AC Measurement of Magnetic Susceptibility. Part 2. Physics 401, Spring 2015 Eugene V. Colla

Transcription

1 AC Measurement of Magnetic Susceptibility. Part 2. Physics 401, Spring 2015 Eugene V. Colla

2 Outline What and how we measuring (week1) Magnetic looses Temperature dependencies of permeability End of semester 4/20/2015 2

3 Magnetic materials. B H M 0 Magnetic induction Permeability of free space Magnetic field M Magnetization H magnetic susceptibility 4/20/2015 3

4 Magnetic materials. M H 0 B H M In general is a function of H and T HT M ( H, T ) H (, ) M H T 4/20/2015 4

5 Magnetic materials. B H H 1 H H; r r < 0 - diamagnetics, r < 1 > 0 - paramagnetics r > 1 >> 0 - ferromagnetics r >> 1 4/20/2015 5

6 Magnetic materials. Diamagnetism. Material χ v (10 5 ) Bismuth 16.6 Carbon (diamond) 2.1 Carbon (graphite) 1.6 Copper 1.0 Lead 1.8 Mercury 2.9 Pyrolytic carbon 40.0 Silver 2.6 Superconductor 10 5 Water 0.91 < 0 - diamagnetics Ideal diamagnetic = -1 Levitation of the pyrolytic carbon Courtesy of Wikipedia 4/20/2015 6

7 Magnetic materials. Ferromagnetism. >> 1 - ferromagnetics M~M s Material r B rem (T) Fe, 99.8% pure M=0 Permalloy 100, Superpermalloy 1,000, Co, 99% pure Ni, 99% pure /20/2015 7

8 Measuring of the permeability. DC field. H = H 0 + H sinωt 1 B 0 B f ( H) DC part of the setup H 0 H 0 = N pi DC 2πr Here Np number of turns in DC primary coil 4/20/2015 8

9 Measuring of the permeability. AC modulation H = H + Hsinωt 0 1 B B w 0 B f ( H) Wavetek reference H 0 H = H 0 + H1sinωt B ω ~ df dh =db dh = 0 r H 1 = N pi AC 2πr R ac Here Np number of turns in AC primary coil 4/20/2015 9

10 Measuring of the permeability. AC modulation Primary coil of N p turns supplied by current I p creates magnetic field H and flux Φ For toroid: H = N pi p 2πr 1 R 2 <r < R 1 R2 I N t dr I N t R2 H da ln 2 r 2 R R 1 da=dr*t 4/20/

11 Measuring of the permeability. Pickup coil. Lock-in measures emf on the pickup coil V lockin N pickup d dt Faraday's law = 0 + 1cosωt 2 I N t R AC dr I N t 1 Hac da 2 r 2 R R 1 ln R 2 1 This is per 1 turn of the pickup coil! Here Ip is ac current in primary coil L3; I p = V 0sin(ωt) R ac N t R di N t R V V N N t 2 AC 2 AC lock in pickup ln pickup ln w cos( w ) 2 R1 dt 2 R1 Rac V N t R r L w cos( wt); where L N pickup ln 2 R AC 0 0 Rac 0 2 4/20/

12 Measuring of the permeability. Pickup coil. N t R di N t R V V N N t 2 AC 2 AC lock in pickup ln pickup ln w cos( w ) 2 R1 dt 2 R1 Rac V N t R r L w cos( wt); where L N pickup ln 2 R AC 0 0 Rac In general r = -j Geometry of toroid Resistor in AC current loop Because of /2 phase shift (cos(wt)) the signal will be delivered to Y channel of the lock-in amplifier. provides the information about the losses in system 4/20/

13 Hysteresis Loops. Remagnetization loses Energy of the magnetic field W = V HdB By cycling around the loop W loop = V HdB=V*Loop_area V here is a volume of the magnetic material 4/20/

14 Calculating of the magnetic induction B B H H H r 0r db ; B 0 r( H ) dh dh Magnetics ZP44715-TC 0.4 After integrating 0.2 B (T) H (A/m) 4/20/

15 Hysteresis Loops. Remagnetization loses W = V HdB W loop = V HdB=V*Loop_area Using Origin Pro for integrating Magnetics ZP44715-TC B (T) H (A/m) 4/20/

16 Hysteresis Loops. Remagnetization loses W = V HdB W loop = V HdB=V*Loop_area Using Origin Pro for integrating Magnetics ZP44715-TC B (T) H (A/m) 4/20/

17 Hysteresis Loops. Remagnetization loses W = V HdB W loop = V HdB=V*Loop_area Using Origin Pro for integrating Magnetics ZP44715-TC B (T) ! H (A/m) 4/20/

18 Hysteresis Loops. Remagnetization loses W = V HdB W loop = V HdB=V*Loop_area Using Origin Pro for integrating Magnetics ZP44715-TC Integr B (T) 0.0 Integrated Y H (A/m) H (A/M) 4/20/

19 Hysteresis Loops. Remagnetization loses W = V HdB W loop = V HdB=V*Loop_area Using Origin Pro for integrating Units : V ( volume) m H( field) A m 3 1 B( magn. induction) kg s A V 2 2 B H m kg s J 2 1 (joule) Power of loses: W/T = W*f, where T is period and f frequency 4/20/

20 Temperature dependence of the magnetic permeability. In this experiment we will measure permeability as a function of T. I DC will be fixed. The default option I DC =0. DMM will measure the emf of T-type thermocouple. 4/20/

21 Measuring of the temperature. Thermocouple. Type Names of Materials T Range B Platinum30% Rhodium (+) Platinum 6% Rhodium (-) F C C W5Re Tungsten 5% Rhenium (+) W26Re Tungsten 26% Rhenium (-) F C E J K N R S T Chromel (+) Constantan (-) Iron (+) Constantan (-) Chromel (+) Alumel (-) Nicrosil (+) Nisil (-) Platinum 13% Rhodium (+) Platinum (-) Platinum 10% Rhodium (+) Platinum (-) Copper (+) Constantan (-) F C F C F C F C F C F C F C Type T (copper-constantan) has thermoemf at 0 C 41.5V/ C; 4/20/

22 Measuring of the temperature. Thermocouple. Type T (copper-constantan) has thermoemf at 0 C 41.5V/ C; 4/20/

23 Measuring of the temperature. Temperature ramp. Option 1: manual by changing the voltage applied to the heater Option 2: by using Omega PID temperature controller 4/20/

24 Measuring of the temperature. Software. 4/20/

25 Measuring of the temperature. Software. AC frequency (1-10kHz) Series resistor in AC loop (fixed) 4/20/

26 Measuring of the temperature. Software. AC frequency (1-10kHz) Series resistor in AC loop (fixed) DMM resolution: Optimal=100nV 4/20/

27 Temperature dependence of the magnetic permeability. Ferroxcube 3E cooling ' (a.u.) T(K) 4/20/

28 Temperature dependence of the magnetic permeability. Ferroxcube 4A T heating cooling 300 heating cooling? ' (a.u.) ' (a.u.) T (K) T (K) Hysteresis. Where it is coming from? 4/20/

29 Temperature dependence of the magnetic permeability. 300 heating cooling? db ( T ) 0r( T ) T dh ' (a.u.) T (K) B (a.u.) /20/

30 Temperature dependence of the magnetic permeability. 300 heating cooling? db ( T ) 0r( T ) T dh ' (a.u.) # B(a.u.) 0.5 B (a.u.) 0-1 #1 T (K) -2 Slope#1 ~0.728 Slope#2 ~ H(a.u.) 4/20/

31 Temperature dependence of the magnetic permeability. Curie-Weiss law. Pierre Curie Pierre Ernest Weiss C ' T T c Curie-Weiss law 4/20/

32 Temperature dependence of the magnetic permeability Ferroxcube 3E C 57C 80C 100C ~130C (T>Tc) B (a.u.) I H (A) 4/20/

33 References Information about magnetic materials can be found in : \\Phyaplportal\PHYCS401\Experiments\AC_Magnetization\Mag netic Materials SR830 manual ibid 4/20/

34 End of semester schedule No Lecture on April 27 th Third week of the Magnetic Laboratory. You can repeat some experiments done during first two weeks + some new challenging experiments like taking B-H dependencies taken at different temperatures or measuring of the permeability as a function frequency with and without DC magnetic field bias. May 13 th Wednesday 11.59pm. Final deadline for submitting of the final report. No extension and no late vouchers. 4/20/