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Infrared and Raman investigations of OH impurities in doped and pure KTaO3 single crystals
Solid State Communications, Prmted in Great Bntam.
INFRARED
Vol. 87, No 1, pp. 63-66, 1993.
0038-1098/93 $6.00 + .OO Pergamon Press Ltd
AND RAMAN INVESTIGATIONS OF OH IMPURITIES SINGLE CRYSTALS
IN DOPED AND PURE KTaOs
S Jandl and J. Rousseau Department
de Physique, Universiti: de Sherbrooke,
Sherbrooke, Qu&ec, Canada, JlK 2Rl
and L.A. Boatner Oak Ridge National Laboratory, (Received
Sohd State Division, Oak Ridge, TN 37831-6056, USA
24 December
1992 by D.J. Lockwood)
Infrared and Raman spectroscopy have been used to investigate the temperature-dependent properties of OH absorption bands m Ni-, Co-, and Nb-doped KTaOs single crystals and m pure KTaOs . Effects on the OH stretching-mode frequency and on broadening of the absorption bands due either to the presence of Ni and Co impurities or to the ferroelectric phase transition that is induced at a critical temperature in the case of the Nb-doped material KT% &%s ~0s were studied. The experimental results are compared to the predictions of two microscopic theoretical models for the location of hydrogen in perovskite-structure oxides of this type
study of SrTiOs and Li-doped KTaOs carried out by Klauer and Wohlecke [lo] For the case of hydrogen m SrTrOs, these workers showed that the symmetry rules were consistent with vibrations of the protons along the O-O bonds. For hydrogen m KTaOs, however, no definitive conclusions could be reached. The present work reports the results of infrared absorption measurements as a function of temperature of hydroxyl radicals m pure KTaOJ single crystals and m KTa03 crystals doped with either Ni, Co, or Nb The objectives of this work are, first, to determine the effects of the different dopants on the OH stretching mode (including the influence of the ferroelectric soft mode m the case of the Nbdoped material), second, to evaluate the validity of the cubic-face (CF) model vs the octahedron-edge (OE) model for the location of the hydrogen, and third, to confirm the infrared active character of the previously observed Raman-active OH stretching mode as affected by the ferroelectrlc soft mode.
1. INTRODUCTION HYDROGEN IMPURITIES are generally present in single crystals of the perovsklte-structure oxides KTa03 and SrTiOs m the “as-grown” state. Hydrogen impurities can also bc intentionally introduced at higher concentrations by annealing these crystals at elevated temperatures in water-vapor-containing ambients. The presence of hydrogen m these materials is manifested m the observation of infrared absorption bands that correspond to the OH stretching mode and that occur m the vicmlty of 3480 cm-‘. Usually, these bands consist of a primary intense absorption plus one or more weaker “satelhte” bands. The fundamental properties of hydrogen in KTaOs and SrTiOs have been the SubJect of a number of previous spectroscopic studies [l-9] that have led to two different proposed crystallographic locations for the mcorporation of hydrogen m the perovskrte lattice. In the work of Houde et al [5], the experimental results were interpreted as being consistent with a model m which hydrogen occupies a position on the cubic unit cell face between the 02- and K+ (Sr2+) ions. Weber er al [3], on the other hand, have assigned the hydrogen sites as lying along the O-O bonds of the oxygen octahedron. These two competmg models have been compared to more recent experimental results obtained m a polarrzed-Raman scattering
2. EXPERIMENTAL The angle-crystal samples employed m this investigation were grown by sohdification from a melt contammg excess K20 In the case of the Ni- and Codoped specimens, the doping level corresponded to the addition of 0.03 g of either nickel or cobalt oxide 63
OH IMPURITIES
64
Vol. 87, No. 1
IN DOPED AND PURE KTaOs ORNL-DWG
92M-15779
KTaO$Co)
0
0 0
4000 6000 2000 ENERGY (cm-l)
8000
2000 4000 6000 ENERGY (cm-l)
0
8000
Fig. 1. Raman spectra of pure and doped KTaOs single crystals at a sample temperature of 23 K. to 20g of Ta20s The composition of the sohdsolutton potassium tantalate niobate (KTN) crystal was KTas &lb0 0603. Raman and luminescence spectra were obtained using the 514 5 run argon-ion laser line at a constant power of 150 mW for excitation and a Spex double monochromator equipped with a photon counting system. The single-crystal samples were mounted in a continuous-flow temperatureregulated helium cryostat. The high-resolution mfrared-transmission spectra were obtained using a Fourier-transform interferometer (BOMEM DA3 002) equipped with a globar source, a Ge bolometer detector, and a KBr beamsplitter.
mtensities for the specimens which were excited at the same incident power are mdicative of non-uniform defect and impurity densities that result m either quenched or enhanced luminescence bands. If the OH stretchmg-mode frequency is impurity dependent as reported previously by Jovanovic et al. [2], then important variations m the correspondmg Infrared absorption-band frequency would be expected. Since, m the present work, the influence of the ferroelectric soft mode on the OH vibrational mode is of particular interest, the KTN sample was mvestigated both above and below the critical transition temperature that occurs at 65K. Figure 2 illustrates the Raman spectra obtained for the cubic phase of
3. RESULTS AND DISCUSSION Figure 1 illustrates the Raman spectra obtained at a sample temperature of 23K for the specimens investigated here. The second-order Raman-active phonons dommate and are identical below 2000 cm-’ for pure KTaOs and both the Ni- and Co-doped KTaOs. For all three samples, the presence of ferroelectric microdomams [1 l] is evidenced by a weak peak that appears around 545cm-‘, and no local modes due to a particular dopmg are observed. Two maJor luminescence bands are present m the spectra. The hmunescence band that IS centered around 65OOcm-’ has previously been associated with Ta3+ ions near an oxygen vacancy [12], while the origin of the second band centered around 3OOOcm-’ remains undetermined. The observed different lummescence
0
200 RAMAN
400 SHIFT(cm-‘)
Fig. 2. Raman spectra of a KTao#bO o6O3 single crystal at a sample temperature of (a) 20 K (below T,) and (b) 300K
Vol. 87, No. 1
OH IMPURITIES
IN DOPED AND PURE KTaOs
the material at a sample temperature of 300 K and at 20K where the KTN sample is in the rhombohedral phase. Below the critical transition temperature, the ferroelectric Raman-active mode is observed at 50 cm-‘. This mode is relatively intense and is characterized by a rather broad half-bandwidth of N 25 cm-’ Interactions between the OH radicals and the ferroelectric mode are expected to result in a broadening of the infrared absorption plus a band multiplicity resulting from the inequtvalent localelectric fields following an onset of the ferroelectric domains. Typical OH absorption bands of various samples for T = 100 K and T = 50 K are shown in Fig. 3(a) and 3(b) respectively. In the temperature interval extending from 1OOK down to 50K, the absorption
II. 3460
I.8
.
3472
5
.
..I
n II
3465
0
III.*..,
t
34975
3510
0
( cmeL)
Fig. 3.(a). Bands 1 and 2. Infrared absorption bands at 100 K of pure KTaOs(-) and of Ni and Co doped KTa03 (---). Bands 3 and 4. Infrared absorption bands of KT%,+,Nbs~03 at 300K. (b). Bands 1 and 2 Infrared absorption bands at 50 K of pure KTa03 (-) and of Ni and Co doped KTa03 (---). Bands 3 and 4. Infrared absorption bands of KTao s4Nb0 0603 at 50K Arrows indicate the Raman frequencies of [lo]. Inset. Band 1 at 15 K of pure KTa03 (-) and of Ni and Co doped KTa03 (---).
65
bands denoted as 1 and 2 in Figs. 3(a) and 3(b) occur at the same frequency for pure KTaOs and for Niand Co-doped KTa03. The only observed manifestation of the Ni and Co doping is represented by an increase in the half-bandwidth. For example, at a sample temperature of 100 K, band 1 in pure KTaOs has a half-bandwidth of 3.25cm-’ which is to be compared with the half-bandwidth of 3.75cm-’ for the Ni- or Co-doped crystals. At a temperature of 15 K, the bandwidth for the pure specimen is 0.25cm-’ while that of the doped specimens is 1 Ocm-‘. These results are not consistent with the concept of strong interactions occurrmg between the OH radicals and the impurity ions In the case of KTN, two bands labeled 3 and 4 are observed that are shifted in frequency relative to bands 1 and 2 as a result of the ferroelectric-mode oscillator strength. The half-bandwidth of these bands is broader than those in the Ni- and Co-doped samples (5.0cm-’ compared to 3.75cm-’ at lOOK). Below the ferroelectric phase transition at T = 50 K, bands 3 and 4 that are observed in KTN split into triplets. As reported m [lo], a triplet band is observed in the Raman spectra of Li-doped KTaOs below the phase transition that 1s associated with the OH stretching mode. In Fig. 3(b), arrows indicate the triplet Raman frequencies that accurately coincide with the strong central infrared-absorption band and the two weaker outer bands observed m band 1 of KTaOs and band 3 of the KTN sample below T,. The low temperature splitting of band 2 wtth intense outer bands coincides in frequency with the triplet of band 4 of the KTN system indicating an important coupling to ferroelectric fluctuations. Three inequivalent positions of the hydrogen sites are accounted for by either the crystal-face (CF) or octahedron-edge (OE) models m relationshtp to the ferroelectrtc-mode atomic displacements along the z-axis [3,5]. They correspond to a central infrared band that is polarized perpendicular to the z-axis with eight equivalent sites for the hydroxyl radicals oriented m the xy plane and to two outer bands with equal polartzation components parallel and perpendicular to the z axis Eight equivalent sites are also associated with each of the outer bands. It should be noted that neither the OE model nor the CF model are capable of accountmg for all of the experimental observations unless degeneracies are invoked It appears that all of the experimental measurements can be consistently interpreted if both types of sites described by the OE and CF models are occupied by hydrogen impurities. The two observed infrared bands labeled 1 and 2 would, therefore, be associated with the two different types of hydrogen
66
OH IMPURITIES
IN DOPED AND PURE KTa03
sites in pure KTa03 as well as m the Ni- or Co-doped material. The reduced intensity of band 2 relative to band 1 would be indicative of a preferential occupation of one site over the other. In the case of KTN, the two bands denoted as 3 and 4 exhibit essentially equal intensities reflecting an equal occupation probability for the two types of sites.
4. CONCLUSIONS Two distinct Infrared absorption bands associated with the stretching mode of OH radicals (labeled 1 and 2 as described above) ‘have been observed in pure KTaOJ and in doped KTaOr single crystals. In the absence of the ferroelectric phase transition that occurs for the KTN case, the effects due to doping are restricted to band broadening without affecting the frequency. The identical three frequencies observed in Raman scattering are also detected in the splitting of band 1 m pure KTa03 at low temperature and in the KTN sample below T,. Bands 1 and 2 are consistent with the occupation of site locations that are described by both the cubic-face and octahedronedge models-both of which predict a triplet structure at low temperatures so that the hydrogen may be located either along the cube face diagonals or along the oxygen-oxygen bonds. The relative intensity of the outer peaks in bands 1 and 2 indicates that the mfluence of the ferroelectric mode on the two sites is uneven, strong in one case and weak in the other.
Vol. 87, No. 1
Acknowledgements - The research performed at I’Universitt de Sherbrooke was supported by the National Sciences and Engineering Research Council of Canada. Research performed at the Oak Ridge National Laboratory, Solid State Division, was supported by the Division of Materials Sciences, U S. Department of Energy, under contract number DE-AC05840R21400 with Martin Marietta Energy Systems, Inc. REFERENCES 1. 2. 3. 4. 5. 6
7. 8. 9. 10. 11. 12.
D. Houde, S Jandl, P. Grenier, C. Pepm k Y. Lepine, Ferroelectrics 77, 55 (1988). A. Jovanovtc, M. Wohlecke, S. Kapphan & B. Hellermann, Ferroelectrics 107, 85 (1990). G Weber, S. Kapphan k M. Wohlecke, Phys. Rev B34, 8406 (1986). R. Waser, 2. Nuturforsch. A42, 1357 (1986). D. Houde, Y. Lepine, C. Pepin, S. Jandl & J L. Brebner, Phys. Rev. B35, 4948 (1987). J.L. Brebner, S. Jandl & Y. Lepine, Phys. Rev B23, 3816 (1981). S. Jandl, M. Banville, P. Dufour, S. Coulombe & L A. Boatner, Phys. Rev. B43, 7555 (1991). H. Engstrom, J.B Bates & L.A. Boatner, J. Chem. Phys. 73, 1073 (1980). R. Gonzalez, M.M. Abraham, L.A. Boatner & Y. Chen, J. Chem. Phys. 78, 660 (1983). S Klauer and M. Wohlecke, Phys. Rev. Lett. 68, 3213 (1992). S Jandl, P. Gremer & L.A. Boatner, Ferroelectrrcs 107, 73 (1990). P. Grenier, G Bernier, S. Jandl, B. Sake & L.A Boatner, J Phys.. Condens. Matter 1, 2515 (1989).
INFRARED
Vol. 87, No 1, pp. 63-66, 1993.
0038-1098/93 $6.00 + .OO Pergamon Press Ltd
AND RAMAN INVESTIGATIONS OF OH IMPURITIES SINGLE CRYSTALS
IN DOPED AND PURE KTaOs
S Jandl and J. Rousseau Department
de Physique, Universiti: de Sherbrooke,
Sherbrooke, Qu&ec, Canada, JlK 2Rl
and L.A. Boatner Oak Ridge National Laboratory, (Received
Sohd State Division, Oak Ridge, TN 37831-6056, USA
24 December
1992 by D.J. Lockwood)
Infrared and Raman spectroscopy have been used to investigate the temperature-dependent properties of OH absorption bands m Ni-, Co-, and Nb-doped KTaOs single crystals and m pure KTaOs . Effects on the OH stretching-mode frequency and on broadening of the absorption bands due either to the presence of Ni and Co impurities or to the ferroelectric phase transition that is induced at a critical temperature in the case of the Nb-doped material KT% &%s ~0s were studied. The experimental results are compared to the predictions of two microscopic theoretical models for the location of hydrogen in perovskite-structure oxides of this type
study of SrTiOs and Li-doped KTaOs carried out by Klauer and Wohlecke [lo] For the case of hydrogen m SrTrOs, these workers showed that the symmetry rules were consistent with vibrations of the protons along the O-O bonds. For hydrogen m KTaOs, however, no definitive conclusions could be reached. The present work reports the results of infrared absorption measurements as a function of temperature of hydroxyl radicals m pure KTaOJ single crystals and m KTa03 crystals doped with either Ni, Co, or Nb The objectives of this work are, first, to determine the effects of the different dopants on the OH stretching mode (including the influence of the ferroelectric soft mode m the case of the Nbdoped material), second, to evaluate the validity of the cubic-face (CF) model vs the octahedron-edge (OE) model for the location of the hydrogen, and third, to confirm the infrared active character of the previously observed Raman-active OH stretching mode as affected by the ferroelectrlc soft mode.
1. INTRODUCTION HYDROGEN IMPURITIES are generally present in single crystals of the perovsklte-structure oxides KTa03 and SrTiOs m the “as-grown” state. Hydrogen impurities can also bc intentionally introduced at higher concentrations by annealing these crystals at elevated temperatures in water-vapor-containing ambients. The presence of hydrogen m these materials is manifested m the observation of infrared absorption bands that correspond to the OH stretching mode and that occur m the vicmlty of 3480 cm-‘. Usually, these bands consist of a primary intense absorption plus one or more weaker “satelhte” bands. The fundamental properties of hydrogen in KTaOs and SrTiOs have been the SubJect of a number of previous spectroscopic studies [l-9] that have led to two different proposed crystallographic locations for the mcorporation of hydrogen m the perovskrte lattice. In the work of Houde et al [5], the experimental results were interpreted as being consistent with a model m which hydrogen occupies a position on the cubic unit cell face between the 02- and K+ (Sr2+) ions. Weber er al [3], on the other hand, have assigned the hydrogen sites as lying along the O-O bonds of the oxygen octahedron. These two competmg models have been compared to more recent experimental results obtained m a polarrzed-Raman scattering
2. EXPERIMENTAL The angle-crystal samples employed m this investigation were grown by sohdification from a melt contammg excess K20 In the case of the Ni- and Codoped specimens, the doping level corresponded to the addition of 0.03 g of either nickel or cobalt oxide 63
OH IMPURITIES
64
Vol. 87, No. 1
IN DOPED AND PURE KTaOs ORNL-DWG
92M-15779
KTaO$Co)
0
0 0
4000 6000 2000 ENERGY (cm-l)
8000
2000 4000 6000 ENERGY (cm-l)
0
8000
Fig. 1. Raman spectra of pure and doped KTaOs single crystals at a sample temperature of 23 K. to 20g of Ta20s The composition of the sohdsolutton potassium tantalate niobate (KTN) crystal was KTas &lb0 0603. Raman and luminescence spectra were obtained using the 514 5 run argon-ion laser line at a constant power of 150 mW for excitation and a Spex double monochromator equipped with a photon counting system. The single-crystal samples were mounted in a continuous-flow temperatureregulated helium cryostat. The high-resolution mfrared-transmission spectra were obtained using a Fourier-transform interferometer (BOMEM DA3 002) equipped with a globar source, a Ge bolometer detector, and a KBr beamsplitter.
mtensities for the specimens which were excited at the same incident power are mdicative of non-uniform defect and impurity densities that result m either quenched or enhanced luminescence bands. If the OH stretchmg-mode frequency is impurity dependent as reported previously by Jovanovic et al. [2], then important variations m the correspondmg Infrared absorption-band frequency would be expected. Since, m the present work, the influence of the ferroelectric soft mode on the OH vibrational mode is of particular interest, the KTN sample was mvestigated both above and below the critical transition temperature that occurs at 65K. Figure 2 illustrates the Raman spectra obtained for the cubic phase of
3. RESULTS AND DISCUSSION Figure 1 illustrates the Raman spectra obtained at a sample temperature of 23K for the specimens investigated here. The second-order Raman-active phonons dommate and are identical below 2000 cm-’ for pure KTaOs and both the Ni- and Co-doped KTaOs. For all three samples, the presence of ferroelectric microdomams [1 l] is evidenced by a weak peak that appears around 545cm-‘, and no local modes due to a particular dopmg are observed. Two maJor luminescence bands are present m the spectra. The hmunescence band that IS centered around 65OOcm-’ has previously been associated with Ta3+ ions near an oxygen vacancy [12], while the origin of the second band centered around 3OOOcm-’ remains undetermined. The observed different lummescence
0
200 RAMAN
400 SHIFT(cm-‘)
Fig. 2. Raman spectra of a KTao#bO o6O3 single crystal at a sample temperature of (a) 20 K (below T,) and (b) 300K
Vol. 87, No. 1
OH IMPURITIES
IN DOPED AND PURE KTaOs
the material at a sample temperature of 300 K and at 20K where the KTN sample is in the rhombohedral phase. Below the critical transition temperature, the ferroelectric Raman-active mode is observed at 50 cm-‘. This mode is relatively intense and is characterized by a rather broad half-bandwidth of N 25 cm-’ Interactions between the OH radicals and the ferroelectric mode are expected to result in a broadening of the infrared absorption plus a band multiplicity resulting from the inequtvalent localelectric fields following an onset of the ferroelectric domains. Typical OH absorption bands of various samples for T = 100 K and T = 50 K are shown in Fig. 3(a) and 3(b) respectively. In the temperature interval extending from 1OOK down to 50K, the absorption
II. 3460
I.8
.
3472
5
.
..I
n II
3465
0
III.*..,
t
34975
3510
0
( cmeL)
Fig. 3.(a). Bands 1 and 2. Infrared absorption bands at 100 K of pure KTaOs(-) and of Ni and Co doped KTa03 (---). Bands 3 and 4. Infrared absorption bands of KT%,+,Nbs~03 at 300K. (b). Bands 1 and 2 Infrared absorption bands at 50 K of pure KTa03 (-) and of Ni and Co doped KTa03 (---). Bands 3 and 4. Infrared absorption bands of KTao s4Nb0 0603 at 50K Arrows indicate the Raman frequencies of [lo]. Inset. Band 1 at 15 K of pure KTa03 (-) and of Ni and Co doped KTa03 (---).
65
bands denoted as 1 and 2 in Figs. 3(a) and 3(b) occur at the same frequency for pure KTaOs and for Niand Co-doped KTa03. The only observed manifestation of the Ni and Co doping is represented by an increase in the half-bandwidth. For example, at a sample temperature of 100 K, band 1 in pure KTaOs has a half-bandwidth of 3.25cm-’ which is to be compared with the half-bandwidth of 3.75cm-’ for the Ni- or Co-doped crystals. At a temperature of 15 K, the bandwidth for the pure specimen is 0.25cm-’ while that of the doped specimens is 1 Ocm-‘. These results are not consistent with the concept of strong interactions occurrmg between the OH radicals and the impurity ions In the case of KTN, two bands labeled 3 and 4 are observed that are shifted in frequency relative to bands 1 and 2 as a result of the ferroelectric-mode oscillator strength. The half-bandwidth of these bands is broader than those in the Ni- and Co-doped samples (5.0cm-’ compared to 3.75cm-’ at lOOK). Below the ferroelectric phase transition at T = 50 K, bands 3 and 4 that are observed in KTN split into triplets. As reported m [lo], a triplet band is observed in the Raman spectra of Li-doped KTaOs below the phase transition that 1s associated with the OH stretching mode. In Fig. 3(b), arrows indicate the triplet Raman frequencies that accurately coincide with the strong central infrared-absorption band and the two weaker outer bands observed m band 1 of KTaOs and band 3 of the KTN sample below T,. The low temperature splitting of band 2 wtth intense outer bands coincides in frequency with the triplet of band 4 of the KTN system indicating an important coupling to ferroelectric fluctuations. Three inequivalent positions of the hydrogen sites are accounted for by either the crystal-face (CF) or octahedron-edge (OE) models m relationshtp to the ferroelectrtc-mode atomic displacements along the z-axis [3,5]. They correspond to a central infrared band that is polarized perpendicular to the z-axis with eight equivalent sites for the hydroxyl radicals oriented m the xy plane and to two outer bands with equal polartzation components parallel and perpendicular to the z axis Eight equivalent sites are also associated with each of the outer bands. It should be noted that neither the OE model nor the CF model are capable of accountmg for all of the experimental observations unless degeneracies are invoked It appears that all of the experimental measurements can be consistently interpreted if both types of sites described by the OE and CF models are occupied by hydrogen impurities. The two observed infrared bands labeled 1 and 2 would, therefore, be associated with the two different types of hydrogen
66
OH IMPURITIES
IN DOPED AND PURE KTa03
sites in pure KTa03 as well as m the Ni- or Co-doped material. The reduced intensity of band 2 relative to band 1 would be indicative of a preferential occupation of one site over the other. In the case of KTN, the two bands denoted as 3 and 4 exhibit essentially equal intensities reflecting an equal occupation probability for the two types of sites.
4. CONCLUSIONS Two distinct Infrared absorption bands associated with the stretching mode of OH radicals (labeled 1 and 2 as described above) ‘have been observed in pure KTaOJ and in doped KTaOr single crystals. In the absence of the ferroelectric phase transition that occurs for the KTN case, the effects due to doping are restricted to band broadening without affecting the frequency. The identical three frequencies observed in Raman scattering are also detected in the splitting of band 1 m pure KTa03 at low temperature and in the KTN sample below T,. Bands 1 and 2 are consistent with the occupation of site locations that are described by both the cubic-face and octahedronedge models-both of which predict a triplet structure at low temperatures so that the hydrogen may be located either along the cube face diagonals or along the oxygen-oxygen bonds. The relative intensity of the outer peaks in bands 1 and 2 indicates that the mfluence of the ferroelectric mode on the two sites is uneven, strong in one case and weak in the other.
Vol. 87, No. 1
Acknowledgements - The research performed at I’Universitt de Sherbrooke was supported by the National Sciences and Engineering Research Council of Canada. Research performed at the Oak Ridge National Laboratory, Solid State Division, was supported by the Division of Materials Sciences, U S. Department of Energy, under contract number DE-AC05840R21400 with Martin Marietta Energy Systems, Inc. REFERENCES 1. 2. 3. 4. 5. 6
7. 8. 9. 10. 11. 12.
D. Houde, S Jandl, P. Grenier, C. Pepm k Y. Lepine, Ferroelectrics 77, 55 (1988). A. Jovanovtc, M. Wohlecke, S. Kapphan & B. Hellermann, Ferroelectrics 107, 85 (1990). G Weber, S. Kapphan k M. Wohlecke, Phys. Rev B34, 8406 (1986). R. Waser, 2. Nuturforsch. A42, 1357 (1986). D. Houde, Y. Lepine, C. Pepin, S. Jandl & J L. Brebner, Phys. Rev. B35, 4948 (1987). J.L. Brebner, S. Jandl & Y. Lepine, Phys. Rev B23, 3816 (1981). S. Jandl, M. Banville, P. Dufour, S. Coulombe & L A. Boatner, Phys. Rev. B43, 7555 (1991). H. Engstrom, J.B Bates & L.A. Boatner, J. Chem. Phys. 73, 1073 (1980). R. Gonzalez, M.M. Abraham, L.A. Boatner & Y. Chen, J. Chem. Phys. 78, 660 (1983). S Klauer and M. Wohlecke, Phys. Rev. Lett. 68, 3213 (1992). S Jandl, P. Gremer & L.A. Boatner, Ferroelectrrcs 107, 73 (1990). P. Grenier, G Bernier, S. Jandl, B. Sake & L.A Boatner, J Phys.. Condens. Matter 1, 2515 (1989).