AC Measurement of Magnetic Susceptibility. Part 2.

Physics 401, Spring 2018

Eugene V. Colla

Outline

• What and how we measuring (week1)

• Magnetic looses

• Temperature dependencies of permeability

• End of semester

4/16/2018 2

Magnetic materials.

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0B H M

Magnetic field

Permeability

of free space

Magnetic inductionMagnetization

M H

– magnetic susceptibility

Magnetic materials.

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0B H M M H

In general is a function of H and T

( , )M H T H ( , )T

MH T

H

Magnetic materials.

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0 0 01 ;

1

r

r

B H H H H

< 0 - diamagnetics, r < 1

> 0 - paramagnetics r > 1

>> 0 - ferromagnetics r >> 1

Magnetic materials. Diamagnetism.

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< 0 - diamagneticsMaterial χv (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 −105

Water −0.91

Levitation of the pyrolytic carbon

Courtesy of WikipediaIdeal diamagnetic = -1

M~Ms

M=0

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Magnetic materials. Ferromagnetism.

>> 1 - ferromagnetics

Material r Brem (T)

Fe, 99.8% pure 5000 1.3

Permalloy 100,000 0.7

Superpermalloy 1,000,000 0.7

Co, 99% pure 250 0.5

Ni, 99% pure 600 0.4

Measuring of the permeability. DC field.

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10H = + H sH inωt

H0

B0( )B f H DC part of the setup

𝑯𝟎 =𝑵𝒑𝑰𝑫𝑪

𝟐𝝅𝒓 Here Np – number of turns in DC primary coil

Measuring of the permeability. AC modulation

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10H H s= H + inωt

0 1H = H + H sinωt

H0

B0Bw

( )B f H

𝑩𝝎~𝒅𝒇

𝒅𝑯=𝒅𝑩

𝒅𝑯=0r

Wavetek

reference

𝑯𝟏 =𝑵𝒑𝑰𝑨𝑪

𝟐𝝅𝒓

Here Np – number of turns in AC primary coil

Rac

Primary coil of Np turns supplied by current Ip creates magnetic field H and flux Φ

For toroid: 𝑯 =𝑵𝒑𝑰𝒑

𝟐𝝅𝒓

R2 <r < R1

2

1

2

1

ln

2 2

R

R

RI N t dr I N tH da

r R

da=dr*t

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Measuring of the permeability. AC modulation

Lock-in measures emf on the pickup coil

lock in pickup

dV N

dt

Here IAC is ac current in primary coil L3; 𝑰𝑨𝑪 =𝑽𝟎𝐬𝐢𝐧(𝝎𝒕)

𝑹𝒂𝒄

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Measuring of the permeability. Pickup coil.

0 1= + cosωt

Faraday's law

2

1

2

1

1

ln

2 2

R

AC

ac

R

I N t Rdr I N tH da

r R

2 2

1 1

0 2

0 0

1

ln ln cos( )2 2

cos( ); where ln2

AC AC

lock in pickup pickup

ac

AC

r pickup

ac

dI VR RN t N tV N N t

R dt R R

V N t RL t L N

R R

w

w

w

w

This is per 1 turn of the pickup coil !

1 ac acB da H da

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Measuring of the permeability. Pickup coil.

2 2

1 1

0 2

0 0

1

ln ln cos( )2 2

cos( ); where ln2

AC AC

lock in pickup pickup

ac

AC

r pickup

ac

dI VR RN t N tV N N t

R dt R R

V N t RL t L N

R R

w

w

w

w

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

Hysteresis Loops. Remagnetization loses

𝑾 = 𝑽න𝑯𝒅𝑩 𝑾𝒍𝒐𝒐𝒑 = 𝑽ׯ𝑯𝒅𝑩=V*Loop_area

Energy of the magnetic field

By cycling around the loop

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V here is a volume of the magnetic material

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Calculating of the magnetic induction B

0 01

rB H H H

0 0; ( )

r r

dBB H dH

dH

-200 0 200-0.4

-0.2

0.0

0.2

0.4

B (

T)

H (A/m)

Magnetics ZP44715-TC

After integrating

Hysteresis Loops. Remagnetization loses

𝑾 = 𝑽න𝑯𝒅𝑩𝑾𝒍𝒐𝒐𝒑 = 𝑽ׯ𝑯𝒅𝑩=V*Loop_area

4/16/2018 15

Using Origin Pro for integrating

-200 0 200-0.4

-0.2

0.0

0.2

0.4B

(T

)

H (A/m)

Magnetics ZP44715-TC

Hysteresis Loops. Remagnetization loses

𝑾 = 𝑽න𝑯𝒅𝑩𝑾𝒍𝒐𝒐𝒑 = 𝑽ׯ𝑯𝒅𝑩=V*Loop_area

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Using Origin Pro for integrating

-200 0 200-0.4

-0.2

0.0

0.2

0.4

B (

T)

H (A/m)

Magnetics ZP44715-TC

Hysteresis Loops. Remagnetization loses

𝑾 = 𝑽න𝑯𝒅𝑩𝑾𝒍𝒐𝒐𝒑 = 𝑽ׯ𝑯𝒅𝑩=V*Loop_area

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Using Origin Pro for integrating

-200 0 200-0.4

-0.2

0.0

0.2

0.4

B (

T)

H (A/m)

Magnetics ZP44715-TC

!

Hysteresis Loops. Remagnetization loses

𝑾 = 𝑽න𝑯𝒅𝑩𝑾𝒍𝒐𝒐𝒑 = 𝑽ׯ𝑯𝒅𝑩=V*Loop_area

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Using Origin Pro for integrating

-200 0 200-0.4

-0.2

0.0

0.2

0.4

B (

T)

H (A/m)

Magnetics ZP44715-TC

-200 0 200-20

0

20

40

60

80

Inte

gra

ted Y

3

H (A/M)

Integrate from -0.0364912 to -0.0250877

Hysteresis Loops. Remagnetization loses

𝑾 = 𝑽න𝑯𝒅𝑩𝑾𝒍𝒐𝒐𝒑 = 𝑽ׯ𝑯𝒅𝑩=V*Loop_area

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Using Origin Pro for integrating

3

1

2 1

2 2

( )

( )

( . )

(joule)

:

volume m

field A m

magn indu

Units

V

H

B

V

c

B H J

tion kg s A

m kg s

Power of loses: W/T = W*f, where T is period and f frequency

Temperature dependence of the magnetic permeability.

In this experiment we will measure permeability

as a function of T. IDC will be fixed. The default

option IDC =0.

DMM will measure the emf of T-type

thermocouple.

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Measuring of the temperature. Thermocouple.

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Type Names of Materials T Range

BPlatinum30% Rhodium (+)

Platinum 6% Rhodium (-)

2500 -3100F

1370-1700C

CW5Re Tungsten 5% Rhenium (+)

W26Re Tungsten 26% Rhenium (-)

3000-4200F

1650-2315C

EChromel (+)

Constantan (-)

200-1650F

95-900C

JIron (+)

Constantan (-)

200-1400F

95-760C

KChromel (+)

Alumel (-)

200-2300F

95-1260C

NNicrosil (+)

Nisil (-)

1200-2300F

650-1260C

RPlatinum 13% Rhodium (+)

Platinum (-)

1600-2640F

870-1450C

SPlatinum 10% Rhodium (+)

Platinum (-)

1800-2640F

980-1450C

TCopper (+)

Constantan (-)

-330-660F

-200-350C

Type T (copper-constantan) has thermoemf at 0°C 41.5V/°C;

Measuring of the temperature. Temperature ramp.

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Option 1: manual by changing the voltage applied to the heater

Option 2: by using Omega PID temperature controller

Measuring of the temperature. Software.

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Series resistor in AC loop (fixed)

AC frequency (1-10kHz)

DMM resolution: Optimal=100nV

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Temperature dependence of the magnetic permeability.

Ferroxcube 3E8

300 350 400 450

0

50

100

150

200

250

cooling

' (a

.u.)

T(K)

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Temperature dependence of the magnetic permeability.

300 320 340 360 380 400 420

0

100

200

300

T (K)

heating

cooling

'

(a.u

.)

376 378 380 382 384 386 388 390

0

100

T (K)

heating

cooling

'

(a.u

.)

T

Ferroxcube 4A20

Hysteresis. Where it is coming from?

?

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Temperature dependence of the magnetic permeability.

300 320 340 360 380 400 420

0

100

200

300

T (K)

heating

cooling

'

(a.u

.)

? 0

( ) ( )r

dBT T T

dH

Slope#1 ~0.728Slope#2 ~0.546

-2 -1 0 1 2

-2

-1

0

1

2

B (

a.u

.)

0.00 0.05 0.10 0.150.0

0.5

1.0

B(a

.u.)

H(a.u.)

#1

#2

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Temperature dependence of the magnetic permeability. Curie-Weiss law.

Pierre Curie5.15.1859-4.19.1906

Pierre Ernest Weiss3.25.1865-10.24.1940

'c

C

T T

Curie-Weiss law

Temperature dependence of the magnetic permeability (week 3)

-0.4 -0.2 0.0 0.2 0.4

-0.4

0.0

0.4 20C

57C

80C

100C

~130C (T>Tc)

B (

a.u

.)

IH (A)

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Ferroxcube 3E8

References

• Information about magnetic materials can be found in :

\\Phyaplportal\PHYCS401\Experiments\AC_Magnetization\Mag

netic Materials

• SR830 manual ibid

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End of semester schedule

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• No Lectures on Aril 23rd and April 30th

• 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 9th Wednesday 11.59pm. Final deadline for

submitting of the final and resubmitted reports. No

extension and no late vouchers!