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УДК 538.9
Electromechanical Properties and Anisotropy of Acoustic Waves Characteristics in Single Crystals YAl3(BO3)4
Pavel P. Turchin*
Institute of Engineering Physics and Radioelectronics, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041 Kirensky Institute of Physics Federal Research Center KSC SB RAS Akademgorodok, 50/38, Krasnoyarsk, 660036
Russia
Sergey I. Burkov Vladimir I. Turchin Sergey V. Yurkevich Pavel O. Sukhodaev Irina S. Raikova
Institute of Engineering Physics and Radioelectronics Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041
Russia
Received 09.08.2019, received in revised form 16.09.2019, accepted 06.10.2019 Velocity of bulk acoustic waves in base and rotated cuts have been measured by the ultrasonic pulse-echo method and values of CEjkl and e-ijk in single crystals YAls(BOs)4 have been calculated. The value of dijk piezoelectric modulus of these single crystals have been determined by quasistatic measurements, and elj dielectric constants have been determined by the flat capacitor method. Experimental values of material constants have been applied for the study of anisotropy of acoustic waves characteristics in single crystals YAls (BO3)4.
Keywords: electromechanical properties, acoustic waves, multiferroics. DOI: 10.17516/1997-1397-2019-12-6-756-771.
Introduction
Globally, a lot of attention is paid to the study of multiferroics [1-3], which include trigonal rare-earth oxyborates RMe3(BO3)4 (where R = Y, La-Lu; Me = Fe, Al, Cr, Ga, Sc). Ferrob-orates (RFe3(BO3)4) [4-6] are characterized by giant magnetoelectric [7] and magnetodielectric [8] effects. Alumoborates RAl3(BO3)4 that combine good luminescent properties and are a promising material for laser technology [9-11] are also of interest for practical applications, and single crystal YAl3(BO3)4 is used as a fourth harmonic generator in Nd:YAG laser [12]. Yttrium alumoborate YAl3(BO3)4 in the oxyborate series is a nonmagnetic single crystal and can characterize the anisotropy of the elastic-electric interaction in them. There are well-known cases of studying electromechanical properties of oxyborates [13-15], but no such studies have been carried out for yttrium alumoborate.
To study electromechanical properties of single crystals YAl3(BO3)4, the ultrasonic pulseecho method [16,17] which allows to determine the velocities of bulk acoustic waves (BAW) with
* pturchin@sfu-kras.ru © Siberian Federal University. All rights reserved
the accuracy of no worse than 10~4, was used. The point group of YAl3 (BO3)4 single crystals YAl3(BO3)4 symmetry is the same as in La3Ga5SiO14 (langasite) 32 (spatial symmetry groups R32 and P321, respectively). Therefore, the choice of the directions for BAW propagation and cuts to determine elastic, piezoelectric and dielectric properties in the single crystals under study correlate with studies [18,19], where the values of linear electromechanical constants of langasite were found. In contrast to [18,19], instead of rotated 45-degree cuts, close to it crystallographic direction [0111] (R facets) and the direction perpendicular to [0111] and to [2110] (R+90 facets) are used in this work.
In addition to pulse-echo measurements of BAW velocities and determination of the values of elastic Cjkl and piezoelectric eijk constants on their basis, quasi-static [20,21] studies of piezoelectric moduli dijk, which are related to ej ratio [22] were carried out
eijk dilmClmjk ■ (1)
To eliminate ambiguity in the signs of piezoelectric constants, direct measurements of the direction of electric polarization of the samples in the direction of the polar axis of the crystal were carried out. All the measurements were performed in the crystal physical coordinate system, where C14<0 [23]. The low-frequency values of dielectric constant ef1 of single crystals YAl3(BO3)4 were determined using the flat capacitor method.
The obtained values of electromechanical constants of single crystals made it possible to analyze the anisotropy of the main characteristics of BAW and surface acoustic waves (SAW). These data make it possible to form an opinion about the magnitude of the elastic-electric interaction for the longitudinal and shear strains in various directions of the crystals under study.
1. Theory
Propagation of BAW in acentric nonmagnetic single crystals is described by the Green-Christoffel equations [23,24]
(Til - XSii)Ui =0, (2)
where the following notations are used: ril = CEjklninj + ppr — the Christoffel symmetric tensor for piezoelectrics, Xi = pv2 — eigenvalues of ril , Sil — the Kronecker tensor, Ul — eigenvectors of ril, el = eplmnpnm and ei = eniknnnk — piezoelectric vectors, e* = e^nns — the convolution of the high-frequency dielectric constant, ni — the unit vector of wave normal.
The orientations of the crystal physical directions used to determine the electromechanical constants are given in Fig. 1. Solutions of equations (2) for directions perpendicular to x, y, and z-cuts (crystal-physics directions [100], [010] and [001] respectively) and rotated cuts R ([0 cosp sinp]) and R+90 ([0 — sinp cosp]) (p = 48.05°) are presented in Tab. 1 and Tab. 2.
Abundant number of solutions for non-piezoelectric active BAW given in Tab. 1 and 2 provides the necessary and verification relations for determining the elastic constants Cijkl. Piezoelectric active modes also allow determining the absolute values and the mutual sign of piezoelectric constants e11 and e14.
The values of e11 and e14 and their sign can also be determined from the equation (1) if CEjkl and piezoelectric modulus dijk, which are given by the equation of state (3) [22, 23] are known
Di = dijk&jk, (3)
where Di is electric induction; ajk is mechanical stress tensor.
[001) [001]
Fig. 1. Crystal physical orientation of directions and cuts. a) basic x, y, z — cuts; b) rotated R and R+90 cuts
Table 1. Relations between BAW velocities and linear material constants in crystals of symmetry 32 for base cuts
№ Xi = pvl n U Mode Relations with material constants
1 Ai [001] [001] L C33
2 X2 S C44
3 A3 [100] [001] L p'2 C + p11 Cii+ n
4 A4 S 1 (Cee+C44)+1 V(Cee - C44)2 +4C2U
5 A5 S 2 (Cee+C44)- 2 V/(Cee — C44)2 + 4Ci4
6 Ae [010] [100] L P'2 C + p11 Cee+,. n &n
7 A7 S 1 (C44+C1O+1 y/(C11 - C44)2 +4C24
8 As S 1 (C44+C11)-1 /(C11 - C44)2 + 4C24
2. Experiment
The block diagram of the ultrasonic pulse-echo method [17] is presented in Fig. 2.
In this method, a nanosecond pulse from generator 1 is transmitted to the piezoelectric transducer 3 and, after repeated reflection in sample 4, a series of reflected pulses is recorded by the oscilloscope 6. The wideband signal limiting amplifier 2, limits the amplitude of the probe pulse to the input voltage level of the oscilloscope 6 and increases sensitivity of the method when recording small amplitude signals. The rubidium frequency standard 7 provides temperature stabilization of the oscilloscope clock frequency 6. The master oscillator 5 synchronizes the start of the oscillator 1 and the sweep of oscilloscope 6. The experimental value of the bulk acoustic wave velocity in the implemented method is found from the known sample length l and the
2l
measured pulse propagation time in the sample t - v = — . An example of a recorded series
Table 2. Relations between BAW velocities and linear material constants in crystals of symmetry 32 for rotated R and R+90 cuts (y = 48.05° )
№ Ai = pv2 n U Mode Relations with material constants
1 AQ [0 cos y sin y] [100] S C66 cos2 y + C44 sin2 y+ +2C14 cos y sin y+ (en cos2 y+e14 cos y sin y)2 e'/1 cos2 y+£33 sin2 y
2 A10 QL 2(Cii cos2 y + C33 sin2 y+ +C44 — 2C14 cos y sin y)+ + 2V(C11 cos2 y + C33sin2 y + C44 — —2C14 cos y sin y)2 — 4[(C11 cos2 y+ +C44 sin2 y — 2C14 cos y sin y) * *(C33 sin2 y + C44 cos2 y) — — ((C13 + C14) cos y sin y — C14 cos2 y)2]
3 Aii QS 2 (C11 cos2 y + C33 sin2 y+ +C44 — 2C14 cos y sin y) — —1 \J(C11 cos2 y + C33 sin2 y + C44 — —2C14 cos y sin y)2 — 4[(C11 cos2 y+ +C44 sin2 y — 2C14 cos y sin y) * *(C33 sin2 y + C44 cos2 y) — — ((C13 + C14) cos y sin y — C14 cos2 y)2]
4 A12 [0 — sin y cos y ] [100] S C66 sin2 y + C44 cos2 y— —2C14 cos y sin y+ (e11 cos2 y+e14 cos y sin y)2 En! cos2 y+e33 sin2 y
5 A13 QL 2 (C11 sin2 y + C33 cos2 y+ +C44 + 2C14 cos y sin y)+ + 2 \J (C11 sin2 y + C33 cos2 y + C44+ +2C14 cos y sin y)2 — 4[(C11 sin2 y+ +C44 cos2 y + 2C14 cos y sin y)* *(C33 cos2 y + C44 sin2 y) —
— ( —(C13 + C14) cos y sin y — C14 sin2 y)2]
6 Al4 QS 2 (C11 sin2 y + C33 cos2 y+ +C44 + 2C14 cos y sin y) — — 2\/ (C11 sin2 y + C33 cos2 y + C44+ +2C14 cos y sin y)2 — 4[(C11 sin2 y+ +C44 cos2 y + 2C14 cos y sin y)* *(C33 cos2 y + C44 sin2 y) —
— ( — (C13 + C14) cos y sin y — C14 sin2 y)2]
of echo pulses is shown in Fig. 3. The resonant frequency of the piezoelectric transducer in the experiments was 28 MHz.
Fig. 2. Block diagram of the automated pulse-echo method. 1 — G5-66 pulse generator, 2 — signal limiting amplifier, 3 — piezoelectric transducer, 4 — sample, 5 — AFG 3252 master generator, 6 — DPO 72004 oscilloscope, 7 — FS725 rubidium frequency standard, 8 — personal computer
H4ffl+H4
rt rz i
h U I i- U -M— K4 b f
F I ' T
1
P
Fig. 3. A series of reflected echo pulses for a longitudinal wave in the direction [100] of the single crystal YAl3(BO3)4
The quasi-static measurements of piezoelectric moduli dn and di4 were carried out at the equipment, the block diagram of which is given in Fig. 4.
When measuring, the test sample 6 is placed in the holder 7 of the DMA 242 C 1 device, and adjustable static Fsiai and dynamic Fdyn loads with a total amplitude in the range of 0^8H with a frequency of up to 100 Hz are applied to it. Electric charges on the surface of the piezoelectric sample under load are converted by the charge amplifier 4 into the voltage recorded by the oscilloscope 3. An example of voltage measurement is shown in Fig. 5.
The value of the piezoelectric modulus is calculated in accordance with the formula:
7 q uSi
^ = F = KoFSe ^ (4)
where di\ is the measured piezoelectric modulus, q is electrodes charge, Fdyn is the dynamic force amplitude, U is the voltage amplitude at the charge amplifier output, Sl is the area of load application, Se is the electrodes area, Ka is the charge amplifier conversion coefficient.
Fig. 4. Block diagram of the experimental method for measuring piezoelectric modules. A variant of measuring of the transverse as related to the direction of the electric polarization pressure is presented. 1 — DMA 242 C, 2 — personal computer, 3 — DPO 7104 oscilloscope, 4 — charge amplifier LE-41, 5 — power supply, 6 — sample, 7 — sample holder
Fig. 5. Recording the voltage U on the sample when measuring piezoelectric moduli at different frequencies
The samples used in the experiments had the orientations given in Fig. 1. The linear dimensions of the samples were about 5-6 mm, the accuracy of the faces orientation was not worse than ±3', the opposite faces flatness was 3 microns. To determine the low-frequency dielectric constant by the flat capacitor method, the plates with x and R cuts with a thickness of less than 0.5 mm and an area of about 1 cm2 were used.
The positive direction of Xi axis of the crystal-physical coordinate system was chosen from the correspondence of the measured BAW velocities to the solutions of equation (2) (Tab. 2) obtained for the R and R+90 cuts (Fig. 1), in such a way that C14<0 was performed in both directions. The sign of piezoelectric constants was controlled by direct measurement of the piezoelectric effect. Mechanical compressive strain was considered negative.
3. Values of electromechanical constants
Experimental values of BAW velocities for the studied directions are given in Tab. 3. Point out high values of the shear and longitudinal BAW velocities at a not very high density of the single crystal 3.72 g/cm3 [25] under study.
Table 3. BAW velocities in YAl3(BO3)4 single crystal at room temperature
n Mode V (v ± Av), m/s
[001] L [001] 8534±5
S 4488±1
[100] L [100] 10587±2
S 4020±1
S 5474±1
010[ S [100] 5412±3
QL 10453±1
QS 4435±1
[0 cos(48.05°) sin(48.05°)] S [100] 4205±1
QL 9202±3
QS 5521±1
[0-sin(48.05°) cos(48.05°)] S [100] 5486±1
QL 8680±3
QS 5610±1
The values of Cjki calculated in accordance with the ratios of Tab. 1 and 2 are given in Tab. 4 compared to the data for other crystals.
In quasi-static measurements, the longitudinal piezoelectric modulus dn was determined according to the formula (4) when mechanical compressive stress was applied along axis Xi (Fig. 1 b) and charge detection was recorded in the same direction. The sign of the piezoelectric modulus was found by determining the direction of the electric induction vector with respect to the positive direction of X1 axis from equation (3). To determine d14, in contrast to d11, a mechanical compressive stress was applied to R and R+90 faces (Fig. 1b). In this case, there were piezoelectric modules d'12 and d' respectively. In this case the value of the piezoelectric modulus d14 can be found from the equations
d'i2 + d'i cos2 y
«14 = -:--(5)
sin y cos y
Table 4. Values of elastic constants YAl3(BO3)4 at room temperature compared to the data for other oxyborate single crystals, C66 = (Cii — Ci2)/2
Elastic constants Values of elastic constants, 1010 N/m2
This work YAl3(BO3)4 [13] [14] [15]*
RFe3(BO3)4 HoMe3 (BO3)4
R=Nd R=Sm Me=Fe Me=Al TbFe3(BO3)4
C11 40.47±0.05 31.9 32.4 37 39.5 27.2
C12 21.14±0.05 17.4 19.4 12.5 13.1 12.2
C13 9.75±0.05 11.7 - 7.2 6.1 -
Cl4 -2.35±0.1 2.96 2.86 3 1 4.76
C33 27.09±0.05 21.4 21.4 15.9 17.3 21.1
C44 7.49±0.01 4.9 5.05 6.8 6.4 7.54
*Measurements are performed at liquid nitrogen temperature
or
= <2 + ¿11 sin2 y , (6)
- Sin y cos y
The results of quasi-static measurements are presented in Tab. 5.
Table 5. The values of the piezoelectric moduli dj^ in single crystal YAl3(BO3)4 at room temperature
Piezoelectric moduli dn d12 d12 d14
Values of moduli, 10~12 C/N -6.0±0.3 -0.9±0.1 7.0±0.2 -7.2±0.4
After determining the values of the piezoelectric moduli and elastic moduli, it becomes possible to determine the values of the piezoelectric constants e11 and e14. This can be done from the equations 3 and 6 of Tab. 1 and the equations 1 and 4 of Tab. 2, as well as using the formula (1), which gives the following equalities
en = 2Ceedii + Ci4di4, (7)
ei4 = 2Ci4dii + C44di4. (8)
Equations (7) and (8) determine the sign of the constants eii and ei4. Note that the obtained values of the piezoelectric constants eii and ei4 from the acoustic measurements, as well as the values calculated from equations (7) and (8) coincided within the experimental error. The values eii and ei4 of the single crystal YAl3(BO3)4 are presented in Tab. 6 compared to the known
data for oxyborates of other authors. The high-frequency values of the dielectric constant ej were calculated on the basis of the experimental values efj using the formula [22]
emn — emn = dmij dnklCijkl■ (9)
Table 6. Values of piezoelectric ejk and dielectric ej constants at room temperature
Constants Values of constants
This work YAl3(BO3)4 [13] [14]
NdFe3 (BO3)4 SmFe3 (BO3)4 HoFe3(BO3)4 HoAl3(BO3)4
Piezoelectric constants eijk, C/m2
eii -1.06±0.07 1.4 1.4 0.99 1.75
ei4 -0.27±0.04 0.4 1.11 0.5
Dielectric constants, ej/e0
e11/e0 11.7±0.1
e33/e0 11.1±0.1
4. Anisotropy of BAW characteristics
Based on the obtained values of the material constants of YAl3(BO3)4 crystal elastic moduli, piezoelectric coefficient and dielectric constant, anisotropy for bulk acoustic waves characteristics in the base planes was calculated. The values of BAW phase velocities were calculated on the basis of the Green-Christoffel equations (2). The calculation of electromechanical coupling coefficients (EMCC) k2 and the angles of deviation of the elastic wave energy flow 7 from the wave normal were calculated using the formulas [26]. To simulate the anisotropy of BAW characteristics, the software package [27], where all calculations are performed in a triaxial orthogonal crystal physical coordinate system (CPCS) was used.
The anisotropy of BAW parameters in the (001) plane is demonstrated in Fig. 6. In this plane, the change in BAW velocities of longitudinal (QL) and fast shear (QFS) waves is relatively small. In particular, the value of the phase velocity QFS in the direction [100] is 5479.8 m/s, but at an angle of 30° it is 5407.3 m/s (Fig. 6a). In the plane (001) all BAW are piezo-active. The maximum EMCC k2 value is close to 0.1 and is reached in the direction at an angle of 30° with the direction [100] for the elastic wave QFS, but, at the same time, the maximum value of the energy flow deviation from the wave normal 7 = 10.7° for QFS is reached as well. The maximum value 7 = 18.5° is reached for a slow shear wave QSS at an angle of 15° with the direction [100]. It should be noted that in the direction [100] for the QL wave, the maximum value of k2, close to 0.03, is reached, but the value is 7 = 0°, which may be of practical importance. In Fig. 6 and in the other figures, the dots indicate the experimental values of BAW velocities.
The similar BAW characteristics of crystal YAl3(BO3)4 in plane (010) are presented in Fig. 7. In Y-cut, all BAW are also piezo-active, but the maximum value of k2 is reached for the QL
wave in the direction [100]. For QFS and QSS waves it is much smaller (Fig. 7 b). However, the energy flow deviation in plane (010) is considerably larger compared to (001). The maximum value for QSS wave is 7 = 32.5° at an angle of 35° with the axis [001] (Fig. 7c).
(a) (b) (c)
Fig. 7. Anisotropy of BAW characteristics in plane (010)
There is a distinctive feature in plane (100) — the presence of 4 acoustic axes (Fig. 8), and only in the direction [001] (the axis of symmetry of order 3) the presence of the acoustic axis is determined by the crystal symmetry. Only one of the shear waves is piezo-active. The solutions "exchange" takes place in the acoustic axes' region at an angle of 25.5° and 143° with the direction [100]. The maximum value of EMCC k2 = 0.12 is reached at an angle of 15° with the direction [100] for QFS. It is necessary to note large values of the energy flow deviation angles from the wave normal to 7 = 29° for a slow shear wave (Fig. 8 c).
The similar BAW characteristics of crystal YAl3(BO3)4 in the plane (110) of CFCS are presented in Fig. 9. In the plane (110) all BAW are also piezo-active, as well as maximum values of k2, close to 0.05 for fast and slow BAW respectively, (Fig. 9 b). However, in these directions, the angles of energy flow deviation from the wave normal are significant (Fig. 9 c).
(V
\ QFS
- QSS 1
40
80 120
160
(a) (b) (c)
Fig. 8. Anisotropy of BAW characteristics in plane (100)
(a) (b) (c)
Fig. 9. Anisotropy of BAW characteristics in plane (110)
5. Anisotropy of SAW characteristics
To calculate SAW characteristics, it is necessary to supplement the equations of motion (2) with boundary conditions, which are equality of the normal components of the stress tensor to
zero and continuity of the electric induction vector at the crystal-vacuum interface: T3j = 0;
xs =0
[28]. The anisotropy of SAW characteristics is analyzed using the software
xs =0
D3 = Dvac
package [29] in the working orthogonal coordinate system, where axis X3 is directed along the outer normal to the layer surface, and axis X1 coincides with the direction of wave propagation. SAW characteristics of crystal YAl3(BO3)4 in plane (001) are presented in Fig. 10. The values of the SAW phase velocity are in the range from 3958.9 m/s to 4276.1 m/s. The maximum value of EMCC k2 = 0.0013 in the direction of elastic wave propagation at an angle of 16° with the axis [100], but the maximum angle of energy flow deviation from the sagittal plane 7 = 12.9° is also reached here.
In plane (010), the maximum value of EMCC k2 = 0.011 is reached in the direction of the elastic wave propagation at an angle of 28° with the axis [001] (Fig. 11), but the angle of the
(a)
(b)
(c)
Fig. 10. Anisotropy of SAW characteristics in plane (001)
energy flow deviation from the sagittal plane is 7 = 5.1°. The maximum value of the angle of the energy flow deviation from the sagittal plane is 7 = 18.1° is achieved at an angle of 17° with the axis [001].
Ai
-1—1—1—1—1 120 160
Yi Ч*' Ч5'
(a) (b) (c)
Fig. 11. Anisotropy of SAW characteristics in plane (010)
The similar SAW characteristics of crystal УА1з(БОз)4 in plane (100) are presented in Fig. 12. The maximum value of EMCC k2 « 0.012 is reached in the direction of the elastic wave propagation at an angle of 29° with the axis [010] (Fig. 12), but the energy flow deviation angle from the sagittal plane is 7 = 10.3°. At an angle of 159° with the axis [010] and the value of k2 = 0.011 the angle 7 = 8.9°.
SAW characteristics of crystal YAl3(BO3)4 in the X boule axis, Euler angles (0°, ф, 0°) are given in Fig. 13. The energy flow deviation angle from the sagittal plane in the entire interval is zero, EMCC reaches values close to 0.008.
SAW characteristics of crystal YAl3(BO3)4 for У cylinder axis, Euler angles (0°, ф, 90°) are presented in Fig. 14. In this case, the symmetry axis 2 is orthogonal to the sagittal plane, therefore, there are two surface waves in this section — the Rayleigh wave polarized in the sagittal plane and the Bleustein-Gulyaev piezo-active wave. The peculiarity of this section is the fact that the phase velocity value of the Rayleigh wave is greater than the slow shear wave in the interval when the fast shear wave becomes piezo-active (Fig. 14). The energy flow deviation
(a) (b) (c)
Fig. 12. Anisotropy of SAW characteristics in plane (100)
angle from the sagittal plane is also zero in the entire interval, but EMCC can exceed the values of k2 =0.013.
Fig. 13. Anisotropy of SAW characteristics for the X boule axis, Euler angles (0°, 0°)
Conclusion
The carried out precision acoustic and quasi-static measurements made it possible to determine the values of linear electromechanical material constant of single crystals YAl3(BO3)4 with good precision. Despite the small value of the single crystal density of 3.72 g/cm3, the shear BAW velocities exceed 4000 m/s, the longitudinal BAW 8000 m/s, and in a number of directions 10000 m/s. The value of the longitudinal modulus of elasticity Cn = 40.5 • 1010N/m2.
Both acoustic ultrasonic pulse-echo method and quasi-static measurements of piezoelectric constants within the margin of error give the same, relatively small values e11 = —1.06 C/m2 and e14 = —0.27 C/m2. At the same time, the study of the anisotropy of BAW characteristics demonstrates the existence of directions in the (100) and (001) planes in the single crystal under study, in which the electromechanical coupling coefficient k for a fast shear BAW exceeds 30%, as in strong piezoelectrics.
(a)
(b)
Fig. 14. Anisotropy of SAW characteristics for Y cylinder axis (0, y, 90)
The study of the anisotropy of the BAW and SAW characteristics demonstrates a number of other features of the yttrium aluminum borates electromechanical properties manifestation. For instance, in plane (100) 4 acoustic axes are observed, and only one of them is symmetrically conditioned. For X boule axis, a range of angles where the velocity of the Rayleigh SAW exceeds the velocity of the slow shear BAW is observed.
The reported study was funded by Russian Foundation for Basic Research project no. 18-42240016, Government of Krasnoyarsk Territory, Krasnoyarsk Regional Fund of Science, to the research project: "Electromechanical Properties and Anisotropy of Acoustic Wave Propagation in Yttrium Aluminoborates Single Crystals".
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Электромеханические свойства и анизотропия характеристик акустических волн в монокристаллах YAl3(BO3)4
Павел П. Турчин
Институт инженерной физики и радиоэлектроники Сибирский федеральный университет Свободный, 79, Красноярск, 660041 Институт физики им. Л. В. Киренского СО РАН Академгородок, 50/38, Красноярск, 660036
Россия
Сергей И. Бурков Владимир И. Турчин Сергей В. Юркевич Павел О. Суходаев Ирина С. Райкова
Институт инженерной физики и радиоэлектроники Сибирский федеральный университет Свободный, 79, Красноярск, 660041
Россия
Эхо-импульсным ультразвуковым методом измерены скорости объемных акустических волн в базовых и повернутых срезах и рассчитаны значения СЕЫ и eijk в монокристаллах УЛ1з(БОз)4. Величины пьезомодулей dijk этих монокристаллов определены квазистатическими измерениями, диэлектрических постоянных e%j — методом плоского конденсатора. Экспериментальные значения материальных постоянных применены для исследования анизотропии характеристик акустических волн в монокристаллах УЛ1з(БОз)4.
Ключевые слова: электромеханические свойства, акустические волны, мультиферроики.
