C and the other close to the sample give differential emf. Corresponding temperature is read out from a calibration chart.
- 9. The sample resistance is computed as ( Ohm ) The resistivity is computed as = ( R S A ) / l Sources of Resistivity : 1. Impurities 2. Phonons 3. Magnons Separate the various contributions from total T total ph o mag Correction of thermo emf arising from local heating 0 RT
- 11. Analysis : <ul><li>1 .Find the slope ( A) of the curve at high temperatures. Then “ ” phonon is determined as ph =AT </li></ul><ul><li>and is plotted against T </li></ul><ul><li>Subtract ph from the total measured . </li></ul><ul><li>This gives 0 + mag . </li></ul><ul><li>Here we neglect can not be , and take this as mag </li></ul><ul><li>( 0 can be determined if versus T is measured close to 0 K) </li></ul><ul><li>3. Plot mag Vs T and also( mag / T) Vs T </li></ul><ul><li>The latter graph is expected to show a peak at the inflection point which gives T c ,the Curie temperature. </li></ul>

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