ac measurement of magnetic susceptibility · 2018. 4. 16. · carbon (diamond) −2.1 carbon...
TRANSCRIPT
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
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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
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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!