- Email: [email protected]
Ultrasonic measurement of the elastic constants of LiKSO4 between 300 and 370 K
Pergamon
Solid State Communications. Vol. 97. No. 7. pp. 635-638. 1996 Copyright cl 1995 Elsevier Science Ltd Printed in Great Britam. All rights reserved 0038 1098196 $12.00 + 00
003%1098(95)00577-3
ULTRASONIC
MEASUREMENT OF THE ELASTIC CONSTANTS BETWEEN 300 AND 370 K L. Godfrey*
Department
and J. Philip
of Physics and Instrumentation Centre, Cochin University Cochin 682 022, India (Received
OF LiKS04
of Science and Technology,
18 July 1995; accepted 21 August 1995 by M.F. Collins)
All five independent elastic constants of LiKS04 have been determined from absolute velocity measurements on single crystal samples using ultrasonic pulse echo overlap technique. The constant Cl3 is reported for the first time. Measurement of the temperature variation of elastic constants between 300 and 370 K indicates no anomaly near 333 K, ruling out a phase transition occurring in the sample at this temperature reported in an earlier Brillouin scattering work. Keywords: ultrasonics.
A. ferroelectrics,
D. elasticity,
1. INTRODUCTION LITHIUM POTASSIUM SULPHATE (LPS). LiKS04, is an extensively studied crystal. It exhibits a sequence of very interesting phase transitions as the temperature is varied from 20K to 998 K (melting point) [l, 21. A variety of experimental techniques such as thermal expansion [3], Raman scattering [l, 4-61, dielectric constant [l, 7, 81, ferroelectricity [9], piezoelectricity [lo], X-ray diffraction [Il. 121, ESR [ 13- 151, thermal analysis [ 161, neutron scattering [ 171, Brillouin scattering [18-211, ultrasonics [2, 221, etc. have been used to investigate the properties of this crystal as the temperature is varied. The interest in this crystal is because of its pyroelectric and ferroelectric behaviour, electro-optic effect [23], existence of a large number of phase transitions, and observation of incommensurate lattice phase in certain temperature regions. The series of phase transitions observed in LPS is said to be very peculiar [24]. There are phase transitions at high temperature, at first from paraphase towards a commensurate state, and then with incommensurate modulation [25, 261. In this state LPS is simultaneously ferroelastic [27,281 and superionic [21, 291. In the range from room
* Permanent address: School of Pure and Applied Physics, Mahatma Gandhi University, Kottayam 686 560, India. 635
D. phase
transitions,
E.
temperature to 708 K, LPS has hexagonal symmetry and belongs to the space group Cz (P63) with two molecules per unit cell. Below room temperature, LPS undergoes a number of phase transitions and shows large thermal hysteresis for the transition temperatures. The crystal symmetry and structure of the modulated phase as well as the phase transition temperatures of LPS are not yet well established [22, 301. The elastic properties of LPS have been studied before using Brillouin scattering [18-21, 311 and acoustic techniques [2, 22, 321. Elastic properties have also been investigated earlier by resonance antiresonance [ 10, 151 and torsion pendulum methods [33]. Drozdowski et al. [18] have reported the values of elastic constants C,, , C33, and C66 of LPS at room temperature measured by Brillouin scattering technique. Later Pimenta et al. [19] used Brillouin scattering to measure the constants Ct,, C33, Cd4, C,, and deduced the value of Cl1 using the relation Cl1 = Cri - 2C66. Kabelka and Kuchler [2] made the first ultrasonic determination of the elastic constants of LPS and compared their values with that of Pirnenta et al. [19]. We find that in none of the previous measurements has the independent elastic constant Ci3 of LPS been reported. So the complete set of five independent elastic constants of this widely investigated crystal is not yet available in literature. Drozdowski et al. [18] have reported a phase
636
ELASTIC
CONSTANTS
transition occurring in this crystal around 333K (60°C) in their Brillouin scattering results. They have reported that the elastic constants CZ2, C3s and Ce6 undergo anomalous changes at this temperature indicative of a phase transition. Later Brillouin scattering study of Pimenta et af. [ 191 could not detect any anomaly in elastic constants at this temperature. But Wan Ji-fang et al. [32], from their ultrasonic studies. reported that there is an abrupt change of Cj3 near 333 K with large temperature hysteresis and that the peak of Cx3 reduces with successive heating and cooling. On examining early investigations, we find that there is a minimum near 333 K in the thermal expansion coefficient curve of LPS in the u-axis direction [3]. The purpose of this communication is twofold: (i) Report all five independent elastic constants of LiKS04 including Cl3 at room temperature. (ii) Determine whether there is a phase transition in LiKS04 at 333 K by measuring the temperature variation of all five independent elastic constants of LPS and ultrasonic attenuation in the temperature interval from 300 K to 370 K. 2. EXPERIMENTAL
METHOD
AND
RESULTS
LiKS04 single crystals are grown from an equimolar mixture of Li2C03 and KHSOj dissolved in distilled water. On mixing, the following reaction takes place 2KHS04
+ Li2C03 -+ 2LiKSOJ
OF LiKS04
Vol. 97, No. 7
Table I. Elastic constants (in GPa) of LiKS04 comparison with previous measurements Cji
Present study (1995)
Kabelka Kuchler (1988)
Cl, Cl1 C,3
57.24 28.66 22.37 67.35 21.51 14.29
c33
c,, C,,
& [2]
in
Pimenta et al. [19] (1986)
Drozdowski et al. [18] (1983)
55.0 26.4 -
57.4 29.2 _
51.6
67.3 20.5 14.3
67.3 21.1 14.2
59.3
_
57.0
pulse modulator and receiver system (Model 7700 with accessories) has been used for the measurements. The McSkimin At criterion [36] has been applied for the correct identification of echo overlap and bond correction. For hexagonal crystals there are nine nonzero elastic constants. of which five are independent, which are related by, c,, = Cl?, C& = css, Cl3 = C,, and C’t? = Ctt - 2C,,. The diagonal constants are determined directly from velocity measurements along symmetry directions using longitudinal and transverse waves. Cl2 is calculated using the relation given above. C13 is obtained by measuring the velocity u of the quasi-longitudinal wave in a-c plane and using the relation,
+ Hz0 + CO?. c,3
Crystals obtained from the solution prepared by the above method are found to be of better quality than from the method of making LPS by mixing equimolar mixtures of LiZSO and K,S04. The crystals are grown at 311 K from a seed crystal by constant temperature solvent evaporation method in a specially designed constant temperature solution growth apparatus. Large single crystals of good optical quality with typical sizes of about 3cm in a and e directions are obtained over a period of 45 days. The crystals have well-developed faces perpendicular to [ 10 01, [0 0 l] and [lo 1] directions. The following choice of axes has been taken for ultrasonic study: the [0 0 l] axis is the hexagonal one, [ 10 0] axis is in the basal plane and perpendicular to a natural face of the crystal and [0 lo] axis is in the basal plane and perpendicular to the other two. The lattice parameters are u = 5.147 A and c = 8.633 A [34]. The density of the crystal is 2.396 gm cmp3 [2]. Velocity of longitudinal and transverse ultrasonic waves of frequency 1OMHz propagating along the symmetry directions have been measured accurately by the Pulse Echo Overlap method [35]. A MATEC
=
(y-Cnj
where ttz = sin’ %C,, + co? %Cu - pv’, n = sin’ %C,+ co? K33 p2. I = sin’ 9~0s’ 9, p = density and 9 is the angle between the propagation direction and the c-axis. For the measurement of C13, the velocity in the [l 0 l] direction is used with 9 = 59.20’. The measured constants at 300K are tabulated in Table 1 in comparison with earlier reports. The accuracy of the
57
x-
h7.l
;
2
++++++
““++++++ **+
57.2.
*+++++
:
*++A+&
-
g ;r k z Q 2
2
++++++.+
5
1
3 -h&L) ++++*+*+ ++++* *++++++*L
+++a++
C/i
**++
.
C
*++++++,, 56hi
-6h.I -
*+++++++ +++i+
i
5 z
+++++++ +++++
*+++++
;
++*++
-h52
g ; 7 r z
1
1
Fig. 1. Temperature and C33 of LiKSO+
variation
of elastic constants
Ct 1
ELASTIC
Vol. 97, No. 7
20.011140 300 310
320
330
340
350
360
CONSTANTS
370
T(K)
Fig. 2. Temperature variation CM, and CG6 of LiKS04.
of elastic constants
Ci3,
present measurements are better than 1% and provide the complete set of elastic constants of LPS. The temperature variation of all the elastic constants have been measured from room temperature to 370 K by keeping the sample in a temperature controlled high temperature cell. Special attention has been paid to temperatures around 333 K where Drozdowski et al. [ 181 and Wang Ji-fang et al. [32] found an anomaly in Brillouin scattering and ultrasonic measurements respectively. The experimental curves of Drozdowski et al. [18] show an anomaly of the order of 0.5GPa variation and an anomaly of this magnitude, if present, can easily be detected in the present ultrasonic measurements which has a precision of 0.01%. The ultrasonic attenuation measurements have also been performed relative to the room temperature value along with the velocity measurements since it is a very sensitive indicator of phase transitions. The results of our measurements in the range from 300K to 370K are displayed in Figs 1 and 2. As is evident from these figures, none of the elastic constants undergo any anomaly at 333 K. The ultrasonic attenuation (not given in the figure) shows a linear variation with temperature and does not show any anomaly near 333 K.
637
we can conclude that LPS does not undergo any phase transition at 333 K. All the elastic constants decrease slightly with increasing temperature which is the general behaviour exhibited by most solids. The difference in observation reported by different workers regarding the anomaly at 333 K needs some explanation. Pimenta et al. [19] have suggested that a possible explanation of this discrepancy could be the existence of two different stable structures of LPS near room temperature. We find that a similar idea has also been proposed by Tomaszewski and Lukaszewicz [ 11, 121 to explain the difference in thermal hysteresis of the low temperature phase transition temperature in LPS. They have suggested that there are two types of crystals. Type A and Type B, which are characterised by the thermal hysteresis of the low temperature transition. We feel that the possibility for the existence of two types of LPS at room temperature may be a correct explanation for the inconsistent experimental results on LPS found in literature. Ackno,vledgement - This work has been supported by Department of Science and Technology (Government of India) through grant No. SP/S2/M06/86.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.
3. DISCUSSION 10. Our values for the elastic constants compare well with the values reported by earlier workers. The value of C,, reported by Drozdowski et al. [18] is abnormally high compared to other reported values. Our results on the temperature variation of elastic constants are in agreement with those of Pimenta et al. [ 191 who could not detect any anomaly at 333 K in the temperature variation of Cii, CJ3 or C,, in their Brillouin scattering results. Since ultrasonics is a more sensitive technique than Brillouin scattering,
OF LiKS04
11. 12. 13. 14.
A.J. Oliveira, F.A. Germano, J. Mendes Filho, F.E.A. Melo & J.E. Moreira, Phys. Rev. B38, 12633 (1988). H. Kabelka & G. Kuchler, Ferroelectrics 88,93 (1988). D.P. Sharma, Pramana 13, 223 (1979). M.L. Bansal & A.P. Roy, Phys. Rev. B30, 7307 (1984). M.L. Bansal, S.K. Deb, A.P. Roy & V.C. Sahni, Solid State Commun. 36, 1047 (1980). M.L. Bansal, S.K. Deb. A.P. Roy & V.C. Sahni. Pramana 20, 183 (1983). R. Cach, P.E. Tomaszewski & J. Bornarel, J. Ph_ys.C: Solid Stare Phys. 18,915 (1985). S. FuJimoto, N. Yasuda & H. Hibino, J. Phys. D: Appl. Phys. 18, 1871 (1985). S. Fujimoto, N. Yasuda, H. Hibino & P.S. Narayanan, J. Phvs. D: Appl. Phys. 17, L35 (1984). B. Mroz, T. Krajewski, T. Breczewsci, W. Chomka & D. Sematowicz, Ferroelectrics 42, 71 (1982). P.E. Tomaszewski & K. Lukaszewicz, Phvs. Status Solidi A71, K53 (1982). P.E. Tomaszewskii & K. Lukaszewicz, Phase Trans. 4, 37 (1983). F. Holuji & M. Drozdowski, Ferroefectrics 36, 379 (1981). C.H.A. Fonseca, G.M. Ribeiro, R. Gazzenelli & AS. Chaves, Solid State Commun. 46, 221 (1983).
638 15. 16. 17. 18. 19. 20.
21.
22.
23. 24. 25.
ELASTIC
CONSTANTS
K. Maezawa, H. Takeuchi & K. Ohi, J. Phys. Sot. Japan 54,3106 (1985). L. Abello. K. Chhor & C. Pommier, J. Chem. Thermodynamics 17, 1023 (1985). S. Bhakay-Tamhane, A. Sequeira & R. Chidambaram, Solid State Commun. 53, 197 (1985). M. Drozdowski, F. Holuj & M. Czajkowski, Solid State Commun. 45, 1005 (1983). M.A. Pimenta, Y. Luspin & G. Hauret, Solid State Commun. 59, 481 (1986). Tu An, Liu Jing-qing, Gu Ben-yuan, MO Yujun, Yang Hua-guang & Wang Yan-yun, Solid State Commun. 61, 1 (1987). M.A. Pimenta. P. Echegut, Y. Luspin, G. Hauret, F. Gervais & P. Alberd, Phys. Rev. B39, 3361 (1989). E.V. Charnaya, B.F. Borisov, T. Krajewski & A.K. Radjabov, Soiid State Commun. 85, 443 (1993). S. Fujimoto, N. Yasuda & H. Hibino, J. Phys. D: Appl. Phys. 18, L135 (1985). N. Choudhury, S.L. Chaplot & K.R. Rao, Phys. Rev. B33, 8607 (1986). Y.Y. Li, Solid State Commun. 51, 355 (1984).
26. 27. 28. 29. 30.
31. 32. 33. 34. 35.
36.
OF LiKS04
Vol. 97, No. 7
MS. Zhang, R.S. Katiyar & J.F. Scott, Ferroelectrics 74, 305 (1987). T. Breczewski, T. Krajewski & B. Mroz, Ferroelectrics 33, 9 (1981). T. Krajewski. T. Breczewski, P. Piskunowicz & B. Mroz, Ferroelectrics Lett. 4, 95 (1985). M.A. Pimenta, P. Echegut, F. Gervais & P. Abelard, Solid State /onics 28-30, 224 (1988). B. Mroz, J.A. Tuczynski, H. Kiefte & M.J. Clouter, J. Phys. Condens. Matter 1, 5965 ( 1989). F. Ganot, B. Kihal, R. Farhi & P. Moth, Jap. J. Appl. Phjx 24, 491 (1985). Wang Ji-fang, Zhang Dao-fan, Wang Ru-ju & Zang Liang-kun, Chin. Phys. Lett. 2,201 (1985). M.E.M. Kassem & B. Mroz, Acta Phys. Polonica 63A, 449 (1983). H. Schulz, U. Zucker & R. Frech, Acta Cryst. B41, 21 (1985). E.P. Papadakis, Physical Acoustics, Vol. 12 (Edited by W.P. Mason & R.N. Thurston). Academic Press, New York (1990). H.J. McSkimin & P. Andreatch, J. Acoust. Sot. Am. 34, 609 (1962).
Solid State Communications. Vol. 97. No. 7. pp. 635-638. 1996 Copyright cl 1995 Elsevier Science Ltd Printed in Great Britam. All rights reserved 0038 1098196 $12.00 + 00
003%1098(95)00577-3
ULTRASONIC
MEASUREMENT OF THE ELASTIC CONSTANTS BETWEEN 300 AND 370 K L. Godfrey*
Department
and J. Philip
of Physics and Instrumentation Centre, Cochin University Cochin 682 022, India (Received
OF LiKS04
of Science and Technology,
18 July 1995; accepted 21 August 1995 by M.F. Collins)
All five independent elastic constants of LiKS04 have been determined from absolute velocity measurements on single crystal samples using ultrasonic pulse echo overlap technique. The constant Cl3 is reported for the first time. Measurement of the temperature variation of elastic constants between 300 and 370 K indicates no anomaly near 333 K, ruling out a phase transition occurring in the sample at this temperature reported in an earlier Brillouin scattering work. Keywords: ultrasonics.
A. ferroelectrics,
D. elasticity,
1. INTRODUCTION LITHIUM POTASSIUM SULPHATE (LPS). LiKS04, is an extensively studied crystal. It exhibits a sequence of very interesting phase transitions as the temperature is varied from 20K to 998 K (melting point) [l, 21. A variety of experimental techniques such as thermal expansion [3], Raman scattering [l, 4-61, dielectric constant [l, 7, 81, ferroelectricity [9], piezoelectricity [lo], X-ray diffraction [Il. 121, ESR [ 13- 151, thermal analysis [ 161, neutron scattering [ 171, Brillouin scattering [18-211, ultrasonics [2, 221, etc. have been used to investigate the properties of this crystal as the temperature is varied. The interest in this crystal is because of its pyroelectric and ferroelectric behaviour, electro-optic effect [23], existence of a large number of phase transitions, and observation of incommensurate lattice phase in certain temperature regions. The series of phase transitions observed in LPS is said to be very peculiar [24]. There are phase transitions at high temperature, at first from paraphase towards a commensurate state, and then with incommensurate modulation [25, 261. In this state LPS is simultaneously ferroelastic [27,281 and superionic [21, 291. In the range from room
* Permanent address: School of Pure and Applied Physics, Mahatma Gandhi University, Kottayam 686 560, India. 635
D. phase
transitions,
E.
temperature to 708 K, LPS has hexagonal symmetry and belongs to the space group Cz (P63) with two molecules per unit cell. Below room temperature, LPS undergoes a number of phase transitions and shows large thermal hysteresis for the transition temperatures. The crystal symmetry and structure of the modulated phase as well as the phase transition temperatures of LPS are not yet well established [22, 301. The elastic properties of LPS have been studied before using Brillouin scattering [18-21, 311 and acoustic techniques [2, 22, 321. Elastic properties have also been investigated earlier by resonance antiresonance [ 10, 151 and torsion pendulum methods [33]. Drozdowski et al. [18] have reported the values of elastic constants C,, , C33, and C66 of LPS at room temperature measured by Brillouin scattering technique. Later Pimenta et al. [19] used Brillouin scattering to measure the constants Ct,, C33, Cd4, C,, and deduced the value of Cl1 using the relation Cl1 = Cri - 2C66. Kabelka and Kuchler [2] made the first ultrasonic determination of the elastic constants of LPS and compared their values with that of Pirnenta et al. [19]. We find that in none of the previous measurements has the independent elastic constant Ci3 of LPS been reported. So the complete set of five independent elastic constants of this widely investigated crystal is not yet available in literature. Drozdowski et al. [18] have reported a phase
636
ELASTIC
CONSTANTS
transition occurring in this crystal around 333K (60°C) in their Brillouin scattering results. They have reported that the elastic constants CZ2, C3s and Ce6 undergo anomalous changes at this temperature indicative of a phase transition. Later Brillouin scattering study of Pimenta et af. [ 191 could not detect any anomaly in elastic constants at this temperature. But Wan Ji-fang et al. [32], from their ultrasonic studies. reported that there is an abrupt change of Cj3 near 333 K with large temperature hysteresis and that the peak of Cx3 reduces with successive heating and cooling. On examining early investigations, we find that there is a minimum near 333 K in the thermal expansion coefficient curve of LPS in the u-axis direction [3]. The purpose of this communication is twofold: (i) Report all five independent elastic constants of LiKS04 including Cl3 at room temperature. (ii) Determine whether there is a phase transition in LiKS04 at 333 K by measuring the temperature variation of all five independent elastic constants of LPS and ultrasonic attenuation in the temperature interval from 300 K to 370 K. 2. EXPERIMENTAL
METHOD
AND
RESULTS
LiKS04 single crystals are grown from an equimolar mixture of Li2C03 and KHSOj dissolved in distilled water. On mixing, the following reaction takes place 2KHS04
+ Li2C03 -+ 2LiKSOJ
OF LiKS04
Vol. 97, No. 7
Table I. Elastic constants (in GPa) of LiKS04 comparison with previous measurements Cji
Present study (1995)
Kabelka Kuchler (1988)
Cl, Cl1 C,3
57.24 28.66 22.37 67.35 21.51 14.29
c33
c,, C,,
& [2]
in
Pimenta et al. [19] (1986)
Drozdowski et al. [18] (1983)
55.0 26.4 -
57.4 29.2 _
51.6
67.3 20.5 14.3
67.3 21.1 14.2
59.3
_
57.0
pulse modulator and receiver system (Model 7700 with accessories) has been used for the measurements. The McSkimin At criterion [36] has been applied for the correct identification of echo overlap and bond correction. For hexagonal crystals there are nine nonzero elastic constants. of which five are independent, which are related by, c,, = Cl?, C& = css, Cl3 = C,, and C’t? = Ctt - 2C,,. The diagonal constants are determined directly from velocity measurements along symmetry directions using longitudinal and transverse waves. Cl2 is calculated using the relation given above. C13 is obtained by measuring the velocity u of the quasi-longitudinal wave in a-c plane and using the relation,
+ Hz0 + CO?. c,3
Crystals obtained from the solution prepared by the above method are found to be of better quality than from the method of making LPS by mixing equimolar mixtures of LiZSO and K,S04. The crystals are grown at 311 K from a seed crystal by constant temperature solvent evaporation method in a specially designed constant temperature solution growth apparatus. Large single crystals of good optical quality with typical sizes of about 3cm in a and e directions are obtained over a period of 45 days. The crystals have well-developed faces perpendicular to [ 10 01, [0 0 l] and [lo 1] directions. The following choice of axes has been taken for ultrasonic study: the [0 0 l] axis is the hexagonal one, [ 10 0] axis is in the basal plane and perpendicular to a natural face of the crystal and [0 lo] axis is in the basal plane and perpendicular to the other two. The lattice parameters are u = 5.147 A and c = 8.633 A [34]. The density of the crystal is 2.396 gm cmp3 [2]. Velocity of longitudinal and transverse ultrasonic waves of frequency 1OMHz propagating along the symmetry directions have been measured accurately by the Pulse Echo Overlap method [35]. A MATEC
=
(y-Cnj
where ttz = sin’ %C,, + co? %Cu - pv’, n = sin’ %C,+ co? K33 p2. I = sin’ 9~0s’ 9, p = density and 9 is the angle between the propagation direction and the c-axis. For the measurement of C13, the velocity in the [l 0 l] direction is used with 9 = 59.20’. The measured constants at 300K are tabulated in Table 1 in comparison with earlier reports. The accuracy of the
57
x-
h7.l
;
2
++++++
““++++++ **+
57.2.
*+++++
:
*++A+&
-
g ;r k z Q 2
2
++++++.+
5
1
3 -h&L) ++++*+*+ ++++* *++++++*L
+++a++
C/i
**++
.
C
*++++++,, 56hi
-6h.I -
*+++++++ +++i+
i
5 z
+++++++ +++++
*+++++
;
++*++
-h52
g ; 7 r z
1
1
Fig. 1. Temperature and C33 of LiKSO+
variation
of elastic constants
Ct 1
ELASTIC
Vol. 97, No. 7
20.011140 300 310
320
330
340
350
360
CONSTANTS
370
T(K)
Fig. 2. Temperature variation CM, and CG6 of LiKS04.
of elastic constants
Ci3,
present measurements are better than 1% and provide the complete set of elastic constants of LPS. The temperature variation of all the elastic constants have been measured from room temperature to 370 K by keeping the sample in a temperature controlled high temperature cell. Special attention has been paid to temperatures around 333 K where Drozdowski et al. [ 181 and Wang Ji-fang et al. [32] found an anomaly in Brillouin scattering and ultrasonic measurements respectively. The experimental curves of Drozdowski et al. [18] show an anomaly of the order of 0.5GPa variation and an anomaly of this magnitude, if present, can easily be detected in the present ultrasonic measurements which has a precision of 0.01%. The ultrasonic attenuation measurements have also been performed relative to the room temperature value along with the velocity measurements since it is a very sensitive indicator of phase transitions. The results of our measurements in the range from 300K to 370K are displayed in Figs 1 and 2. As is evident from these figures, none of the elastic constants undergo any anomaly at 333 K. The ultrasonic attenuation (not given in the figure) shows a linear variation with temperature and does not show any anomaly near 333 K.
637
we can conclude that LPS does not undergo any phase transition at 333 K. All the elastic constants decrease slightly with increasing temperature which is the general behaviour exhibited by most solids. The difference in observation reported by different workers regarding the anomaly at 333 K needs some explanation. Pimenta et al. [19] have suggested that a possible explanation of this discrepancy could be the existence of two different stable structures of LPS near room temperature. We find that a similar idea has also been proposed by Tomaszewski and Lukaszewicz [ 11, 121 to explain the difference in thermal hysteresis of the low temperature phase transition temperature in LPS. They have suggested that there are two types of crystals. Type A and Type B, which are characterised by the thermal hysteresis of the low temperature transition. We feel that the possibility for the existence of two types of LPS at room temperature may be a correct explanation for the inconsistent experimental results on LPS found in literature. Ackno,vledgement - This work has been supported by Department of Science and Technology (Government of India) through grant No. SP/S2/M06/86.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.
3. DISCUSSION 10. Our values for the elastic constants compare well with the values reported by earlier workers. The value of C,, reported by Drozdowski et al. [18] is abnormally high compared to other reported values. Our results on the temperature variation of elastic constants are in agreement with those of Pimenta et al. [ 191 who could not detect any anomaly at 333 K in the temperature variation of Cii, CJ3 or C,, in their Brillouin scattering results. Since ultrasonics is a more sensitive technique than Brillouin scattering,
OF LiKS04
11. 12. 13. 14.
A.J. Oliveira, F.A. Germano, J. Mendes Filho, F.E.A. Melo & J.E. Moreira, Phys. Rev. B38, 12633 (1988). H. Kabelka & G. Kuchler, Ferroelectrics 88,93 (1988). D.P. Sharma, Pramana 13, 223 (1979). M.L. Bansal & A.P. Roy, Phys. Rev. B30, 7307 (1984). M.L. Bansal, S.K. Deb, A.P. Roy & V.C. Sahni, Solid State Commun. 36, 1047 (1980). M.L. Bansal, S.K. Deb. A.P. Roy & V.C. Sahni. Pramana 20, 183 (1983). R. Cach, P.E. Tomaszewski & J. Bornarel, J. Ph_ys.C: Solid Stare Phys. 18,915 (1985). S. FuJimoto, N. Yasuda & H. Hibino, J. Phys. D: Appl. Phys. 18, 1871 (1985). S. Fujimoto, N. Yasuda, H. Hibino & P.S. Narayanan, J. Phvs. D: Appl. Phys. 17, L35 (1984). B. Mroz, T. Krajewski, T. Breczewsci, W. Chomka & D. Sematowicz, Ferroelectrics 42, 71 (1982). P.E. Tomaszewski & K. Lukaszewicz, Phvs. Status Solidi A71, K53 (1982). P.E. Tomaszewskii & K. Lukaszewicz, Phase Trans. 4, 37 (1983). F. Holuji & M. Drozdowski, Ferroefectrics 36, 379 (1981). C.H.A. Fonseca, G.M. Ribeiro, R. Gazzenelli & AS. Chaves, Solid State Commun. 46, 221 (1983).
638 15. 16. 17. 18. 19. 20.
21.
22.
23. 24. 25.
ELASTIC
CONSTANTS
K. Maezawa, H. Takeuchi & K. Ohi, J. Phys. Sot. Japan 54,3106 (1985). L. Abello. K. Chhor & C. Pommier, J. Chem. Thermodynamics 17, 1023 (1985). S. Bhakay-Tamhane, A. Sequeira & R. Chidambaram, Solid State Commun. 53, 197 (1985). M. Drozdowski, F. Holuj & M. Czajkowski, Solid State Commun. 45, 1005 (1983). M.A. Pimenta, Y. Luspin & G. Hauret, Solid State Commun. 59, 481 (1986). Tu An, Liu Jing-qing, Gu Ben-yuan, MO Yujun, Yang Hua-guang & Wang Yan-yun, Solid State Commun. 61, 1 (1987). M.A. Pimenta. P. Echegut, Y. Luspin, G. Hauret, F. Gervais & P. Alberd, Phys. Rev. B39, 3361 (1989). E.V. Charnaya, B.F. Borisov, T. Krajewski & A.K. Radjabov, Soiid State Commun. 85, 443 (1993). S. Fujimoto, N. Yasuda & H. Hibino, J. Phys. D: Appl. Phys. 18, L135 (1985). N. Choudhury, S.L. Chaplot & K.R. Rao, Phys. Rev. B33, 8607 (1986). Y.Y. Li, Solid State Commun. 51, 355 (1984).
26. 27. 28. 29. 30.
31. 32. 33. 34. 35.
36.
OF LiKS04
Vol. 97, No. 7
MS. Zhang, R.S. Katiyar & J.F. Scott, Ferroelectrics 74, 305 (1987). T. Breczewski, T. Krajewski & B. Mroz, Ferroelectrics 33, 9 (1981). T. Krajewski. T. Breczewski, P. Piskunowicz & B. Mroz, Ferroelectrics Lett. 4, 95 (1985). M.A. Pimenta, P. Echegut, F. Gervais & P. Abelard, Solid State /onics 28-30, 224 (1988). B. Mroz, J.A. Tuczynski, H. Kiefte & M.J. Clouter, J. Phys. Condens. Matter 1, 5965 ( 1989). F. Ganot, B. Kihal, R. Farhi & P. Moth, Jap. J. Appl. Phjx 24, 491 (1985). Wang Ji-fang, Zhang Dao-fan, Wang Ru-ju & Zang Liang-kun, Chin. Phys. Lett. 2,201 (1985). M.E.M. Kassem & B. Mroz, Acta Phys. Polonica 63A, 449 (1983). H. Schulz, U. Zucker & R. Frech, Acta Cryst. B41, 21 (1985). E.P. Papadakis, Physical Acoustics, Vol. 12 (Edited by W.P. Mason & R.N. Thurston). Academic Press, New York (1990). H.J. McSkimin & P. Andreatch, J. Acoust. Sot. Am. 34, 609 (1962).