Magneto-Electric Test Procedure A Charge-Based Magneto- Electric Test Procedure Scott P. Chapman &...

Radiant Technologies, Inc.Magneto-Electric Test Procedure

A Charge-Based Magneto-Electric Test Procedure

Scott P. Chapman & Joseph T. Evans, Jr.

Radiant Technologies, Inc.

Aug 9, 2011

IWPMA 2011


Summary

The goal is to describe an experiment to characterize the charge response of a piezoelectric or multiferroic sample in the presence of a magnetic (B) field by:

P = H

B = H

P = /B

For a multiferroic, H induces P directly. For our piezoelectric sample, P results from direct force (dc) or torque (d) applied to the sample ferroelectric.


SummaryI will present:

• Mathematics and theory relating predictive and measured polarization response to the magnetic field and magnetic field geometry.

• Experimental considerations.• Experimental design and configuration.• Measured results.• Measured comparison to predictive.


Magnetic ForceThese three statements apply to understanding Magnetic Force:

• Magnetic force is generated only by moving electric charges.

• For two objects to exert magnetic force both must contain moving charges.

• Magnetic force calculation proceeds as follows:

• Calculate a mathematical field, H, that sums the motion of all charge particles at the point of interest in the field.

• Multiply H by the magnetic permeability factor, , to convert it to a force field, B.

• Use B to calculate magnetic force on the target. This requires the calculation of both the HH coil force and the target force, and their multiplication.


Geometry

Bsingle coil = 0NIR2 x 0.5(R2+x2)-3/2 (1)

BHHC = 0.5 0NIR2 / [(R2+(x+K/2)2)3/2+[(R2+(x-K/2)2) 3/2] (2)

N = Number of Coils R = Coil Radius (m)I = Current Through Loop (Amps) K = Coil Separation (m)

B = 0.716 0NI/R (3)

For: K = R and x = 0 (Centered Between Coils)


Basic Test Configuration - Orientation 1


Plot Measured Charge Vs Field

H

P

P is Measured but H may be inferred

Arbitrary Data


Independent Field Values

The independent (Field) axis in the data presentation can be determined by:

• Assumed Field by DRIVE Volts into the Current Amplifier. This experiment presented here uses this approach.

• Assumed Field by Measured Current into the Helmholtz Coil. This reduces the number of error sources in the first option by half.

• Field Measured Field by magnetic sensor. Most accurate.


Some Field Profiles


Improved Test Configuration - Measure HH Coil Input Current


Improved Test Configuration - Direct Field Measurement at Sample


Advanced Test Configuration - Introduce a DC Bias Field


Program Entry Parameters


Measurement Configuration


Data Presentation Configuration


Direct Force (dc) Measurement


Direct Force (dc) Response


Torque (d) Measurement


Torque (d) Response


Measured Piezo ConstantsThe constants we measured:

• Parallel to the magnetic axis:

* 61.2 pC/N (10 g = 0.98 N)

* 71.4 pC/N (20 g = 1.96 N)

* 71.4 pC/N (50 g = 4.9 N)

* 68.0 pC/N (Average)

• Torque: 765.0 pC/N

When applying magnetic torque, the force must be calculated from the lever arm length and then multiplied by the equivalent torque piezo constant


Primary Error Sources

There are three primary sources of error:

• Frequency response of the current amplifier with the attached HH coil. Slow the measurement to ensure the amplifier can provide the requested HH coil input power.

• Parasitic charge resulting from magnetic induction in the RETURN cable. This effect is reduced by slowing the measurement. Measure the effect and subtract from the final measurement.

• Charge measurement accuracy reduced by charge deterioration over long tests. This effect is reduced by speeding the test.


Pre-Measurement Steps

To prepare for the Magneto-Electric Response Task measurement, perform these steps:

• Calculate the magnetic field at the point where the sample is located.

• Measure the induced current in the cable, under measurement test conditions, and retain to subtract from the measured data.

• Reduce the test speed to reduce inductive current, but no slower than 1000.0 ms.

• Determine through experimentation the maximum frequency and ensure 1/Test Period does not exceed this value.


Predictive Modelm || B - Centered in HH Coil

Define, for our force inducing magnet:

m = MV

M = Magnetization of Magnet V = Volume

For B || m

F = [m B] (1)

For constant m, as with our magnets:

F = m B/ x (2)

For constant B, as in the center of the Helmholtz coil:

F = 0 => Q = 0


Predictive Modelm B - Centered in HH Coil

Piezo Constant:

d = 0.75 V x 100 pC/10g (Sense Capacitor) =

75 pC/0.098 N = 765 pC/N

Ftorque ():

m = 4 x 1.08 T/4x10-7 x (0.00252 x 0.006) = 0.4 A/m

Estimated Charge (Q) at 45.0 Gauss:

Q = d x 0.4 A/m x B / Height

= 765 pC/N x 0.4 A/m x 45 e-4 T / 0.006 m

= 229.5 pC


Predictive Model m || B - At 1 K From Closest Coil

x = 1.5 K = 1.5 R

B = -0.319 0NI/R2

Q = dc x 0.4 A/m x B = d33 x 0.037 x I

What is d33, is 0.037 the Amps/Gauss and How do I use this to predict Q?


Predictive Modelm B - At 1 K From Closest Coil

At x = 0:

B = 0.716 0NI/R

=> 0NI/R = B/0.716 = 45.0/0.716 = 62.85 G

At x = 1.5 K = 1.5 R:

BHHC = 0.5 0NIR2/(R2+(x+K/2)2)3/2+ 0.5 0NIR2/(R2+(x-K/2)2) 3/2 G

= 0.5 0NIR2/(R2+(1.5R + R/2)2)3/2+ 0.5 0NIR2/(R2+(1.5R-K/2)2)3/2

= 0.1727 0NI/R G = 10.855 G

Q = d x 0.4 A/m x B / Height

= 765 pC/N x 0.4 A/m x 10.855 e-4 T / 0.006 m

= 55.36 pC/m3


Experiment


Measured Data - Centered || BAverag ed C harg e

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

-60 -40 -20 0 20 40 60

Averag ed Induc tive C urrent

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

-60 -40 -20 0 20 40 60

C orrec ted C harg e

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

-60 -40 -20 0 20 40 60


Measured Data - Centered B


-0.00015

-0.0001

-0.00005

0

0.00005

0.0001

0.00015

-60 -40 -20 0 20 40 60


-0.00015

-0.0001

-0.00005

0

0.00005

0.0001

0.00015

-60 -40 -20 0 20 40 60

Averag ed C harg e

-0.00015

-0.0001

-0.00005

0

0.00005

0.0001

0.00015

-60 -40 -20 0 20 40 60


Measured Data - x = R || BAverag ed C harg e

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

-60 -40 -20 0 20 40 60


-0.03

-0.02

-0.01

0

0.01

0.02

0.03

-60 -40 -20 0 20 40 60


-0.03

-0.02

-0.01

0

0.01

0.02

0.03

-60 -40 -20 0 20 40 60


Measured Data - x = R BAverag ed C harg e

-0.00004

-0.00003

-0.00002

-0.00001

0

0.00001

0.00002

0.00003

0.00004

-60 -40 -20 0 20 40 60


-0.00004

-0.00003

-0.00002

-0.00001

0

0.00001

0.00002

0.00003

0.00004

-60 -40 -20 0 20 40 60


-0.00004

-0.00003

-0.00002

-0.00001

0

0.00001

0.00002

0.00003

0.00004

-60 -40 -20 0 20 40 60


Summarize ResultsExperiment Predicted

ResultsMeasuredResults


Error Sources• Amps/DRIVE Volts conversion for the KEPCO 36-6M

current amplifier. -1.75 Volts/Amp used. Expected current = 45.0 G X 0.0373 Amps/Gauss = 1.68 Amps. Post-data measurement showed 1.799 Amps. Generated 48.15 G.

• Current/Gauss conversion for the Lakeshore MH-6 Helmholtz coil. Used the Lakeshore published conversion of 26.76 G/A => 0.0373 A/G. Did not measure the actual ratio.

• Manual dc and d measurements.

• Unstable measurement surface.

• Unfixed sample subject to bending an shear.

• Joe, please add.


Conclusion

• Radiant successfully tested the magneto-electric response of a piezoelectric force sensor coupled to a magnet using Radiant’s Magnetoelectric Response Task

• The system was able to cleanly capture the measurements that generated 100 pC of Response

• The sample response differed from our predictions but there were several possible error sources in the test fixture and predictive models.

Magneto-Electric Test Procedure A Charge-Based Magneto- Electric Test Procedure Scott P. Chapman &...

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