A Charge-Based Magneto-Electric Test Procedure

1. A Charge-Based Magneto-Electric Test Procedure Scott P. Chapman & Joseph T. Evans, Jr. Radiant Technologies, Inc. Aug 9, 2011 IWPMA 2011

2. 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 = aH B = mH P = a/mB For a multiferroic, H induces P directly. For our piezoelectric sample, P results from direct force (dc) or torque (dt) applied to the sample ferroelectric with a magnet attached.

3. 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. Experiment Experiment – Stimulate sample with magnetic field and measure charge. Simple. Characterize sample independently, calculate B Field and predict charge. Hard. Compare the two.

5. 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.

6. Magnetic Force 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, m, 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.

7. Geometry (Along Field Axis) Bsingle coil = m0NIR2 x 0.5(R2+x2)-3/2 (1) BHHC = 0.5 m0NIR2 x 1/(R2+(x+K/2)2)3/2 + 0.5 m0NIR2 x 1/(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) x = Location of interest measured from midway between the coils (m) B = 0.716 m0NI/R (3) For: K = R and x = 0 (Centered Between Coils)

8. Basic Test ConfigurationOrientation 1 – Centered – m || B

9. Basic Test ConfigurationOrientation 2 – Centered – m^ B

10. Basic Test ConfigurationOrientation 3 – x = 1.5 R – m^ B

11. Plot Measured Charge Vs Field Arbitrary Data P H P is Accurately Measured but H may be inferred

12. Independent Field Values • The independent (Field) axis in the data presentation can be determined by: • AssumedFieldby DRIVE Volts into the Current Amplifier. This experiment presented here uses this approach. • AssumedFieldby Measured Current into the Helmholtz Coil. This reduces the number of error sources in the first option by half. • Measured Field by magnetic sensor. Most accurate.

13. Some Field Profiles

14. Improved Test Configuration - Measure HH Coil Input Current

15. Improved Test Configuration - Direct Field Measurement at Sample

16. Advanced Test Configuration - Introduce a DC Bias Field

17. Program Entry Parameters

18. Measurement Configuration

19. Data Presentation Configuration

20. Direct Force (dc) Measurement

21. Direct Force (dc) Response

22. Torque (dt) Measurement

23. Torque (dt) Response

24. Measured Piezo Constants • The constants we measured: Numbers are high (~10 x) due to substrate bending. • Parallel to the magnetic axis (dc): • 612 pC/N (10 g = 0.098 N) • 688 pC/N (20 g = 0.196 N) • 653 pC/N (50 g = 0.49 N) • 650 ±40 pC/N (Average)

25. Measured Piezo Constants Torque (dt): 765 pC/N When applying magnetic torque, the force must be calculated from the lever arm length and then multiplied by the equivalent torque piezoelectric constant

26. Primary Measurement 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 limiting the length of the test. 1000.0 ms is optimal and well within equipment capabilities. Significantly limits inductive charge.

27. 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.

28. Pre-Measurement Steps Reduce the test speed to reduce inductive current, but no slower than 1000.0 ms. Determine through experimentation the maximum frequency and ensure 1000/Test Period (ms) does not exceed this value.

29. 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 = Ñ[m ·B] (1) For constant m, as with our reference sample magnets: F = mdB/ dx (2) For constant B, as in the center of the Helmholtz coil: F = 0 => DQ = 0 pC

30. Predictive Modelm ^B - Centered in HH Coil Piezo Constant: dt = 0.75 V x 100 pC/10g (Sense Capacitor) = 75 pC/0.098 N = 765 pC/N Ftorque (t): m = 4 x 1.08 T/4p x10-7 x (0.00252px 0.006) = 0.4 A/m Estimated Charge (DQ) at 45.0 Gauss: DQ = dt 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

31. Predictive Model m ||B - At 1 K From Closest Coil • x = 1.5 K = 1.5 R • ÑB = -0.319 m0NI/R2 • DQ = dc x 0.4 A/m x ÑB • = 650 pC/N x 0.4 A/m x-0.093I T/m • At 45 Gauss, I = 1.68 Amps • DQ = 650 pC/N x 0.4 A/m x-0.093 x 1.68 A T/m • = -4.06 pC

32. Predictive Modelm ^B - At 1 K From Closest Coil At x = 0: B = 0.716 m0NI/R => m0NI/R = B/0.716 = 45.0/0.716 = 62.85 G At x = 1.5 K = 1.5 R: BHHC = 0.5 m0NIR2/(R2+(x+K/2)2)3/2+ 0.5 m0NIR2/(R2+(x-K/2)2) 3/2 G = 0.5 m0NIR2/(R2+(1.5R + R/2)2)3/2+ 0.5 m0NIR2/(R2+(1.5R-K/2)2)3/2 = 0.1727 m0NI/R G = 10.855 G DQ = dt 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

33. Experiment

34. Measured Data - Centered || B Measured: 1 pC Inductive: 1 pC Corrected: 2 pC Signal Smaller than Noise

35. Measured Data - Centered ^ B Measured: 100 pC Inductive: -1 pC Corrected: 101 pC

36. Measured Data - x = 1.5 R || B Measured: -0.75 pC Inductive: -1.5 pC Corrected: 0.5 pC Signal Smaller than Noise

37. Measured Data - x = 1.5 R ^ B Measured: 30 pC Inductive: -2 pC Corrected: 32 pC

38. Summarize Results @ 45 G

39. Possible 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.

40. Possible Error Sources Manual dc and dt measurements. Primary Unstable measurement surface. Unfixed sample subject to bending an shear. Primary

41. 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 30 pC of response. • The sample response differed from our predictions most likely due to several possible error sources in the test fixture and piezo constants. • To properly utilize the MT Task and achieve accurate results, these error sources must be mitigated.