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Crystals 2014, 4(3), 241-261; doi:10.3390/cryst4030241

Review
Rare-Earth Calcium Oxyborate Piezoelectric Crystals ReCa4O(BO3)3: Growth and Piezoelectric Characterizations
Fapeng Yu 1, Xiulan Duan 1, Shujun Zhang 2,*, Qingming Lu 3 and Xian Zhao 1,*
1
State Key Laboratory of Crystal Materials and Institute of Crystal Materials, Shandong University, Jinan 250100, Shandong, China; E-Mails: fapengyu@sdu.edu.cn (F.Y.); xlduan@sdu.edu.cn (X.D.)
2
Materials Research Institute, Pennsylvania State University, University Park, PA 16802, USA
3
School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100, Shandong, China; E-Mail: qmlu@sdu.edu.cn
*
Authors to whom correspondence should be addressed; E-Mails: soz1@psu.edu (S.Z.); zhaoxian@icm.sdu.edu.cn (X.Z.); Tel.: +1-814-863-2639 (S.Z.); +86-531-8836-4068 (X.Z.).
Received: 12 April 2014; in revised form: 15 June 2014 / Accepted: 24 June 2014 /
Published: 8 July 2014

Abstract

: Rare-earth calcium oxyborate crystals, ReCa4O(BO3)3 (ReCOB, Re = Er, Y, Gd, Sm, Nd, Pr, and La ), are potential piezoelectric materials for ultrahigh temperature sensor applications, due to their high electrical resistivity at elevated temperature, high piezoelectric sensitivity and temperature stability. In this paper, different techniques for ReCOB single-crystal growth are introduced, including the Bridgman and Czochralski pulling methods. Crystal orientations and the relationships between the crystallographic and physical axes of the monoclinic ReCOB crystals are discussed. The procedures for dielectric, elastic, electromechanical and piezoelectric property characterization, taking advantage of the impedance method, are presented. In addition, the maximum piezoelectric coefficients for different piezoelectric vibration modes are explored, and the optimized crystal cuts free of piezoelectric cross-talk are obtained by rotation calculations.
Keywords:
ReCOB crystals; crystal growth; dielectric; piezoelectric; sensor

1. Introduction

High temperature sensors are desirable in aerospace and automotive industries for monitoring component conditions to optimize the propulsion system, with operations at temperatures up to 1000 °C, to enable safer, more fuel-efficient and more reliable vehicles; in addition, they are important for nondestructive in situ inspection of the structure health of the furnace component or systems in electric generation plants, to improve the safety and reduce life-cycle costs. Compared with the commercial strain gauge and optical fiber sensors, etc., piezoelectric sensors have greater potentials in realizing high temperature (>600 °C) sensing with the merits of high accuracy, fast response time and ease of integration [1,2,3,4].

Of all the investigated high temperature piezoelectric materials up to date, crystals in trigonal, tetragonal and monoclinic systems have been extensively investigated. Among these materials, the trigonal lithium niobate (LiNbO3, LN) crystals with 3m symmetry were reported to possess high piezoelectric coefficient, being on the order of 6–70 pC/N at room temperature, approximately 3–30 times that of commercial α-quartz (SiO2) (2–3 pC/N). However, the maximum operating temperature of LN-based piezoelectric devices, restricted by their low electrical resistivity (a requirement of >106 Ohm·cm was proposed for comparison, where the materials with low resistivity yet can be used for high frequency applications [1]) at elevated temperature is limited to <600 °C, though the Curie temperature is above 1150 °C [5]. Other important trigonal piezoelectric crystals include the langasite family with the general formula of A3BC3D2O14 [6,7,8,9,10,11,12] and gallium orthophosphate GaPO4, in the point group of 32 [13,14,15,16,17,18,19], these crystals were reported to show modest piezoelectric coefficients (5–7 pC/N) and high melting points (1300–1500 °C for langasite family crystals and ~1670 °C for GaPO4), prior to which, there are no phase transitions observed for langasite family crystals (the phase transition for GaPO4 is about 970 °C). However, the costly component Ga2O3 restricted their further implements. The newly developed Ca3TaAl3Si2O14 (CTAS) crystals, substituting the Ga with Al elements, were found to possess improved higher temperature properties than La3Ga5SiO14 (LGS) and to significantly decrease the cost of raw materials; nevertheless, the crystal quality needs to be improved, due to the core defect observed inside the crystals [12]. The tetragonal melilite crystals (point group 42m, such as SrLaGa3O7 (SLG), Ca2Al2SiO7 (CAS), etc.) and fresnoite crystals (point group 4mm, such as Ba2TiSi2O8) were investigated for piezoelectric applications. These crystals show the merits of high melting points (1400–1700 °C) and high effective piezoelectric coefficients deff (5–18 pC/N) [20,21,22,23,24,25,26]; the evaluations of the temperature dependence of dielectric, piezoelectric and electromechanical properties, however, are limited. Of particular significance is that the monoclinic rare-earth calcium oxyborate crystals (ReCa4O(BO3)3, ReCOB, Re: rare earth), which have been extensively investigated for nonlinear optical applications in the last two decades [27,28,29,30,31,32,33], were reported to exhibit good piezoelectric properties and high electrical resistivity at an elevated temperature of 1000 °C, with no phase transition prior to their melting points (~1400–1520 °C) [1,2,3,34,35,36,37,38].

Table 1 summarizes the basic characteristics of various high temperature piezoelectric crystals in monoclinic, trigonal and tetragonal systems, where the monoclinic ReCOB crystals were found to exhibit relatively high melting points, as well as relatively large piezoelectric coefficients, promising high temperature piezoelectric sensor applications.

In this review article, crystal growth, dielectric, elastic and piezoelectric property characterizations of the monoclinic ReCOB crystals are surveyed. Different crystal growth techniques, including the Bridgman and Czochralski (Cz) pulling methods, are discussed in Section 2. The crystal orientation related to the physical axes and crystallographic axes for electro-elastic property investigations is studied in Section 3. In Section 4, characterizations of the dielectric, elastic and piezoelectric properties of ReCOB crystals are reviewed. In Section 5, the maximum piezoelectric coefficients for different crystal cuts and the optimized crystal cuts free of cross-talk are discussed. Finally, the significance and challenges of ReCOB crystals are summarized; future research is proposed in Section 6.

Table Table 1. A comparison of different high temperature piezoelectric crystals. LGS, La3Ga5SiO14; CTGS, Ca3TaGa3Si2O14; CTAS, Ca3TaAl3Si2O14; SLG, SrLaGa3O7; CAS, Ca2Al2SiO7; BTS, Ba2TiSi2O8; ReCOB, ReCa4O(BO3)3.

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Table 1. A comparison of different high temperature piezoelectric crystals. LGS, La3Ga5SiO14; CTGS, Ca3TaGa3Si2O14; CTAS, Ca3TaAl3Si2O14; SLG, SrLaGa3O7; CAS, Ca2Al2SiO7; BTS, Ba2TiSi2O8; ReCOB, ReCa4O(BO3)3.
SymmetryCrystalsGrowth MethodTc/Tm (°C)deff (pC/N)
TrigonalLGSCz1430 [39]6~7
CTGSCz~1370 [40]~10
CTASCz~5
GaPO4Flux/hydrothermal970 [41] #~5
LNCz1150~70 [42]
TetragonalSLGCz~1650 [43]~14 [44]
CASCz1500~6 [22]
BTSCz1445~18 [23]
MonoclinicReCOBCz/Bridgman1400~1520 [1]~15

Notes: Cz, Czochralski pulling method; # α–β phase transition temperature.

2. Crystal Growth

2.1. Polycrystalline Preparation

The ReCOB polycrystalline materials were prepared by high purity (99.99%) CaCO3, Re2O3 (Pr6O11) and H3BO3 powders. They were weighed according to their nominal compositions. Considering the evaporation of B2O3 during crystal growth, an excess of H3BO3 (1–3 wt%) was added to the starting components, which will benefit the crystal growth [38,45,46]. The starting materials were mixed completely, followed by the calcination ~1000 °C for 5–10 h to decompose the H3BO3 and CaCO3, after which, the calcined powders were ground, remixed and then pressed into tablets to fabricate ReCOB polycrystalline components at 1100–1200 °C for 10–20 h; the solid state reaction follows the equation below:

Re2O3 + 6H3BO3 + 8CaCO3 = 2ReCa4O(BO3)3 + 8CO2↑ + 9H2O↑

2.2. Approaches for ReCOB Crystal Growth

Different techniques have been applied for ReCOB crystal growth, including the high temperature flux, Bridgman and Cz approaches [47,48,49]. At the early stage of ReCOB crystal studies, the high temperature flux method was adopted for the crystal growth, where the selection of appropriate flux agent (high temperature solvent) is vital, especially for the crystals with incongruent features. Among ReCOB crystals (except CeCOB and YbCOB), ErCOB, YCOB, GdCOB, SmCOB, NdCOB, PrCOB and LaCOB are congruent melting compounds, while TbCOB and TmCOB were found to possess a very narrow congruent region. Lead oxide was firstly selected as the flux agent for ReCOB crystal growth, with limited success, where the grown crystals were at centimeter scale [47]. Later, the Bridgman and Cz methods, which are favorable for growing crystals with congruent melting features, were utilized. In the following, the growth of ReCOB crystals by the Bridgman and Cz methods is introduced.

2.2.1. Bridgman Method

The Bridgman method, which is also called the Bridgman-Stockbarger method, involves heating polycrystalline materials in a platinum or iridium crucible above its melting point and slowly cooling it from one end, where an oriented seed crystal is located. The crucible is translated from the high temperature region to the low temperature region at a special designed speed; the single crystal is progressively formed along the length of the crucible. Figure 1 shows a schematic set-up of the Bridgman growth system.

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Figure 1. Schematic set-up of the Bridgman growth system.

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Figure 1. Schematic set-up of the Bridgman growth system.
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By the Bridgman method [50], the feed materials were prepared by thoroughly mixing the stoichiometric oxides, which were charged into a cylindrical platinum crucible. The material was heated to about 50 °C above its melting point, maintained for more than 10 h to make a homogeneous melt. The seeding process (along the <010> or <001> orientation) was performed by adjusting the crucible position and furnace temperature gradient, so that only the top part of the seed was melted. Growth was then driven by lowering the crucible at a rate of 0.2–0.6 mm/h, and the temperature gradient near the solid/liquid interface was normally kept at 30–50 °C/cm. Recently, large YCOB crystals with a diameter up to 3–4 inches have been reported, using the modified Bridgman furnace [48].

2.2.2. Cz Pulling Method

Cz method is named after Polish scientist, Jan Czochralski, who invented this method in 1916. In the Cz pulling technique, iridium, platinum, molybdenum and graphite crucibles are generally selected and heated in a low–medium radio-frequency furnace. Particularly, for ReCOB crystal growth, an iridium crucible is mostly utilized, due to its high melting point (~2450 °C) and chemical inertia to the raw materials. Figure 2 gives the schematic set-up of the Cz pulling system.

YCOB and GdCOB single crystals have been grown by the Cz method [27,33,49]. ReCOB materials were melted and kept 30–80 °C above their respective melting points for more than 10 h to ensure the homogeneity of the melts. A <010>-oriented crystal seed was selected for the growth, which will benefit the large diameter crystals. The pulling speed was controlled at 0.4–2.0 mm/h, and the rotation speed was varied from 10 to 30 rpm during the crystal growth. When the growth was finished, the crystal was cooled down to room temperature at a low rate of 10–50 °C/h, to avoid the crystal cracks induced by inner thermal stress. Figure 3 shows the large YCOB single crystals grown by the Cz method (Figure 3a,c) and the Bridgman method (Figure 3b) with a diameter being on the order of 3–4 inches. The obtained crystals were reported to possess X-ray diffraction with a very low full-width at half maximum (FWHM) (~30ʺ) [51] and high optical homogeneity (10−6) [52], exhibiting high crystal quality.

Crystals 04 00241 g002 1024
Figure 2. Schematic set-up of the Cz method for crystal growth.

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Figure 2. Schematic set-up of the Cz method for crystal growth.
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Crystals 04 00241 g003 1024
Figure 3. Large YCOB single crystals grown by the Cz method and the Bridgeman method (crystal (a) was grown by Crystal Photonics Inc. using Cz method, reprinted with permission from [53]. Copyright 2006 Elsevier; Crystal (b) was grown using Bridgeman method, reprinted with permission from [48]. Copyright 2013 Elsevier; and crystals (c) were grown using Cz method, reprinted with permission from [46]. Copyright 2013 Chinese Ceramic Society.

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Figure 3. Large YCOB single crystals grown by the Cz method and the Bridgeman method (crystal (a) was grown by Crystal Photonics Inc. using Cz method, reprinted with permission from [53]. Copyright 2006 Elsevier; Crystal (b) was grown using Bridgeman method, reprinted with permission from [48]. Copyright 2013 Elsevier; and crystals (c) were grown using Cz method, reprinted with permission from [46]. Copyright 2013 Chinese Ceramic Society.
Crystals 04 00241 g003 1024

3. Orientation of Monoclinic ReCOB Crystals

ReCOB are monoclinic biaxial crystals belonging to the point group m. Therefore, three different orientation systems exist due to the crystal symmetry, including the crystallographic, optical and physical systems. For piezoelectric characterizations, the relationship between the crystallographic and physical axes should be determined, where the physical Y-axis is parallel to the crystallographic b-axis, Z- to the c-axis, and the X-axis is perpendicular to the Y and Z axes to form a right-hand orthogonal system according to the IEEE Standard on Piezoelectricity [54], as shown in Figure 4.

The initial orientation step is to verify the (010), (201) an (101) faces using X-ray analysis, possessing relatively strong diffraction peaks, from which, the crystallographic axes, a, b and c, can be determined according to the relationships between the interfacial angle and crystallographic plane. Then, the physical axes can be easily determined based on the IEEE standards. Taking YCOB crystals, for example, the angle between the Z-axis and (101) face was calculated to be around 57.1°, while the angle between the X-axis and (201) face was close to 34.6° (Figure 4). It is noteworthy that these angles (interfacial angles, etc.) are varied for different ReCOB crystals, due to their different lattice parameters (Table 2). After the orientation of the X, Y and Z axes, the positive X and positive Z axes can be further confirmed by using a quasi-static piezoelectric d33 meter, according to the IEEE Standard on Piezoelectricity [54].

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Figure 4. Schematic of the cross-section of Cz-grown YCOB crystals, with the relationship of the crystallographic and physical axes.

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Figure 4. Schematic of the cross-section of Cz-grown YCOB crystals, with the relationship of the crystallographic and physical axes.
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Table Table 2. Unit cell parameters and interfacial angles for different ReCOB crystals in space group Cm.

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Table 2. Unit cell parameters and interfacial angles for different ReCOB crystals in space group Cm.
CrystalsTmCOBErCOBYCOBTbCOBGdCOBSmCOBNdCOBPrCOBLaCOB
Parameters (Å/Å3/°) *a8.0688.0758.0788.0728.1048.1148.1458.1778.173
b16.0116.0116.0216.0016.0316.0616.0716.1616.09
c3.5223.5303.5343.5453.5583.5793.6073.6293.627
β101.11101.43101.19101.25101.25101.38101.37101.40101.40
V446.56447.25448.01449.06453.38457.24462.81469.95467.41
Formula weight *521.33519.74441.65511.33509.99502.78496.98493.33491.68
∠1 (°) #112.59112.45112.46112.41112.26111.99111.78111.66111.62
∠2 (°) #34.7434.7034.7734.7534.8534.9435.0835.1435.14
∠3 (°) #45.8546.1345.9646.0046.1046.3246.4546.5446.57

* PDF #: 00-050-0403 (YCOB); 01-077-0951 (GdCOB); 01-079-1378 (SmCOB); 00-050-0399 (NdCOB); 01-070-7385 (LaCOB); TmCOB [55]; TbCOB [56]; PrCOB [38]; # ∠1: the interfacial angle between (101) and (201); ∠2: the interfacial angle between (201) and the X-axis; ∠3: the interfacial angle between (201) and (001).

4. Electro-Elastic Material Constants Determination

Due to the crystal symmetry, there are two different sets of electro-elastic component matrix for monoclinic crystal, relating to point group m and point group 2. The piezoelectric crystals in point group 2 possess eight independent piezoelectric strain coefficients dij, while crystals in point group m exhibit ten independent piezoelectric strain coefficients dij, four dielectric permittivities εij and thirteen elastic compliances sij. The electro-elastic component matrix for piezoelectric crystals in point group m can be written as:

Crystals 04 00241 i001

Taking advantage of the impedance method based on the IEEE standard, all of the electro-elastic parameters for ReCOB crystals can be determined. Meanwhile, the elastic stiffness cij and piezoelectric stress coefficient eij can be obtained based on the determined elastic compliance sij and piezoelectric strain coefficient dij, following the equations below:

c = 1/s
e = dc

Based on the IEEE standard [54], the dielectric permittivities εii (i = 1, 2 and 3) can be evaluated by measuring the capacitance of X-, Y- and Z-cut square plates, respectively. Piezoelectric d11 and d33 can be obtained by measuring the longitudinal vibration mode of the X and Z rods, while elastic compliances sii (i = 1–6) can be calculated from the extensional and shear vibration modes, relating to the piezoelectric coefficient d12, d13, d15, d24, d26, d31, d32, d33 and d35. On the contrary, the dielectric cross permittivity ε13 and elastic cross compliances sij (ij; i, j = 1–6) can be evaluated by employing oblique crystal cuts that do not lie along or normal to any of the three physical axes. Figure 5 presents different crystal cuts designed for the electro-elastic parameter determination, including the dielectric permittivities, elastic compliances and piezoelectric coefficients. The aspect ratios of the samples (X-, Y- and Z-square plates) for dielectric measurement ranged from 1:8:8 to 1:10:10, whereas for elastic measurement, rectangular samples were used with aspect ratios, t (thickness):w (width):l (length), ranging from 1:2:10 to 1:3:15 and an orientation accuracy <30ʺ. For each crystal cut, 3–5 pieces of samples were prepared for parameter determination.

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Figure 5. Crystal cuts for electro-elastic parameter determination ((a) X rod; (b) Z rod; (c) XZ plate; (d) XY plate; (e) ZY plate; (f) ZX plate; (g) (XZw)45°; (h) (XZw)30°; (i) (XZw)−45°; (j) Z-square plate; (k) X-square plate; (l) Y-square plate; (m) (XYt)45°; (n) (ZXt)45°; (o) (YZtw) 45°/−45°).

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Figure 5. Crystal cuts for electro-elastic parameter determination ((a) X rod; (b) Z rod; (c) XZ plate; (d) XY plate; (e) ZY plate; (f) ZX plate; (g) (XZw)45°; (h) (XZw)30°; (i) (XZw)−45°; (j) Z-square plate; (k) X-square plate; (l) Y-square plate; (m) (XYt)45°; (n) (ZXt)45°; (o) (YZtw) 45°/−45°).
Crystals 04 00241 g005 1024

4.1. Dielectric Permittivity

ReCOB crystals possess four independent dielectric permittivities, where the dielectric permittivities ε11, ε22, ε33 can be determined from X-, Y-, and Z-cut samples (k, l and j), while for the determination of ε13, sample (g) was used (Table 3), following the formulae below:

Crystals 04 00241 i002
Crystals 04 00241 i003
where C is the capacitance of the crystal sample measured at 100 kHz, t is the thickness, A is the area of the measured plate and Crystals 04 00241 i022 is the dielectric permittivity for the -axis.

Table Table 3. A summary of different crystal cuts for material constants’ determination, reprinted with permission from [57]. Copyright 2014 Wiley-VCH.

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Table 3. A summary of different crystal cuts for material constants’ determination, reprinted with permission from [57]. Copyright 2014 Wiley-VCH.
Crystal CutsModesMaterial constants
X rod (a)longitudinal extensiond11
Z rod (b)d33
ZX plate (f)transverse extensions11, d31,
s22, d12, d32,
s33, d13
XY plate (d)
ZY plate (e)
XZ plate (c)
XZ plate (c)width shear *s44, d24
ZX plate (f)s66, d26
(XZw)45° (g)s46
XZ plate (c)thickness shears55, d15, d35
ZX plate (f)
(XZw)45° (g)transverse extensions13, s15, s35
(XZw)30° (h)
(XZw)−30° (i)
(XYt)45° (m)transverse extensions12, s23, s25
(ZXt)45° (n)
(YZtw)45°/−45° (o)
X cut (k)ε11, ε22, ε33, ε13
Y cut (l)
Z cut (j)
(XZw)45° (g)

* d24 (d223) and d26 (d212) are thickness shear vibration modes; however, XZ and ZX cut samples with electrodes on the Y faces were used to determine their values, due to the achievable clean d24/d26 vibration modes using the impedance method.

4.2. Piezoelectric Coefficients and Elastic Compliances

For determining the complete set of elastic compliances, piezoelectric coefficients, as well as electromechanical coupling factors, crystal cuts with different orientations were designed, as given in Figure 5. In addition, different crystal cuts with corresponding piezoelectric vibration modes and electro-elastic parameters are summarized in Table 3.

4.2.1. Piezoelectric Coefficients d11 and d33

Piezoelectric coefficients d11, d33 and elastic compliances s11 and s33 were determined using the longitudinal mode of X and Z rods (samples (a) and (b)), relating to the equations below:

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Crystals 04 00241 i005
d = k(εs)1/2
where ρ, fr, fa and k are the crystal density, resonance frequency, anti-resonance and electromechanical coupling factor, respectively.

4.2.2. Piezoelectric Coefficients d12, d13, d31, and d32

Using the transverse extensional mode of XY, XZ, ZX and ZY crystal cuts (samples (c)–(e)), piezoelectric coefficients d12, d13, d31 and d32 and elastic compliances s22, s33 and s11 were calculated by Equations (9)–(11).

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Crystals 04 00241 i007

4.2.3. Piezoelectric Coefficients d15, d35, d24, and d26

d15, d35, d24 and d26 are thickness shear piezoelectric coefficients; thus, XZ and ZX crystal cuts (samples (c) and (f)) with electrodes on the X and Z faces, respectively, were designed for piezoelectric d15 and d35 and elastic compliance s55 evaluation. However, for the piezoelectric d24 and d26 and elastic compliance s44 and s66 determinations, XZ and ZX cut samples with an electrode on the Y faces were used (equivalent to YZ and YX cut samples with an electrode on Y faces), due to the fact that clean width shear vibrations can be obtained. The shear piezoelectric coefficients d15, d35, d24 and d26 and elastic compliances of s55, s44 and s66 can be determined by using Equations (8), (9), (12) and (13).

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Crystals 04 00241 i009

4.2.4. Elastic Compliances s12, s13, s15, s23, s25, s35 and s46

Except the dielectric, piezoelectric and elastic constants above, there are cross-elastic compliances s12, s13, s15, s23, s25, s35 and s46 remaining unsolved, requiring the oblique crystal cuts. Crystal cuts (g–i) with transverse extensional modes were employed to determine the elastic compliances s13, s15 and s35, based on Equations (10) and (14), while for the compliance s23, s12 and s25 evaluations, crystal cuts (m–o) were designed, combining Equations (10) and (15)–(17). Particularly, the elastic compliance s46 was obtained using Equations (13) and (18) by measuring the shear vibration mode of sample (g).

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Utilizing the crystal cuts listed in Table 3, all of the dielectric permittivities and elastic compliances were obtained, and the results are given in Table 4.

Table Table 4. Dielectric, piezoelectric and elastic constants of ReCOB (Re = Er, Y, Gd, Nd, Pr and La) crystals.

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Table 4. Dielectric, piezoelectric and elastic constants of ReCOB (Re = Er, Y, Gd, Nd, Pr and La) crystals.
Elastic Compliances sEij (pm2/N)
Crystalss11s12s13s15s22s23s25s33s35s44s46s55s66
ErCOB7.36.78.931.221.616.6
YCOB a7.2−0.8−2.47−0.47.00.550.548.9−0.1234.5−0.3721.016.3
YCOB b7.15−0.35−2.80.746.91−0.68−0.468.79−1.235.03.523.015.0
GdCOB b7.6−1.2−3.90.47.15−4.6−1.58.940.3228.01.723.018.0
GdCOB c7.6−0.92−0.95−0.997.1−0.92−148.9−0.3317.014.019.018.0
GdCOB7.6−1.0−1.0−0.47.31.22.88.9−0.631.7−0.920.018.0
NdCOB d8.3−1.4−3.72.07.4−0.71.89.4−0.430.90.322.420.5
NdCOB e8.3−2.0−3.5−0.97.5−1.60.59.40.934.01.022.020.0
PrCOB9.07.910.433.918.7
LaCOB f8.82−1.1−2.61.14.78−1.23.410.1−1.334.01.319.018.0
Relative Dielectric Permittivities εTij0
Crystalsε11ε13ε22ε33
ErCOB9.511.810.0
YCOB a9.650.9511.89.55
YCOB b9.57−0.9611.49.52
GdCOB b10.50.814.010.4
GdCOB c9.030.7512.3510.25
GdCOB9.40.913.39.4
NdCOB d9.9−1.615.510.2
NdCOB e9.9−0.815.010.0
PrCOB9.815.310.1
LaCOB b9.871.214.39.87
LaCOB f9.87−1.2414.99.87
Piezoelectric Coefficients dij (pC/N)
Crystalsd11d12d13d15d24d26d31d32d33d35
ErCOB1.73.4−4.3−1.43.97.6−0.7−2.81.5−5.5
YCOB a1.73.9−4.2−1.14.47.9−0.77−2.51.4−5.0
YCOB b1.43.8−4.2−7.2−2.68.0−0.22−2.30.832.2
GdCOB b2.84.8−3.8−6.90.4511−0.77−2.42.5−4
GdCOB c2.44.0−4.50.66−2.82.4−1.1−2.22.0−2.7
GdCOB2.44.1−4.7−2.25.111.1−1.1−2.52.0−3.8
NdCOB d2.74.1−4.83.04.115.0−1.9−3.72.12.3
NdCOB e1.73.9−4.9−1.4−2.51.5-
PrCOB2.5 *3.9−5.2−1.93.115.8−1.5−2.52.0 *3.3
LaCOB2.4 *4.74.011.82.0 *
LaCOB b2.13.9−3.9−0.55−2.21.5
LaCOB f1.283.89−3.890.626.418.73−0.55−2.221.10

Data (a−f) were from [57,58,59,60,61,62]; * measured by a quasi-static d33 meter.

4.2.5. Determination of the Sign of the Piezoelectric Coefficients

According to the IEEE standard [54], the longitudinal piezoelectric d11 and d33 are positive, while the transverse and shear piezoelectric coefficients are either positive or negative. Therefore, more crystal cuts (rotated around physical axes) are desired to discuss the sign of the piezoelectric coefficient dij (ij) for ReCOB crystals. In this subsection, piezoelectric coefficients for YCOB a in Table 4 are discussed.

It is noticed that the piezoelectric d35 is a function of d11, d13, d31, d33 and d15 when rotated around the Y-axis, as expressed below:

Crystals 04 00241 i015
Crystals 04 00241 i016

Figure 6 shows the variation of piezoelectric d35 for YCOB crystals as a function of the rotation angle around the Y-axis (curve (a) in Figure 6). For verification, the experimental shear piezoelectric d35 values measured from rotated crystal cuts (ZXw)θ (θ = −60°, −30°, 30° and 60°) were plotted and found to be in good agreement with the calculations, from which, the maximum d35 value was determined to be on the order of 6.4 pC/N for (ZXw)−55° crystal cuts. In addition, different d35 curves plotted by presuming the opposite sign of the related piezoelectric coefficients in Equation (19) were given as curves (b)–(g), where large discrepancies were observed. The consistency between the calculation and measurement of d35 values for YCOB crystals indicates the validity of the reported piezoelectric coefficients d11, d13, d31, d33, d15 and d35.

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Figure 6. Variation of piezoelectric d35 as a function of rotation angle around the Y-axis for YCOB crystals ((a) d35, (b) presuming positive d15, (c) presuming positive d35, (d) presuming positive d13, d31, d15 and d35, (e) presuming positive d13 and d31, (f) presuming negative d13 and (g) presuming positive d13, d31, d15 and d35). Reprinted with permission from [57]. Copyright 2014 Wiley-VCH.

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Figure 6. Variation of piezoelectric d35 as a function of rotation angle around the Y-axis for YCOB crystals ((a) d35, (b) presuming positive d15, (c) presuming positive d35, (d) presuming positive d13, d31, d15 and d35, (e) presuming positive d13 and d31, (f) presuming negative d13 and (g) presuming positive d13, d31, d15 and d35). Reprinted with permission from [57]. Copyright 2014 Wiley-VCH.
Crystals 04 00241 g006 1024

Similarly, the variations of piezoelectric d31, d32, d33 and d35 for different crystal cuts rotated around the Y-axis were plotted and compared in Figure 7, where piezoelectric d31 was selected for verifications by measuring the transverse extensional modes of different (ZXw)θ crystal cuts (θ = −60°, −45°, −30°, 30° and 60°). The piezoelectric coefficients Crystals 04 00241 i023 were determined by Equations (9)–(11), and the results were plotted in Figure 7. It is noted that the measured Crystals 04 00241 i023 for different crystal cuts is in good agreement with the calculated results (Equation (20)).

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Figure 7. Variations of piezoelectric coefficients d31, d32, d33, and d35 as a function of the rotation angle around the Y-axis. Reprinted with permission from [57]. Copyright 2014 Wiley-VCH.

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Figure 7. Variations of piezoelectric coefficients d31, d32, d33, and d35 as a function of the rotation angle around the Y-axis. Reprinted with permission from [57]. Copyright 2014 Wiley-VCH.
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5. The Investigation of Optimum Crystal Cuts

According to the crystal symmetry, ReCOB crystals possess two independent longitudinal piezoelectric coefficients (d11 and d33), four transverse piezoelectric coefficients (d12, d13, d31 and d32) and four thickness shear piezoelectric coefficients (d15, d35, d24 and d26). For piezoelectric sensing applications, various crystal cuts with different piezoelectric vibration modes might be utilized, including the longitudinal (compression) and shear vibration modes, etc. Therefore, it is necessary to discuss the optimum crystal cuts with a high piezoelectric coefficient and free of piezoelectric cross-talk.

5.1. Rotated Crystal Cuts with Maximized Values

It is noticed that the maximum values of longitudinal piezoelectric d11 and d33 for ReCOB crystals should be equal, due to the fact that the Z rods (d33) can be obtained by the rotation of X rods around the Y-axis for −90°, analogous to the thickness shear piezoelectric d15 (d35) and d26 (d24). Similarly, the transverse piezoelectric d12 and d13, d31 and d32 should be equal from the viewpoint of crystal cut rotation. Equations (21)–(25) reveal the relationships between d11 and d33, d15 and d35, d26 and d24, d12 and d13 and d31 and d32. Evidently, the effective piezoelectric coefficients Crystals 04 00241 i024, Crystals 04 00241 i025 and Crystals 04 00241 i026 equal to d33, d35 and d24, respectively, when rotated around the Y-axis for ±90°. Meanwhile, when rotated around the X- and Z-axes for ±90°, Crystals 04 00241 i027 and Crystals 04 00241 i023 equal to d13 and d32, respectively.

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Crystals 04 00241 i018
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Crystals 04 00241 i020
Crystals 04 00241 i021

Therefore, the orientation dependence of the longitudinal piezoelectric d11, transverse piezoelectric d12 and d31 and thickness shear piezoelectric coefficients d15 and d26 for YCOB crystals were discussed (data refer to YCOB a in Table 4). The maximum d11 (4.9 pC/N) was obtained from the X plate rotated 1° around the X-axis and then rotated 52° around the Z-axis, whereas the maximum d12 and d31 were observed for (XYl)33° and (ZXlt)90°/123°, respectively, being on the order of ~4.6 pC/N. Meanwhile, the highest piezoelectric d15 (9.0 pC/N) was obtained for (XZlt)90°/60° crystal cuts, and the maximum piezoelectric d26 (9.0 pC/N) was achieved in (YXlt)180°/30° [(YXt)-30°] crystal cut, as reported in [63]. The crystal cuts with maximum d11, d12, d31 and d15 (the same as d26) values are illustrated in Figure 8a–d, respectively.

For comparison, the maximum values of shear piezoelectric coefficient d26 for different ReCOB crystals were studied based on the determined piezoelectric d24 and d26 values; results are given in Table 5, where PrCOB crystals were found to possess the maximum shear piezoelectric d26 value, being on the order of 16.1 pC/N, nearly two times that of ErCOB crystals. The increase of the piezoelectric coefficient for ReCOB crystals was reported to be associated with the difference of the diameter of rare-earth cations (Re3+) and the disorder distribution of Ca2+ and Re3+ ions in ReCOB crystals [34,47].

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Figure 8. The crystal cuts with maximum d11, d12, d31 and d15 (the same as d26) values for YCOB crystals (a) (XYtw)1°/52°; (b) (XYl)33°; (c) (ZXlt)90°/123°; and (d) (XZlt)90°/60°, respectively.

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Figure 8. The crystal cuts with maximum d11, d12, d31 and d15 (the same as d26) values for YCOB crystals (a) (XYtw)1°/52°; (b) (XYl)33°; (c) (ZXlt)90°/123°; and (d) (XZlt)90°/60°, respectively.
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Table Table 5. Optimum crystal cuts (d26 mode) obtained for ReCOB crystals at room temperature.

Click here to display table

Table 5. Optimum crystal cuts (d26 mode) obtained for ReCOB crystals at room temperature.
Crystalsd24 (pC/N)d26 (pC/N)Crystal CutsMaximum d26 (pC/N)
ErCOB3.97.6(YXt)-25°~8.5
YCOB4.47.9(YXt)-30°~9.0
GdCOB4.711.5(YXt)-20°~12.0
SmCOB4.112.7(YXt)-20°~13.3
NdCOB4.115.0(YXt)-15°~15.5
PrCOB3.115.8(YXt)-10°~16.1
LaCOB4.011.8(YXt)-20°~12.4

5.2. Rotated Crystal Cuts without Piezoelectric Cross-Talk

For ideal piezoelectric sensors, only the output (charge, current or voltage) is desired when they are loaded (such as force, vibration, pressure or acceleration) along their sensitivity axis; meanwhile, the load normal to that axis should not produce any output. However, real sensors may give an output also to a force normal to their sensitive axis, which may have significant influence on the accuracy of the measuring results, this is called cross-talk (transverse sensitivity) [64]. The cross-talk effect can be weakened or reduced by device structure design; however, minimizing the piezoelectric cross-talk by using the crystal cut design is desirable for improving the accuracy of the sensors. In the following subsection, piezoelectric cross-talk for the longitudinal modes (d11) and thickness shear modes (d15 and d26) were discussed, based on the piezoelectric coefficients of YCOB crystals (YCOB a in Table 4).

The X plates or X rods with the first 130° rotation angle around the Y-axis and the second 225° rotation angle around the X-axis exhibit a relatively good longitudinal piezoelectric response, giving an effective piezoelectric coefficient d11 being on the order of ~3.0 pC/N, while other coefficients were found to be −0.8~−1.2 pC/N.

Interestingly, the thickness shear piezoelectric d15 and d26 were found to possess optimal crystal cuts with negligible piezoelectric cross-talk. Figure 9 presents the variation of piezoelectric coefficients d1j (j = 1–6) for (XZlw)45°/θ crystal cuts, where the optimal crystal cut was achieved for (XZlw)45°/35°, of which, the shear piezoelectric coefficient d15 was determined to be on the order of 8.8 pC/N, with minimized d11, d12, and d13 being close to zero, d14 and d16 < 2.0 pC/N.

Figure 10 gives the variation of piezoelectric coefficients d24 and d26 as a function of rotation angle around the Y-axis, based on the determined piezoelectric coefficients d24 (4.4 pC/N) and d26 (7.9 pC/N) for YCOB listed in Table 5. It was found that the (YXt)330° crystal cut, which equals to the crystal cut (YXt)−30°, possess the maximum d26 value, being around 9.0 pC/N, with zero piezoelectric d24 value, demonstrating free piezoelectric cross-talk. On the contrary, the highest piezoelectric d24 (9.0 pC/N) was achieved from the (YXt)60° crystal cut, with the d26 value being zero. Of particular importance is that these crystal cuts were found to possess the maximum thickness shear piezoelectric coefficients, without the interference from other piezoelectric vibrations, due to the fact that the monoclinic symmetry plane is vertical to the Y-axis.

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Figure 9. Thickness shear piezoelectric d15 for the (XZlw)45°/θ crystal cut as a function of rotation angle θ. The inset shows the schematic of the crystal cut (XZlw)45°/35°.

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Figure 9. Thickness shear piezoelectric d15 for the (XZlw)45°/θ crystal cut as a function of rotation angle θ. The inset shows the schematic of the crystal cut (XZlw)45°/35°.
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Figure 10. Thickness shear piezoelectric d26 for the (YXt)θ crystal cut as a function of rotation angle θ. The inset shows the schematic of crystal cut (YXt)−30°.

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Figure 10. Thickness shear piezoelectric d26 for the (YXt)θ crystal cut as a function of rotation angle θ. The inset shows the schematic of crystal cut (YXt)−30°.
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6. Summary and Future Research

6.1. Significance of ReCOB Crystals

The monoclinic ReCOB crystals are promising materials for high temperature piezoelectric sensing. The desirable material merits include the low-cost, reproducible crystals with high quality and large dimension, high piezoelectric coefficient, high electrical resistivity, as well as the high thermal stability of the piezoelectric and electromechanical properties, etc. Relevant to this paper, crystal growth and piezoelectric characterization were discussed. Then Bridgman and Cz methods for ReCOB crystal growth were introduced. The relationship between the crystallographic axes and physical axes for ReCOB was discussed for piezoelectric property determination. In addition, procedures for the characterization of the dielectric, elastic and piezoelectric parameters were established, the independent electro-elastic constants were determined, where the highest piezoelectric coefficients d26 were achieved, being on the order of 7.6, 7.9, 11.5, 12.7, 15.0, 15.8 and 11.8 pC/N for ErCOB, YCOB, GdCOB, SmCOB, NdCOB, PrCOB and LaCOB, respectively. Of particular significance is that (YXt)θ crystal cuts not only possess maximum d26 coefficients, but also exhibit no cross-talk from other piezoelectric vibrations.

6.2. Future Research

ReCOB piezoelectric crystals are potential materials for high temperature sensor applications. However, several challenges remain for future investigations, including: (1) temperature stability evaluation of the electro-elastic properties, to explore the optimized ReCOB crystals with high thermal stability; (2) structure-property investigation of ReCOB crystals for further improving of the properties at elevated temperatures; and (3) reliability testing of the electro-elastic properties under harsh environments, including high temperature, hard radiation (Gamma and neutron radiations), low oxygen partial pressure, high/low pressure and corrosive/erosive conditions, etc.

Acknowledgments

Thomas R. Shrout from Pennsylvania State University is acknowledged for the helpful discussions. Shiyi Guo from Shandong University is thanked for his kind helps during ErCOB crystal growth. Fapeng Yu and Xian Zhao would like to thank the National Natural Science Foundation of China (Grant Nos. 91022034, 51202129, 51372168) and the Natural Science Foundation of Shandong Province (ZR2012EMQ004). This work is also supported by the China postdoctoral Science Foundation (2012M511019).

Author Contributions

Fapeng Yu grew the ReCOB single crystals and evaluated their dielectric and piezoelectric properties. Xiulan Duan studied the crystal structures. Qingming Lu prepared the crystal cuts of different ReCOB crystals for property characterization. Shujun Zhang and Xian Zhao directed this research. Fapeng Yu and Xiulan Duan prepared the manuscript. All the authors contributed to revising the manuscript.

Conflicts of Interest

The authors declare no conflict of interest.

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