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Cite This: Cryst. Growth Des. XXXX, XXX, XXX−XXX
Electroelastic Features of Piezoelectric Bi2ZnB2O7 Crystal Feifei Chen, Chao Jiang, Shiwei Tian, Fapeng Yu,* Xiufeng Cheng, Xiulan Duan, Zhengping Wang, and Xian Zhao Institute of Crystal Materials and Advanced Research Center for Optics of Shandong University, Jinan 250100, P. R. China
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S Supporting Information *
ABSTRACT: A Bi2ZnB2O7 single crystal measuring 45 mm × 35 mm × 15 mm was grown by using the Kyropoulos method. The as-grown crystal showed distinct crystal facets (001), (010), and (110), among others, which were consistent with the ideal growth morphology predicted by the BravaisFriedel and Donnay-Harker method. The electric, elastic, and piezoelectric properties of the Bi2ZnB2O7 single crystal were examined, using the impedance and pulse-echo methods for the first time. The independent piezoelectric coefficients d15, d24, d31, d32, and d33 were evaluated and found to be of the value of 1.4, −5.5, 2.5, −6.4, and 1.1 pC/N, respectively. The contributions of the crystal symmetry space group to the piezoelectric property were analyzed from the viewpoint of polyhedral distortion and net dipole moment. The temperaturedependent behaviors of the electroelastic properties were characterized in the temperature range from room temperature to 500 °C. Within this temperature range, the highest electromechanical coupling factor k32 (14.5%) and piezoelectric coefficient d33 (1.1 pC/N) exhibited temperature-independent behavior.
1. INTRODUCTION The development of electronic technology toward higher frequency and wider bandwidth has drawn interest in exploring new piezoelectric crystal materials with high mechanical coupling factor, large piezoelectric coefficient, and good temperature stability over a broad usage temperature range.1−7 During the past several years, the search for highperformance and low-cost piezoelectric materials was persistently pursued to develop and/or extend their application. Among the studied piezoelectric single crystals, the oxyborate crystals have received significant attention because of the distinct structural characteristics of boron−oxygen groups, particularly for oxyborate crystals containing bismuth. These elements are included in the well-known monoclinic bismuth triborate α-BiB3O6 (α-BIBO) crystal, which was reported to exhibit excellent nonlinear optical (NLO) and piezoelectric properties.8−13 Bi2ZnB2O7 (abbreviated as BZBO) is a type of oxyborate crystal that contains bismuth. This compound was first synthesized and studied in 2005.14 Subsequently, the synthesis and optical properties of the BZBO crystal were widely studied. In 2009, Li et al. successfully grew the BZBO crystal with a millimeter size and reported on the powder secondharmonic generation (SHG) effect. The powder SHG effect was about 3−4 times that of KH2PO4 (KDP) and larger than that of LiB3O5.15−17 In 2011, the NLO coefficients of the BZBO crystal were evaluated in which the BZBO crystal showed relatively large NLO coefficients [d31 = (2.34 ± 0.05) d36 (KDP), d32 = (7.90 ± 0.16) d36 (KDP), and d33 = (2.60 ± 0.06) d36 (KDP)]. The large NLO coefficients indicate that the BZBO crystal is a potential NLO crystal material.18 In 2013, © XXXX American Chemical Society
the structural and electronic properties of the crystal were evaluated using first-principles calculations on the basis of the density functional theory. Results indicated that the contributions of the (BiO6)9− and (B2O5)4− groups were dominant in the production of large microscopic secondorder susceptibilities.19 In the same year, the polarized Raman spectra of the BZBO crystals were recorded in the spectral range 10−1600 cm−1, and the normal modes of vibrations were analyzed.20 In the subsequent years, the optical properties of the BZBO crystal were characterized, including optical homogeneity, conoscopic interferogram, and third-order NLO properties.21 The luminescence, spectroscopic properties, and powder SHG effect were further studied for the pure BZBO and RE3+-doped BZBO powders. The doped BZBO crystals showed improved SHG response.22,23 The electrical and optical properties of the BZBO crystal as a type of crystal material with a noncentrosymmetric structure are worthy of a comprehensive study. However, the literature mostly focuses on the synthesis and optical properties of the crystal, studying on the electroelastic properties of this crystal is very limited. In the present study, large-size and high-quality BZBO crystals were grown by the Kyropoulos method. The electroelastic properties, including the dielectric, elastic, and piezoelectric properties, were characterized at room temperature. The contributions of the crystal symmetry space group to the piezoelectric property were analyzed from viewpoint of polyhedral distortion and net dipole moment. Moreover, the Received: March 5, 2018 Revised: April 29, 2018 Published: June 4, 2018 A
DOI: 10.1021/acs.cgd.8b00342 Cryst. Growth Des. XXXX, XXX, XXX−XXX
Crystal Growth & Design
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d33 meter (model ZJ-2, Institute of Acoustics Academia Sinica, Beijing, China). For the measurement of electroelastic constants by using the impedance method, different crystal cuts measuring 1 mm × 8 mm × 8 mm, 1 mm × 3.5 mm × 13 mm, and 2 mm × 2 mm × 8 mm were prepared for the square plates [(samples (a), (b), (c), and (g) in Figure 2], rectangular plates [samples (e), (f), (h), (i), and (j) in
temperature-dependent behaviors of the electroelastic properties were evaluated from room temperature to 500 °C.
2. EXPERIMENTAL SECTION 2.1. Single Crystal Growth. Prior to single crystal growth, polycrystalline BZBO powder was synthesized by traditional solidstate reaction techniques. Raw materials of Bi2O3 (99.99%, Alfa Aesar), ZnO (99.8%, Aladdin), and H3BO3 (99.99%, Alfa Aesar) were weighed according to their stoichiometric ratio (molar ratio of Bi2O3:ZnO:H3BO3 = 1:1:2). The stoichiometric raw materials were ground thoroughly into fine powders and fully mixed for more than 12 h. To determine the optimum sintering temperature for polycrystalline BZBO powders, the mixed powders were pressed into small blocks and then heated in air from room temperature to 450−600 °C for 4−10 h, respectively. The crystal phase of the sintered blocks was identified by X-ray powder diffraction (XRPD). The synthesized BZBO polycrystalline blocks were placed into a platinum (Pt) crucible at the center of a vertical and temperatureprogrammable furnace, where the longitudinal temperature gradient above the melt of 692 °C was nearly 2−3 °C/cm. The crucible was heated to 800 °C progressively and held on for at least 24 h to turn the raw materials into a homogeneous liquid solution. The temperature of the melt was then slowly decreased to 692 °C for crystal seeding. In the first run, a specially designed Pt wire was used as the seed and dipped into the solution after a stabilization period (2−5 h). The rotation speed of the Pt wire was maintained at 15 rpm. The polycrystalline BZBO surrounding the Pt wire was obtained by spontaneous crystallization with a slow cooling at a fairly low rate (0.1−0.2 °C/day). The high-quality BZBO crystal seed was selected and prepared from the grown polycrystalline BZBO bulks. In the following runs, the BZBO single crystals were grown using the selected BZBO crystal seeds. The growth condition and parameters were the same as for the spontaneous crystallization. The seed was soaked in the melt and the BZBO crystal was slowly grown into large size without pulling during the cooling process. The growth period was controlled within 2 weeks. When the growth procedure was finished, the temperature was gradually cooled to room temperature at a rate ranging from 5 °C/h to 20 °C/h. 2.2. Crystal Orientation and Sample Preparation. With regard to the requirements of the electroelastic property evaluation, the relationship between the crystallographic axes and the piezoelectric axes of the BZBO crystal was determined for the sample preparation. The BZBO crystal belongs to the orthorhombic system and space group Pba2 (mm2 point group). According to the IEEE standard on piezoelectricity,24 the relations between the crystallographic axes and the piezoelectric axes can be expressed as a//X, b// Y, and c//Z for the BZBO orthorhombic crystal. The X, Y, and Z axes form a right-handed orthogonal coordinate system. The coordinate system for the BZBO single crystal is presented in Figure 1. The polar direction [001] is defined as axis 3, and the [010] and [100] directions are defined as axes 2 and 1, respectively. The crystallographic axes were determined by X-ray diffraction, and the positive direction of the Z axis was determined by a quasi-static piezoelectric
Figure 2. Schematic of BZBO samples used to evaluate the electric, elastic, and piezoelectric constants: (a) X square plate; (b) Y square plate; (c) Z square plate; (d) Z bar; (e) ZX plate; (f) ZY plate; (g) Y′45° square plate; (h) ZYw/θ plates (θ = 60°, 70°, and 80°); (i) ZXw/θ plates (θ = 30°, 45°, and 60°); (j) ZXt/θ plates (θ = 30°, 45°, and 60°).
Figure 2], and rod samples [sample (d) in Figure 2], respectively. For the measurement of electroelastic constants by using the pulse-echo method, a rectangular sample measuring 4.9 (X) mm × 5.5 (Y) mm × 5.8 (Z) mm was designed. 2.2.1. Determination of Electroelastic Constants by Impedance Method. The BZBO crystal has 17 independent nonzero characteristic constants, including 3 dielectric constants (εT11, εT22, and εT33), 9 elastic constants (sE11, sE12, sE13, sE22, sE23, sE33, sE44, sE55, and sE66), and 5 piezoelectric coefficients (d15, d24, d31, d32, and d33). The dielectric constants were obtained by measuring the capacitance of samples (a), (b), and (c) by using a multifrequency LCR meter (Agilent 4263B). The 14 independent electroelastic constants were obtained by measuring the resonance and antiresonance frequencies with the use of the Impedance Phase Gain Analyzer HP4194A. All samples presented in Figure 2 were divided into 2 types: noncircumgyrate and circumgyrate. For the crystal cut (such as XYw/ θ), the first and second letters denote the directions of the thickness and the length of the sample, respectively. The third letter represents the rotation axis and the corresponding rotation angle θ of the circumgyrate sample. All samples were sputtered with platinum films in the direction of the applied electric field. Table 1 summarizes the different crystal cuts, vibration modes, and related equations used to determine the electroelastic constants of the BZBO crystal. 2.2.2. Evaluation of the Electroelastic Constants by Ultrasonic Pulse-Echo Method. To improve the accuracy of the electroelastic constants of the BZBO crystal, the ultrasonic pulse-echo method was used to analyze the elastic constants.25,26 Different from the impedance method, the elastic constants could be obtained with fewer samples. In the current study, only one cube-shaped sample was designed and prepared (Figure 1) for the ultrasonic test. Electric pulses used to excite the transducer (a 15 MHz longitudinal wave transducer and a 20 MHz shear wave transducer) were generated by a 200 MHz pulse/receiver (Panametrics, America), and the time-offlight between echoes was detected using a Tektronix 3054 digital oscilloscope. With the use of a crystal cube, 6 elastic stiffness constants (cE11, cE22, cD33, cE44, cE55, and cE66) can be determined from the measured phase velocities of ultrasonic waves propagating along different crystallographic directions. Relevant equations are presented as follows: Along direction 1
Figure 1. Relationships of the crystallographic and piezoelectric axes of the BZBO single crystal. B
DOI: 10.1021/acs.cgd.8b00342 Cryst. Growth Des. XXXX, XXX, XXX−XXX
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Table 1. Crystal Cuts, Vibration Modes, and Related Equations Used to Determine the Electroelastic Constants of BZBO Crystals samples
vibration modes
constants
X square plate
/
εT11/ε0
Y square plate Z square plate
/ /
εT22/ε0 εT33/ε0
related equations
εiiT C·t = A ·ε0 ε0 (under 1 kHz)
π fr π ji f − fr yzzz tan jjjj a z 2 fa 2 j fa zz { k 1 E sii = 4ρ(lfa )2 (1 − kii2)
kij2 = Z bar
d33, sE33
longitudinal
dij = kij εiiT sjjE X square plate Y square plate Y′(45°) square plate
d15, sE55 d24, sE44 sE66
thickness shear
π fr π ij f − fr yzzz tan jjjj a z 2 fa 2 j fa zz { k 1 E sii = 4ρ(tfa )2 (1 − kij2)
kij2 =
dij = kij εiiT sjjE ZX plate ZY plate
d31, sE11 d32, sE22
length extension
kij2 1 − kij2 siiE =
=
π fa π ji f − fr zyzz tan jjjj a z 2 fr 2 j fa zz { k
1 4ρ(lfr )2
dij = kij εiiT sjjE
v1(1) L =
ZXt/θ
sE12
E E s11E′ = s11E cos 4 θ + s22 sin 4 θ + (2s12E + s66 )sin 2 θ cos2 θ
ZYw/θ
sE23
E′ E E E E s22 = s22 cos 4 θ + s33 sin 4 θ + (2s23 + s44 )sin 2 θ cos2 θ
ZXw/θ
sE13
E E s11E′ = s11E cos 4 θ + s33 sin 4 θ + (2s13E + s55 )sin 2 θ cos2 θ
c11E (2) , v1T = ρ
E c66 , v1(3) T = ρ
D c55 ρ
(1)
E c66 , v2(3) T = ρ
D c44 ρ
(2)
E c55 , v3(2) T = ρ
E c44 ρ
(3)
Along direction 2 v2(2) L =
E c 22 , v2(1) T = ρ
Along direction 3
v3(3) L =
D c33 , v3(1) T = ρ
where the superscript of shear velocity v represents the direction of particle displacement perpendicular to the direction of wave propagation. The elastic stiffness constants are derived from the measured phase velocities.
3. RESULTS AND DISCUSSION 3.1. XRPD Phase Analysis and Morphology Calculations. The polycrystalline BZBO compounds were obtained by sintering the stoichiometric raw materials at 600 °C using solid-state reaction method. The sintering temperature was slightly higher than the reported Pechini systhesis method.27 Below 600 °C, the BZBO phase was found difficult to obtain using solid-state reaction method (Figure 3a). The XRPD pattern of the raw materials sintered at 600 °C for 4 h (Figure 3b) was consistent with the standard powder diffraction pattern (Figure 3f, ICSD Card No. 164635), with impurity
Figure 3. XRPD characterization of the BZBO: (a) XRPD pattern of the powder materials sintered at 450 °C for 4 h; (b) XRPD pattern of the powder materials sintered at 600 °C for 4 h; (c) XRPD pattern of the powder materials sintered at 600 °C for 10 h; (d) polycrystalline XRPD pattern; (e) single crystal XRPD pattern; (f) standard powder XRPD pattern.
peaks expected within the 20−30° range for the BZBO crystal. When the raw materials were sintered at 600 °C for 10 h, pure C
DOI: 10.1021/acs.cgd.8b00342 Cryst. Growth Des. XXXX, XXX, XXX−XXX
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piezoelectric charge coefficients dij of the BZBO crystal were larger than those of the α-BTMO and α-SiO2 crystals. The relative dielectric constants εT11/ε0, εT22/ε0, and εT33/ε0 were equal to 36.8, 18.5, and 18.3, respectively. The piezoelectric charge coefficient d32 was −6.4 pC/N, which was nearly 3.6 times higher that of α-BTMO. The signs of the piezoelectric coefficients were further discussed taking advantage of the anisotropy of piezoelectric crystals. The dependence of the orientation of piezoelectric coefficients d31 and d32 was investigated using eqs 4−6 (α, β, and γ are the rotation angles around the physical X-, Y-, and Zaxes, respectively).
BZBO phase was synthesized (Figures 3c). Thus, in this study, all polycrystalline BZBO compounds were prepared after they were sintered at 600 °C for at least 10 h. The BZBO bulk single crystal with dimension of 45 mm × 35 mm × 15 mm was obtained by the Kyropoulos method. Figure 4a,b present the photographs and morphology of the as-
′ = d32cos3 α + (d33 − d 24)sin 2 α cos α d32
(4)
′ = d31cos3 β + (d33 − d15)sin 2 β cos β d31
(5)
′ = d31cos 2 γ + d32 sin 2 γ d31
(6)
With the ZXt/θ crystal cut as an example, variations in effective piezoelectric d′31 as a function of the rotation angle around the Z axis were plotted by presuming the signs of the related piezoelectric coefficients d31 and d32 given in eq 6 (Figure 5a− d), where discrepancies were observed. The experimental piezoelectric d′31 values (θ = 45° and 60°) were obtained (as denoted by violet circles in Figure 5), where the consistency of the experimental d′31 values and curve (c) indicate that d31 and d32 have opposite signs. Therefore, the variations in d′31 value could be described using curve (c), and the effect d′31 value varied from 2.5 pC/N to −6.4 pC/N as a function of the rotation angle around the Z axis. The maximum d′31 value was determined to be on the order of −6.4 pC/N when the rotation angle reached ±90°. The minimum d′31 value was observed at 0° and determined to be equal to 2.5 pC/N. By using the same method, the signs of the other piezoelectric coefficients d15 and d24 were discussed and obtained from the circumgyrate samples (samples h−j in Figure 2). The results are presented in Figure 5, together with the measured values for verification, where the effective piezoelectric coefficients measured from ZXt/θ, ZYw/θ, and ZXw/θ crystal cuts were plotted in violet, black, and green solid spheres, respectively. The measured piezoelectric values were found to be in good agreement with the calculated values (the hollow sphere in Figure 5), indicating the validity of the determined piezoelectric coefficients. Table 2 shows that the magnitude of the piezoelectric coefficients of the BZBO crystal differs from those of α-BIBO. However, both types of crystal possess the same bismuth and boron elements. The piezoelectric properties were considered related to the asymmetric polyhedral structure. The distortion of the asymmetric polyhedra could be quantified by calculating the polyhedral distortions and dipole moments. On the basis of the crystal structure, the BZBO crystals contained BiO6 octahedron, ZnO4 tetrahedron and BOx (x = 3 and 4) polyhedron. For the BiO6 polyhedral distortions, the magnitude was quantified by considering the 6 BiO bond lengths. For the BiO6 octahedral distortion, Δd is defined as follows:31
Figure 4. Photographs and morphology of the BZBO single crystals grown along the [001] directions (a) and (b); Ideal growth morphology of the BZBO crystal by the BFDH method (c).
grown BZBO crystals with different habitual facets. By using the X-ray orientation apparatus, the indices of the distinguishable habitual facets were determined to be (001), (010), (100), (110), and so on. The ideal morphology of the BZBO crystal was established according to the Bravais-Friedel and Donnay-Harker (BFDH) method by using the Mercury Calculate program with its structural parameters. Figure 4c shows the ideal morphology of the BZBO crystal with habitual (001), (010), and (110) facets, which were in accordance with the practically grown crystals. The (100) facet was not predicted but observed from the as-grown crystals. The differences between the observed morphology and the theoretical morphology may be associated with growth conditions, such as seed orientation, growth speed, the level of undercooling, convection of flows (natural or forced or even both of them) and thermal gradient. If the growth conditions were further optimized, unrevealed facets might be observed. 3.2. Electroelastic Properties of BZBO Crystal. Table 2 lists the dielectric constants, elastic constants, and piezoelectric coefficients of the BZBO crystals determined using the impedance and ultrasonic pulse-echo methods at room temperature. The electroelastic constants for the α-BaTeMo2O9 (α-BTMO),28 α-SiO2,29,30 and α-BIBO12 crystals were also listed for comparison. It was revealed that the elastic constants cEij (i, j = 1−6) evaluated by impedance and pulseecho methods were comparable to themselves, except for cE66; the relative uncertainty was found to be Δdα‑BIBO (BiO) > ΔdBZBO (Bi1O). The larger distortions contribute to strong piezoelectric properties. The dipole moment is another important parameter to which dielectric and piezoelectric properties are attributable. The bond-valence approach was used to calculate the direction
Figure 5. Variations in piezoelectric coefficient as a function of the rotation angle presuming (a) +d31 and +d32; (b) −d31 and +d32; (c) +d31 and −d32; (d) −d31 and −d32; (e) piezoelectric coefficient d32 around the X-axis; (f) piezoelectric coefficient d31 around the Y-axis.
where the pairs (O1, O4), (O2, O5), and (O3, O6) are the oxygen atoms that constitute the octahedron and are located opposite each other. Their bond angles are θ1 = ∠O1−Bi−O4, E
DOI: 10.1021/acs.cgd.8b00342 Cryst. Growth Des. XXXX, XXX, XXX−XXX
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Table 3. Dipole Moments Calculated for BZBO and α-BIBO Crystalsa dipole moments crystals BZBO
α-BIBO
Bi1O6 Bi2O6 B1O3 B2O4 ZnO4 BiO6 B1O4 B2O3
x(a)
y(b)
z(c)
Debye
×10−4 edu cm/Å3
−5.3493 12.4261 −1.5424 −0.6783 −0.2942 −0.0001 −3.5527 × 10−15 0.9708
−13.3602 7.5161 0.2477 −0.9517 −0.8908 16.1242 −0.5725 1.8804
3.2347 1.8402 0.2502 −2.7206 1.8982 3.5527 × 10−15 1.3323 × 10−15 −1.7435
14.75 14.64 1.58 2.96 2.12 16.12 0.57 2.57
1013.71 1006.03 110.00 203.49 145.52 1451.24 51.53 231.59
The crystallographic data of BZBO and α-BIBO were referred to ICSD, no 16463516 and no 245889,37 respectively.
a
Figure 7. Directions of the net dipole moment for the polyhedra and unit cell of BZBO (a) and α-BIBO (b) crystals (The black arrows indicate the approximate directions of the dipole moment for the BiO6, BO3, BO4, and ZnO4 polyhedra. The green arrows indicate the net dipole moments.).
and magnitude of the dipole moments.32−36 Table 3 summarizes the calculated dipole moments for each polyhedron in the BZBO crystals, as well as the α-BIBO crystal for comparison. The magnitude of the dipole moment for BiO6 was larger than those for BO3 and BO4. The bond distances for Bi1O6 and Bi2O6 were in the ranges 2.167−2.669 and 2.133−2.779 Å, respectively. Meanwhile, the bond distances for B1O3, B2O4, and ZnO4 were in the ranges 1.33−1.41, 1.46−1.52, and 1.93−1.95 Å, respectively. The strong piezoelectric properties were attributed to the larger dipole moments of BiO6. The magnitude of the net dipole moment in the unit cell for the BZBO crystal was calculated and found to be 18.01 D, nearly half that of the α-BIBO crystal (35.04 D) (for detailed calculation, see the Supporting Information, Tables S1 and S2). The net dipole moment direction of the BZBO crystal was along the crystallographic c axis, whereas that of the α-BIBO crystal was along the b axis (green arrows in Figure 7). In addition, the directions of the dipole moment for each type of polyhedron in BZBO and α-BIBO crystals are shown in Figure 7. The calculated polyhedral distortions and dipole moments indicated that the BiO6 octahedron showed the larger polarization and contributed to the piezoelectric properties of the α-BIBO crystal. However, the directions of the dipole
moment for the two types of BiO6 octahedron in the BZBO crystal were nearly opposite. Therefore, the net dipole moment weakened. This occurrence might be the reason the piezoelectric properties of the BZBO crystal are weaker than those of the α-BIBO crystal. 3.3. Temperature Dependence of Electric and Electroelastic Properties. 3.3.1. Electrical Resistivity at Elevated Temperatures. Figure 8 shows the variation in electrical resistivity as a function of temperature for the BZBO crystal. The resistivity values along different orientations of the BZBO crystals range from 1.1 × 107 Ω cm to 9.8 × 107 Ω cm at 500 °C. The resistivity along the X-axis is higher than that along the Y- and Z-axes. The resistivity of the BZBO crystal along the X-axis is 1.27 × 1012 Ω cm at 300 °C, nearly 2 orders of magnitude higher than that of quartz (∼2.0 × 1010 Ω cm) and 4 orders higher than the La3Ga5TaO14 (LGTO) crystal.38 3.3.2. Temperature-Dependent Behaviors of Electroelastic Constants. The temperature dependence of the electroelastic properties of the BZBO crystal at temperature ranging from room temperature to 500 °C was determined. Figure 9 presents the variations in relative dielectric constants as a function of temperature. The relative dielectric constants εT11/ ε0, εT22/ε0, and εT33/ε0, which were determined to be of the value of 36.8, 18.5, and 18.3 at room temperature, respectively, F
DOI: 10.1021/acs.cgd.8b00342 Cryst. Growth Des. XXXX, XXX, XXX−XXX
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Figure 10. Variations in resonance frequency as a function of temperature (f r0 is the resonance frequency at room temperature).
Figure 8. Electrical resistivity of BZBO crystals along the X-, Y-, and Z-axes.
in the vicinity of resonant frequency and obtained to be 5100 at room temperature and then shifted to 3500 at 500 °C. 1 Qm = 2πfr R sCs (8) The variations in elastic compliance sEij as a function of temperature are examined for the BZBO piezoelectric crystal (Figure 11). The variation in sE33 is difficult to study because of
Figure 9. Relative dielectric constants of the BZBO crystal as a function of temperature.
shifted to 44.5, 23.5, and 27.5 at 500 °C, respectively. The variations were 20.9%, 26.7%, and 50.3%, respectively. In addition, the dielectric loss along the physical X axis (tan δ11) of the BZBO crystals is considerably lower than the losses along the physical Y- and Z-axes, as depicted in Figure 9. The low dielectric loss tan δ11 is associated with the high resistivity of the BZBO crystal. The temperature dependence of the resonance frequencies of the different crystal cuts was evaluated up to 500 °C. The results are shown in Figure 10. The resonance frequencies shift downward with increasing temperature, exhibiting a linear variation within the tested temperature range. The variations in resonance frequency were nearly equal −3.8%, −3.7%, −3.6%, and −3.4% for the ZX, ZY, ZXt/-30°, and ZYw/70° plates, respectively. The mechanical quality factor Qm is an important quantity reflecting the piezoelectric performance and can be evaluated by using eq 8, based on the Butterworth-Van Dyke equivalent circuit, where the Rs and Cs are the series components of the equivalent circuit and have the physical meaning of motional resistance and capacitance. For the ZX crystal plate, the mechanical quality factors Qm were evaluated
Figure 11. Variations in the elastic compliance of the BZBO crystal as a function of temperature.
the weak vibration resonance frequency. Considering that the elastic compliance of the ZYw/80° plate was close to sE33 (inset in Figure 11), the variation in sE33 for the BZBO crystal was approximately evaluated using the ZYw/80° crystal cut. The elastic compliances increased linearly with increasing temperature, showing positive temperature coefficients. The variations were 8.0%, 7.8%, 8.0%, 8.1%, and 7.5% for sE11, sE22, sE33, sE44, and sE55, respectively. The variations in electromechanical coupling factors obtained based on the measured resonance and anti-resonance frequencies of the BZBO crystals are presented in Figure 12. Among the electromechanical coupling factors, the length extension electromechanical coupling factor k32 is the largest, G
DOI: 10.1021/acs.cgd.8b00342 Cryst. Growth Des. XXXX, XXX, XXX−XXX
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other piezoelectric coefficients d31 and d24 decreased from 2.5 and 5.5 pC/N at room temperature to 1.5 and 5.4 pC/N at 500 °C, respectively. Notably, the piezoelectric coefficient d33 was small but remained constant at 1.1 pC/N at temperatures ranging from room temperature to 500 °C.
4. CONCLUSIONS In this study, transparent and large Bi2ZnB2O7 crystals measuring 45 mm × 35 mm × 15 mm were grown by the Kyropoulos method. The electroelastic constants of the Bi2ZnB2O7 crystal and their temperature-dependent behaviors were studied. Full set of electroelastic properties were evaluated by using the impedance and ultrasonic pulse-echo methods. The piezoelectric coefficients d15, d24, d31, d32, and d33 were 1.4, −5.5, 2.5, −6.4, and 1.1 pC/N, respectively, which were comparable to those of α-BTMO but larger than those of α-SiO2. The structural distortions (1.162 and 1.665 of the two Bi−O octahedra) and the dipole moment (18.01 D) of the BZBO crystal were analyzed, where the values assigned for the BiO6 octahedra appear to affect the piezoelectric properties of BZBO crystal. Moreover, the BZBO crystal maintained the same piezoelectric coefficient d33 from room temperature to 500 °C.
Figure 12. Variations in the electromechanical coupling factors of the BZBO crystal as a function of temperature.
of the value 14.5% at room temperature, and maintaining the same value up to 500 °C. The coupling factors k32 and k15 also exhibit good temperature stability within the tested temperature range. The variations are 2.4% and 13.8%, respectively. By contrast, k31, k33, and k24 of the BZBO crystal slightly decrease with increasing temperature, showing variations equal to −50.9%, −27.9%, and −16.2%, respectively. Combined with the determined dielectric constants, elastic compliances, and electromechanical coupling factors, the variations in piezoelectric coefficient were investigated. Figure 13 shows the temperature stability of the piezoelectric
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.8b00342. Table S1. Calculation of the dipole moment of the BZBO crystal (XLSX) Table S2. Calculation of the dipole moment of the αBIBO crystal (XLSX)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Feifei Chen: 0000-0001-7175-9119 Xian Zhao: 0000-0002-1523-4534 Funding
This work was supported by the Primary Research & Development Plan of Shandong Province (2017CXGC0413) and the National Natural Science Foundation of China (Grant Nos. 51202129, 51502158 and 51672160). Notes
The authors declare no competing financial interest.
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REFERENCES
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Figure 13. Variation of piezoelectric coefficients (absolute values) of the BZBO crystal as a function of temperature.
coefficients of the BZBO crystal. For comparison, the absolute values were presented. The largest piezoelectric coefficient d32 was 6.4 pC/N for the ZY plate at room temperature, which slightly increased with increasing temperature up to 8.0 pC/N at 500 °C. The shear piezoelectric coefficients d24 and d15, which were 5.5 and 1.4 pC/N at room temperature, respectively, slightly increased to 6.1 and 1.8 pC/N at 500 °C, respectively. In contrast, with increasing temperature, the H
DOI: 10.1021/acs.cgd.8b00342 Cryst. Growth Des. XXXX, XXX, XXX−XXX
Crystal Growth & Design
Article
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DOI: 10.1021/acs.cgd.8b00342 Cryst. Growth Des. XXXX, XXX, XXX−XXX
