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Elastic and piezoelectric constants of Bi12TiO20 crystals
January1995
Optical Materials4 (1995) 179-181
ELSEVIER
Elastic and piezoelectric constants of Bi12TiO20 crystals N. B u r i m o v a, A. M a n d e l a, A. R e s h e t ' k o a, S. S h a n d a r o v a, V. V o l k o v b, Yu. K a r g i n b a State Academy o f Control Systems and Radioelectronics, 40, Lenin Avenue, Tomsk 634050, Russian Federation b Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Moscow I 17907, Russian Federation
Abstract
The elastic constants and piezoelectric coefficient of Bi12TiO2ocrystal have been determined. The material constants have been calculated from the experimental data of the phase velocities of acoustic waves at the acoustooptical interaction.
The cubic crystals Bil2SiO20 (BSO), Bil2GeO2o (BGO), Bi12TiO2o (BTO) belong to the 23 class symmetry. These crystals are widely used in spatial light modulators [1], acoustic delay lines [2], for hologram recording and phase conjugation [ 3,4 ] because of their interesting electrooptic and acoustic properties. The effect of acoustic wave photogeneration at recording of a holographic grating in BSO crystal was found some years ago [ 5 ]. This effect gives new possibilities for optical signal processing. Due to investigations of optical amplification effects in such crystals [6,7 ], optical generators have been created on the basis of photorefractive crystals [ 8 ]. The knowledge of the elastic constants and piezoelectric coefficients is necessary for the design and optimization of real devices. For example, the considerable influence of the piezoelectrical effect on photorefractive gratings in BSO, BGO, BTO, GaAs has been demonstrated in Refs. [ 9, l 0 ]. In this paper elastic constants and a piezoelectric coefficient of BTO crystals have been determined at room temperature at acoustooptical interaction. A set of these constants was found from the experimental data of phase velocities for longitudinal and shear acoustic waves. Pure and vanadium-doped BTO crystals were used in our experiments. Acoustic waves
propagated along the [001 ], [ 1]0], [ 111 ] directions in different crystal samples. Shear and longitudinal acoustic waves were launched by lithium niobate piezoelectric plate transducers of X-cut and Y+ 36 ° cut, respectively. A HeNe laser (2 = 633 nm) was used at the acoustooptical interaction as light source. The velocities of the acoustic waves were found from the experimental determination of Bragg diffraction angles. The velocity of the longitudinal acoustic waves was found from the Schaefer-Bergmann diffraction pictures (Fig. 1 ). Such pictures take place at acoustooptical interaction of light beam and acoustic waves with a wide spatial spectrum that is caused by their multiple reflections from the crystal boundaries. For the measurement of the diffraction angles a rotating table with a precision positioning was used. The acoustic frequency was varied in the range from 30 MHz at 70 MHz in our experiments. The following expression was used for the calculation of acoustic wave velocities, V=
where 0 is the angle between diffracted and undiffracted light beams andfstands for the acoustic wave frequency. The experimental data of acoustic wave
0925-3467/95/$09.50 @ 1995 ElsevierScienceB.V. All fightsreserved SSD10925-3467 ( 94 )00099-9
2f 2 sin 0/2 '
180
N. Burimov et al. / Optical Materials 4 (1995) 179-181
Table 3 Elastic constants and piezoelectric coefficient of Bit2TiO2ocrystal by Ref. [ 11 ] and our new values
Crnn(101°N/m2)
C11
CI2
C4E4
el4 ( C / m 2)
Pure Bil2TiO2o V-doped Bil2TiO2o Ref. [11]
12.5 12.56 13.7
2.75 2.77 2.8
2.42 2.43 2.6
1.1 1.1 1.1
2 _ pVLtl,0J = ~ (Cll + Cl2 +2CE4) 2 pVL[oOI 1 i~.Cll ~ p V s [20 0 1 ] -~- CE4
Fig. 1. Schaefer-Bergrnann diffraction picture in the (110) crystallographic plane. Longitudinal acoustic wave was excited along the [ 111 ] direction.
Table 1 Acoustic wave velocities in vanadium-doped Bil2TiO2ocrystal Direction of the propagation acoustic wave
Acoustic wave
Polarization
Velocity (m/ s)
[001 ] [111] [111] [1|0]
Longitudinal Longitudinal Shear Longitudinal
[001 ] [111] [li0] [li0]
3735 + 18 3269+16 2118+11 3374+17
Table 2 Acoustic wave velocities in pure Bi~2TiO2ocrystal Direction of the propagation acoustic wave
Acoustic wave
Polarization
Velocity (m/s)
[001] [001 ] [1i0] [111]
Longitudinal Shear Longitudinal Longitudinal
[001] [ l |0 ] [li0] [111]
3714+20 1636 + 8 3332+16 3253+16
velocities in pure and V-doped BTO crystals are listed in Tables 1, 2. The elastic constants Cmn and piezoelectric coefficient e14 o f Bi~2TiO2o crystals were calculated by the following relations: p V 2 p x t l = ~ (Cll +2C12 +4C4E4 + 4e2,/eoe~ ) 2 pVst1111 = x3(C,, +C4~4- C,2),
where p = 9 0 7 4 k g / m 3 is the crystal mass density, eUl = 44 is the clamped (zero strain) dielectric constant [ 11 ], VL, Vs are the longitudinal and shear ultrasound velocities in the corresponding directions. The calculated values o f the material constants o f pure and V-doped crystals are listed in Table 3. In this table are also listed material constants from Ref. [ 11 ] measured by the resonance method [ 12 ]. The precision of the elastic constants measurements by the resonance method is comparable with the precision o f their measurements by the acoustooptic one. The distinction between the mean elastic constant C11 from Ref. [ 11 ] and our data may result from an inexact crystal orientation in the Ref. [ 11 ]. In our method the crystal orientation and the needed direction o f acoustic wave propagation were determined from Schaefer-Bergmann diffraction pictures. Our measurements have shown that the elastic constants and piezoelectric coefficient of pure and Vdoped Bil2TiO20 crystals do not differ.
References [ 1] M. Petrov, S. Stepanov and A. Khomenko, Photorefractive crystals in coherent optical systems (Springer, Berlin, 1991). [ 2 ] V. Rechicki, Acoustoelectronicradiocomponents: elements and devices on surfaceacoustic waves (Sov. Radio, Moscow, 1980). [3] P. Gunter and J.-P. Huignard, eds., Photorefractive Materials and their Application I and II (Springer, Berlin, 1988, 1989). [ 4 ] S. Stepanov and M. Petrov, Pisma Zh. Tekh. Fiz. 10 (1984) 1356. [ 5 ] P. Piatakov, V. Deev, R. Dochikyan and S. Karinski, Pisma Zh. Tekh. Fiz. l0 (1984) 483. [ 6 ] S. Stepanov, in: Optical holographywith recording in threedimensional media, (Nauka, Leningrad, 1988).
N. Burimov et al. / Optical Materials 4 (1995) 179-181
[7]Ph. Refregier, L. Solymaz, H. Rajbenbach and J.-P. Huignard, J. Appl. Phys. 58 (1985) 45. [ 8 ] S. Odulov, M. Soskin and K. Khizniak, Dynamic Grating Lalers (Nauka, Moscow, 1990). [ 9 ] S. Stepanov, S. Shandarov and N. Khatkov, Fiz. Tverd. Tela. 29 (1987) 3054. [ 10] V. Shepelevich, S. Shandarov and A. Mandel, Ferroelectrics, 110 (1990) 235.
181
[ 11 ] M. Verhinin, S. Davidov and S. Leonov, in: Proc. Intern. Sympos. on Surface Waves in Solids and Layered Structures, USSR, Novosibirsk, 2 (1986) 407. [ 12 ] M. Onoe, A.W. Warner and A.A. Ballman, IEEE Tr., SU- 14 (1967) p. 165.
Optical Materials4 (1995) 179-181
ELSEVIER
Elastic and piezoelectric constants of Bi12TiO20 crystals N. B u r i m o v a, A. M a n d e l a, A. R e s h e t ' k o a, S. S h a n d a r o v a, V. V o l k o v b, Yu. K a r g i n b a State Academy o f Control Systems and Radioelectronics, 40, Lenin Avenue, Tomsk 634050, Russian Federation b Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Moscow I 17907, Russian Federation
Abstract
The elastic constants and piezoelectric coefficient of Bi12TiO2ocrystal have been determined. The material constants have been calculated from the experimental data of the phase velocities of acoustic waves at the acoustooptical interaction.
The cubic crystals Bil2SiO20 (BSO), Bil2GeO2o (BGO), Bi12TiO2o (BTO) belong to the 23 class symmetry. These crystals are widely used in spatial light modulators [1], acoustic delay lines [2], for hologram recording and phase conjugation [ 3,4 ] because of their interesting electrooptic and acoustic properties. The effect of acoustic wave photogeneration at recording of a holographic grating in BSO crystal was found some years ago [ 5 ]. This effect gives new possibilities for optical signal processing. Due to investigations of optical amplification effects in such crystals [6,7 ], optical generators have been created on the basis of photorefractive crystals [ 8 ]. The knowledge of the elastic constants and piezoelectric coefficients is necessary for the design and optimization of real devices. For example, the considerable influence of the piezoelectrical effect on photorefractive gratings in BSO, BGO, BTO, GaAs has been demonstrated in Refs. [ 9, l 0 ]. In this paper elastic constants and a piezoelectric coefficient of BTO crystals have been determined at room temperature at acoustooptical interaction. A set of these constants was found from the experimental data of phase velocities for longitudinal and shear acoustic waves. Pure and vanadium-doped BTO crystals were used in our experiments. Acoustic waves
propagated along the [001 ], [ 1]0], [ 111 ] directions in different crystal samples. Shear and longitudinal acoustic waves were launched by lithium niobate piezoelectric plate transducers of X-cut and Y+ 36 ° cut, respectively. A HeNe laser (2 = 633 nm) was used at the acoustooptical interaction as light source. The velocities of the acoustic waves were found from the experimental determination of Bragg diffraction angles. The velocity of the longitudinal acoustic waves was found from the Schaefer-Bergmann diffraction pictures (Fig. 1 ). Such pictures take place at acoustooptical interaction of light beam and acoustic waves with a wide spatial spectrum that is caused by their multiple reflections from the crystal boundaries. For the measurement of the diffraction angles a rotating table with a precision positioning was used. The acoustic frequency was varied in the range from 30 MHz at 70 MHz in our experiments. The following expression was used for the calculation of acoustic wave velocities, V=
where 0 is the angle between diffracted and undiffracted light beams andfstands for the acoustic wave frequency. The experimental data of acoustic wave
0925-3467/95/$09.50 @ 1995 ElsevierScienceB.V. All fightsreserved SSD10925-3467 ( 94 )00099-9
2f 2 sin 0/2 '
180
N. Burimov et al. / Optical Materials 4 (1995) 179-181
Table 3 Elastic constants and piezoelectric coefficient of Bit2TiO2ocrystal by Ref. [ 11 ] and our new values
Crnn(101°N/m2)
C11
CI2
C4E4
el4 ( C / m 2)
Pure Bil2TiO2o V-doped Bil2TiO2o Ref. [11]
12.5 12.56 13.7
2.75 2.77 2.8
2.42 2.43 2.6
1.1 1.1 1.1
2 _ pVLtl,0J = ~ (Cll + Cl2 +2CE4) 2 pVL[oOI 1 i~.Cll ~ p V s [20 0 1 ] -~- CE4
Fig. 1. Schaefer-Bergrnann diffraction picture in the (110) crystallographic plane. Longitudinal acoustic wave was excited along the [ 111 ] direction.
Table 1 Acoustic wave velocities in vanadium-doped Bil2TiO2ocrystal Direction of the propagation acoustic wave
Acoustic wave
Polarization
Velocity (m/ s)
[001 ] [111] [111] [1|0]
Longitudinal Longitudinal Shear Longitudinal
[001 ] [111] [li0] [li0]
3735 + 18 3269+16 2118+11 3374+17
Table 2 Acoustic wave velocities in pure Bi~2TiO2ocrystal Direction of the propagation acoustic wave
Acoustic wave
Polarization
Velocity (m/s)
[001] [001 ] [1i0] [111]
Longitudinal Shear Longitudinal Longitudinal
[001] [ l |0 ] [li0] [111]
3714+20 1636 + 8 3332+16 3253+16
velocities in pure and V-doped BTO crystals are listed in Tables 1, 2. The elastic constants Cmn and piezoelectric coefficient e14 o f Bi~2TiO2o crystals were calculated by the following relations: p V 2 p x t l = ~ (Cll +2C12 +4C4E4 + 4e2,/eoe~ ) 2 pVst1111 = x3(C,, +C4~4- C,2),
where p = 9 0 7 4 k g / m 3 is the crystal mass density, eUl = 44 is the clamped (zero strain) dielectric constant [ 11 ], VL, Vs are the longitudinal and shear ultrasound velocities in the corresponding directions. The calculated values o f the material constants o f pure and V-doped crystals are listed in Table 3. In this table are also listed material constants from Ref. [ 11 ] measured by the resonance method [ 12 ]. The precision of the elastic constants measurements by the resonance method is comparable with the precision o f their measurements by the acoustooptic one. The distinction between the mean elastic constant C11 from Ref. [ 11 ] and our data may result from an inexact crystal orientation in the Ref. [ 11 ]. In our method the crystal orientation and the needed direction o f acoustic wave propagation were determined from Schaefer-Bergmann diffraction pictures. Our measurements have shown that the elastic constants and piezoelectric coefficient of pure and Vdoped Bil2TiO20 crystals do not differ.
References [ 1] M. Petrov, S. Stepanov and A. Khomenko, Photorefractive crystals in coherent optical systems (Springer, Berlin, 1991). [ 2 ] V. Rechicki, Acoustoelectronicradiocomponents: elements and devices on surfaceacoustic waves (Sov. Radio, Moscow, 1980). [3] P. Gunter and J.-P. Huignard, eds., Photorefractive Materials and their Application I and II (Springer, Berlin, 1988, 1989). [ 4 ] S. Stepanov and M. Petrov, Pisma Zh. Tekh. Fiz. 10 (1984) 1356. [ 5 ] P. Piatakov, V. Deev, R. Dochikyan and S. Karinski, Pisma Zh. Tekh. Fiz. l0 (1984) 483. [ 6 ] S. Stepanov, in: Optical holographywith recording in threedimensional media, (Nauka, Leningrad, 1988).
N. Burimov et al. / Optical Materials 4 (1995) 179-181
[7]Ph. Refregier, L. Solymaz, H. Rajbenbach and J.-P. Huignard, J. Appl. Phys. 58 (1985) 45. [ 8 ] S. Odulov, M. Soskin and K. Khizniak, Dynamic Grating Lalers (Nauka, Moscow, 1990). [ 9 ] S. Stepanov, S. Shandarov and N. Khatkov, Fiz. Tverd. Tela. 29 (1987) 3054. [ 10] V. Shepelevich, S. Shandarov and A. Mandel, Ferroelectrics, 110 (1990) 235.
181
[ 11 ] M. Verhinin, S. Davidov and S. Leonov, in: Proc. Intern. Sympos. on Surface Waves in Solids and Layered Structures, USSR, Novosibirsk, 2 (1986) 407. [ 12 ] M. Onoe, A.W. Warner and A.A. Ballman, IEEE Tr., SU- 14 (1967) p. 165.