1. 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

2. Magneto-Electric Test Procedure 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 (d c ) or torque (d  ) applied to the sample ferroelectric.

3. Magneto-Electric Test Procedure Summary I 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.

4. Magneto-Electric Test Procedure Magnetic Force These 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.

5. Magneto-Electric Test Procedure Geometry B single coil =  0 NIR 2 x 0.5(R 2 +x 2 ) -3/2 (1) B HHC = 0.5  0 NIR 2 / [(R 2 +(x+K/2) 2 ) 3/2 +[(R 2 +(x-K/2) 2 ) 3/2 ] (2) N = Number of CoilsR = Coil Radius (m) I = Current Through Loop (Amps)K = Coil Separation (m) B = 0.716  0 NI/R (3) For: K = R and x = 0 (Centered Between Coils)

6. Magneto-Electric Test Procedure Basic Test Configuration - Orientation 1

7. Magneto-Electric Test Procedure Basic Test Configuration - Orientation 2

8. Magneto-Electric Test Procedure Basic Test Configuration - Orientation 3

9. Magneto-Electric Test Procedure Plot Measured Charge Vs Field H P P is Measured but H may be inferred Arbitrary Data

10. Magneto-Electric Test Procedure 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.

11. Magneto-Electric Test Procedure Some Field Profiles

12. Magneto-Electric Test Procedure Improved Test Configuration - Measure HH Coil Input Current

13. Magneto-Electric Test Procedure Improved Test Configuration - Direct Field Measurement at Sample

14. Magneto-Electric Test Procedure Advanced Test Configuration - Introduce a DC Bias Field

15. Magneto-Electric Test Procedure Program Entry Parameters

16. Magneto-Electric Test Procedure Measurement Configuration

17. Magneto-Electric Test Procedure Data Presentation Configuration

18. Magneto-Electric Test Procedure Direct Force (d c ) Measurement

19. Magneto-Electric Test Procedure Direct Force (d c ) Response

20. Magneto-Electric Test Procedure Torque (d  ) Measurement

21. Magneto-Electric Test Procedure Torque (d  ) Response

22. Magneto-Electric Test Procedure Measured Piezo Constants The 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

23. Magneto-Electric Test Procedure 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.

24. Magneto-Electric Test Procedure 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.

25. Magneto-Electric Test Procedure Predictive Model m || B - Centered in HH Coil Define, for our force inducing magnet: m = MV M = Magnetization of MagnetV = 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

26. Magneto-Electric Test Procedure Predictive Model m  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 F torque (  ): m = 4 x 1.08 T/4  x10 -7 x (0.0025 2  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

27. Magneto-Electric Test Procedure Predictive Model m || B - At 1 K From Closest Coil x = 1.5 K = 1.5 R  B = -0.319  0 NI/R 2  Q = d c x 0.4 A/m x  B = d 33 x 0.037 x I What is d 33, is 0.037 the Amps/Gauss and How do I use this to predict  Q?

28. Magneto-Electric Test Procedure Predictive Model m  B - At 1 K From Closest Coil At x = 0: B = 0.716  0 NI/R =>  0 NI/R = B/0.716 = 45.0/0.716 = 62.85 G At x = 1.5 K = 1.5 R: B HHC = 0.5  0 NIR 2 /(R 2 +(x+K/2) 2 ) 3/2 + 0.5  0 NIR 2/ (R 2 +(x-K/2) 2 ) 3/2 G = 0.5  0 NIR 2 /(R 2 +(1.5R + R/2) 2 ) 3/2 + 0.5  0 NIR 2/ (R 2 +(1.5R-K/2) 2 ) 3/2 = 0.1727  0 NI/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/m 3

29. Magneto-Electric Test Procedure Experiment

30. Magneto-Electric Test Procedure Measured Data - Centered || B

31. Magneto-Electric Test Procedure Measured Data - Centered  B

32. Magneto-Electric Test Procedure Measured Data - x = R || B

33. Magneto-Electric Test Procedure Measured Data - x = R  B

34. Magneto-Electric Test Procedure Summarize Results

35. Magneto-Electric Test Procedure 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 d c and d  measurements. Unstable measurement surface. Unfixed sample subject to bending an shear. Joe, please add.

36. Magneto-Electric Test Procedure 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.