Name: characterization of full set material constants and their temperature dependence for piezoelectric materials using resonant ultrasound spectroscopy
Uploaded: 2016-04-27T13:00:00
Description: Watch this Scientific Journal Video about Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy at JoVE.co

This work was supported by the National Natural Science Foundation of China (Grant No. 11374245), the NIH under Grant No. P41-EB2182, the Natural Science Foundation of Fujian Province, China (Grant No. 2013J01163), and the Open Research Fund of the State Key Laboratory of Acoustics, Chinese Academy of Science (Grant No. SKLA201306).

1. Sample Preparation
Note: PZT-4 ceramic samples of the desired size can be directly ordered from many PZT ceramic manufacturers. One may also cut the sample from a larger PZT ceramic block using a diamond cutting machine, then repole the sample to restore depoling caused by cutting and polishing. Here, the sample shape is a parallelepiped with each dimension between 3 mm and 10 mm. Larger size samples are not necessary but accuracy might be compromised if samples are too small.
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The RUS technique described here can measure the full set material constants using only one sample, which eliminates errors caused by property variation from sample to sample so that self-consistency can be guaranteed. The method can be used for any solid material with a high quality factor Q, no matter if they are piezoelectric or not. All other standard characterization techniques require several samples to get the full set data and are difficult to achieve self-consistent data.
It is import...

Lead zirconate titanate (PZT) piezoelectric ceramics, (1-x)PbZrO3-xPbTiO3, and its derivatives have been widely used in ultrasonic transducers, sensors and actuators since the 1950s1. Many of these electromechanical devices are used at high temperature ranges, such as for space vehicles and underground well logging. Moreover, high power devices, such as therapeutic ultrasonic transducers, piezoelectric transformers and sonar projectors, often heat-up during operation. Such temperature rises will change the resonance frequencies and the focal point of transducers, causing severe performance degradation. High intensity focused ultrasound (HIFU) technology, already used in clinical practice for the treatment of tumors, uses ultrasonic transducers made of PZT ceramics. During operation, the temperature of these transducers will increase, causing a change of the material constants of the PZT resonator, which in turn will change the HIFU focal point as well as the output power2,3. The shift of focal point may lead to serious unwanted results, i.e., healthy tissues being destroyed instead of cancer tissues. On the other hand, if the focal point shift can be predicted, one could use electronic designs to correct such shift. Therefore, measuring the temperature dependence of the full set material properties of piezoelectric materials is very important for the design and evaluation of many electromechanical devices, particularly high power devices.
Poled ferroelectric materials are the best piezoelectric materials known today. In fact, nearly all piezoelectric materials currently in use are ferroelectric materials, including solid solution PZT ceramics and (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-PT) single crystals. The IEEE (Institute of Electrical and Electronics Engineers) impedance resonance method requires 5-7 samples with drastically different geometries in order to characterize the full set material constants4. It is nearly impossible to obtain self-consistent full set matrix data using the IEEE impedance resonance method for ferroelectric materials because the degree of poling depends on the sample geometry (boundary conditions), while sample properties depend on the level of poling. To avoid problems caused by sample to sample variations, all constants should be measured from one sample. Li et al. reported the successful measurement of all constants from one sample at room temperature by using a combination of pulse-echo ultrasound and inverse impedance spectroscopy5. Unfortunately, this technique is hard to perform at elevated temperatures because it is not possible to perform ultrasonic measurements directly inside the furnace. There are also no commercially available shear transducers that can work at high temperatures. In addition, the coupling grease that bound the transducer and the sample cannot work at high temperatures.
In principle, the RUS technique has the capability to determine the full set material constants of piezoelectric materials and their temperature dependence using only one sample6,7. But there are several critical steps for proper implementation of the RUS technique. First, the full set of tensor properties at room temperature should be accurately determined using a combination of pulse-echo and RUS techniques. Second, this room temperature data set can be used to predict the resonance frequencies and to match the measured ones in order to identify the corresponding modes. Third, for each small increment of temperature from room temperature up, one needs to perform spectrum reconstruction against the measured resonance spectrum in order to retrieve the full set constants at this new temperature from the measured resonance spectrum. Then, using the new data set as the new starting point, we can increase the temperature by another small temperature step to get the full set constants at the next temperature. Continuing this process will allow us to obtain the temperature dependence of the full set material constants.
Here, a PZT-4 piezoceramic sample is used to illustrate the measurement procedure of the RUS technique. The poled PZT-4 ceramic has &#8734;m symmetry with 10 independent material constants: 5 elastic constants, 3 piezoelectric constants and 2 dielectric constants. Because the dielectric constants are insensitive to the change of resonance frequencies, they were measured separately using the same sample. The temperature dependence of clamped dielectric constants <img alt="Equation 3" src="/files/ftp_upload/53461/image003.jpg" /> and <img alt="Equation 4" src="/files/ftp_upload/53461/image004.jpg" /> were measured directly from the capacitance measurements, while the free dielectric constants &#160;<img alt="Equation 5" src="/files/ftp_upload/53461/image005.jpg" /> and&#160;<img alt="Equation 2" src="/files/ftp_upload/53461/image002.jpg" /> measured at the same time were used as data consistency checks. The temperature dependence of elastic stiffness constants at a constant electric field <img alt="Equation 6" src="/files/ftp_upload/53461/image006.jpg" />, <img alt="Equation 7" src="/files/ftp_upload/53461/image007.jpg" />, <img alt="Equation 8" src="/files/ftp_upload/53461/image008.jpg" />, <img alt="Equation 9" src="/files/ftp_upload/53461/image009.jpg" /> and <img alt="Equation 10" src="/files/ftp_upload/53461/image010.jpg" />, and piezoelectric stress constants e15,&#160;e31 and e33 were determined by the RUS technique using the same sample.

<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>PZT-4</td>
			<td>TRS</td>
			<td></td>
		</tr>
		<tr>
			<td>paraffin</td>
			<td>MTI Corporation</td>
			<td>8002-74-2</td>
		</tr>
		<tr>
			<td>conductive silver paint</td>
			<td>MG Chemicals</td>
			<td>842-20G</td>
		</tr>
		<tr>
			<td>Al2O3 Powder</td>
			<td>MTI Corporation</td>
			<td></td>
		</tr>
		<tr>
			<td>coupling grease</td>
			<td>Panametrics</td>
			<td></td>
		</tr>
	</tbody>
</table>

characterization of full set material constants and their temperature dependence for piezoelectric materials using resonant ultrasound spectroscopy

During the operation of high power electromechanical devices, a temperature rise is unavoidable due to mechanical and electrical losses, causing the degradation of device performance. In order to evaluate such degradations using computer simulations, full matrix material properties at elevated temperatures are needed as inputs. It is extremely difficult to measure such data for ferroelectric materials due to their strong anisotropic nature and property variation among samples of different geometries. Because the degree of depolarization is boundary condition dependent, data obtained by the IEEE (Institute of Electrical and Electronics Engineers) impedance resonance technique, which requires several samples with drastically different geometries, usually lack self-consistency. The resonant ultrasound spectroscopy (RUS) technique allows the full set material constants to be measured using only one sample, which can eliminate errors caused by sample to sample variation. A detailed RUS procedure is demonstrated here using a lead zirconate titanate (PZT-4) piezoceramic sample. In the example, the complete set of material constants was measured from room temperature to 120 &#176;C. Measured free dielectric constants <img alt="Equation 1" src="/files/ftp_upload/53461/image001.jpg" /> and&#160;<img alt="Equation 2" src="/files/ftp_upload/53461/image002.jpg" /> were compared with calculated ones based on the measured full set data, and piezoelectric constants d15 and d33 were also calculated using different formulas. Excellent agreement was found in the entire range of temperatures, which confirmed the self-consistency of the data set obtained by the RUS.

The LM algorism used in the inversion is a local minimum finder. Therefore, the initial values of elastic stiffness constants <img alt="Equation 6" src="/files/ftp_upload/53461/image006.jpg" />, <img alt="Equation 7" src="/files/ftp_upload/53461/image007.jpg" />, <img alt="Equation 8" src="/files/ftp_upload/53461/image008.jpg" />, <img alt="Equation 9" src="/files/ftp_upload/53461/image009.jpg" />, and <img alt="Equation 10" src="/files/ftp_upload/53461/image010.jpg" />,&#160; and piezoel...

Watch this Scientific Journal Video about Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy at JoVE.co

Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy

This protocol describes the procedure of measuring the temperature dependence of the full set material constants of piezoelectric materials using resonant ultrasound spectroscopy (RUS).

During the operation of high power electromechanical devices, a temperature rise is unavoidable due to mechanical and electrical losses, causing the ...

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