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# 4.electrical resistivity of ferromagnetic nickel

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electrical resistivity of ferromagnetic nickel

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### 4.electrical resistivity of ferromagnetic nickel

1. 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. 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. 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. 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. 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. 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. 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. 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. 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
10. 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>