High-Temperature Piezoelectric Crystals for Acoustic Wave Sensor Applications.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TUFFC.2016.2527599, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

1

High-Temperature Piezoelectric Crystals for Acoustic Wave Sensor Applications Hongfei Zu, Member, IEEE, Huiyan Wu, Member, IEEE, and Qing-Ming Wang, Member, IEEE

Abstract—In this review article, nine different types of high-temperature piezoelectric crystals and their sensor applications are overviewed. The important materials properties of these piezoelectric crystals including dielectric constant, elastic coefficients, piezoelectric coefficients, electromechanical coupling coefficients and mechanical quality factor are discussed in details. The determination methods of these physical properties are also presented. Moreover, the growth methods, structures and properties of these piezoelectric crystals are summarized and compared. Of particular interest are langasite and oxyborate crystals, which exhibit no phase transitions prior to their melting points ~1500°C and possess high electrical resistivity, piezoelectric coefficients and mechanical quality factor at ultrahigh temperature (~1000°C). Finally, some research results on surface acoustic wave (SAW) and bulk acoustic wave (BAW) sensors developed using this high temperature piezoelectric crystals are discussed.

Keywords—piezoelectric crystals, high-temperature crystals, high-temperature sensors, SAW sensors, BAW sensors

I. INTRODUCTION

A

CCORDING to Cady’s [1] definition, piezoelectricity is “electric polarization produced by mechanical strain in crystals belonging to certain classes, the polarization being proportional to the strain and changing sign with it”. It

takes a long time for human beings to discover, comprehend and make use of piezoelectricity: As early as 1703, it was found that tourmaline crystals could attract and repel hot ashes. And in 1842, Brewster observed the same phenomenon with various other kinds of crystals and introduced the name “pyroelectricity”. Haüy and Becquerel did lots of experiments to determine whether electricity could be generated by pressure as well as temperature, however, their results were inconclusive [2]. In 1880, when studying the relation between pyroelectricity and crystal symmetry, the brothers Pierre and Jacques Curie discovered the phenomenon of piezoelectricity. Moreover, they predicted successfully in which types of crystals the phenomenon could be observed and along which directions the force should be applied. By applying pressure to properly cut plates, they observed the related deflections in zinc blende, sodium chlorate, boracite, tourmaline, quartz, calamine, topaz, tartaric acid, cane sugar and Rochelle salt. More importantly, they obtained the quantitative result that the generated charge was proportional to the applied pressure. Then, in 1881, W. Hankel first proposed the name “piezoelectricity”, which was soon widely accepted. The effect described above is This work was partially supported in part by the U.S. National Science Foundation under award No. ECCS 0925716. The authors are with the Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, PA 15261 (email: [email protected]).

0885-3010 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.


2

now known as “direct piezoelectric effect”. There is also “converse (or inverse) piezoelectric effect” which is associated with the mechanical displacement generated by the applied electrical field [3]. The “converse piezoelectric effect” was first predicted by Lippmann [4] in 1881 and demonstrated by Curie brothers later. Curie brothers also pointed out that the magnitude of converse piezoelectric effect constant of quartz was the same with that of direct piezoelectric effect. Piezoelectricity only could be observed in anisotropic dielectric materials whose structures should not possess a center of symmetry. The basic relation between piezoelectricity and the crystal symmetry was established by Voigt [5] who clearly showed in which of the 32 crystal classes piezoelectric effects might exist, and he presented which of the possible 18 piezoelectric coefficients might have non-zero values for each class [1]. Of the 32 crystal classes, 21 do not possess a center of symmetry, and 20 classes of them (the 20 classes and the related crystal systems are as following: 1, Triclinic; 2 and m, Monoclinic; 222 and mm2, Orthorhombic; 4, 4 , 422, 4mm and 4 2m, Tetragonal; 3, 32 and 3m, Trigonal; 6, 6 , 622, 6mm and 6 m2, Hexagonal; 23 and 4 3m, Cubic) exhibit the piezoelectric effect (crystal class 432 has no center of symmetry, but its piezoelectric effect degenerates because of its high symmetry). The “crystallography applied to piezoelectric crystals” has been laid down conventionally by the IEEE [6]. Both direct and converse piezoelectric effects are widely used and a series of applications could be found in present-day devices. The success of piezoelectric materials’ applications highly results from the fact that these materials can be easily adapted to useful and reliable devices [3]. According to which type of physical effect is used, the piezoelectric devices could be divided into four general categories: generators, sensors, actuators and transducers. Generators and sensors make use of the direct piezoelectric effect, which means that they transform the mechanical energy into electric signals, while actuators work based on the converse effect by transforming electrical energy into mechanical energy. And in transducers, both effects are utilized within the same device [7], [8]. The specific applications and the related effects are summarized in table I. This review focuses on sensor applications of high-temperature piezoelectric crystals. Here crystals mean single crystals, so the piezoelectric polycrystalline materials, like ceramics, will not be included. Compared to polycrystalline materials, piezoelectric single crystals can avoid domain-related aging behavior, while possessing high electrical resistivity, low losses and excellent thermal property stability [9]. Sensors that could function at high temperatures without failure play a significant role and are in great demand in many industrial and scientific fields. In the aircraft and aerospace industries, where high temperature actuators and sensors used for structural control and health monitoring would allow development of safer, less weight, more fuel efficient and reliable vehicles, the high temperature sensors are urgently needed and irreplaceable [9]-[11]. Also, energy industry, including coal-fired electric generation plants, nuclear plants, wind power and geothermal power plants, is another beneficiary of high-temperature sensors for the health monitoring of furnace components and reactor systems [10], [12]. Furthermore, in automotive electronics and some other engine-related fields, high-temperature sensors would help to improve engine efficiency and reliability as well as reduce the maintaining cost [9], [13]. To date, extensive effort has been carried out and many kinds of piezoelectric crystal materials have been investigated for the high-temperature sensor applications. Quartz, with the α-β phase transition temperature at 573°C,



3

is the best known and most widely used piezoelectric crystals in electronic devices, such as oscillators, resonators and filters, because of its ultralow mechanical loss (high mechanical QM), narrow bandwidth [9], [14]. Some quartz analogues, represented by GaPO4, are reported to have higher phase transition temperatures than quartz (970°C for GaPO4) while exhibiting high resistivities, low dielectric losses and high mechanical quality factors [15]-[16]. Recently, langasite family crystals, especially the ordered ones, such as Ca3TaGa3Si2O14 (CTGS), have been considered one of the most promising candidates for high temperature sensors for their high piezoelectric coefficients, electromechanical coupling factors, resistivities and thermal stability of dielectric properties [17]-[18]. Besides the materials mentioned above, there are many other important piezoelectric crystal materials, such as the tourmalines, lithium niobate (LN), lithium tetraborate (LTB), oxyborate crystals and PMN-PT crystals, etc. And all of them will be discussed in details later. In this review, the basic parameters and properties of the piezoelectric crystals which are critical to the high temperature sensor applications will be discussed first, including the different analyzing and calculating methods. Furthermore, various types of piezoelectric crystals which are used for high-temperature sensors will be overviewed, together with the preparation methods, structures, properties, applications and so on. Finally, the specific applications of high-temperature sensors, such as the surface acoustic wave (SAW) sensors, bulk acoustic wave (BAW) sensors, accelerometers, cantilever sensors, acoustic emission sensors will be summarized by category. II. BASIC PROPERTIES AND CORRESPONDING METHODS FOR THEIR DETERMINATION “Piezoelectricity”, “Pyroelectricity” and “Ferroelectricity”, should be distinguished firstly in order to realize and analyze material properties further. The definition of “piezoelectricity” was given in previous section, where the “pyroelectricity” was also mentioned. Pyroelectricity is the ability of the spontaneous polarization of certain solids which may be either single crystals or polycrystalline aggregates, when they are heated or cooled [19]. The solids with spontaneous polarization are pyroelectric materials and 10 of the 21 crystal classes which are without a center of symmetry may generate spontaneous polarization (the 10 classes are: 1, m, mm2, 2, 3, 3m, 4, 4mm, 6, 6mm). Ferroelectricity is defined as a physical phenomenon in which a spontaneous electric dipole moment can be reoriented from one crystallographic direction to another by an applied electric field [20]. Therefore, all ferroelectrics are pyroelectric materials while all pyroelectric crystals have piezoelectric effect, not vice versa [21]-[22]. Some relevant properties and parameters will be discussed later in details. A. Dielectric, Elastic and Piezoelectric Constants The dielectric, elastic and piezoelectric constants are the most important parameters for the piezoelectric crystals and should be taken into serious consideration when choosing proper crystals for sensor fabrication. In this section, the linear piezoelectricity, which means the dielectric, elastic and piezoelectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric field will be adopted [6].



4

1) The dielectric constant The dielectric constant is a quantity measuring the ability of a substance to store electrical energy in an electric field. It is associated with the electric displacement in the dielectric material and the applied electrical field by (1) [23]:

Di = ε ij E j

(1)

where Di (C/m2) is the electric displacement, εij (F/m) is the dielectric constant, and Ej (V/m) is the electric field. Another more commonly used parameter is the relative permittivity εr, which is the ratio of the electrical energy stored in a certain material and in vacuum by the same applied voltage:

εr =

ε ε0

(2)

where ε0 is the vacuum permittivity (or permittivity of free or electric constant) and its value is:

= ε 0 8.85 × 10−12 ( F / m)

(3)

Thus, the relative permittivity εr is a dimensionless number. Sometimes, the dielectric impermeability βij (m/F) is used [24]. The relative permittivity εr differs a lot among different crystals, for example, it is 4.65 for quartz [25] while it could be as high as 8783 for PMN-30%PT [26]. For sensors, a large dielectric permittivity is desirable to overcome the losses associated with the electrical circuit, however, it leads to the decrease of piezoelectric voltage coefficient [9], [27]. Thus, for specific applications, comprehensive consideration should be taken. The temperature dependence of the dielectric constant for non-ferroelectric piezoelectric crystals is dominated by three factors: a direct volume expansion effect, the influences of volume expansion and of temperature on polarizability, which follows the Clausius-Mosotti equation [28]:

ε − 1 4πα m = ε +2 3V

(4)

where ε is the dielectric constant and αm is the polarizability of a macroscopic small sphere with a volume V, which sphere is large in comparison with the lattice dimensions. The differentiation of (4) with respect to temperature shows that the temperature coefficient of dielectric permittivity could be evaluated by (5):

TCε =

(ε − 1)(ε + 2)

ε

( A + B + C ) + 0.05 tan δ

(5)

where (A+B), C and tanδ are the effective volume expansion, temperature dependence of polarizability of the intrinsic ions and electrons, and dielectric loss related to inhomogeneity, respectively. For ferroelectric crystals, some others factors, such as the phase transitions, polarization rotation, and domain wall mobility, play a dominant role [9].



5

2) The elastic constant The stresses applied on any elementary cube of material whose edges are along the three orthogonal axes x, y and z (right-handed orthogonal coordinate system, also could be denoted as axes 1, 2 and 3, respectively) can be decomposed into stresses exerted on each face [29]. And, the stresses could be denoted as Tij (N/m2, i = 1, 2, 3; j = 1, 2, 3), where the subscript i designates the direction of the stress component and j denotes the face of the cubic normal to the axis of j. According to the balance of moment, it could be known that:

Tij = T ji

(6)

And there is a short-hand method for reducing the number of indices in the stress tensor. The reduced indices 1 to 6, correspond to the tensor indices if we replace: 11 by 1, 22 by 2, 33 by 3, 23 by 4, 13 by 5 and 12 by 6. T11 T12 T  21 T22 T31 T32

T13   T1 T23  = T6 T33  T5

T6 T2 T4

T5  T4  T3 

(7)

Similarly, the strain components could be expressed in the form:

 S11 S  21  S31

S12 S 22 S32

  S1 S13   S S 23  =  6 2 S33   S  5  2

S6 2 S2 S4 2

S5  2  S4  2  S3  

(8)

For small displacements, Hooke’s Law illustrates that the stresses are proportional to the strains:

Ti = cij S j

(9)

It is sometimes advantageous to express the strains in terms of the stresses:

S ji = s jiTi

(10)

where cij (N/m2) and sji (m2/N) (i, j = 1 to 6) are elastic stiffness constant and elastic compliance constant, respectively. For different crystals, the elastic constants vary greatly, and even for the same crystal, the values of each component could be quite different. For example, for Rochelle salt, s23 = -10.3 while s55 = 328 (pm2/N) [29]. Therefore, the material types, orientations and vibration modes are significant factors which should be paid attention to in the sensor design. The temperature dependent elastic constants (TDEC) could be studied by the method of combining continuum elasticity theory and first principles calculations in which the strain derivatives of the Helmholtz free energy are needed and could be expressed formally as follows:



6

 F1 ( D1P ,T , C11P ,T , , CijP ,T , C66P ,T ) = 0     Fi ( DiP ,T , C11P ,T , , CijP ,T , C66P ,T ) = 0     F ( D P ,T , C P ,T ,  , C P ,T ,  C P ,T ) = 0 11 66 ij  21 21    21 

(11)

𝑃,𝑇 𝑃,𝑇 𝑃,𝑇 where 𝐷1𝑃,𝑇 ···𝐷𝑖𝑃,𝑇 ···𝐷21 and 𝐷11 ···𝐷𝑖𝑗𝑃,𝑇 ···𝐷66 represent the second-order strain derivatives of the Helmholtz

free energy under different deformation modes, and the elastic constants at given temperature and pressure, respectively [30-31]. 3) The piezoelectric coefficients Piezoelectric properties are described in terms of the parameters D (electric displacement), E (electric field), T (stress), and S (strain). The electrical response due to the direct effect can be expressed in terms of stain by:

 Di = eip S p   Ei = hip S p

(12)

And the converse effect can be expressed by:

 Si = gip D p   Si = dip E p

(13)

where eip, hip, gip, and dip (i = 1 to 3, p = 1 to 6) are four types of piezoelectric coefficients and their definitions are as follows [32]:

 ∂Di dip = = ∂Tp   ∂E  gip = − i ∂Tp   ∂E h = − i  ip ∂S p   ∂Di = eip = ∂ Sp 

∂S p ∂Ei

(C / N )

∂S p = (m 2 / C ) ∂Di ∂Tp = − (N / C) ∂Di −

∂Tp ∂Ei

(14)

(C / m 2 )

Each coefficient of the four has its specific application conditions which could be known from their definitions. The most commonly used constant is d33, which represents the electric displacement or field in 3 (or z) direction related to the stress or strain applied in the same direction. Similar with the elastic constants, piezoelectric constants vary largely for different crystals and components. For example, d11 of quartz is about -2.25 (pC/N) [29] while d33 of 70PMN-30PT single crystals is about 1500 [33]. Piezoelectric coefficients reflect the materials



7

sensitivity of the piezoelectric effect. For most sensor applications, such as the pressure sensor, the piezoelectric coefficients should be sufficiently high so that the generated signal could be detected easily. The temperature dependent piezoelectric constants for many crystals have been studied, such as the Lithium Tantalate and Lithium Niobate [34], YCOB [18], and NdCOB [35]. Some materials perform a positive variation while some others possess a negative one. 4) Relations of the materials constant tensors Dielectric constants relate the two first-order tensors: Electric field and electric displacement; elastic constants reflect the relations between the two second-order tensors: Stress and Strain; piezoelectric coefficients present the association of one first-order tensor: Electric field or electric displacement and one second-order tensor: Stress or Strain. Correspondingly, they are second-order, fourth-order, and third-order tensors, and generally possess 9, 81, and 27 components, respectively. And:  ε ij = ε ji  S= S= S= S= S= S= Slkji  S= ijkl jikl ijlk jilk klij lkij klji  dijk = dikj 

(15)

where i, j = 1, 2, 3. Hence, for the most unsymmetrical medium (crystal class 1), the number of independent dielectric, elastic, and piezoelectric constants are 6, 21 and 18, respectively. With the improvement of the symmetry, the numbers will reduce correspondingly. Crystals with the highest symmetry (class 432, 2 / m3 , and

4 / m32 / m ) have 1, 3 and 0 components, respectively. The components for all the crystal classes could be found in Table VIII of IEEE Std 176-1987 [6]. The dielectric, elastic and piezoelectric constants are related by the constitutive equations. Depending on which two of the four parameters: E or D, T or S are considered as the independent variables, there are four types of constitutive equations [6]. 5) The determination of the constants The earliest method for determining the elastic and piezoelectric constants of piezoelectric materials was static measurement. However, it is seldom used now except for determining the positive sense of coordinate axes, because it is difficult to control the electrical boundary conditions [6]. Quasistatic measurement, which is made by applying an alternating stress or electric field to the samples, is an effective improvement of static techniques, for the alternating electric signals are easier to measure and could avoid the influence of pyroelectric effects [36]. The static and quasistatic methods are useful for testing poled ferroelectric ceramics, while they are not suggested for the study of new crystals, especially the crystals with low symmetry, where a more accurate technique—dynamic method should be applied. The electrical properties of a piezoelectric vibrator are associated with the dielectric, elastic, and piezoelectric constants. Thus, by measuring the properties (resonance and anti-resonance frequencies, the capacitance, and sometimes the dissipation factor) of a specified number of crystal plates at various orientations, the constants could be obtained [6], [29], [37]-[38].



8

The dielectric constants could be evaluated from measurements of the capacitance of the samples provided with electrodes covering the major surfaces. In order to ensure the accuracy of the measurements, they are best made at a frequency significantly lower than the lowest resonance frequency of the crystal samples (≤ 0.01 × fr, and the most commonly used measurement frequency is 1 K Hz), in which case the dielectric permittivities are obtained at constant stress and called “free” dielectric permittivities 𝜀𝑖𝑗𝑇 . As discussed in part 4), for the most unsymmetrical 𝑇 𝑇 𝑇 𝑇 𝑇 𝑇 , 𝜀12 , 𝜀13 , 𝜀22 , 𝜀23 , and 𝜀33 . The three dielectric crystals, there are 6 independent dielectric constants: 𝜀11

𝑇 𝑇 𝑇 permitivities 𝜀11 , 𝜀12 , and 𝜀13 could be determined directly by measuring the capacitances and the dimensions of

the square samples of X-cut, Y-cut and Z-cut, respectively (the notation for designating the orientation of crystals follows the rules formulated in part 3.6 of IEEE Std 176-1987), according to (16) as follows:

= ε iiT

Cii ⋅ t = , (i 1, 2,3) A

(16)

where Cii, t and A are the capacitance, thickness and area with electrode of the samples. The other three constants could be obtained from the rotated cut samples according to the transformation of the coordinate system (refer chapter 5 of [29]), and all the cuts and equations used for determining all the dielectric constants will be summarized later in Table II. Besides the “free” dielectric permittivities 𝜀𝑖𝑗𝑇 , there is another type of dielectric

constants—“𝜀𝑖𝑗𝑆 ”, which are measured corresponding to the constant strain and called “clamped” dielectric permittivities. The relations between the two types of dielectric constants are as follows: E e jq ε ijT − ε ijS= diq e jq= eip S pq

(17)

Hence, the “clamped” dielectric constants could be calculated from the related “free” dielectric, elastic, and piezoelectric constant (the determination of elastic and piezoelectric constants will be discussed later). Moreover, the dielectric impermeability βij can be obtained from the permittivities on the basis of (18) as follows:

βij =

(−1)i + j ∆ i , j ∆

(18)

where ∆ is the determinate of the dielectric constants matrix, and ∆𝑖,𝑗 is the minor obtained by suppressing the i th row and j th column. So far, all the dielectric permitivities and impermeabilities could be determined and the

results are summarized in Table II. In order to determine the 21 elastic constants sij and cij, the dynamic method could be applied, in which the resonance and anti-resonance frequencies are obtained from the measurement of the impedance of piezoelectric crystal vibrators first. Then, the elastic constants can be calculated from the resonance and anti-resonance frequencies together with the densities and dimensions of the vibrators. The longitudinal mode of motion is the easiest one that could be related to the fundamental elastic constants of the crystal. Flexure modes and torsional modes are another two simple modes, however, complicated plating arrangements are required to drive them, which restricts their applications [29]. With 15 independently oriented bars cut from an asymmetric material, 9



9

elastic compliances (s11, s22, s33, s15, s16, s24, s26, s34, and s35) and 6 combinations of the remaining twelve compliances (s44+2s33, s55+2s13, s66+2s12, s14+s56, s25+s46, s36+s45) could be determined. The remaining 12 constants couldn’t be obtained from the longitudinal mode vibrators, the determination of which requires other 6 independently oriented samples of face-shear modes or thickness-shear modes [6], [29]. Table III presents the 𝐸 can be got from the ZX-cut bar sample-cuts and formulas used to determine the elastic constants. For example, 𝑠11

with the electrodes are at the faces which are perpendicular to the Z direction, according to (19):

fr =

1 (19)

2l ρ s11E

where fr, l, and ρ and are the resonance frequency, length, and density of the vibrator, respectively. Here, the 𝑠𝑖𝑗𝐸

means the compliances are measured when the electric field is applied perpendicular to the length of the bar. And there is another type of elastic constants—𝑠𝑖𝑗𝐷 , which indicates the electric field is parallel to the length. The

relation between the two types of compliances is:

sE ε T 1 = = D S ε s 1− k 2

(20)

where k is the electromechanical coupling factor, which will be discussed later. The elastic stiffness constants cij are related to sij by (21):

cij =

(−1)i + j ∆ i , j ∆

(21)

where ∆ is the determinate of the elastic compliance constants matrix, and ∆𝑖,𝑗 is the minor obtained by suppressing the i th row and j th column. So far, all the elastic constants could be determined and the results are summarized in Table III. 𝑇 𝐸 The piezoelectric constants d31 could be calculated from 𝜀33 , 𝑠11 , resonance and anti-resonance frequency through

(22) as follows:

= d31 k

ε 33T E π ∆f s11 ≅ 4π 2 fr

ε 33T E s11 4π

(22)

where:

∆f = f a − f r

(23)

With the same coordinate transformation method as the determination of the elastic constants, the relation between ′ 𝑑31 and the 18 piezoelectric constants could be acquired (the equation will be showed in Table IV). Thus, all the 18

dip could be obtained by measuring 18 crystals with independent direction cosines. It is worth mentioning that longitudinal mode vibrators are enough to determine the piezoelectric constants and the 15 sample-cuts used for calculating the elastic constants could be used here. With the dielectric constants, elastic constants and



10

piezoelectric constants d, the other three types of piezoelectric constants e, g and h could be obtained. The formulas will also be showed in Table IV. Up to now, the determination of all the dielectric, elastic and piezoelectric constants have been presented. It should be noted that this is one of the general methods and the sample-cuts and equations used are not unique for the determination of the related parameters. With the increase of the crystal symmetry, the number of non-zero parameters will reduce correspondingly.

B. Other Crucial Parameters

1) The electromechanical coupling factors The electromechanical coupling factors kij (the first subscript represents the direction of the applied electrodes and the second one denotes the direction of the applied or developed mechanical energy) are defined as “non-dimensional coefficients which characterize the efficiency of transforming the stored energy into mechanical or electric work of a particular piezoelectric material under a specific stress and electric field configuration” by 𝑙 IEEE Std 176-1987 [6]. The coefficients here are known as static or quasistatic material coupling factors kmat (𝑘𝑖𝑗 ,

𝑤 𝑡 , 𝑘𝑖𝑗 or kp), for they refer to a static or quasisitatic lossless energy transformation cycle of a piezoelectric 𝑘𝑖𝑗

specimen [39] and could be expressed as follows: 2 kmat =

Wc W

(24)

where Wc and W are the converted energy and the total stored energy, respectively. Similarly, in dynamic conditions, the coupling factors are defined as follows [39]-[40]:

kw2 =

Ec Etot

(25)

where Ec and Etot are the converted energy and the total energy involved in the vibration cycle, respectively. And kw is proportional to kmat by (26):

kw2 =

8 2 kmat π2

(26)

From the piezoelectric constitutive equation: = Si sijE T j + d mi Em T = Dm d miTi + ε mk Ek

(27)

= (i, j 1,= 2,...6; m, k 1, 2,3)

The internal energy U of a piezoelectric device could be obtained:



11

= U

∫ SdT + ∫ DdE

1 1 1 1 T =[ SijE T j Ti + d mi EmTi ] + [ d miTi Em + ε mk Ek Em ] 2 2 2 2

(28)

𝑇 where, the 1/2𝑠𝑖𝑗𝐸 TjTi, 1/2𝜀𝑚𝑘 EkEm, and 1/2 dmiEmTi (or 1/2 dmiTiEm) represent the purely mechanical energy Um,

purely electrical energy Ue and the energy transduction from electrical to mechanical or vica versa Uem through the

piezoelectric effect, respectively. The coupling coefficient can also be defined as: k2 =

2 U em U eU m

(29)

There is a very commonly used coupling factor—“effective coupling factor”, which could be easily obtained from the electrical impedance:

keff2 =

f p2 − f s2 = f p2

f a2 − f r2 f a2

(30)

where fp is the frequency of maximum resistance and fs is the frequency of maximum conductance, and the second relation works for the lossless piezoelectric specimens. The determination of some important static and quasistatic coupling factors are shown in Table X of IEEE Std 176-1987 [6]. The electromechanical coupling factors for different crystals have great discrepancies, for example, they could be smaller than 1% for quartz, while for some relaxor based ferroelectric single crystals, such as Pb(Zn1/3Nb2/3)O3-PbTiO3, the k33 is larger than 90% [41]. The coupling factors are less sensitive to temperature than the dielectric and piezoelectric constants [9], [42]. 2) The mechanical quality factor The mechanical quality factor (Q factor) is a dimensionless parameter which reflects a resonator’s bandwidth relative to its center frequency and shows how under-damped the resonator is [43]-[44]. It presents the relationship between stored and dissipated energy of an oscillatory system and could be expressed by (31) as follows:

Q = 2π ×

Energy Stored Energy Dissipated Per Cycle

(31)

There are two types of Q factors: electrical quality factor QE and mechanical quality factor QM. The former one is related to off resonance devices where the dielectric loss generates most of the heat, while the latter one which determines whether the peak is narrow and sharp enough is pivotal for resonance devices [9]. QM is more commonly used and high QM which means high sensing precision is desirable for sensors. It is related to the frequency by (32) as follows [29]:

Q= M

fr = ∆f

fr f 2 − f1

(32)



12

where f2 and f1 are the frequencies at -3 dB of the maximum admittance. In many cases, especially for the MEMS devices, the quality factor-frequency product Q×f is used to evaluate the performance of the resonators [45]-[46]. The mechanical quality factor could be as large as 105-108 for AT-cut quartz [47], while it is as small as 20 for lead metaniobate [48]. Piezoelectric crystals usually show high mechanical quality factor, but exhibit low piezoelectric coefficients and coupling factors at the same time. Therefore, for specific sensor applications, some compromise should be made. And generally, due to the damping or phonon scattering, the quality factors are found to decrease with the increasing temperature [9]. 3) The complex dielectric, elastic and piezoelectric coefficients The methods stated in part II.A for determining the dielectric, elastic and piezoelectric constants are for lossless or low loss materials, such as Alpha-Quartz, lithium niobate and barium titanate single crystals. However, when they are directly applied to lossy materials, serious errors would be introduced [49]-[51]. From the general acoustic field equations and piezoelectric constitutive equations, Du, Wang, and Uchino deduced the impedance and admittance equations for a thin bar and a thin plate which could be used to determine the complex coefficients:

Z (ω ) =

3 1  2 tan(ωΛ i a )  1 − ∑ ki  jωC  i =1 ωΛ i a 

(33)

Y (ω ) =

3 1  2 tan(ωΛ i a )  1 + ∑ ki  jωC  i =1 ωΛ i a 

(34)

And

where a is half of the thickness for a plate or half of the length for a bar, and C, ki and Ʌi are complex constants which are known functions of the materials coefficients for a specified vibration mode as described in [51]. III. A GENERAL SURVEY OF PIEZOELECTRIC CRYSTALS In this section, various high-temperature piezoelectric crystals are discussed from their structures, preparation methods, properties to the applications. This section is divided into three parts: The first part presents some classic piezoelectric crystals, which have been widely studied, however, whose temperature ranges are restricted by certain factors; the second area details three types of new crystals which could be used up to 1000°C or more; the final section introduces some other particular piezoelectric crystals, which have specific applications. A. Classic High-temperature Piezoelectric Crystals

1) Quartz Quartz (silicon dioxide SiO2) is the second most abundant mineral in the earth’s crust and is the earliest and most widely used piezoelectric crystal. It undergoes the α-β phase transition at about 573 °C [52], at which temperature the α or low-temperature quartz (belongs to the trigonal crystal system) transforms into the β or high-temperature



13

quartz (belongs to the hexagonal crystal system) and the piezoelectric constant d11 vanishes [53]. Quartz in the earth’s crust is usually found in the polycrystalline state or small crystals, however, for piezoelectric applications, the large crystals reasonably free from twinning and flaws are needed. The hydrothermal synthesis method is developed and successfully used to synthesize the large quartz crystals [54] and even quartz nanocrystals [55]. Extensive studies about the properties of quartz crystals have been done [25, 29, 47, 56-60]. Quartz possesses excellent properties: high QM (105-108), high electrical resistivity (˃1017 Ω·cm at room temperature) and low-temperature coefficient, which make it widely used in the control of the frequency of oscillators and very selective filters [9, 29]. Different cuts of quartz crystals have their specific characteristics and applications, which are summarized in Table V. However, the drawbacks of quartz crystals: small dielectric (relative permittivity is about 4.65 [25]) and piezoelectric coefficients （d11 is about -2.25 (pC/N) [29]), low α-β phase transition temperature (573°C) and even lower mechanical twinning temperature (300°C) restrict their applications [9]. 2) Tourmaline Tourmaline belongs to the trigonal crystal system, 3m crystal class and is a complex and even Byzantine mineral with the general chemical formula [62]-[64]:

XY3 Z 6 [T6 O18 ][ BO3 ]V3W

(35)

where X = (vacancy ), Na, K , Ca, Pb 2 + , Y = Li, Mg , Fe 2 + , Mn 2 + , Cu 2 + , Al , V 3+ , Cr 3+ , Fe3+ , Mn3+ , Ti 4 + , Z = Mg , Fe 2 + , Al , V 3+ , Cr 3+ , Fe3+ , T = Si, B, Al , B = B, V = OH , O, W = OH , F , O.

(36)

And most of the compositional variability takes place at the X, Y, Z, W and V sites. There are about 27 minerals in the tourmaline group recognized by the International Mineralogical Association. The diversity of the components results in tourmaline crystals having a variety of colors and a large range of the electrical resistivity. In the laboratories, tourmaline could grow from specific hydrothermal solutions at a range of temperatures 350-750°C depending on the solutions and pressures [65]-[67]. The properties of tourmaline crystals have been widely studied and some results are reported as follows: dielectric constants ε11 and ε33 are about 7-8 and 6, respectively [68]; 𝐸 𝐸 elastic constants 𝑐11 and 𝑐33 are around 300 and 160-180 Gpa, respectively; piezoelectric constants e33 is about 30

(×10-2 C·m-2) [69]; pyroelectric coefficients 𝑝3𝜎 range between ~1.8 and 5.4 (μC/(m2·K)) [70]. Moreover, there is no signature of any phase transition up to 1400 K [69], however, the resistivity limitation restricts its applied



14

temperature range. It was found that tourmaline could be used as shock wave and blast pressure sensor up to 700°C. 3) Lithium niobate, lithium tantalite and lithium tetraborate Both Lithium Niobate (LiNbO3, LN) and Lithium Tantalate (LiTaO3, LT) belong to the trigonal crystal system, 3m crystal class and they are the ABO3-type ferroelectrics with oxygen octahedral like Barium Titanate (BaTiO3, BT). In addition, their crystals are colorless, insoluble in water and organic solvents with high melting points [71]. As for Lithium Tetraborate (also named Lithium Borate, Li2B4O7, LTB), it belongs to tetragonal system, 4mm crystal class and unlike LN and LT crystals, the LTB crystals don’t display ferroelectricity. They could be grown by Czochralski, Bridgman-Stockbarger or Stepanov techniques and the growth rates depend on the methods and temperatures applied [72]-[74]. LN and LT crystals exhibit excellent optical, piezoelectric and pyroelectric properties, and LTB crystals possess zero temperature coefficients of resonance frequency and some other superior piezoelectric properties. A selection of essential properties relative to piezoelectric applications is given in Table VI. LN crystals have a broad homogeneity range with various compositions from congruent to stoichiometric and the electrical and electromechanical properties of related Z-cut and X-cut crystals have been investigated by A. Weidenfelder et al. [77]. Fig. 1 shows the bulk conductivities of three types of Z-cut LN samples as a function of temperature, which illustrates that the conductivities decrease with the increase of the Li2O concentration and they possess linear relationships with temperature from 500°C to 900°C. The total conductivity is composed of the ionic conductivity and electronic conductivity, and the increase of the concentration of Li2O will lead to the decrease of the lithium vacancy concentration, which would certainly result in the decrease of the ionic conductivity. In the meanwhile, the electronic conductivity also shows a dependence on the lithium vacancy concentration (𝜎𝑒 ~([𝑉𝐿𝑖′ ])𝑛 , with n≤0.31), which means the electronic conductivity also decreases with the increase of the

concentration of Li2O. Therefore, the total conductivity decreases with the increase of Li2O concentration. The temperature dependent resonance frequency and the inverse Qf product for X-cut and Z-cut LN crystals could be found from Fig. 2, which indicates a material dependent loss at about 700°C. Samples 1 to 3 are all Z-cut crystals with the Li2O concentration 48.3, 49.5 and 50.0 mol.%, respectively and sample 4 is X-cut with 49.5 mol.% Li2O concentration [77]. LN and LT crystals are excellent materials for mobile phones, piezoelectric sensors and optical applications. Especially, they are widely used in surface acoustic wave (SAW) devices for their low acoustic losses. However, the temperature range of their applications is limited by their phase transitions. Compared to LN and LT, LTB crystals have no phase transition prior to their melting point and own better piezoelectric properties, but the poor levels of ionic conductivity restrict their high temperature applications [13], [71].



15

B. New High-temperature Piezoelectric Crystals

1) Quartz analogues Quartz-like materials with the structure MXO4 (M=B, Al, Ga, Fe, Mn and X=P, As) have been extensively studied for applications supplementary to quartz [78]. Among these materials, Boron phosphate (BPO4) and arsenate (BAsO4) are “isostructural with quartz” and belong to tetragonal crystal system; Aluminum arsenate (AlAsO4) is reported in tetragonal system and in α-quartz forms; Gallium orthophosphate (GaPO4), Berlinite (AlPO4) and Gallium arsenate (GaAsO4) are in the trigonal crystal system as α-quartz and Gallium arsenate is reported only in the α-quartz form, while Berlinite possess α-β phase transition and Gallium orthophosphate transforms into another structure similar with cristobalite at about 970°C [79]. The M-X distance, which is defined as the non-bonded radius sum, is the most important factor in controlling the structure packing [80]-[81]. The M-O-X angle (θ) will decrease and the tilt angle (δ) will increase with the M-O and X-O distances increase, which will result in the increase of the distortion of the tetrahedral chain [82]. And the energy needed for the α-β phase transition increases with the increased distortion, and when θ ≤136° or δ ≥ 22° the transition will not occur, which is reflected in Fig. 3 [80]. Also, the distortion could be indicated by the c/a ratio as shown in Fig. 4. It is found that the ratio ranges from 2.20 (SiO2) to 2.28 (GaAsO4) for the quartz-like structures, and more importantly, the larger the ratio, the more the distortions [78].

Some significant properties for high-temperature sensor applications of SiO2 and quartz-like crystals have been summarized by Shujun Zhang et al. [9]. Among the quartz analogues, GaPO4, which could be grown by hydrothermal method [83]-[84] or flux method [85], possesses most of the excellent performances of quartz, such as high electric resistivity (ρ > 1017 Ω·cm at room temperature and > 107 Ω·cm at 900°C [86]) and high mechanical quality factor (~20000 [87]), while exhibiting stronger piezoelectric effect (d11 = 4.5 pC/N [88]), higher thermal 𝑇 stability, larger dielectric constants (𝜀33 /ε0 = 6.6 [89]) and larger electromechanical coupling factor (k~16% [87]).

The variations of quality factor and coupling factor of an AT-cut resonator with temperature could be seen from Fig. 5. GaPO4 crystals have been widely used for sensors up to 900°C in some harsh environments, and the temperature is restricted by the phase transition. 2) Langasite family crystals Since the synthesis of Ca3Ga2Ge4O14 (CGG) in 1979 [90], which served as the starting point of the langasite (La3Ga5SiO14) family crystals, the langasite family crystals have attracted great attention for their promising piezoelectric, luminescent, laser and photorefractive properties [91]-[93]. To date, about 180 compounds in the family are known [91], [94]. Langasite family crystals belong to the trigonal crystal system, 32 crystal class with the chemical formula as {E}3[A](F)32O14 (using the modified Wyckoff letter notation), whose crystal structure is schematically shown in Fig. 6 [95]. Where, the notations {E} and [A] represent a decahedral site coordinated by eight oxygen and an octahedral site coordinated by six oxygen, respectively. (F) and represent two types of



16

tetrahedral sites coordinated by four oxygen and the size of (F) site is larger than that of site. In La3Ga5SiO14 (LGS) and La3Ga5GeO14 (LGG) crystals, La3+ occupies the {E} sites, Ga3+ occupies [A], (F) and part of sites, and Si4+/ Ge4+ occupies the remaining of [D] sites; while in its isomorphs, such as langanite (La3Ga5.5Nb0.5O14 , LGN or LNG) and langatate (La3Ga5.5Ta0.5O14 , LGT or LTG) crystals, La3+ occupies the {E} sites, Ga3+ occupies (F), and half of the [A] sites, and Nb5+ or Ta5+ occupies the other half of the [A] sites [94]-[95]. The langasite family crystals have been widely exploited as surface acoustic wave (SAW) and bulk acoustic wave (BAW) devices, for their brilliant properties, such as large electromechanical coupling factor, large quality factor, high resistivity, wide pass-band, temperature stability, low acoustic loss and no phase transition prior to their melting points (~1500°C) [93], [96]-[99]. Czochralski method [97], [100]-101] and the modified Bridgman method [102] are found to be two effective ways to grow langasite family crystals. Many substitutions of langasite-type crystals have been investigated, such as incorporation Na+, K+, Ba2+, Sr2+, Ca2+, Pb2+, Bi3+, Pr3+, Nd3+ into the {E} sites and Li+, Mg2+, Zn2+, Ga3+, Al3+, In3+, Ti4+, Zr4+, Hf4+, Nb5+, Ta5+, Sb5+, Mo6+, W6+ into [A] sites [97], [103]. Among these tries, Al3+ modified crystals are found to exhibit larger coupling factors (k12, k25, k26), lower temperature dependence and higher value of piezoelectric constant d11 and higher electric resistivity ρ, for the smaller Al3+ ions replace larger Ga3+ ions and results in the increasing of {E}–O distance [95], [104]-[105]. Fig. 7 shows the temperature dependences of the electric resistivity of Y-cut LGS, LGAS0.9, LTG and LTGA0.5 crystals, which illustrates that compared to LGS and LTG, the LGAS0.9 and LTGA0.5 crystals exhibit high ρ values of one order of magnitude [95]. As in the LGS, LGG, LGN, and LGT crystals discussed above, Ga3+ could occupy (F), and [A] sites. Then, those kinds of langasite-type crystals are so called “disordered” langasite crystals and the disorder structure leads to higher acoustic losses, lower acoustic velocity and non-uniform mechanical properties [106]. Recently, a few “ordered” langasite-type crystals have been studied and 4 compositions are identified based on the structural analysis and the stability constraints: Ca3NbGa3Si2O14 (CNGS), Ca3TaGa3Si2O14 (CTGS), Sr3NbGa3Si2O14 (SNGS) and Sr3TaGa3Si2O14 (STGS), in which Ca2+/Sr2+, Nb5+/Ta5+, Ga3+, and Si4+ occupy the {E}, [A], (F), and sites, respectively [18], [106]-[110]. Additionally, Al3+ modified crystals Ca3TaAl3Si2O14 (CTAS) were grown successfully by Czochralski method, which possesses similar piezoelectric performance with STGS, SNGS and CTGS, and reduce the cost [111]. Fig. 8 presents the dielectric loss of SNGS, STGS, CTGS and CTAS as a function of temperature, from which it could be obtained that the losses of the “ordered” langasite-type crystals are very small (< 0.001) when temperature is below 500°C [18]. The main properties of 10 kinds of commonly used langasite-type crystal could reference Table I in [18]. 3) Rare earth (Re)-calcium oxyborate crystals Rare Earth (Re)-Calcium crystals belong to the monoclinic crystal system, m crystal class, with the chemical formula ReCa4O(BO3)3 (ReCOB, Re are rare earth elements, such as Er, Y, Gd, Sm, Nd, Pr and La) and they were first reported in 1992 [112]. The ReCOB crystals possess the same crystal structure, in which there are three types of distorted octahedral sites: Ca(1), Ca(2)) and Re(1) and they are occupied by two kinds of Ca2+ and one kind of Re3+, respectively. In each octahedron sites, there are six O2-, two of which occupy the vertex angles of the



17

octahedron, while the other four O2- form a parallelogram as shown in Fig. 9 [113]. Similar to langasite family crystals, ReCOB crystals could be grown by the Czochralski method and the Bridgman method [114]-[117]. ReCOB crystals are considered as excellent nonlinear optical materials, for they have lots of wonderful laser and other optical-related performance. For instance, GdCOB crystals are easy to grow and absolutely non-hygroscopic, and YCOB crystals possess large birefringence [118]. Meanwhile, ReCOB family crystals exhibit exceptional 𝑇 piezoelectric properties, especially at elevated temperatures: 𝜀22 is about 15.5 for NdCOB, k26 is about 31.5% for

PrCOB, and d26 is about 15.8 pC/N for PrCOB; of particularly significance, they have no phase transformations

prior to their melting points (~1500°C) and the electric resistivity is ultrahigh (~108 Ω·cm at 1000°C for ErCOB) [113], [119-122]. Fig. 10 gives the electrical resistivities of Y-cut ReCOB samples as a function of temperature and the extrapolated room-temperature resistivities are shown in the inset. It could be seen that with the increasing of the Re3+, the electrical resistivities decrease (except for the LaCOB). And the values of the resistivity go from 106 to 108 Ω·cm for different ReCOB crystals at 1000°C [122]. 𝑇 𝐸 Together with the electrical resistivity (ρ), the dielectric permittivity 𝜀22 /ε0, elastic compliance 𝑠66 , the

piezoelectric coefficient d26, the electromechanical coupling factor k26 and the mechanical quality factor Q26 of the ReCOB family crystals are affected by two factors: the Re3+ ion radius and the disorder distribution of Re3+ and Ca3+. The former factor could change the length of Re-O bond, the volume of the Re-O oxygen octahedron and

further the S6 strain, while the latter one would result in the phonon scattering like the defects [122]. Fig. 11(a) 𝑇 shows the 𝜀22 /ε0 and d26 as a function of the absolute value of the radius difference between the Re3+ ion and the

Ca2+ ion (│R(Re3+)-R(Ca2+)│) and Fig. 11(b) presents the k26 and Q26 as a function of that value. It could be seen 𝑇 that with the increasing of the value, 𝜀22 /ε0, d26 and k26 decrease and Q26 increase. It is worth mentioning that the

radius of La3+ is larger than that of Ca2+ (1.00 Angstrom) and the radii of Pr3+, Nd3+ , Sm3+ , Gd3+ , Y3+ , Er3+ are 𝑇 smaller than Ca2+ ion’s. That’s why the four parameters (𝜀22 /ε0, d26 , k26 and Q26) of LaCOB are a little unsocial

[113], [122].

C. Some Other Piezoelectric Crystals

AlN (Aluminum nitride) was first synthesized in 1877 and found the application in microelectronics in the middle of 1980s for its high thermal conductivity (200 W/(m·K) for AlN ceramic [123]-[124], and about 319 W/(m·K) for single crystal [125]). Also, AlN exhibits high electrical resistivity, low density and matches well with silicon, which make it attract lots of attention. It is reported that the surface oxidation occurs above 700°C in air [126] and AlN stays stable in hydrogen and carbon dioxide atmospheres up to 980°C [127]. AlN single crystal could be grown by the sublimation technique at about 2300°C [128] or physical vapor transport (PVD) [129]. AlN bulk single crystals are promising candidate for UV applications [130], while its thin films are widely used in surface acoustic wave (SAW) devices and thin film bulk acoustic resonator (FBAR) [131]. Relaxor

based

ferroelectric

single

crystals,

such

as

Pb(Zn1/3Nb2/3)O3-PbTiO3

(PZNT)

and

Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMNT), are investigated for electromechanical actuators results from their low



18

dielectric loss (2500 pC/N), and large electromechanical coupling factor (k33 >90%) [33], [41-42]. However, the low Curie temperature (~170°C) and even low rhombohedral to tetragonal phase transition temperate (~120°C) restrict their high-temperature applications [42]. The crystals could be grown from flux growth technique and modified Bridgman technique [132]-[134]. The general properties of 9 kinds of representative single crystals are summarized in Table VII (only ferroelectrics have the Curie point).

IV. SENSING APPLICATIONS OF HIGH-TEMPERATURE PIEZOELECTRIC CRYSTALS It was in the 1950s that the piezoelectric effect began to be considered for sensing applications. Compared to other types of sensing techniques, such as piezoresistive, capacitive and fiber optic sensors, piezoelectric sensors exhibit higher resolution of strain, larger frequency range, better temperature stability, shorter response times, easier to integrate and lower cost [135]. Moreover, piezoelectric crystals have a higher long-term stability and lower loss than the piezoelectric ceramics and the high-temperature sensors are in great demand in aircraft, aerospace, energy and automotive industries [9]-[13]. High-temperature piezoelectric crystals are therefore extensively studied and widely used. According to whether the acoustic waves are applied to sense the physical or chemical changes, the piezoelectric sensors could be divided into Acoustic Wave (AW) sensors and Non-Acoustic Wave sensors. Among the AW sensors, Surface Acoustic Wave (SAW) sensors and Bulk Acoustic Wave (BAW) sensors are resonant-based sensors and have been most extensively investigated and applied. On the other hand, in the light of the functions, the piezoelectric sensors could be classified as temperature sensors, pressure sensors, mass sensors, gas sensors, flow sensors, chemical sensors, bio-sensors and so on. In this section, high-temperature piezoelectric crystal sensors are discussed on the basis of the principals, especially the SAW and BAW sensors, and certain corresponding functional sensors will be described. A. Surface Acoustic Wave (SAW) Sensors

Surface acoustic wave (SAW) is an acoustic wave propagating along the surface of materials exhibiting elasticity, which was first described by Lord Rayleigh in 1885 [136]. SAWs have a longitudinal and a vertical shear components coupling with any media on the surfaces, which would change the amplitude and velocity of the SAWs and make the SAW sensors could sense the temperature, pressure, mass and other properties accordingly. The SAW sensors transduce an input electrical signal into a mechanical wave by the input interdigitated transducers (IDTs) [137], and the wave, which could be affected in amplitude, phase or frequency by the physical parameters to be detected, could be transduced back into the electrical signal by the output IDTs. Then, the changes between the input and output signals could reflect the desired physical parameters [138]-[140]. Concretely, through the IDTs fabricated on the surface of the substrate, the SAW devices could generate Rayleigh waves, which consist of two particle displacement components: surface particles move in paths with the surface parallel or normal to the direction of the propagation. The energies of the waves are confined into the area within several wavelengths depth from the surface. Two sets of



19

IDTs are needed: one to launch the SAW, while the other one to detect it. All the physical or chemical changes loaded between the two sets of IDTs would be reacted by the differences between the launched and detected waves [138]. Depending on the line-width of the IDTs, the frequency range of the SAWs could cover 50 MHz to a few GHz [141] and the IDTs are usually fabricated by the lithography technique [142]. The decisive advantage of the SAW sensors is the possibility of processing wireless without using cables and energy sources, even in the harsh environments [143]-[145]. Thus, piezoelectric crystal SAW sensors are suitable for high-temperature measurement and have been found a wide range of applications. R. Hauser et al. have investigated the acoustic attenuation loss and the aging of the LiNbO3 SAW devices up to 450 °C for more than 10 days [146]. As shown in Fig. 12(a), the aging of LiNbO3 exhibits a continuous decrease below 450°C, which maybe resulted from the decomposition over the congruent melting point (300°C). Furthermore, the tested economic life-time at 400°C is more than 10 days and the predicted lift-time at 300°C based on ARHENIUS equation is as long as 10000 days, which are given in Fig. 12 (b) [146]. M.N. Hamidon et al. have successfully fabricated a kind of SAW sensor based on GaPO4, which could be operated up to 600°C inside the ISM-band (around 434 MHz) [147]-[148]. The IDTs of their devices were fabricated according to the e-beam lithography with lift-off technique and have 50 fingers, 50 wavelength aperture, 200 strips short circuit reflectors and 1.4 μm finger width with the 1:1 finger to space ratio. The Y-Boule orientations with a 5° cut with the dimension of 3.5 cm × 4.5 cm GaPO4 crystal wafers were used. And the electrode metallization was platinum (Pt) with titanium (Ti) or zirconium (Zr) as the adhesion layer [147]. They reported that for the devices with Zr adhesion layer and 82 nm Pt electrode there was no oxidation at 600°C and the resonate frequencies were stable for more than 3500 hours with a small drift 0.03 ppm/h [148]. These gratifying results provide evidences for the conclusion that GaPO4 based SAW sensors could be used up to 600°C for a long time. LGS crystals based high-temperature SAW sensors also have been widely investigated. Cunha et al. have studied the two-port LGS SAW sensors up to 850°C [149]. The Pt/10%Rh/ZrO2 electrode which was deposited through the e-beam evaporation method was used. And the IDTs fabricated by the lift-off techniques possessed 80 fingers, 50 wavelength aperture, 500 electrode short circuit reflectors, 4 μm finger width with 1:1 finger to space ratio. The center frequency response of this type sensor cycled six times between room temperature and 850°C was measured and the result is shown in Fig. 13 [149]. As could be seen, the center frequency stays relatively stable from room temperature to 850°C (less than 5 MHz drift occurred compared to the 170 MHz center frequency) and the major changes take place in the 550°C-850°C. Also, long term (4080 hours) operation for this kind device at 800°C was taken and the results support its stability. Thiele et al. have made detecting the H2 and C2H4 in N2 up to 250°C and 450°C, respectively, by the LGS SAW gas sensor to be a reality [150]. B. Bulk Acoustic Wave (BAW) Sensors

Analogously, bulk acoustic wave (BAW) sensors also utilize the acoustic waves as the sensing mechanisms to detect the physical or chemical quantities (mass, gas, chemical, viscosity et al.) by measuring the changes of the



20

velocity, frequency, phase or amplitude of the acoustic waves. Unlike the surface acoustic waves, the bulk acoustic waves propagate through the entire devices [151]. In general, according to the structures, orientations of the substrate materials, and the directions of the applied electrical excitations, the substrates would be excited to lots of different vibration modes (usually, thickness shear mode and shear-horizontal mode are utilized). With certain vibration modes, the basic parameters of the BAW would be determined. Once the physical or chemical quantities are loaded to the substrates, the parameters would change, and the parameters change of the wave could be used to determine the loaded quantities. There are many different types of BAW sensors with a variety of vibration modes. For example, the piezoelectric plate sensors could be excited to several extensional modes, face-shear modes, thickness shear modes, flexural modes and twist modes; the long thin rod sensors can be exploited as the extensional, bending or torsional modes [141]. The most commonly used BAW sensors are the thickness shear mode (TSM) and the shear-horizontal acoustic plate mode (SH-APM) sensors [151]. The TSM sensors, usually referred to as the quartz crystal microbalance (QCM), are the earliest and most extensively used BAW sensors since they do not generate compressive waves in the surrounding medium [152-153]. QCM has lots of chemistry and electrochemistry applications for its large detection range (from monolayer surface to large masses), high mass sensitivity (measurable mass density down to 1 μg/cm2) and wide applicable environment (gas and liquid phases) [154]-[156]. SH-APM sensors utilize a thin piezoelectric plate to confine the energy between the two surfaces, which results in that both surfaces undergo displacement and are detectable [151]. In addition, thin film bulk acoustic resonator (FBAR or TFBAR) is widely investigated for its small size, high quality factor and high targeted frequency (radio frequency 1 GHz ~ 10 GHz) [157]. In 1959, QCM was first reported in the sensing mode in one paper of Sauerbrey, where he obtained the linear relationship between the mass of deposited metal on quartz crystal and its frequency decrease [158]. Seh et al. from MIT developed high sensitive NOx gas sensor (up to 400°C) by exploiting QCM and the schematic of the sensor is shown in Fig. 14(a) [159]. Through the PMMA templating technique, BaCO3 films (800nm or 400nm in diameter) were deposited on one gold electrode of the QCM (5 MHz, AT-cut). BaCO3 was selected as the active film for it reacts with NO2 to form Ba(NO3)2 with the mass change. The mass sensitivity of this QCM sensor was found to be 1 ng/(cm2·Hz) and the largest change in Δf0 was -2000 Hz (at 400°C and 100 ppm NO2) which is shown in Fig. 14(b) [159]. GaPO4 and LGS are investigated as alternatives to quartz, which could be used at higher temperatures and are also called QCM even though they are not made of quartz. Thanner et al. reported that they used Y-11° cut GaPO4 (diameter 7.4 mm, resonant frequency near 6.2 MHz) as the QCM mass sensor and measured the mass change of lube oil deposited on its surface up to 720°C [160]. Seh et al. also investigated the 1%Sr-LGS, 5%Nb-LGS and updoped LGS BAW gas sensors’ performance from 700°C to 1000°C and presented their bulk conductivities as functions of temperature and oxygen partial pressure, from which they demonstrated that the LGS BAW sensors were possible to operate to 800°C from oxygen partial pressures of 1 atm down to 10-12 atm with Q≥500 [161]-[162]. SH-APM devices possess two major advantages: they could work in a liquid medium without excessive acoustic loss and could work in an aggressive medium [163]. Déjous et al. studied the temperature-compensated properties of ST-cut quartz SH-APM sensors up to 200°C and showed their performance in biological media (sodium chloride and tris(hydroxymethyl)aminomethane) [163]-[164]. FBARs are extensively used as filters in cell phones and other wireless applications and the common materials for FBARs are AlN [165]-[167] and ZnO [168]-[170]. As for single



21

crystal FBARS, Osugi et al. studied the LN FBARs (45° Y-cut, 1μm thickness) with the resonance frequency at 2.12 GHz and Δf of 159 MHz and presented that they had higher coupling factor and Δf/fr (30.6% and 12.4%, respectively) than AlN (6.54~7% and 2.7~2.8%, respectively) [171]. However, few reports about the applications of high temperature crystal FBARs. C. Non-resonant Piezoelectric Crystal sensors

Piezoelectric accelerometers employ the piezoelectric effect of some piezo-materials and first convert the acceleration into a force or displacement through a seismic mass and then convert them into an electrical quantity. Piezoelectric accelerometers are widely used in industry and science to measure the dynamic changes in the vibration and shock. High-temperature piezoelectric crystal acceleration with high sensitivity and stability are in great demand in the engine field where the accelerometers should work in the harsh environments with high temperature, high pressure and high oscillation [172]-[173]. Tian et al. designed and developed a quartz-flexure accelerometer operating in low frequency range based on the capacitive sensing and electrostatic control technology and the results showed that the resolution was about 8 ng/Hz1/2 [174]. Zhang et al. fabricated and tested the accelerometer made by thickness mode (XYlw)-15°/45° cut YCOB crystals up to 1000°C and over a frequency range of 100-600 Hz [175]. It was found that, the accelerometer possessed a high sensitivity (2.4±0.4 pC/g) across the temperature and frequency range, which is shown in Fig. 15, and it could stay stable at 900°C for more than 3 hours. Cantilever which has been extensively used for energy harvesting [176],[177], or as biosensors and chemical sensors is a common structure in microelectromechanical systems (MEMS). Cantilevers are often made from silicon, silicon nitride or polymers, and PMN-PT is the widely used piezoelectric single crystal for cantilevers for its high coupling coefficient and piezoelectric constant [177]-[179]. In addition, unimorphs [180] and bimorphs [181] cantilevers are also commonly used. Acoustic emissions (AE) are the sound waves generated by dynamic stress in a material and the AE sensors play a significant role in the non-destructive inspection field [182]. Kirt et al. developed the lithium niobate 1-3 piezocomposites (with high-temperature-resistant cement) acoustic emission sensors by using the dice and fill method [183]. According to their test, the 4 mm thick sensor with 45% volume fraction of y/36° cut presented the best results and could work over the temperature range from room temperature to 400°C. Johnson et al. designed, fabricated and tested the YCOB single crystal AE sensors and acquired the following result: the sensitivity of the sensor had small to no degradation with the increasing temperature, which demonstrated the ability of YCOB crystal AE sensors to detect zero symmetric and antisymmetric modes up to 1000°C [184]-[185].

V. CONCLUSIONS AND FUTURE WORK High-temperature piezoelectric crystal sensors are important and in great demand in aircraft, aerospace, and energy-related industries, since they possess high electrical resistivity, low losses and excellent thermal property stability and could improve the structural control, health monitoring and improve engine efficiency. Dielectric, elastic and piezoelectric properties are the most basic and significant properties for piezoelectric crystal sensors and generally



22

the number of their independent constants are 6, 21 and 18, respectively. In order to determine all the parameters, 6, 21 and 18 types of samples with independent orientations are needed, respectively. Among the methods for determining the constants of linear and lossless piezoelectric crystals, the dynamic method is most widely used. The coupling factors and quality factor are also pivotal, while the former parameter reflects the energy conversion efficiency and the latter one provides the bandwidth of the sensors. Both of the factors could be obtained through dynamic method. The classic piezoelectric crystals have been extensively investigated and applied, however, their usage temperature ranges are not high enough: quartz (~300°C, restricted by phase transition and mechanical twinning); tourmaline (~700°C, limited by the strong pyroelectric effects); LN (~700°C, restricted by the phase transition and loss). Recently, some new types of piezoelectric crystals have attracted much attention of the researchers for their excellent high-temperature performance. For example, GaPO4 (one kind of quartz analogues) could be used as sensors up to 900°C. Langasite and oxyborate family crystals, which exhibit no phase transitions prior to their melting points (~1500°C) and possess high electrical resistivity, piezoelectric coefficients and quality factor under high temperature (~1000°C) are considered the most promising candidates for the ultrahigh-temperature sensors. In addition, the resonator-based piezoelectric crystal sensors: SAW sensors and BAW sensors, are the most widely used ones, since they exhibit a series of advantages over other types of sensing technologies, such as the temperature sensitivity and stability. However, the high-temperature sensing applications of the piezoelectric crystals are not only limited by the usage temperature ranges of the crystals, but also restricted by the associated measurement technologies, especially the electrodes. Thus, the film electrodes (100nm ~ 200nm) which could resist high temperature, oxidation and corrosion call for serious investigation in the future. Furthermore, the performance of the piezoelectric crystal sensors in harsh conditions other than high temperature, such as the corrosive and radioactive environments, needs to be studied and presented.

ACKNOWLEDGMENT This research work was partially supported US National Science Foundation (NSF) award No. ECCS 0925716.

REFERENCES [1]

W.G. Cady, Piezoelectricity. New York, NY: McGraw-Hill, 1946, pp. 1-8.

[2]

C. S. Brown, R. C. Kell, L. A. Thomas, “Piezoelectric materials, a review of progress,” IRE Transactions on Component Parts, vol. 9, pp. 193-211, 1962.

[3]

R. C. Buchanan, Ceramic Materials for Electronics: Processing, Properties, and Applications, 2nd ed., New York, NY: Marcel Dekker Inc, 1991, pp. 129-133.

[4]

G. Lippmann, “Principe de la conservation de l'électricité, ou second principe de la théorie des phénomènes électriques,” J. Phys. Theor. Appl., vol. 10, pp. 381-394, 1881.

[5]

W. Voigt, Lehrbuch Der Kristallphysik, Leipzig, Germany: B.G. Teubner: 1910, pp. 801-944.



23

[6]

IEEE Standard on Piezoelectricity, ANSI/IEEE Std 176-1987, 1988.

[7]

J. Nuffer, T. Bein, “Application of piezoelectric materials in transportation industry,” Global Symposium on Innovative Solutions for the Advancement of the Transport Industry, San Sebastian, Spain, Oct. 4-6, 2006.

[8]

G. H. Haertling, “Ferroelectric ceramics: History and technology,” J. Am. Ceram. Soc., vol. 82, pp. 797-818, 1999.

[9]

S. J. Zhang, F. P. Yu, “Piezoelectric materials for high temperature sensors,” J. Am. Ceram. Soc., vol. 94, pp. 3153-3170, 2011.

[10] M. J. Schulz, M. J. Sundaresan, J. Mcmichael, D. Clayton, R. Sadler, B. Nagel, “Piezoelectric materials at elevated temperature,” J. of Intell. Mater. Syst. And Struct., vol. 14, pp. 693-705, 2003. [11] G. W. Hunter, J. D. Wrbanek, R. S. Okojie, P. G. Neudeck, G. C. Fralick, L. Y. Chen, J. Xu. G. M. Beheim, “Development and application of high-temperature sensors and electronics for propulsion applications,” Proc. SPIE 6222, Sensors for Propulsion Measurement Applications, 622209, Orlando, FL, USA, Apr. 17, 2006. [12] R. C. Turner, P. A. Fuierer, R. E. Newnham, T. R. Short, “Materials for high temperature acoustic and vibration sensors: A review,” Appl. Acoust., vol. 41, pp. 299-324, 1994. [13] D. Damjanovic, “Materials for high temperature piezoelectric transducers,” Curr. Opinion Solid State Mater. Sci., vol. 3, pp. 469-473, 1998. [14] J. Tichy, J. Erhart, E.; Kittinger, J. Privratska, Fundamentals of Piezoelectric Sensorics, New York, NY: Springer-Verlag, 2010, pp. 119-176. [15] E. Philippot, A. Ibanez, A. Goiffon, M. Cochez, A. Zarka, B. Capelle, J. Schwartzel, J. Detaint, “A quartz-like material: gallium phosphate (GaPO4); crystal growth and characterization,” J. Cryst. Growth., vol. 130, pp. 195-208, 1993. [16] H. Fritze, “High temperature piezoelectric materials: Defect chemistry and electro-mechanical properties,” J. Electroceram, vol. 17, pp. 625-630, 2006. [17] H. Fritze, “High-temperature bulk acoustic wave sensors,” Meas. Sci. Tehcnol., vol. 22, 012002, 28pp, 2011. [18] S. J. Zhang, Y. Q. Zheng, H. K. Kong, J. Xin, E. Frantz, T. R. Shrout, “Characterization of high temperature piezoelectric crystals with an ordered langasite structure,” J. Appl. Phys., vol. 105, 114107, 6pp, 2009. [19] S. B. Lang, Sourcebook of Pyroelectricity, New York, NY: Gordon and Breach, Science Publishers, Inc:, 1974, pp. 1-80. [20] R. E. Newnham, L. E. Cross, “Ferroelectricity: The foundation of a field from form to function,” MRS Bull., vol. 30, pp. 845-848, 2005. [21] R. G. Kepler, “Piezoelectricity, pyroelectricity, and ferroelectricity in organic materials,” Ann. Rev. Phys. Chem., vol. 29, pp. 497-518, 1978. [22] G. H. Haertling, “Ferroelectric ceramics: History and technology,” J. Am. Ceram. Soc., vol. 82, pp. 797-818, 1999. [23] R. E. Newnham, Properties of Materials-Anisotropy, Symmetry, Structure, NEW YORK, NY: Oxford University Press, 2005, pp. 58-69. [24] K. C. Kao, Dielectric Phenomena in Solids, San Diego, CA: Elsevier Academic Press, 2004, pp. 41-162. [25] M. R. Stuart, “Dielectric constant of quartz as a function of frequency and temperature,” J. Appl. Phys., vol. 26, pp. 1399-1404, 1955. [26] E. W. Sun, S. J. Zhang, J. Luo, T. R. Shrout, W. W. Cao, “Elastic, dielectric, and piezoelectric constants of Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 single crystal poled along [011]c,” Appl. Phys. Lett., vol. 97, 032902, 3pp, 2010. [27] G. Gautschi, Piezoelectric Sensorics: Force, Strain, Pressure, Acceleration and Acoustic Emission Sensors Materials and Amplifiers, New York, NY: Springer-Verlag, 2002, pp. 73-90. [28] E. E. Havinga, “The temperature dependence of dielectric constants,” J. Phys. Chem. Solids., vol. 18, pp. 253-255, 1961. [29] W. P. Mason, Piezoelectric crystals and their application to ultrasonics, NEW YORK, NY: D. Van Nostrand Company, Inc., 1950. [30] J. J. Zhao, J. M. Winey, Y. M. Gupta, “First-principles calculations of second- and third-order elastic constants for single crystals of arbitrary symmetry,” Phys. Rev. B., vol. 75, 094105, 7pp, 2007.



24

[31] T. J. Shao, B. Wen, R. Melnik, S. Yao, Y. Kawazoe, Y. J. Tian, “Temperature dependent elastic constants for crystals with arbitrary symmetry: Combined first principles and continuum elasticity theory,” J. Appl. Phys., vol. 111, 083525, 7pp, 2012. [32] A. J. Moulson, J. M. Herbert, Electroceramics: Materials, properties, applications, NEW YORK, NY: Chapman and Hall, 1990, pp. 265-317. [33] S. E. Park, T. R. Shrout, “Characteristics of relaxor-based piezoelectric single crystals for ultrasonic transducers,” IEEE Tran, Ultrason. Ferroelectri. Freq. Control., vol. 44, pp. 1140-1147, 1997. [34] R. T. Smith, F. S. Welsh, “Temperature dependence of the elastic, piezoelectric, and dielectric constants of lithium tantalate and lithium niobate,” J. Appl. Phys., vol. 42, pp. 2219-2230, 1971. [35] F. P. Yu, S. J. Zhang, X. Zhao, D. R. Yuan, L. F. Qin, Q. M. Wang, T. R. Shrout, “Dielectric and electromechanical properties of rare earth calcium oxyborate piezoelectric crystals at high temperatures,” IEEE Tran, Ultrason. Ferroelectri. Freq. Control., vol. 58, pp. 868-873, 2011. [36] W. P. Mason, H. Jaffe, “Methods for measuring piezoelectric, elastic, and dielectric constants of crystals and ceramics,” Proceeding of the IRE., vol. 42, pp. 921-930, 1954. [37] W. P. Mason, Electromechanical Transducers and Wave Filters, NEW YORK, NY: D. Van Nostrand Company, Inc., 1948. [38] M. Redwood, J. Lamb, “On the measurement of attenuation and ultrasonic Delay Lines,” Proceeding of the IRE., vol. 103, pp. 773-780, 1956. [39] A. Caronti, R. Carotenuto, M. Pappalardo, “Electromechanical coupling factor of capacitive micromachined ultrasonic transducers,” J. Acoust. Soc. Am., vol. 113, pp. 279-288, 2003. [40] N. Lamberti, M. Pappalardo, “The electromechanical coupling factor in static and dynamic conditions,” Acoustics, vol. 85, pp. 39-46, 1999. [41] S. E. Park, T. R. Shrout, “Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals,” J. Appl. Phys., vol. 82, pp. 1804-1811, 1997. [42] S. J. Zhang, T. R. Shrout, “Relaxor-PT single crystals: Observations and developments,” IEEE Tran. Ultrason. Ferroele. Freq. Control., vol. 57, pp. 2138-2146, 2010. [43] J. H. Harlow, Electric Power Transformer Engineering, 3rd ed., Boca Raton, FL: CRC Press, 2004, pp. 1-216. [44] M. Tooley, M. H. Tooley, Electronic circuits: Fundamentals and applications, Oxford, UK: Newnes, 2006, pp. 77-78. [45] C. T. -C. Nguyen, “MEMS Technology for timing and frequency control,” IEEE Tran. Ultrason. Ferroele. Freq. Control., vol. 54, pp. 251-270, 2007. [46] D. T. Nguyen, C. Baker, W. Hease, S. Sejil, P. Senellart, A. Lemaître, S. Ducci, G. Leo, I. Favero, “Ultrahigh q-frequency product for optomechanical disk resonators with a mechanical shield,” Appl. Phys. Lett., vol. 103, 241112, 5pp, 2013. [47] L. B. M. Sliva, E. J. P. Santos, “Modeling quality factor in AT-cut quartz-crystal resonators,” 2013 Symposium on Microelectronics Technology and Devices (SBMicro), Curitiba, Brazil, Sep. 2-6, 2013. [48] J. Soejima, K. Nagata, “PbNb2O6 Ceramics with tungsten bronze structure for low Qm piezoelectric material,” Jpn. J. Appl. Phys., vol. 40, pp. 5747-5750, 2001. [49] R. Holland, E. P. EerNisse, “Accurate measurement of coefficients in a ferroelectric ceramic,” IEEE Trans. Sonics Ultrason., vol. SU-16, pp. 173-181, 1969. [50] X. H. Du, Q. -M. Wang, K. Uchino, “Accurate determination of complex materials coefficients of piezoelectric resonators,” IEEE Tran. Ultrason. Ferroele. Freq. Control., vol. 50, pp. 312-320, 2003. [51] X. H. Du, Q. -M. Wang, K. Uchino, “An accurate method for the determination of complex coefficients of single crystal piezoelectric resonators І: Theory,” IEEE Tran. Ultrason. Ferroele. Freq. Control., vol. 51, pp. 227-237, 2004. [52] H. L. Chatelier, “Sur la dilatation du quartz,” C.R. Acad. Sci., vol. 108, pp. 1046, 1889.



25

[53] R. K. Cook, P. G. Weissler, “Piezoelectric constants of Alpha- and Beta-quartz at various temperatures,” Phys. Rev., vol. 80, pp. 712-716, 1950. [54] A. C. Walker, “Hydrothermal synthesis of quartz crystals,” J. Am. Ceram. Soc., vol. 36, pp. 250-256, 1953. [55] J. F. Bertone, J. Cizeron, R. K. Wahi, J. K. Bosworth, V. L. Colvin, “Hydrothermal synthesis of quartz nanocrystals,” Nano. Lett., vol. 3, pp. 655-659, 2003. [56] R. Bechmann, “Elastic and piezoelectric constants of Alpha-Quartz,” Phys. Rev., vol. 110, pp. 1060-1061, 1958. [57] A. J. Mullen, “Temperature Variation of the piezoelectric constant of quartz,” J. Appl. Phys. vol. 40, pp. 1693-1696, 1969. [58] A. De, K. V. Rao, “Dielectric properties of synthetic quartz crystals,” J. Mater. Sci., vol. 23, pp. 661-664, 1988. [59] H. F. Tiersten, The Redetermination of The Elastic, Piezoelectric and Dielectric Constants of Quartz and Their Variation With Temperature, NEW YORK, NY: Rome Air Development Center, Air Force Systems Command, 1989, 46pp. [60] P. Heyliger, H. Ledbetter, S. Kim, “Elastic constants of natural quartz,” J. Acoust. Soc. Am., vol. 114, pp. 644-650, 2003. [61] C. S. Lam, “A review of the recent development of temperature stable cuts of quartz for SAW applications,” Fourth International Symposium on Acoustic Wave Devices for Future Mobile Communication Systems, Chiba, Japan, Mar. 3-5, 2010. [62] F. C. Hawthorne, D. J. Henry, “Classification of the minerals of the tourmaline group,” Eur. J. Mineral., vol. 11, pp. 201-215, 1999. [63] D. J. Henry, M. NovÁk, F. C. Hawthorne, A. Ertl, B. L. Dutrow, P. Uher, F. Pezzotta, “Nomenclature of the tourmaline-supergroup minerals,” Am. Mineral., vol. 96, pp. 895-913, 2011. [64] F. C. Hawthorne, D. M. Dirlam, “Tourmaline the indicator mineral: From atomic arrangement to viking navigation,” Elements, vol. 7, pp. 307-312, 2011. [65] C. Frondel, R. L. Collette, “Synthesis of tourmaline by reaction of mineral grains with NaCl-H3BO3 solution, and its implications in rock metamorphism,” Am. Mineral., vol. 42, pp. 754-758, 1957. [66] T. Setkova, Y. Shapovalov, V. Balitsky, “Growth of tourmaline single crystals containing transition metal elements in hydrothermal solutions,” J. Cryst. Growth., vol. 318, pp. 904-907, 2011. [67] T. V. Setkova, V. S. Balitskiy, “Epitaxial growth of Ga-rich tourmaline on natural elbaite seed In boric hydrothermal solutions,” 17th International Conference On Crystal Growth and Epitaxy-ICCGE-17, Warsaw, Poland, Aug. 11-16, 2013. [68] C. S. Pandey, S. Jodlauk, J. Schreuer, “Correlation between dielectric properties and chemical composition of the tourmaline single crystals,” Appl. Phys. Lett., vol. 99, 142906, 3pp, 2011. [69] C. S. Pandey, J. Schreuer, “Elastic and piezoelectric constants of tourmaline single crystals at Non-ambient temperatures determined by resonant ultrasound spectroscopy,” J. Appl. Phys., vol. 111, 013516, 7pp, 2012. [70] K. T. Hawkins, “Influence of chemistry on the pyroelectric effect In tourmaline,” Am. Mineral., vol. 80, pp. 491-501, 1995. [71] T. Volk, M. Wöhlecke, Lithium Niobate: Defects, Photorefraction and Ferroelectric Switching, New York, NY: Springer-Verlag, 2008, pp. 1-8. [72] K. Nassau, H. J. Levinstein, G. M. Loiacono, “Ferroelectric lithium niobate. 1. Growth, domain structure, dislocations and etching,” J. Phys. Chem. Solids., vol. 27, pp. 983-988, 1966. [73] V. N. Kurlov, B. S. Red’kin, “Growth of shaped lithium tantalate crystals,” J. Cryst. Growth., vol. 104, pp. 80-83, 1990. [74] T. Shiosaki, M. Adachi, A. Kawabata, “Growth and properties of piezoelectric lithium tetraborate crystal for BAW and SAW devices,” IEEE Int. Appl. Ferroelec. Symp., pp. 455-464, 1986. [75] K. Uchino, Advanced Piezoelectric Materials: Science and Technology; Sawston, Cambridge, UK: Woodhead Publishing, 2010, pp. 204-238.



26

[76] S. J. Fan, “Properties, Production and application of new piezoelectric crystal lithium tetraborate Li2B4O7,” IEEE International Frequency Control Symposium, Salt Lake City, UT, Jun. 2-4, 1993, pp. 353-358. [77] A. Weidenfelder, J. Shi, P. Fielitz, G. Borchardt, K. D. Becker, H. Fritze, “Electrical and electromechanical properties of stoichiometric lithium niobate at High-temperatures,” Solid State Ionics, vol. 225, pp. 26-29, 2012. [78] E. Philippot, D. Palmier, M. Pintard, A. Goiffon, “A general survey of quartz and quartz-like materials: Packing distortions, temperature, and pressure effects,” J. Solid State Chem., vol. 123, pp. 1-13, 1996. [79] J. H. Sherman, “Quartz analogues.” 40th Annual Frequency Control Symposium, Philadelphia, PA, May 28-30, 1986. [80] E. Philippot, A. Goiffon, A. Ibanez, M. Pintard, “Structure deformations and existence of the α-β transition in MXO4 quartz-like materials,” J. Solid State Chem., vol. 110, pp. 356-362, 1994. [81] C. Glidewell, “Some chemical and structural consequences of non-bonded interactions,” Inorg. Chim. Acta., vol. 12, pp. 219-227, 1975. [82] H. Grimm, B. Dorner, “On the mechanism of the α-β phase transformation of quartz,” J. Phys. Chem. Solids., vol. 36, pp. 407-413, 1975. [83] E. Philippot, A. Ibanez, A. Goiffon, M. Cochez, A. Zarka, B. Capelle, J. Schwartzel, J. Détaint, “A quartz-like material: Gallium phosphate (GaPO4); crystal growth and characterization,” J. Cryst. Growth., vol. 130, pp. 195-208, 1993. [84] O. Cambon, P. Yot, D. Balitsky, A. Goiffon, E. Philippot, B. Capelle, J. Detaint, “Crystal growth of GaPO4, a very promising material for manufacturing BAW devices,” Ann. Chim. Sci. Mat., vol. 26, pp. 79-84, 2001. [85] G. G. Xu, H. Z. Cui, J. Li, J. Y. Wang, “Investigation of single crystal growth of GaPO4 by the flux method,” Crystallography Reports, vol. 58, pp. 195-197, 2013. [86] P. M. Worsch, P. W. Krempl, W. Wallnöfer, “GaPO4 crystals for sensor applications,” Sensors, 2002. Proceedings of IEEE, Orlando, FL, Jun. 12-14, 2002. [87] J. Haines, O. Cambon, N. Prudhomme, G. Fraysse, D. A. Keen, L. C. Chapon, M. G. Tucker, “High-temperature, structural disorder, phase transitions, and piezoelectric properties of GaPO4,” Phys. Rev. B., vol. 73, 014103, 10pp, 2006. [88] F. Krispel, C. Reiter, J. Neubig, F. Lenzenhuber, P. W. Krempl, W. Wallnöfer, P. M. Worsch, “Properties and Applications of Singly Rotated GaPO4 Resonators,” 2003 IEEE Int. Frequency Control Symposium & 17th European Frequency and Time Forum, Tampa, May 5-8, 2003. [89] C. Reiter, P. W. Krempl, H. Thanner, W. Wallnöfer, P. M. Worsch, “Material properties of GaPo4 and their relevance for applications,” Ann. Chim. Sci. Mat., vol. 26, pp. 91-94, 2001. [90] B. V. Mill, A. V. Butashin, A. M. Ellern, A. A. Maier, “Formation de phases dans le System CaO-Ga2O3-GeO2,” Izvest. Akad. Nauk Sssr, Neorg. Mater., vol. 17, pp. 1648-1653, 1981. [91] B. V. Mill, “Formation of phase with the Ca3Ga2Ge4O14 structure in the AO-TeO3-Ga2O3-XO2 (A=Pb, Ba, Sr; X=Si, Ge) and PbO-TeO3-MO-GeO2 (M=Zn, Co) Systems,” Zhurnal Neorganicheskoi Khimii, vol. 55, pp. 1706-1711, 2010. [92] A. P. Dudka, V. I. Simonov, “Structural conditionality of the piezoelectric properties of langasite family crystals,” Crystallography Reports, vol. 56, pp. 980-985, 2011. [93] I. A. Andreev, “Single Crystals of the Langasite Family: An intriguing combination of properties promising for Acoustoelectronics,” Zhurnal Tekhnicheskoĭ Fiziki, vol. 76, pp. 80-86, 2006. [94] B. V. Mill, Y. V. Pisarevsky, “Langasite-type materials: From discovery to present state,” Proceedings of 2000 IEEE/EIA International Frequency Control Symposium, Kansas City, Missouri, Jun. 7-9, 2000. [95] H. Takeda, J. Yamaura, T. Hoshina, T. Tsusrumi, “Growth, structure and electrical properties of aluminum substituted langasite family crystals,” IOP Conf. Ser.: Mater. Sci. Eng., vol. 18, 092020, 4pp, 2011.



27

[96] H. Yoshida, O. Eguchi, Y. Ohashi, J. I. Kushibiki, “Applications of langasite family crystals to piezoelectric devices,” The 33rd Symposium on UltraSonic Electronics, Chiba, Japan, Nov. 13-15, 2012. [97] T. Fukuda, H. Takeda, K. Shimamura, H. Kawanaka, M. Kumatoriya, S. Murakami, J. Sato, M. Sato, “Growth of new langasite single crystals for piezoelectric applications,” Proceedings of the 11th IEEE International Symposium on Applications of Ferroelectrics, Montreux, Switzerland, Aug. 24-27, 1998. [98] S. Georgescu, A. M.; Voiculescu, C. Matei, O. Toma, L. Gheorghe, A. Achim, “Reflectance measurements on europium-doped langasite, langanite and langatate powders,” Rom. Rep. Phys., vol. 62, pp. 128-133, 2010. [99] F. P. Yu, X. Zhao, L. H. Pan, F. Li, D. R. Yuan, S. J. Zhang, “Investigation of zero temperature compensated cuts in langasite-type piezocrystals for high temperature applications,” J. Phys. D: Appl. Phys., vol. 43, 165402. 7pp, 2010. [100] B. Chai, H. Qiu, Y. Y. Ji, J. L. Lefaucheur, “Growth of high quality single domain crystals of langasite family compounds,” Frequency and Time Forum, 1999 and the IEEE International Frequency Control Symposium, 1999., Proceedings of the 1999 Joint Meeting of the European, Besancon, France, Apr. 13-16, 1999. [101] A. Masatoshi, S. Yuzuru, F. Takeo, K. Tomoaki, “Growth of langasite family compounds for bulk and saw applications,” Ferroelectrics, vol. 273, pp. 89-94, 2002. [102] A. H. Wu, “Bridgman Growth of langasite-type piezoelectric crystals,” Cryst. Res. Technol., vol. 42, pp. 862-866, 2007. [103] M. Adachi, T. Funakawa, T. Karaki, “Growth of substituted langasite-type Ca3NbGa3Si2O14 single crystals, and their dielectric, elastic and piezoelectric properties,” Applications of Ferroelectrics, 2002. ISAF 2002. Proceedings of the 13th IEEE International Symposium on, Nara, Japan, May 28 - Jun. 1, 2002. [104] T. Kuze, H. Takeda, T. Nishida, K. Uchiyama, T. Shiosaki, “Synthesis and electric properties of aluminum substituted langasite-type La3Nb0.5Ga5.5O14 single crystals,” Applications of Ferroelectrics, 2007. ISAF 2007. 16th IEEE International Symposium on, Nara, Japan, May 27-31, 2007. [105] M. Kumatoriya, H. Sato, J. Nakanishi, T. Fujii, M. Kadota, Y. Sakabe, “Crystal growth and electromechanical properties of Al substituted langasite (La3Ga5-xAlxSiO14),” J. Cryst. Growth., vol. 229, pp. 289-293, 2001. [106] B. H. T. Chai, A. N. P. Bustamante, M. C. Chou, “A new class of ordered langasite structure compounds,” Frequency Control Symposium and Exhibition, 2000. Proceedings of the 2000 IEEE/EIA International, Kansas, MO, Jun. 07-09, 2000. [107] H. F. Zu, H. Y. Wu, Y. Z. Wang, Q. -M. Wang, S. J. Zhang, T. R. Shrout, “Properties of Piezoelectric Single crystals Ca3TaGa3Si2O14 at high temperature and high vacuum conditions,” 2013 Joint UFFC, EFTF and PFM Symposium, Prague, Czech Republic, Jul. 21-25, 2013. [108] Z. M. Wang, D. R. Yuan, Z. X. Cheng, X. L. Duan, H. Q. Sun, X. Z. Shi, X. C. Wei, Y. Q. Lü, D. Xu, M. K. Lü, L. H. Pan, “Growth of a new ordered langasite structure compound Ca3TaAl3Si2O14 single crystal,” J. Cryst. Growth., vol. 253, pp. 398-403, 2003. [109] H. Ohsato, T. Iwataki, H. Morikoshi, “Mechanism of piezoelectricity for langasite based on the framework crystal structure,” Trans. Electr. Electron. Mater., vol. 13, pp. 51-59, 2012. [110] I. A. Kaurova, G. M. Kuz’micheva, V. B. Rybakov, A. Cousson, O. Zaharko, E. N. Domoroshchina, “Growth and neutron diffraction investigation of Ca3NbGa3Si2O14 and La3Ga5.5Nb0.5O14 crystals,” J. Mater., vol. 2013, 191626, 6pp, 2013. [111] J. Xin, Y. Q. Zheng, H. K. Kong, H. Chen, X. N. Tu, E. Shi, “Growth of a new ordered langasite structure crystal Ca3TaAl3Si2O14,” Cryst. Growth Des., vol. 8, pp. 2617-2619, 2008. [112] R. Norrestam, M. Nygren, J. -O. Bovin, “Structural investigations of new calcium-rare earth (R) oxyborates with the composition Ca4RO(BO3)3,” Chem. Mater., vol. 4, pp. 737-743, 1992. [113] F. P. Yu, S. J. Zhang, X. Zhao, S. Y. Guo, X. L. Duan, D. R. Yuan, T. R. Shrout, “Investigation of the dielectric and piezoelectric properties of ReCa4(BO3)3 crystals,” J. Phys. D: Appl. Phys., vol. 44, 135405, 6pp, 2011.



28

[114] Y. T. Fei, B. H. T. Chai, C. A. Ebbers, Z. M. Liao, K. I. Schaffers, P. Thelin, “Large-aperture YCOB crystal growth for frequency conversion in the high average power laser System,” J. Cryst. Growth., vol. 290, pp. 301-306, 2006. [115] R. A. Kumar, “Borate crystals for nonlinear optical and laser applications: A review,” Journal of Chemistry, vol. 2013, 154862, 6pp, 2013. [116] M. Iwai, T. Kobayashi, H. Furuya, Y. Mori, T. Sasaki, “Crystal growth and optical characterization of rare-earth (Re) calcium oxyborate ReCa4O(BO3)3 (Re=Y or Gd) as new nonlinear optical material,” Jpn. J. Appl. Phys., vol. 36, pp. L1562-L1562, 1997. [117] Y. Q. Zheng, X. N. Tu, J. J. Chen, P. Gao, E. W. Shi, “Piezoelectric acceleration sensors based on LGX and ReCOB crystals for application above 645°C,” 2013 Joint UFFC, EFTF and PFM Symposium, Prague, Czech Republic, Jul. 21-25, 2013. [118] C. T. Chen, T. Sasaki, R. K. Li, Y. C. Wu, Z. S. Lin, Y. Mori, Z. G. Hu, J. Y. Wang, G. Aka, M. Yoshimura, Y. Kaneda, Nonlinear Optical Borate Crystals, Hoboken, NJ: John Wiley & Sons, 2012, pp. 117-343. [119] S. J. Zhang, F. P. Yu, R. Xia, Y. T. Fei, E. Frantz, X. Zhao, D. R. Yuan, B. H. T. Chai, D. Snyder, T. R. Shrout, “High temperature ReCOB piezocrystals: Recent developments,” J. Cryst. Growth., vol. 318, pp. 884-889, 2011. [120] S. J. Zhang, E. Frantz, R. Xia, W. Everson, J. Randi, D. W. Snyder, T. R. Shrout, “Gadolinium calcium oxyborate piezoelectric single crystals for ultrahigh temperature (>1000°C) applications,” J. Appl. Phys., vol. 104, 084103, 7pp, 2008. [121] S. J. Zhang, Y. T. Fei, E. Frantz, D. W. Snyder, B. H. T. Chai, T. R. Shrout, “High-temperature piezoelectric single crystal ReCa4O(BO3)3 for sensor applications,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control., vol. 55, pp. 2703-2708, 2008. [122] F. P. Yu, S. Hou, X. Zhao, S. J. Zhang, “High-temperature piezoelectric crystals ReCa4O(BO3)3: a review,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control., vol. 61, pp. 1344-1356, 2014. [123] A. V. Virkar, T. B. Jackson, R. A. Cutler, “Thermodynamic and kinetic effects of oxygen removal on the thermal conductivity of aluminum nitride,” J. Am. Ceram. Soc., vol. 72, pp. 2031-2042, 1989. [124] Y. Kurokawa, K. Utsumi, H. Takamizawa, “Development and microstructural characterization of high-thermal-conductivity aluminum nitride ceramics,” J. Am. Ceram. Soc., vol. 71, pp. 588-594, 1988. [125] G. A. Slack, R. A. Tanzilli, R. O. Pohl, J. W. Wandersande, “The intrinsic thermal conductivity of AlN,” J. Phys. Chem. Solids., vol. 48, pp. 641-647, 1987. [126] T. Aubert, O. Elnazria, B. Assouar, E. Blampain, A. Hamdan, D. Genève, S. Weber, “Investigations on AlN/sapphire piezoelectric bilayer structure for high-temperature SAW applications,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control., vol. 59, pp. 999-1005, 2012. [127] L. I. Berger, Semiconductor Materials, Boca Raton, FL: CRC Press, 1997, pp. 123-124. [128] R. Schlesser, R. Dalmau, Z. Sitar, “Seeded growth of AlN bulk single crystals by sublimation,” J. Cryst. Growth., vol. 241, pp. 416-420, 2002. [129] D. Zhuang, Z. G. Herro, R. Schlesser, Z. Sitar, “Seeded growth of AlN single crystals by physical vapor transport,” J. Cryst. Growth., vol. 287, pp. 372-375, 2006. [130] I. Satoh, S. Arakawa, K. Tanizaki, M. Miyanaga, T. Sakurada, Y. Yamamoto, H. Nakahata, “Development of aluminum nitride single-crystal substrates,” SEI Technical Review 71, vol. 79, pp. 78-82, 2010. [131] M. A. Dubois, P. Muralt, “Properties of aluminum nitride thin films for piezoelectric transducers and microwave filter applications,” Appl. Phys. Lett., vol. 74, pp. 3032-3034, 1999. [132] Z. W. Yin, H. S. Luo, P. C. Wang, G. S. Xu, “Growth, characterization and properties of relaxor ferroelectric PMN-PT single crystals,” Ferroelectrics, vol. 229, pp. 207-216, 1999. [133] T. R. Shrout, Z. P. Chang, N. Kim, S. Markgraf, “Dielectric behavior of single crystals near the (1-x)Pb(Mg1/3Nb2/3)O3-(x)PbTiO3,” Ferroelectrics, vol. 12, pp. 63-69, 1990.



29

[134] H. S. Luo, G. S. Xu, P. C. Wang, Z. W. Yin, “Growth and characterization of relaxor ferroelectric PMNT single crystals,” Ferroelectrics, vol. 231, pp. 97-102, 1999. [135] X. N. Jiang, K. Kim, S. J. Zhang, J. Johnson, G. Salazar, “High-temperature piezoelectric sensing,” Sensors, vol. 14, pp. 144-169, 2014. [136] L. Rayleigh, “On waves propagated along the plane surface of an elastic solid,” Proc. London Math. Soc., vol. s1-17, pp. 4-11, 1885. [137] R. M. White, F. W. Voltmer, “Direct coupling to surface acoustic wave,” Appl. Phys. Lett., vol. 7, pp. 314-316, 1965. [138] M. Hoummady, A. Campitelli, W. Wlodarski, “Acoustic wave sensors: Design, sensing mechanisms and applications,” Smart Mater. Struct., vol. 6, pp. 647-657, 1997. [139] M. F. Hribšek, D. V. Tošić, M. R. Radosavljević, “Surface acoustic wave sensors in mechanical engineering,” FME Transactions., vol. 38, pp. 11-18, 2010. [140] E. Benes, M. Gröschl, F. Seifert, A. Pohl, “Comparison between BAW and SAW sensor principles,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control., vol. 45, pp. 1314-1330, 1998. [141] E. Benes, M. Gröschl, W. Burger, M. Schmid, “Sensors based on piezoelectric resonators,” Sensor. Actuat. A-Phys., vol. 48, pp. 1-21, 1995. [142] M. R. Zakaria, U. Hashim, R. M. Ayub, T. Adam, “Design and fabrication of IDT SAW by using conventional lithography technique,” Middle-East Journal of Scientific Research, vol. 18, pp. 1281-1285, 2013. [143] A. Pohl, “A review of wireless SAW sensors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control., vol. 47, pp. 317-332, 2000. [144] J. Hornsteiner, E. Born, G. Fischerauer, E. Riha, “Surface acoustic wave sensors for high-temperature applications,” In Proceedings of the IEEE International Frequency Control Symposium, Pasadena, CA, May 29, 1998, pp. 615-620. [145] W. E. Bulst, G. Fischerauer, “State of the art in wireless sensing with surface acoustic waves,” IEEE Trans. on Industrial Electronics., vol. 48, pp. 265-271, 2001. [146] R. Hauser, L. Reindl, J. Biniasch, “High-temperature stability of LiNbO3 based SAW devices,” 2003 IEEE Symposium on Ultrasonics, Honolulu, HI, Oct. 5-8, 2003, vol. 1, pp. 192-195. [147] M. N. Hamidon, V. Skarda, N. M. White, F. Krispel, P. Krempl, M. Binhack, W. Buff, “Fabrication of high temperature surface acoustic wave devices for sensor applications,” Sensor. Actuat. A-Phys., vol. 123-124, pp. 403-407, 2005. [148] M. N. Hamidon, V. Skarda, N. M. White, F. Krispel, P. Krempl, M. Binhack, W. Buff, “High-temperature 434 MHz surface acoustic wave devices based on GaPO4,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control., vol. 53, pp. 2465-2470, 2006. [149] M. P. Da Cunha, R. J. Lad, T. Moonlight, G. Bernhardt, D. J. Frankel, “High-temperature stability of langasite surface acoustic wave devices,” 2008 IEEE Ultrasonics Symposium, Beijing, China, Nov. 2-5, 2008, vol. 1, pp. 205-208. [150] J. A. Thiele, M. P. Da Cunha, “High temperature LGS SAW gas sensor,” Sensor. Actuat. B-Chem., vol. 113, pp. 816-822, 2006. [151] B. Drafts, “Acoustic wave technology sensor,” IEEE Transactions on Microwave Theory and Techniques., vol. 49, pp. 795-802, 2001. [152] H. Fritze, “High-temperature bulk acoustic wave sensors,” Meas. Scil Technol., vol. 22, 012002, 28pp, 2011. [153] P. Hauptmann, R. Lucklum, J. Schroder, “Recent trends in bulk acoustic wave resonator sensors,” 2003 IEEE Symposium on Ultrasonics, Honolulu, HI, Oct. 5-8, 2003, vol. 1, pp. 56-65. [154] K. A. Marx, “Quartz Crystal Microbalance: A useful tool for studying thin polymer films and complex biomolecular systems at the solution-surface interface,” Biomacromolecules, vol. 4, pp. 1109-1120, 2003. [155] R. Lucklum, P. Hauptmann, “The quartz crystal microbalance: Mass sensitivity, viscoelasticity and acoustic amplification,” Sensor. Actuat. B-Chem., vol. 70, pp. 30-36, 2000.



30

[156] E. Uttenthaler, M. Schräml, J. Mandel, S. Drost, “Ultrasensitive quartz crystal microbalance sensors for detection of M13-Phages in liquids,” Biosens. Bioelectron., vol. 16, pp. 735-743, 2001. [157] M. A. Dubois, “Thin film bulk acoustic wave resonators: A technology overview,” MEMSWAVE 03, Toulouse, France, Jul. 2-4, 2003. [158] G. Sauerbrey, “Verwendung von schwingquarzen zur wägung düneer schichten und zur mikrowägung,” Zeitschrift für Physik, vol. 155, pp. 206-222, 1959. [159] H. Seh, T. Hyodo, H. L. Tuller, “Bulk acoustic wave resonator as a sensing platform for NOx at high temperatures,” Sensor. Actuat. B-Chem., vol. 108, pp. 547-552, 2005. [160] H. Thanner, P. W. Krempl, R. Selic, W. Wallnöfer, P. M. Worsch, “GaPO4 high temperature crystal microbalance demonstration Up to 720°C,” J. Therm. Anal. Cal., vol. 71, pp. 53-59, 2003. [161] H. Seh, H. L. Tuller, H. Fritze, “Langasite for High-temperature Acoustic Wave Gas Sensors,” Sensor. Actuat. B-Chem., vol. 93, pp. 169-174, 2003. [162] H. Seh, H. L. Tuller, H. Fritze, “Defect properties of langasite and effects on BAW gas sensor performance at high temperatures,” J. Eur. Ceram. Soc., vol. 24, pp. 1425-1429, 2004. [163] C. Déjous, I. Esteban, D. Rebière, J. Pistré, R. Planade, “Temperature-compensated SH-APM sensors: New theoretical and experimental results,” 1997 IEEE International Frequency Control Symposium, Orlando, FL, May. 28-30, 1997. [164] C. Déjous, M. Savart, D. Rebière, J. Pistré, “A Shear-horizontal acoustic plate mode (SH-APM) sensor for biological media,” Sensor. Actuat. B-Chem., vol. 27, pp. 452-456, 1995. [165] R. B. Karabalin, M. H. Matheny, X. L. Feng, E. Defaÿ, G. L. Rhun, C. Marcoux, S. Hentz, P. Andreucci, M. L. Roukes, “Piezoelectric nanoelectromechanical resonators based on aluminum nitride thin films,” Appl. Phys. Lett., vol. 95, 103111, 3pp, 2009. [166] T. Y. Lee, J. T. Song, “Detection of carcinoembryonic antigen using AlN FBAR,” Thin Solid Films, vol. 518, pp. 6630-6633, 2010. [167] C. -M. Yang, K. Uehara, S. -K. Kim, S. Kameda, H. Nakase, K. Tsubouchi, “Highly C-Axis-Oriented AlN film using MOCVD for 5 GHz-Band FBAR filter,” 2003 IEEE Symposium on Ultrasonics, Honolulu, HI, Oct. 5-8, 2003, vol. 1, pp. 170-173. [168] Z. Yan, X. Y. Zhou, G. K. H. Pang, T. Zhang, W. L. Liu, J. G. Cheng, Z. T. Song, S. L. Feng, L. H. Lai, J. Z. Chen, Y. Wang, “ZnO-based film bulk acoustic resonator for high sensitivity biosensor applications,” Appl. Phys. Lett., vol. 90, 143503, 3pp, 2007. [169] Q. -X. Su, P. Kirby, E. Komuro, M. Imura, Q. Zhang. R. Whatmore, “Thin-film bulk acoustic resonators and filters using ZnO and Lead-Zirconium-Titanate thin films,” IEEE Transactions on Microwave Theory and Techniques. vol. 49, pp. 769-778, 2001. [170] W. C. Xu, X. Zhang, S. Choi, J. Chae, “A high-quality-factor film bulk acoustic resonator in liquid for biosensing applications,” Journal of Microelectromechanical Systems, vol. 20, pp. 213-220, 2011. [171] Y. Osugi, T. Yoshino, K. Suzuki, T. Hirai, “Single crystal FBAR with LiNbO3 and LiTaO3 piezoelectric substance layers,” 2007 IEEE/MTT-S International Microwave Symposium, Honolulu, HI, Jun. 3-8, 2007, pp. 873-876. [172] O. Boubai, “Knock detection in automobile engines,” IEEE Instrum. Meas. Mag., vol. 3, pp. 24-28, 2000. [173] S. Szwaja, K. Bhandary, J. Naber, “Comparisons of hydrogen and gasoline combustion knock in a spark ignition engine,” Int. J. Hydrog. Energy., vol. 32, pp. 5076-5087, 2007. [174] W. Tian, S. C. Wu, Z. B. Zhou, S. B. Qu, Y. Z. Bai, J. Luo, “High resolution space quartz-flexure accelerometer based on capacitive sensing and electrostatic control technology,” Rev. Sci. Instrum., vol. 83, 095002, 6pp, 2012. [175] S. J. Zhang, X. N. Jiang, M. Lapsley, P. Moses, T. R. Shrout, “Piezoelectric accelerometers for ultrahigh temperature application,” Appl. Phys. Lett., vol. 96, 013506, 3pp, 2010.



31

[176] L. Zhou, J. Sun, X. J. Zheng, S. F. Deng, J. H. Zhao, S. T. Peng, Y. Zhang, X. Y. Wang, H. B. Cheng, “A model for the energy harvesting performance of shear mode piezoelectric cantilever,” Sensor. Actuat. A-Phys., volume 179, pp. 185-192, 2012. [177] G. Tang, J. -Q. Liu, B. Yang, J. -B. Luo, H. -S. Liu, Y. -G. Li, C. -S. Yang, V. -D. Dao, K. Tanaka, S. Sugiyama, “Piezoelectric MEMS low-level vibration energy harvester with PMN-PT single crystal cantilever,” Electron. Lett., volume 48, 2pp, 2012. [178] C. D. Xu, B. Ren, W. N. Di, Z. Liang, J. Jiao, L. Y. Li, L. Li, X. Y. Zhao, H. S. Luo, D. Wang, “Cantilever driving low frequency piezoelectric energy harvester using single crystal material 0.71Pb(Mg1/3Nb2/3)O3-0.29PbTiO3,” Appl. Phys. Lett., vol. 101, 033502, 4pp, 2012. [179] S. Hur, S. Q. Lee, H. S. Choi, “Fabrication and characterization of PMN-PT single crystal cantilever array for cochlear-like acoustic sensor,” J. Mech. Sci. Technol., vol. 24, pp. 181-184, 2010. [180] O. Bilgen, M. A. Karami, D. J. Inman, M. I. Friswell, “The actuation characterization of cantilevered unimorph beams with single crystal piezoelectric materials,” Smart. Mater. Struct., vol. 20, 055024, 9pp, 2011. [181] J. Zhang, Z. Wu, Y. M. Jia, J. W. Kan, G. M. Cheng, “Piezoelectric bimorph cantilever for vibration-producing-hydrogen,” Sensors. vol. 13, pp. 367-374, 2013. [182] V. Giurgiutiu, A. Cuc, “Embedded non-destructive evaluation for structural health monitoring, damage detection, and failure prevention,” Shock and Vibration Digest, vol. 37, pp. 83-105, 2005. [183] K. Kirk, C. Scheit, N. Schmarje, “High-temperature acoustic emission test using lithium niobate piezocomposite transducers,” Insight Non Destr. Test. Cond. Monit., vol. 49, pp. 142-145, 2007. [184] J. A. Johnson, K. Kim, S. J. Zhang, D. Wu, X. N. Jiang, “High-temperature (>1000°C) acoustic emission sensor,” Proc. SPIE 8694, Nondestructive Characterization for Composite Materials, Aerospace Engineering, Civil Infrastructure, and Homeland Security 2013, San Diego, CA, Mar. 10, 2013. [185] J. A. Johnson, K. Kim, S. J. Zhang, X. N. Jiang, “Crack propagation testing using a YCOB acoustic emission sensor,” Proc. SPIE 9063, Nondestructive Characterization for Composite Materials, Aerospace Engineering, Civil Infrastructure, and Homeland Security 2014, San Diego, CA, Mar. 9, 2014.



32

CAPTION OF FIGURES AND TABLES Fig. 1. Arrhenius diagram of the total electrical conductivities of LN samples with different lithium content in the temperature range from 500 °C to 900 °C [77] (copyright 2012 by the ELSEVIER). Fig. 2. Temperature dependent frequency and inverse Qf product of sample 3 and 4. The full squares and the full triangles present sample 3; the blank squares and the blank triangles present sample 4 [77] (copyright 2012 by the ELSEVIER). Fig. 3. Evolution of the bridging angle M–O–X, θ, in terms of the mean value of the tilt angle, δ, of MO4 and XO4 tetrahedra [80] (copyright 1994 by the ELSEVIER). Fig. 4. Evolution of the c/a ratio in terms of the bridging angle M–O–X, θ, [78] (copyright 1996 by the ELSEVIER). Fig. 5. Quality factor Q (hollow triangles) and coupling factor k (solid squares) of an AT-cut GaPO4 resonator as a function of temperature [87] (copyright 2006 by the APS Physics). Fig. 6. Schematic illustration of the langasite crystal structure viewed along [001] direction [95] (copyright 2011 by the Authors). Fig. 7. Resistivity ρ as a function of temperature for pure and Al-substituted crystals [95] (copyright 2011 by the Authors). Fig. 8. Dielectric loss as a function of temperature for ordered langasite-type piezoelectric crystals [18] (copyright 2009 by the AIP Publishing). Fig. 9. Schematic crystal structure of ReCOB crystals (from ICDD database; Nd could be replaced by other Re elements, (a) observed from the a-axis, (b) observed from the b-axis and (c) schematic of ionic displacement movement) [113] (copyright 2011 by the IOP Science). Fig. 10. Electrical resistivity (ρ) of Y-cut ReCOB (Re = Er, Y, Gd, Sm, Nd, Pr, and La) crystals at room temperature (inset) and elevated temperatures [122] (copyright 2014 by the IEEE). Fig. 11. (a)The dielectric/piezoelectric constants and (b) the electromechanical coupling/mechanical quality factors of the ReCOB family crystals, as a function of the absolute value of the radius difference between the Re3+ ion and the Ca2+ ion (│R(Re3+)-R(Ca2+)│) (data obtained from reference [113, 122]). Fig. 12. (a)Long time ageing of the investigated ID-tag at 400°C (b) Measurements of the long-time thermal stability of LiNbO3 SAW devices up to 450°C and the predicted lift-time at 300 °C [146] (copyright 2003 by the IEEE). Fig. 13. Measured center frequency for a Pt/10%Rh/ZrO2 deposited two-port LGS SAW sensor while being cycled from room temperature to 850°C six times [149] (copyright 2008 by the IEEE). Fig. 14. (a)Schematic of NO2 QCM sensor (b) Comparing responses to NO2 at different temperatures and two different BaCO3 microstructures [159] (copyright 2005 by the ELSEVIER). Fig. 15. Sensitivity of the YCOB accelerometer as function of temperature up to 1000°C at different frequencies [175] (copyright 2010 by the AIP).

Table I.

Specific applications and related effects of piezoelectric materials.

Table II.

The determination of the dielectric permitivities and impermeabilities.

Table III. The determination of the elastic constants. Table IV. The determination of the piezoelectric constants [29]. Table V.

Characteristics and applications of principal cuts of quartz crystals.

Table VI. General properties of LN, LT and LTB crystals. Table VII. General properties of 9 kinds of representative piezoelectric single crystals.



33

Fig. 1. Arrhenius diagram of the total electrical conductivities of LN samples with different lithium content in the temperature range from 500 °C to 900 °C [77] (copyright 2012 by the ELSEVIER).



34

Fig. 2. Temperature dependent frequency and inverse Qf product of sample 3 and 4. The full squares and the full triangles present sample 3; the blank squares and the blank triangles present sample 4 [77] (copyright 2012 by the ELSEVIER).



35

Fig. 3. Evolution of the bridging angle M–O–X, θ, in terms of the mean value of the tilt angle, δ, of MO4 and XO4 tetrahedra [80] (copyright 1994 by the ELSEVIER).



36

Fig. 4. Evolution of the c/a ratio in terms of the bridging angle M–O–X, θ, [78] (copyright 1996 by the ELSEVIER).



37

Fig. 5. Quality factor Q (hollow triangles) and coupling factor k (solid squares) of an AT-cut GaPO4 resonator as a function of temperature [87] (copyright 2006 by the APS Physics).



38

Fig. 6. Schematic illustration of the langasite crystal structure viewed along [001] direction [95] (copyright 2011 by the Authors).



39

Fig. 7. Resistivity ρ as a function of temperature for pure and Al-substituted crystals [95] (copyright 2011 by the Authors).



40

Fig. 8. Dielectric loss as a function of temperature for ordered langasite-type piezoelectric crystals [18] (copyright 2009 by the AIP Publishing).



41

Fig. 9. Schematic crystal structure of ReCOB crystals (from ICDD database; Nd could be replaced by other Re elements, (a) observed from the a-axis, (b) observed from the b-axis and (c) schematic of ionic displacement movement). [113] (copyright 2011 by the IOP Science).



42

Fig. 10. Electrical resistivity (ρ) of Y-cut ReCOB (Re = Er, Y, Gd, Sm, Nd, Pr, and La) crystals at room temperature (inset) and elevated temperatures [122] (copyright 2014 by the IEEE).



43

Fig. 11. (a) The dielectric/piezoelectric constants and (b) the electromechanical coupling/mechanical quality factors of the ReCOB family crystals, as a function of the absolute value of the radius difference between the Re3+ ion and the Ca2+ ion (│R(Re3+)-R(Ca2+)│) (data obtained from reference [113, 122]).



44

Fig. 12. (a) Long time ageing of the investigated ID-tag at 400°C (b) Measurements of the long-time thermal stability of LiNbO3 SAW devices up to 450°C and the predicted lift-time at 300 °C [146] (copyright 2003 by the IEEE).



45

Fig. 13. Measured center frequency for a Pt/10%Rh/ZrO2 deposited two-port LGS SAW sensor while being cycled from room temperature to 850°C six times [149] (copyright 2008 by the IEEE).



46

Fig. 14. (a) Schematic of NO2 QCM sensor (b) Comparing responses to NO2 at different temperatures and two different BaCO3 microstructures [159] (copyright 2005 by the ELSEVIER).



47

Fig. 15. Sensitivity of the YCOB accelerometer as function of temperature up to 1000°C at different frequencies [175] (copyright 2010 by the AIP)).



48

Devices Categories Generator

Sensor

Actuator Transducer

TABLE I SPECIFIC APPLICATIONS AND RELATED EFFECTS OF PIEZOELECTRIC MATERIALS Piezoelectric Principles of the Work Specific Applications Effect Direct Generate voltages when mechanically Spark igniter, energy harvesting, activated gas stove, welding equipment, etc. Direct Convert a physical parameter into an Accelerometer, hydrophone, electrical signal flaw detector, auto diagnostic, etc. Converse Convert an electrical signal into a Ultrasonic motor, finely adjust physical displacement machining tools, etc. Both Convert energy between electrical and Ultrasonic sonar devices, mechanical antenna, magnetic cartridge, etc.



49

Dielectric Parameters

TABLE II THE DETERMINATION OF THE DIELECTRIC PERMITIVITIES AND IMPERMEABILITIES Sample-cuts Calculation Formulas

ε11T

X-cut

ε

T 22

Y-cut

ε

T 33

Y-cut

ε12T

(XYw)ө

ε13T

(XZw)ө

T ε 23

(YZw)ө

Comment

i = 1, 2,3 T ε= Cii ⋅ t / A ii T ε11T = ε11T cos 2 θ + 2ε12T cos θ sin θ + ε 22 sin 2 θ '

T ε11T = ε11T cos 2 θ − 2ε13T cos θ sin θ + ε 33 sin 2 θ '

T ε= Cii ' ⋅ t ' / A' The ii sample-cuts and formulas used are not unique '

T T T T ε 22 = ε 22 cos 2 θ + 2ε 23 cos θ sin θ + ε 33 sin 2 θ '

ε ijS

E ε ijT − ε ijS= diq e jq= eip S pq e jq

β ij

(−1)i + j ∆ i , j β ij = ∆

Ref [29]

ε11 ε12 ε13 ∆ = ε12 ε 22 ε 23

ε13 ε 23 ε 33 Ref [29]



50

Elastic Parameters

Sample-cuts

E , s34E , and s26

Comment

E s11E ' = s11E l14 + (2 s12E + s66 )l12 m12 + (2 s13E + s55E )l12 n12

E , s33E , s11E , s22 E , s15E , s16E , s24

TABLE III THE DETERMINATION OF THE ELASTIC CONSTANTS Calculation Formulas

15 arbitrary independent orientations

s35E

E +(2 s14E + 2 s56E )l12 m1n1 + 2 s15E l13 n1 + 2 s16E l13 m1 + s22 m14 E E E E E E +(2 s23 + s44 + 2 s46 )m12 n12 + 2 s24 m13 n1 + (2 s25 )m12l1n1 + 2 s26 m13l1 E + s33E n14 + 2 s34E n13 m1 + 2 s35E n13l1 + 2( s36E + s45 )n12l1m1 E E or s66 = s44

9 elastic compliances and 6 combinations could be obtained Ref [6, 29]

'

E E , s23 s44

XY-cut or (XYt)ө

4s22E m12 m22 + 8s23E m1m2 n1n2 + 4s24E m1m2 (m1n2 + m2 n1 ) s66E ' = +4 s n n + 4 s n n (m1n2 + m2 n1 ) + s (m1n2 + m2 n1 ) E 2 2 33 1 2

E 34 1 2

E 44

2

E E or s66 = s55 '

s55E , s13E

YZ-cut or (YZt)ө

4s11E l12l22 + 8s13E l1l2 n1n2 + 4 s15E l1l2 (l1n2 + l2 n1 ) s66E ' = +4s33E n12 n22 + 4s35E n1n2 (l1n2 + l2 n1 ) + s44E (l1n2 + l2 n1 ) 2 E E or s66 = s66 '

E , s12E s66

s14E , s56E

E E , s25 s46

E s36E , s45

ZX-cut or (ZXt)ө (ZXl)ө

(ZYl)ө (ZXlw)өҩ

s66E ' = 4s11E l12l22 + 8s12E l1l2 m1m2 + 4s16E l1l2 (l1m2 + l2 m1 ) +4s22E m12 m22 + 4s26E m1m2 (l1m2 + l2 m1 ) + s66E (l1m2 + l2 m1 ) 2

The method of calculating '

E follows that in s66E and s66

chapter 5 of Ref [29], li , mi and ni are direction cosines of two related coordinate system, Ref (5.65) of [29], The sample-cuts and formulas used are not unique and may not be the best choices for specific crystals

s66E ' = s55E (l1n2 + l2 n1 ) 2 + s66E (l1m2 + l2 m1 ) 2 +2 s56E (l1m2 + l2 m1 )(l1n2 + l2 n1 ) s66E ' = s44E (m1n2 + m2 n1 ) 2 + s66E (l1m2 + l2 m1 ) 2 +2 s46E (l1m2 + l2 m1 )(m1n2 + m2 n1 ) Equation 5.72 in Ref [29]

sijD

sijD= (1 − k 2 ) sijE

Ref [29]

cij

cij =

(−1)i+ j ∆ i , j ∆

Ref [29]



51

Dielectric Parameters

Sample-cuts

TABLE IV THE DETERMINATION OF THE PIEZOELECTRIC CONSTANTS [29] Calculation Formulas

d31' = d11l3l12 + d12l3 m12 + d13l3 n12 + d14l3 m1n1 + d15l3l1n1

d nj

enj

18 arbitrary independent orientations

+ d16l3l1m1 + d 21m3l12 + d 22 m3 m12 + d 23 m3 n12 + d 24 m3 m1n1 + d 25 m3l1n1 + d 26 m3l1m1 + d31n3l12 + d32 n3 m12 + d33 n3 n12 + d34 n3 m1n1 + d35 n3l1n1 + d36 n3l1m1

= enj

S ε mn = hmj d ni cijE 4π

g nj

T g nj 4= d mj hni sijD = πβ mn

hnj

S = hnj 4= πβ mn emj g ni cijD

Comment

li , mi and ni are direction cosines of two related coordinate system, Ref (5.65) of [29], The sample-cuts and formulas used are not unique m, n = 1, 2,3 i, j = 1, 2,3, 4,5, 6



52

Sample-cuts X-cut Y-cut

TABLE V CHARACTERISTICS AND APPLICATIONS OF PRINCIPAL CUTS OF QUARTZ CRYSTALS Characteristics Applications High frequency but poor temperature coefficient Produce ultra-sonic vibration High frequency but poor temperature coefficient Generate shear vibration

AT and BT-cut CT and DT-cut GT-cut

High frequency with zero temperature coefficient zero temperature coefficient Both positive and negative temperature coefficient

Control of high frequency oscillator Frequency modulated oscillator Stable oscillators with little aging

ST-cut SC-cut

Narrow band low phase noise and good aging characteristics

Narrow band SAW filter/resonator/oscillator Oven-controlled crystal oscillator

K-cut LST-cut

Good 2nd order temperature coefficient Good frequency-temperature performance

100-150 MHz fixed frequency SAW oscillator High frequency oscillator with stable frequency-temperature performance

Ref [29]

[61]



53

Crystals LN LT LTB

Density (gcm-1)

Melting point(°C)

4.647 7.456 2.439

1255 1650 849

TABLE VI GENERAL PROPERTIES OF LN, LT AND LTB CRYSTALS T Curie ε11T / ε 0 ε 33 / ε0 s11E point(°C) (pm2/N) 1140 85.2 28.7 5.831 605 53.6 43.4 4.93 -9.33 9.93 8.81

s33E

d33

Ref

(pm2/N) 5.026 4.317 24.6

(pC/N) 6.0 5.7 19.4

[71, 75] [71, 75] [74, 76]



54

Crystals

Quartz Tourmaline LN GaPO4 LGS CTGS YCOB AlN PMNT

TABLE VII GENERAL PROPERTIES OF 9 KINDS OF REPRESENTATIVE PIEZOELECTRIC SINGLE CRYSTALS Melting Curie ρ (Ω·cm) keff ceff (GPa) d eff Qeff ε r ,eff point (°C) point (pC/N) (%) (°C) 1670 1102 1255 1670 1470 1350 1510 2200 1270

--1140 -----170

4.65 6-8 28~85 6.6 19 18.2 12 9 ~5000

6~106 160~300 53~245 4.6~67 14~268 0.4~178 0.7~155 ~330 3~16

2.25 1.8~3.6 1~69 4.5 6 4.6 3~10 ->2500

90

105~108 -102~104 ~104 ~104 ~104 ~104 ~104 ~102

>1017 -~1010 ~1017 ~1015 ~1017 ~1017 >1014 ~109

Temp range (°C)

Ref

~300 ~700 ~700 ~900 ~1100 ~1100 ~1250 ~500 ~120

[25,29, 56-60] [65-70] [71-77] [83-88] [91-106] [107-111] [119-122] [122-131] [132-134]



55

Authors’ Biographies

Hongfei Zu was born in Linyi, Shandong, China, in 1986. He received B.S. in Department of Microelectronics from Xi’an Jiaotong University, Xi’an, China, in 2009 and M.S. in Department of Electronics Science and Technology from Xi’an Jiaotong University, Xi’an, China, in 2012. He is now a PhD student in the Department of Mechanical Engineering and Materials Science at University of Pittsburgh. His research interest includes high temperature sensor and surface acoustic wave (SAW) and bulk acoustic wave (BAW) sensor applications.

Huiyan Wu was born in Yangzhou, Jiangsu, China, in 1986. She received B.S. and M.S in Material Science & Engineering from Xi’an Jiaotong University, Xi’an, China. She is now a PhD student in Department of Mechanical Engineering and Materials Science at University of Pittsburgh. Her research interests include nano-materials, film materials, biomaterials, and corresponding BAW sensor, SAW sensor, biosensor applications.

Qing-Ming Wang (M’00) is a professor in the Department of Mechanical Engineering and Materials Science, the University of Pittsburgh, Pennsylvania. He received the B.S. and M.S. degrees in Materials Science and Engineering from Tsinghua University, Beijing, China, in 1987 and 1989, respectively, and the Ph.D. degree in Materials from the Pennsylvania State University in 1998. Prior joining the University of Pittsburgh, Dr. Wang was an R&D engineer and materials scientist in Lexmark International, Inc., Lexington, Kentucky, where he worked on piezoelectric and electrostatic microactuators for inkjet printhead development. From 1990 to 1992, he worked as a development engineer in a technology company in Beijing where he participated in the research and development of electronic materials and piezoelectric devices. From 1992 to 1994, he was a research assistant in the New Mexico Institute of Mining and Technology working on nickel-zinc ferrite and ferrite/polymer composites for EMI filter application. From 1994 to 1998, he was a graduate assistant in the Materials Research Laboratory of the Pennsylvania State University working toward his Ph.D. degree in the areas of piezoelectric ceramic actuators for low frequency active noise cancellation and vibration damping, and thin film materials for microactuator and microsensor applications. Dr.Wang’s primary research interests are in microelectromechanical systems (MEMS) and microfabrication; thin film bulk acoustic wave resonators (FBAR) and acoustic wave sensors; functional nanomaterials and devices; and piezoelectric and electrostrictive thin films and composites for transducer, actuator, and sensor applications. He is a member of IEEE, IEEE-UFFC, the Materials Research Society (MRS), ASME, and the American Ceramic Society.


Piezoelectric single crystals for ultrasonic transducers in biomedical applications.

Phonon-electron interactions in piezoelectric semiconductor bulk acoustic wave resonators.

Iridium interdigital transducers for high-temperature surface acoustic wave applications.

Enhanced sensitive love wave surface acoustic wave sensor designed for immunoassay formats.

Palladium nanoparticle-based surface acoustic wave hydrogen sensor.

Starch viscoelastic properties studied with an acoustic wave sensor.

Piezoelectric cell growth sensor.

transmission at vertical borders of piezoelectric substrates.

A novel optimal sensitivity design scheme for yarn tension sensor using surface acoustic wave device.

ZnO Bilayer Structure for Room Temperature Hydrogen Detection.

A surface acoustic wave sensor functionalized with a polypyrrole molecularly imprinted polymer for selective dopamine detection.

A wireless demodulation system for passive surface acoustic wave torque sensor.

Piezoelectric crystals generate NMR-like signals for rapid spectrometer troubleshooting.

Detection of third-hand smoke on clothing fibers with a surface acoustic wave gas sensor.

Mass Sensitivity Optimization of a Surface Acoustic Wave Sensor Incorporating a Resonator Configuration.

Longitudinal modes along thin piezoelectric waveguides for liquid sensing applications.

Periodical Microstructures Based on Novel Piezoelectric Material for Biomedical Applications.

Multiphysics Simulation of Low-Amplitude Acoustic Wave Detection by Piezoelectric Wafer Active Sensors Validated by In-Situ AE-Fatigue Experiment.

Effects of interface bonding on acoustic wave generation in an elastic body by surface-mounted piezoelectric transducers.

The Use of Phononic Crystals to Design Piezoelectric Power Transducers.

Growth and Characterization of Lead-free Piezoelectric Single Crystals.

Nanosized microporous crystals: emerging applications.

Spin wave nonreciprocity for logic device applications.

Molecularly Imprinted Nanomaterials for Sensor Applications.