A Magentoelectric Coefficient Measurement System with a Free-Stress Sample Holder

With less extra stress on the testing sample, a free-stress sample holder was designed to place the sample horizontally. With the free-stress sample holder, a magnetoelectric (ME) coefficient measurement system was developed based on dynamic method. This measurement system has the hardware part and the software part, integrated by the DC magnetic field generation module, the AC magnetic field generation module, the induced ME voltage detecting module and PC software module. Then, a sample of Terfenol-D/PZT/Terfenol-D trilayer was designed and fabricated, and the relationships of its ME coefficient influenced by the DC magnetic field and the frequency of the AC magnetic field were tested using the measurement system. And the results showed that the free-stress sample holder was proven to improve the accuracy of the measurement system by less stress interference.


Introduction
In magnetoelectric (ME) composites, electric field can control its magnetic properties and magnetic field can control its electric properties. In recent years, the potential application of the ME composites with the considerable ME coefficient at room temperature has attracted wide attention in the memorizers [1] [2], sensors [3] [4] and the MEMS devices [5] [6]. To improve the performance of the ME composite in their applications, the ME coefficient has to be discussed very often.
In the ME composite, the ME effect arises from the magnetostrictive and piezoelectric constituents via interfacial strain [7]. When magnetic field is applied on the ME composite, the stress or strain, generated in the magnetostrictive part, passes to the piezoelectric part, in which the induced voltage is generated and detected, and vice versa. Therefore, the ME coefficients is defined by E dE d d dH dE dH α σ σ = × = , E, H and σ are the electric field, the magnetic field and the stress, respectively [8]. The stresses, generated in the magnetostrictive constituents or in the piezoelectric constituents or passed through the interfaces of the two constituents, influence the ME coefficient seriously. Especially, when the ME coefficient is being tested by the ME coefficient measurement system, any extra stress, not from the ME effect, will affect the testing results. It is always the significant problem to design a preferable ME coefficient measurement system for the experimenters.

Theory
The ME coefficient measurement has two methods, static method [9] and dynamic method [10], in which the latter one is more popular nowadays. The static method uses a DC magnetic field and detects the induced ME voltage, every data of which needs almost half an hour to get the stable data [9]. In the dynamic method, a DC magnetic field and an AC magnetic field are superimposed to get an output ME voltage, which is an AC voltage with the same frequency of the  (2), where, d is the thickness of the piezoelectric layer.
Considering the extra stress σ ext , Equation (2) should be where, out V is the measurement value of the induced voltage, the item of out V ′ is caused by the applied magnetic field and The item of x g σ ∆ is caused by the extra stress. So E α ′ is the true ME coefficient of the ME effect and σ α is the error from the clamping ways of the sample holder. Here, in order to decrease the extra stress σ ext from the clamping ways, a free-stress sample holder is designed to makes the ME coefficient measurement system as accurate as possible.

Measurement System Design
Based on the dynamic method of ME coefficients, the measurement system is equipped with DC magnetic field generation module, AC magnetic field generation module, the induced ME voltage detecting module, a sample holder and PC software module, shown in Figure 1(a). In the system, the components and their connections are shown in Figure 1(b). PC software can give the instructions to control the output of DC and AC magnetic fields and their signal feedback, process the induced ME voltage signal, calculate and export the ME coefficient data.

DC Magnetic Field Generation Module
In    Oe alternating magnetic field is achieved when the current is 1 A. In Figure   3(b), at the different frequencies the values of the AC magnetic field is about 1

AC Magnetic Field Generation Module
Oe with the current 1 A.

The Induced ME Voltage Detecting Module
As the sample size becomes smaller, the fundamental resonance frequency of the sample will increase, that is sometimes over a testing frequency range of one detected device. Here, Lock-in amplifier SR850, with the frequency range of 0.01 -100 kHz, and FLUKE8846A multi-meter, with the frequency range of 3 -300 kHz, are used to detect the induced ME voltage together, because the resonance frequency of our sample is over 100 kHz. When testing the small voltage output

The Sample Holder
In the ME coefficient measurement systems, the sample holder always applied a force on the sample vertically [17] or horizontally [19], as shown in Figure 5(a) and Figure 5(b). Either manually or automatically install the sample, it is difficult to keep the extra force constant, which is a source of error about the testing results. In this paper, without extra force on the sample is a way to decrease the influence of the sample holder and the testing error, as in Figure 5(c).
In order to decrease the extra stress from the sample holder clamping, a sample holder is shown in Figure 5, by which little stress is applied on the sample. It   Figure   6(d) is fit for a PCB board in Figure 6(c). The PCB is embedded in the recess so that a pair of pin header on PCB happens to match a female header on the top of grooving in Figure 6(b). The electrodes of the sample connected to circuit outputs the voltage signal of the piezoelectric layer. The chassis is fixed and the pallet is rotatable with angle scale engraved on the center pillar. By rotating the stage in a horizontal plane angle, the ME coefficient can be tested in the different directions.

PC Software Module
The main working flow chart of PC software is shown in Figure 7. PC software can calculate the ME coefficient data and display them by a graphical form in real time, and then export them by Excel or Txt formats. Two different line chart panels are designed to display the α-H dc relationship and the α-f ac relationship.
Finally, in the measurement system, all of the instruments are equipped with RS232 interface and PC software controls each device via USB hub.

Test Results
The ME coefficient of a trilayer composite sample Terfenol-D/PZT/Terfenol-D,  with the size of 7.6 × 5.7 × 0.9 mm 3 of Terfenol-D and 7.6 × 5.7 × 1.0 mm 3 of PZT was tested five times with each clamping ways by the ME coefficient measurement system. By three holding ways, clamping vertically (Figure 8(a)), clamping horizontally (Figure 8(b)) and free-stress holding (Figure 8(c)), Figure 8 shows the relationships between the ME coefficient and the DC magnetic field at the AC magnetic field of 1 kHz. When H dc is small, the ME coefficient changes rapidly with the DC magnetic field increasing, reaches the maximum ME coefficient near the DC magnetic field of 1100 Oe, and then decreases slowly. These experimental results have the same trend with the theoretical and the experimental results in literatures [11]. This phenomenon is due to the dynamic magnetostriction coefficient of magnetostrictive material Terfenol-D changed by the DC magnetic field H dc . Compared the tree clamping ways in Table 1, the averages of the maximum ME coefficients are similar, different within 0.8%. It is believed that the results are effective under the three clamping ways. The averages under the free-stress holding are slightly smaller, because the extra stress from the first two clamping ways is mostly compressive stress. In the equation (3), substitute the material parameters of Terfenol-D and PZT, the coefficient g x is a positive term on the testing direction, so the testing results under the first two clamping ways is some larger than by the free-stress holding way. The standard deviation of the free-stress holding is smallest under the three clamping ways. Because the uncertainty of the extra stress caused by the clamping ways will add a new error sauce of the ME coefficient testing results, the dispersion of the results increases, in other words, the accuracy of the results is reduced. Therefore, the free-stress holder improved the accuracy of the testing results of the measurement system.   Figure 9. The ME coefficient vs. the frequency of AC magnetic field at DC magnetic field of 600 Oe, (a) clamping vertically, (b) clamping horizontally and (c) free-stress holding.  Table 2. The extra stresses under the clamping ways increase the error sauce and increase the dispersion of the testing results, which results in reducing the accuracy of the results using the measurement system.

Conclusion
In this paper, a ME coefficient measurement system was designed with a freestress sample holder. Compared with the other clamping ways, the free-stress sample holder reduced the extra stress from the clamping ways, resulting in improving the accuracy of the testing result of the measurement system. Finally, a ME coefficient measurement system was designed including the five modules, DC magnetic field generation module, AC magnetic field generation module, the induced ME voltage detecting module, a sample holder and PC software module, and the performance of the system were as follows: bias magnetic field range is 0 -4000 Oe; AC magnetic field amplitude is 1 Oe and the frequency is 0.01 -300 kHz; the ME coefficient's accuracy is 0.01 mV/cm·Oe by lock-in amplifier and 0.05 mV/cm·Oe by the multi-meter.