Ultrahigh‐Temperature Piezoelectric Crystal YbBa3(PO4)3 for Vibration Sensing Application

High‐temperature vibration sensors are of great importance for accurate monitoring of dynamic mechanical conditions in automotive, aerospace and energy‐generation‐related systems. Currently, piezoelectric crystals with ultrahigh operational temperature and good piezoelectric performance for high‐temperature sensing applications are attracting considerable attention. Herein, a novel piezoelectric crystal YbBa3(PO4)3 with cubic symmetry and a high melting point of ≈1850 °C is explored, and grown by using the Czochralski method. The temperature‐dependent behaviors of electro‐elastic constants and electrical resistivity are investigated ranging from 25 to 800 °C, where the dielectric loss of the YbBa3(PO4)3 crystal is found to be ≈15% at 800 °C. In addition, an optimal crystal cut with a pure thickness shear vibration mode is designed. The optimal crystal cut presents a good piezoelectric activity ( d26∗$d_{26}^ * $ = 12.6 pC N−1) as well as good temperature stability. Furthermore, a high‐temperature accelerometer with shear piezoelectric mode is designed and fabricated using the YbBa3(PO4)3 crystal, and the sensing performance at elevated temperature are evaluated. The average sensitivity is found to be 1.16 pC g−1, with a small temperature deviation (≈7.7%), exhibiting a good temperature stability. All these results indicate that YbBa3(PO4)3 piezoelectric crystal is a promising candidate for high‐temperature piezoelectric sensing applications.


Introduction
Structure health monitoring is very important for many industrial applications, e.g. in engines, automotive combustion DOI: 10.1002/adsr.202200090[3][4] With the growing demands for structure health monitoring, there is a pressing need on piezoelectric sensors with comprehensive performances for in situ monitoring such as industrial systems for feedback control and system optimization, as well as the structural components health monitoring to improve their service safety.
To date, different types of vibration sensors have been designed for hightemperature sensing applications, including capacitive, fiber optic, piezoresistive, and piezoelectric sensors.0] Piezoresistive sensors are less susceptible to electromagnetic interference than other types of sensors.However, this type of sensor is not suitable for elevated environment due to the inherent temperature dependence of materials resistivity. [11,12]n comparison with above mentioned sensors, piezoelectric sensors possess many advantages, such as simple structure, fast response time, compact sensor size, and easy integration with other parts.Furthermore, additional power sources are not necessary demand for this type of sensor, which is beneficial for high-temperature applications.
For achieving high-temperature sensing, various types of piezoelectric crystals have been developed, including LiNbO 3 , langatate (LGT), Gallium orthophosphate (GaPO 4 ), Ba 2 TiSi 2 O 8 (BTS), aluminum nitride (AlN) and rare earth calcium oxyborate (RECOB) crystals.Among them, LiNbO 3 crystal has attracted wide attention because of high curie temperature (≈1150 °C) and high electromechanical coupling factors. [13]However, this material possesses pyroelectric property and undergo chemical decomposition (starting at 300 °C), resulting in the decreased resistivity, which greatly restricts the use of temperature below 600 °C. [14,15]Langatate crystals have been considerably investigated resulting from its lack of phase transition before the meltingtemperature of ≈1470 °C, none pyroelectric behavior as well as the achievable large size bulk crystal. [16,17]However, the sensing performances of LGT based piezoelectric devices can be restricted since the fact that the decreased resistivity and quality factor at elevated temperatures caused the transport and diffusion of oxygen ion in the lattice. [18]GaPO 4 crystal was investigated for sensing applications owing to the advantages of high mechanical quality factor and greater piezoelectric sensitivity. [19]owever, this material can suffer from a high temperature cristobalite-phase transition (≈970 °C) and the mechanical quality factor heavily decreases at temperatures above 700 °C due to the structure disorder increases. [20][23] However, pyroelectric behavior and commensurate-incommensurate phase transition could affect the performance of sensors.AlN crystal has also obtained widely attention for high-temperature piezoelectric devices applications due to its high melting point (>2000 °C) and achievable piezoelectric activity up to 1150 °C. [24,25]However, the temperature coefficients of the independent piezoelectric coefficient are all positive, thus it is hard to realize good stability of piezoelectric sensitivity. [26][29][30] However, RECOB crystals belong to monoclinic symmetry with Cm space group, the pyroelectric behavior and the cross-talk of different vibration modes could affect the performance of the piezoelectric sensors.Hence, exploring novel high-performance piezoelectric crystals with high melting point, low-cost, none pyroelectricity, and pure vibration mode are pressed for high-temperature sensing applications.
[33][34] However, the piezoelectric sensing applications of these crystals are barely concerned.Very recent studies reveal that the REM 3 (PO 4 ) 3 type crystals exhibit attractive structural stability and piezoelectric properties.For example, these crystals undergo none phase transition prior to their high melting points (>1850 °C) and possess good piezoelectric activity (d 14 ≈ 12 pC N −1 ). [35,36]In addition, the REM 3 (PO 4 ) 3 type crystals with a 43m point group are none-pyroelectric material, which is beneficial for high-temperature sensing applications.Furthermore, the REM 3 (PO 4 ) 3 type crystals were found to be readily grown with high quality and large crystal size using the Czochralski (Cz) pulling method.Of particular significance is that these type crystals with high symmetry can obtain pure piezoelectric vibration mode, thus potential for high-temperature sensing applications.
YbBa 3 (PO 4 ) 3 (YbBP) single crystal belonging to the family of REM 3 (PO 4 ) 3 was firstly reported as a laser material due to its disordered crystal structure. [37]Recent study has also been confirmed that the YbBP crystal possesses good piezoelectric activ-ity and allows for the design of optimum crystal cut. [38]However, there are very limited reports on the use of YbBP crystal for sensing applications, except for the acoustic wave sensor application.In this paper, the YbBP crystal was grown by using the Cz method.The temperature dependence of the electro-elastic constants and electrical resistivity were investigated.In addition, the optimal crystal cut with a pure thickness shear vibration mode and good piezoelectric response was designed.Furthermore, a shear-mode piezoelectric vibration sensor based on the YbBP single crystal was fabricated, and its sensing performance at elevated temperatures were studied.

Single Crystal Growth
The YbBa 3 (PO 4 ) 3 bulk crystal was grown by using the Cz pulling method under an Ar atmosphere.High purity chemical reagents Yb 2 O 3 (99.99%),BaCO 3 (99.99%),and NH 4 H 2 PO 4 (99.99%) were used as the raw materials.YbBa 3 (PO 4 ) 3 polycrystalline sample was afforded via the high temperature solid-state reaction method.The weighed starting materials were fully mixed for more than 24 h, and then calcined at 1200 °C for 20 h.After sintering, the oxides were ground, remixed, pressed into tablets, and sintered at 1400 °C for 40 h to synthesize the polycrystalline YbBP compounds.In the growth process of single crystal, the pulling speed and rotation ratio were set to be 0.3-0.8mm h −1 and 8-12 rpm, respectively, where the seed used is <001> orientation.When the growth finished, as-grown YbBa 3 (PO 4 ) 3 bulk crystal was slowly cooled down to ambient temperature taking advantage of a rate of 30-50 °C h −1 .

Crystalline Quality Characterization
The crystalline quality for the YbBP crystal was assessed by using the high-resolution X-ray diffractometer quipped with a 4-bounce Ge-220 monochromator set for Cu K radiation ( = 1.54056Å).The accelerating voltage and tube current were set to be 40 kV and 40 mA, respectively.The scan range was 0.2°with the speed of 0.001°s −1 .A (001)-oriented wafer was finely polished on both large sides for the measurement.

Electrical Characterization
The YbBa 3 (PO 4 ) 3 piezoelectric crystal is of cubic family crystalizing in the crystal symmetry of 43m point group, and thus five independent material constants in total, i.e., three independent elastic constants (s E 11 , s E 12 , s E 44 ), one dielectric permittivity ( T 11 ), and one piezoelectric coefficient (d 14 ).They can be written as matrices in following equations: where the superscripts E and T represent the condition of constant electrical field and stress, respectively.
Based on the Institute of Electrical and Electronics Engineers (IEEE) standard, [39] three samples with different configurations were designed, including one X-cut square plate with a dimension of 6 mm × 6 mm × 1 mm and two long stripes, i.e., XYt/30°a nd XYt/45°, where the long stripes samples possess the following dimensions: t × w × l = 10 mm × 2 mm × 1 mm.All the measured specimens were deposited with Pt electrode (200 nm thick) on the required parallel surfaces by using a radio-frequency magnetron sputtering for the electric property's measurements.
The capacitance and dielectric loss for the X-cut sample were measured by using a multifrequency HP4284A LCR meter (Agilent) over the temperature range of 25-800 °C, connected to a high-temperature furnace (KSL-1200X, KJGROUP), and dielectric permittivity was determined using the follow equation: where the C represents the capacitance, t and A are the thickness and area of sample, respectively.Based on the XYt/30°cut, the elastic compliance constant s ′ E 22 (30 • ) of the obtained transverse extension sample can be expressed as: and it can be measured directly by using the XYt/30°cut sample based on: where  is the density, which is determined using the lattice parameters of the YbBP crystal, l and f r represent the length of the transverse extension bar and measured resonance frequency of the extension mode, respectively.Similarly, the elastic compliance constant s ′ E 22 (45 • ) can be measured by using the XYt/45°s ample and it follows: Combining equations ( 5) and (7), the values of s E 11 and 2s E 12 +s E 44 can be determined.The elastic compliance constant s E 44 was obtained by using a X-cut square plate sample, where the corresponding formula are as follows: where l is the edge length of the face-shear plate, f r is the measured resonance frequency for the face-shear mode.After getting s E 44 , the value of s E 12 can be obtained.The electromechanical coupling factor k′ 12 is ascertained using the following formula: where f a is the measured anti-resonance frequency of the length extension mode.Then the piezoelectric coefficient can be given by: The piezoelectric coefficient d 14 was determined according to the following conversion formula: In which the value of  is 45°in this work.The different temperatures were obtained by using a program-controlled high temperature furnace with a resolution of ± 1 °C.
In addition, the electrical resistivity of the YbBP piezoelectric crystal was ascertained from the resistance over the range of 25-800 °C, taking advantage of a 2410 Source Meter (Keithley Instruments), where the applied voltage is 100 V.For the high-temperature measurements, a specially designed specimen holder was utilized.

Shear-Mode Accelerometer Design
A shear-mode accelerometer based on YbBP single crystal was designed and fabricated using the thickness shear mode d 26 .
A prototyped shear-mode piezoelectric vibration sensor, including piezoelectric elements, center post, seismic masses, bolt as well as pedestal, is illustrated in Figure 1a.For the sensor components, two pieces of YbBP crystals were selected with a dimension of 10 (outer side) mm × 4.5 (inner radius) mm × 1.1 (thickness) mm, as shown in Figure 1b.Surface roughness and wafer parallelism for the piezoelectric elements were equal to 0.1 μm and 0.05 mm, respectively.Piezoelectric elements vacuum-sputtered with Pt electrodes on the parallel large surfaces were symmetrically on both sides of the center post and rigidly secured by the masses of the seismic using a bolt, where the washer and nut without utilizing an adhesive connection.In this design, the mass of each seismic mass is 7.5 g and the total mass is 30.5 g.Inconel 601 alloy was applied for the whole structure because of its outstanding resistance to high temperature oxidation and corrosion as well as its excellent electrical conductivity. [40]

Experimental Setup
Figure 2 presents the schematic of the experimental setup for assessing vibration sensor performance at high temperature condition.The bolt was applied a clamping torque by using a Model 285-50 torque control driver (Wiha Quality Tools).The accelerometer was connected in a CTG-5KG vibration shaker by an aluminum oxide rod and put into a program controlled high temperature tube furnace, where the temperature is controlled by the accuracy of ±1 °C.A sinusoidal signal was excited using an AFG 1022 function generator and then amplified via a power amplifier (CT5701-100W).The signal was introduced into the vibration shaker to produce a desired vibration signal.The output charge signal generated via the accelerometer was further amplified using a p CT5852 preamplifier with a gain of 1000.The amplified signal was subsequently digitized using a (NI USB-6009) data acquisition card and presented on a desktop by using a LABVIEW interface.Additionally, a commercial PE 352C22 accelerometer (PCB) was utilized as a reference vibration sensor to calibrate the acceleration at ambient temperature, where the acceleration information is also collected on the desktop.To obtain the value of accuracy, the fabricated and reference vibration sensors were attentively installed side by side on the center of the vibration shaker, and the calculation was implemented at the reference frequency (160 Hz) and reference acceleration.For each temperature point, sensing tests were measured three times, and then the mean value was used.

Single Crystal Growth and Crystalline Quality
An YbBP crystal with a size of 30 mm in diameter and 55 mm in length was obtained by using the Cz pulling technique, as presented in Figure 3a.It is free of crack and inclusions.In addition, the rocking curve measured was implemented to evaluate the crystalline quality of as-grown crystal and the corresponding result is presented in Figure 3b.It can be observed that the shape of rocking curve is symmetric and the full width at half maximum is determined to be on the order of 35.13 arcsec, suggesting the good crystalline quality.

Electrical Properties
The temperature dependence of relative dielectric permittivity and corresponding dielectric loss for the YbBP piezoelectric crystal is presented in Figure 4a, where the measured frequency is set to be 100 kHz.It can be observed that the dielectric permittivity slightly increased as the temperature increases, where the variation is found to be ≈8% from room temperature up to 800 °C (Figure 4b), exhibiting good temperature stability.For the dielectric loss of the YbBP piezoelectric crystal, the value is found to be around 15% at the temperature of 800 °C, suggesting a low dielectric loss behav-ior.The temperature dependence of the electromechanical coupling factor k 14 was also investigated, as seen by the results in the inset of Figure 4b.The electromechanical coupling factor k 14 slightly first decreases and then nearly remain constant over the test temperature ranges.In addition, Figure 4c gives the temperature dependence of the elastic compliance constants.As can be seen, the elastic compliance constants s E ij (,s E 12 and s E 44 ) are shifted slightly as the temperature increases.The elastic constants s E 11 and s E 12 show negative temperature coefficient from room temperature up to 800 °C, while s E 44 increases with increased temperatures, exhibiting a positive temperature coefficient.Considering the frequency of limiting for the sensors is inversely proportional to the constant of time (product of the resistivity and permittivity). [29]Electrical resistivity is extremely important parameter for piezoelectric sensing applications, especially in high temperature condition.Therefore, it is highly significant to estimate the resistivity for the piezoelectric crystal.Figure 5 presents the temperature independence of the electrical resistivity of the YbBP crystal, where the purple dashed line is fitted linearly of experimental data.For comparison, the resistivity of high-temperature piezoelectric crystals LiNbO 3 , La 3 Ga 5 SiO 14 (LGS), Ca 3 TaGa 3 Si 2 O 14 (CTGS), and YCa 4 O(BO 3 ) 3 (YCOB) were also presented.As shown, YbBP piezoelectric crystal exhibited a high electrical resistivity at temperature of 500 °C, being on the order of 5.7 × 10 8 Ω cm, which is two orders of magnitude higher than LGS and LN crystals. [41]And even at elevated temperature, the resistivity of YbBP crystal is found to be 5 × 10 6 Ω cm at 800 °C, which reveals a good insulation property.This value is the same level of the CTGS crystal, while the resistivity is slightly lower than the YCOB crystal. [42]In principle, high electrical resistivity of the YbBP crystal makes it promising for serving as a hightemperature sensor.In addition, the activation energy value for the YbBP crystal is estimated on the basis of the Arrhenius law: where represents the resistivity at infinite temperature, E a is the activation energy, k B and T are the Boltzmann's constant and absolute temperature, respectively.From the least square fit, the activation energy for the YbBP piezoelectric crystals is determined to 1.08 eV.

Orientation Dependence of the Piezoelectric Constants
Based on the principle of Neumann, there are three nonzero piezoelectric strain constants for the YbBP crystal because of their cubic symmetry.Among these, only one piezoelectric constant is independent, i.e. face-shear piezoelectric strain constant (d 14 = d 25 = d 36 ).Apart from these, transverse and thickness-shear piezoelectric coefficients can be obtained by using the rotation method.
The relationship between the piezoelectric strain constants and orientation angles using the following equation: ijk (, , ) = a il a jm a kn d lmn (14)   where , , and  represent the angles of Euler for the sample orientation, a ij are required matrix of the Euler describing the rotation on the basis of Euler angles, "d" and d* denote the initial matrix of piezoelectric coefficient and matrix obtained after rotation, respectively.For the 43m symmetry, the value of the thickness-shear piezoelectric coefficients d * 26 can be achieved from the Y-cut plate by using a single rotation around the x-axes.Relationship between the piezoelectric strain constants d * 26 and rotation angle can be expressed using the following formula: The orientation dependence of the piezoelectric strain constant d * 26 is investigated and the corresponding result is presented in Figure 6.It can be seen from that the maximum thicknessshear piezoelectric strain constant d * 26 is realized with the use of Y-cut rotated 45°around the x-axes, corresponding to the crystal cut YXl/45°.The maximum value is of 12.6 pC N −1 , which is equal to the face-shear piezoelectric strain constant d 14 .

Piezoelectric Crosstalk Behavior
An ideal piezoelectric vibration sensor should generate a signal output, such as charge, voltage, or current, only for the load appearing along their axis of sensitivity.Unfortunately, additional signal outputs may also occur because of a load normal to axis of their sensitivity, which extremely disturbs the accuracy of measurement.This undesired production of the signal output is called the piezoelectric crosstalk phenomenon, owing to the coupling behavior between the different piezoelectric vibration modes.Hence, it is further essential to design a pure piezoelectric vibration mode for the piezoelectric crystals to minimize this crosstalk and enhance the measurement accuracy.
To obtain an optimal crystal cut, the piezoelectric crosstalk behavior of the YbBP crystal is investigated and the corresponding result is illustrated in Figure 7a, where the rotation angle is around the x-axis.As shown, the thickness-shear mode (d * 26 ) value firstly increased with increasing rotation angle, and then exhibited decreased tendency.The maximum thickness-shear mode (d * 26 ) value is found to be 12.6 pC N −1 , with a rotation angle of 45°.More importantly, all other values of the piezoelectric coefficients, d 2i (i = 1-5), are equal to zero for the YXl/45°crystal cut, indicating a pure thickness-shear vibration mode, which is much beneficial for the design of the sensors.
In addition, the temperature dependence of piezoelectric coefficient d * 26 is further investigated.As shown in Figure 7b, the piezoelectric coefficient d * 26 slightly first decreases and then nearly remain constant over the test temperature range from 25 °C up to 800 °C, exhibiting a good temperature stability.

Prototype Vibration Sensor Test
On the basis of the pure thickness-shear vibration mode for the YbBP piezoelectric crystal, the YXl/45°crystal cut was selected for the design and fabrication of the vibration sensor prototype.Temperature dependence of the charge sensitivity at frequency of 160 Hz was investigated and the corresponding result was presented in Figure 8.It is observed that the YbBP based vibration sensor exhibits a good stability in the tested temperature range of 25 to 650 °C, where the average sensitivity is determined to be on the order of 1.16 pC g −1 .In addition, the temperature deviation  was calculated by following the formula: in which S i and S A are the sensor sensitivity at each temperature point and the average sensitivity, respectively.The temperature deviation of the YbBP based vibration sensor was found to be ≤7.7%, as shown in Figure 8 (inset), suggesting good temperature stability.Thus, the YbBP-based vibration sensor is a promising candidate for elevated temperature structure health monitoring.Some inadequacies remain in the current research.The YbBP based vibration sensor is needed to be hermetically packaged to evaluated comprehensively the performances of the sensors.Besides, the long-term performance of the sensor and thermal shock resistance need to be further evaluated to probe the sensing capability of the sensor.In the future study, the performance of the packaged sensor will be investigated.And the sensing performance in harsh conditions, including the radiation and low pressure, will be focused.

Conclusion
In this paper, a novel piezoelectric crystal YbBa 3 (PO 4 ) 3 with a cubic symmetry and high melting point of ≈1850 °C was grown by using the Cz method.The temperature dependence of relative dielectric permittivity and electrical resistivity were investigated in the temperature range of 25-800 °C, where the variation of dielectric permittivity is found to be ≈8% and the dielectric loss of the YbBP crystal is equal to ≈15% at 800 °C.In addition, an optimal crystal cut with a pure thickness shear vibration mode was designed.The optimal crystal cut presents a good piezoelectric activity (d * 26 = 12.6 pC N −1 ) as well as good temperature stability.Furthermore, a prototyped shear-mode piezoelectric vibration sensor based on the YbBP crystal was designed and fabricated, and the sensing performance at high temperature was evaluated.The average sensitivity was found to be order of 1.16 pC g −1 and the temperature deviation is found to be on the order of 7.7%, exhibiting a good stability.All these results suggest that YbBa 3 (PO 4 ) 3 single crystal is a promising candidate for elevated temperature piezoelectric sensing applications.

Figure 1 .
Figure 1.a) The expanded view of the shear-mode accelerometer assembly, b) piezoelectric elements of square for the YbBP crystal.

Figure 2 .
Figure 2. Experimental setup for evaluating accelerometer performance at high temperature condition.

Figure 3 .
Figure 3. a) Photograph of the as-grown YbBP single crystal, b) X-ray rocking curve recorded for the (001) wafer.

Figure 4 .
Figure 4. a) Dielectric permittivity and dielectric loss, b) variation of the dielectric permittivity, c) elastic compliance constants as a function of temperature for YbBP piezoelectric crystal.

Figure 5 .
Figure 5. Temperature dependence of resistivity of the YbBP crystal, compared with other high-temperature piezoelectric crystals.

Figure 6 .
Figure 6.Orientation dependence of the piezoelectric strain constant d * 26

Figure 7 .
Figure 7. a) Piezoelectric crosstalk behavior of the YbBP crystal versus rotation angle around the x-axis, b) temperature dependence of piezoelectric coefficient d * 26 .

Figure 8 .
Figure 8. Sensitivity of the YbBP based vibration sensor as a temperature function at frequency of 160 Hz, the inset gives the temperature deviation.