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Soft mode behavior in PbTi1−xZbxO3
Vol. 14, pp. 1137—1139, 1974.
Solid State Communications,
Pergamon Press.
Printed in Great Britain
SOFT MODE BEHAVIOR IN PbTi1.~Zr~O3 D. Bäuerle* Y. Yacobyt, and W. Richter Max-Planck-Institut für Festkorperforschung, Stuttgart, Federal Republic of Germany (Received 21 December 1973 by M. Cardona)
Raman scattering experiments were performed in the system PbTii_~Zr~Os. The substitution of Ti by Zr leads to a softening of the lowest E(TO)mode in PbTiO3, and to the creation of an additional mode, which appears to interact with the soft mode.
THE SOLID solution of PbTit_~Zr~O3 (PZT) shows a structural phase transition in which a ferroelectric phase with tetragonal structure transforms into a ferroelectric phase with rhombohedral structure. This phase transition is only slightly dependent on temperature and occurs for T = 295 K at x = 0.52.1 Several properties of PZT such as the elastic, piezoelectric, and dielectric constants undergo strong anomalies for values of x near x~.These anomalies are responsible for strong electromechanical activity and explain the increasing technical interest in PZT materials. On the other hand, little is known about the microscopic mechanisms which are responsible for this tetragonal-rhombohedral phase transition. Some lattice dynamical aspects of this transition have been studied using Raman techniques. Such measurements 2 who observed first performed by Burns Scott, for concenawere softening of the lowest E(TO)and phonon trations up to x ~ 0.24. Based on these measurements, and an additional measurement for x = 0.25, Pinczuk3 recently mentioned that the tetragonalrhombohedral phase transition is directly correlated with the softening of this lowest E(TO) phonon. Furthermore, Pinczuk suggests that the square of the E(TO) mode frequency is linear in the concentration *
x, and goes to zero as the concentration approaches the critical concentration x~.l’his suggestion would imply that the tetragonal-rhombohedral phase transition in PZT is of second order. In this paper, we report on an investigation of the frequency dependence of the lowest E(TO) mode over the whole range of concentrations 0 ~x ~ 0.5. The measurements were performed on powder samples by using the Raman backscattering technique. Figure 1 shows the Stokes spectra for various concentrations of x. The mode labeled byA is the lowest E(TO) mode in pure PbTiO3. The second peak, B, is not present in the x = 0 sample, and it was notintensity resolvedwith in previous investigations. Peak Bthe increases in increasing x. Figure 2 shows analyzed line positions. The dots show the present experimental values, whereas the crosses present the results obtained by Burns and Scott. Each of our experimental points represents an average of Stokes and Antistokes frequencies. The full lines in the figure are just guides for the eye. For values of x ~ 0.25 the frequency dependence of line A on x is consistent with the relation c~,2(x)=1(xo—x)
On leave from Philips Forschungslaboratorium, Aachen.
(1)
where ~yis a constant and x 0 ~ 0.62.
t On leave from the Physics Department, Hebrew
For x> 0.35, the frequency of mode A levels
University, Jerusalem, Israel.
off, while mode B starts to soften more rapidly. The 1137
1138
SOFT MODE BEHAVIOR IN PbTi1..~Zr~O3
‘faster’ decrease in the mode frequency, as observed by Burns and Scott (see crosses in Fig. 2), can be explained by the fact that peaks A and B were not resolved in their measurements. Furthermore, linear
PbTi~,,Zr~O3 I • 295 K
I
05
extrapolation Pinczuk, seemsoftothe be data not likely tox = either. xe,, as suggested by The frequency dependence of line A cannot be understood on the basis of the presently available 4 have calculated the dependence of the soft mode frequency on the theory.Dvofalc and Glogar concentration of impurities. Assuming that the only change caused by the impurity ions takes place in
z
Ui
~
Ui
Vol. 14, No. 11
~.02
u U.,
A
z
the short range harmonic force constant, these authors find that
4
FRE~JENOYlcr&l
where ~ is independent of x and T~(x)= T 0+~T.,. = ‘y(T~—T) (2) T0 is the critical temperature for x = 0, while the change in critical temperature, T1 is proportional to the concentrationx over a wide range. Since the long range Coulomb forces are also harmonic, their addition will not alter the form of equation (2). ~
FIG. 1. Raman spectra of PbTi.,_~Zr~O3 for different concentrations x (Stokes component). The spectra are shifted vertically. The scattering background is about the same for all of them. _____________________
1-295K PbTii~Zr~O3
,
However, they will lead to an additional contribution to the change in the critical temperature, ~T2, which has terms linear and quadratic in x. The dependence 1 and has the of the critical temperature on form x was established experimentally, T~(x)= 1 17x~ 1 32x + 490 (3) —
—
E
for 0
4 U) ~53O00 0 Ui Ui U1000
az
0
01
02
03
0~
05
CONCENTRATION x
FIG. 2. Concentration dependence of the square of the mode frequencies: Open and full circles indicate measured values for line A and B, respectively, Dotted line is calculated from equations (2) and (3). Crosses indicate results obtained by Burns and Scott. The dashed line is the extrapolation of the slope of A at = 0.
therefore thatexperimental cannot explain our results value temperature of~yfor from pureequations PbTiO (2)2.and (3), using 2(x) the follows theconclude dotted line inweFig. This result isWe in disagreement with our results. 3, with we find that w on the basis of equation (2) y independent of x and T. This leads to the conclusion that the change of the anharmonic parts of the potential with the concentration should be taken into account in this case, The leveling off of the frequency of line A and the ‘faster’ decrease in the frequency of line B for x > 0.25 is not yet clear. One possibility is that the two modes strongly interact and repel each other. Such a behavior was observed previously in ‘pure’ systems as, for example, SbSI5 or SrTiO 3 ,6 where the soft mode frequency changes with temperature in a manner similar to equation (1).
Vol. 14, No. 11
SOFT MODE BEHAVIOR IN PbTi1~Zr~O3
Line B can be interpreted in one of the following ways: This mode could be a zone boundary TA mode, which becomes Raman active due to the Zr ‘impurity’, The energyinof the zone boundary TA mode was measured inelastic neutron scattering experiments on pure PbTiO 7 and was found to be slightly higher than the3energy of mode B extrapolated to x = 0. Another possibility is that mode B is an impurity mode associated with the Zr doping. This mode may have an eigenvector similar to that of the E(TO) mode in pure PbTiO3, except that the Ti ion is substituted by the ‘heavier’ Zr ion. This second possibility would be consistent with the level repulsion, which takes place only between modes of the same symmetry. Qualitatively, an increase in the static dielectric constant perpendicular to the polar axis can be understood from the softening of mode A. However,
1139
we do not have, at present, reliable dielectric measurements for single PZT crystals. Moreover, it is not clear, whether 8 the Lyddane—Sachs—Teller relation really holds. In conclusion, we may say that the softening of mode A may play an important role in the tetragonal. rhombohedral phase transition of 1~Ti 1_~Zr~O3. However, the experimental results have clearly shown that the square of the soft mode frequency does not vanish as the concentration approaches the critical concentration x~.On the contrary, because of the finite mode frequencies for x xe,, we suggest that this phase transition could be of first order. —~
Acknowledgements We wish to thank H. Bilz, and T.P. Martin for valuable discussions, and KB. Hardtl for PZT material. —
REFERENCES 1. 2.
JAFFE B., COOK R.W. and JAFFE H.,Piezoelectric Ceramics, p. 136. Academic Press, New York (1971). BUR.NS C. and SCOTT B.A.,Phys. Rev. Lett. 25,1191(1970).
3. 4.
PINCZUK A., Solid State Commun. 12, 1035 (1973). DVORAK V. and GLOGAR P.,Phys. Rev. 143,344(1966).
5.
STEIGMEIER E.F., HARBEKE G. and WEHNER R.K., in Light Scattering in Solids, p. 396 (edited by BALKANSKI M.) Flarnmarion Sci. Paris (1971).
6.
FLEURYP.A., SCOTT I.F. and WORLOCK 1.M., Phys. Rev. Lett. 21, 16 (1968).
7. 8.
SHIRANE G., AXE J.D. and HARADA J.,Phys. Rev. 2, 155 (1970). BURNS G. and SCOTT B.A., Solid State Commun. 13,417(1973).
An PbTi1_~Zr~O3 wurden Ramanstreuexperimente durchgefuhrt. Die Substitution von Ti durch Zr führt zu einem Erweichen der niedrigsten E(TO) Schwingung in PbTIO3. DarUber hinaus tritt in den Ramanspektren eine Schwingungsbande auf, deren Intensitat mit wachsender Zr Konzentration zunimmt. Es gibt Anzeichen für eine Wechselwirkung der Schwingungen.
Solid State Communications,
Pergamon Press.
Printed in Great Britain
SOFT MODE BEHAVIOR IN PbTi1.~Zr~O3 D. Bäuerle* Y. Yacobyt, and W. Richter Max-Planck-Institut für Festkorperforschung, Stuttgart, Federal Republic of Germany (Received 21 December 1973 by M. Cardona)
Raman scattering experiments were performed in the system PbTii_~Zr~Os. The substitution of Ti by Zr leads to a softening of the lowest E(TO)mode in PbTiO3, and to the creation of an additional mode, which appears to interact with the soft mode.
THE SOLID solution of PbTit_~Zr~O3 (PZT) shows a structural phase transition in which a ferroelectric phase with tetragonal structure transforms into a ferroelectric phase with rhombohedral structure. This phase transition is only slightly dependent on temperature and occurs for T = 295 K at x = 0.52.1 Several properties of PZT such as the elastic, piezoelectric, and dielectric constants undergo strong anomalies for values of x near x~.These anomalies are responsible for strong electromechanical activity and explain the increasing technical interest in PZT materials. On the other hand, little is known about the microscopic mechanisms which are responsible for this tetragonal-rhombohedral phase transition. Some lattice dynamical aspects of this transition have been studied using Raman techniques. Such measurements 2 who observed first performed by Burns Scott, for concenawere softening of the lowest E(TO)and phonon trations up to x ~ 0.24. Based on these measurements, and an additional measurement for x = 0.25, Pinczuk3 recently mentioned that the tetragonalrhombohedral phase transition is directly correlated with the softening of this lowest E(TO) phonon. Furthermore, Pinczuk suggests that the square of the E(TO) mode frequency is linear in the concentration *
x, and goes to zero as the concentration approaches the critical concentration x~.l’his suggestion would imply that the tetragonal-rhombohedral phase transition in PZT is of second order. In this paper, we report on an investigation of the frequency dependence of the lowest E(TO) mode over the whole range of concentrations 0 ~x ~ 0.5. The measurements were performed on powder samples by using the Raman backscattering technique. Figure 1 shows the Stokes spectra for various concentrations of x. The mode labeled byA is the lowest E(TO) mode in pure PbTiO3. The second peak, B, is not present in the x = 0 sample, and it was notintensity resolvedwith in previous investigations. Peak Bthe increases in increasing x. Figure 2 shows analyzed line positions. The dots show the present experimental values, whereas the crosses present the results obtained by Burns and Scott. Each of our experimental points represents an average of Stokes and Antistokes frequencies. The full lines in the figure are just guides for the eye. For values of x ~ 0.25 the frequency dependence of line A on x is consistent with the relation c~,2(x)=1(xo—x)
On leave from Philips Forschungslaboratorium, Aachen.
(1)
where ~yis a constant and x 0 ~ 0.62.
t On leave from the Physics Department, Hebrew
For x> 0.35, the frequency of mode A levels
University, Jerusalem, Israel.
off, while mode B starts to soften more rapidly. The 1137
1138
SOFT MODE BEHAVIOR IN PbTi1..~Zr~O3
‘faster’ decrease in the mode frequency, as observed by Burns and Scott (see crosses in Fig. 2), can be explained by the fact that peaks A and B were not resolved in their measurements. Furthermore, linear
PbTi~,,Zr~O3 I • 295 K
I
05
extrapolation Pinczuk, seemsoftothe be data not likely tox = either. xe,, as suggested by The frequency dependence of line A cannot be understood on the basis of the presently available 4 have calculated the dependence of the soft mode frequency on the theory.Dvofalc and Glogar concentration of impurities. Assuming that the only change caused by the impurity ions takes place in
z
Ui
~
Ui
Vol. 14, No. 11
~.02
u U.,
A
z
the short range harmonic force constant, these authors find that
4
FRE~JENOYlcr&l
where ~ is independent of x and T~(x)= T 0+~T.,. = ‘y(T~—T) (2) T0 is the critical temperature for x = 0, while the change in critical temperature, T1 is proportional to the concentrationx over a wide range. Since the long range Coulomb forces are also harmonic, their addition will not alter the form of equation (2). ~
FIG. 1. Raman spectra of PbTi.,_~Zr~O3 for different concentrations x (Stokes component). The spectra are shifted vertically. The scattering background is about the same for all of them. _____________________
1-295K PbTii~Zr~O3
,
However, they will lead to an additional contribution to the change in the critical temperature, ~T2, which has terms linear and quadratic in x. The dependence 1 and has the of the critical temperature on form x was established experimentally, T~(x)= 1 17x~ 1 32x + 490 (3) —
—
E
for 0
4 U) ~53O00 0 Ui Ui U1000
az
0
01
02
03
0~
05
CONCENTRATION x
FIG. 2. Concentration dependence of the square of the mode frequencies: Open and full circles indicate measured values for line A and B, respectively, Dotted line is calculated from equations (2) and (3). Crosses indicate results obtained by Burns and Scott. The dashed line is the extrapolation of the slope of A at = 0.
therefore thatexperimental cannot explain our results value temperature of~yfor from pureequations PbTiO (2)2.and (3), using 2(x) the follows theconclude dotted line inweFig. This result isWe in disagreement with our results. 3, with we find that w on the basis of equation (2) y independent of x and T. This leads to the conclusion that the change of the anharmonic parts of the potential with the concentration should be taken into account in this case, The leveling off of the frequency of line A and the ‘faster’ decrease in the frequency of line B for x > 0.25 is not yet clear. One possibility is that the two modes strongly interact and repel each other. Such a behavior was observed previously in ‘pure’ systems as, for example, SbSI5 or SrTiO 3 ,6 where the soft mode frequency changes with temperature in a manner similar to equation (1).
Vol. 14, No. 11
SOFT MODE BEHAVIOR IN PbTi1~Zr~O3
Line B can be interpreted in one of the following ways: This mode could be a zone boundary TA mode, which becomes Raman active due to the Zr ‘impurity’, The energyinof the zone boundary TA mode was measured inelastic neutron scattering experiments on pure PbTiO 7 and was found to be slightly higher than the3energy of mode B extrapolated to x = 0. Another possibility is that mode B is an impurity mode associated with the Zr doping. This mode may have an eigenvector similar to that of the E(TO) mode in pure PbTiO3, except that the Ti ion is substituted by the ‘heavier’ Zr ion. This second possibility would be consistent with the level repulsion, which takes place only between modes of the same symmetry. Qualitatively, an increase in the static dielectric constant perpendicular to the polar axis can be understood from the softening of mode A. However,
1139
we do not have, at present, reliable dielectric measurements for single PZT crystals. Moreover, it is not clear, whether 8 the Lyddane—Sachs—Teller relation really holds. In conclusion, we may say that the softening of mode A may play an important role in the tetragonal. rhombohedral phase transition of 1~Ti 1_~Zr~O3. However, the experimental results have clearly shown that the square of the soft mode frequency does not vanish as the concentration approaches the critical concentration x~.On the contrary, because of the finite mode frequencies for x xe,, we suggest that this phase transition could be of first order. —~
Acknowledgements We wish to thank H. Bilz, and T.P. Martin for valuable discussions, and KB. Hardtl for PZT material. —
REFERENCES 1. 2.
JAFFE B., COOK R.W. and JAFFE H.,Piezoelectric Ceramics, p. 136. Academic Press, New York (1971). BUR.NS C. and SCOTT B.A.,Phys. Rev. Lett. 25,1191(1970).
3. 4.
PINCZUK A., Solid State Commun. 12, 1035 (1973). DVORAK V. and GLOGAR P.,Phys. Rev. 143,344(1966).
5.
STEIGMEIER E.F., HARBEKE G. and WEHNER R.K., in Light Scattering in Solids, p. 396 (edited by BALKANSKI M.) Flarnmarion Sci. Paris (1971).
6.
FLEURYP.A., SCOTT I.F. and WORLOCK 1.M., Phys. Rev. Lett. 21, 16 (1968).
7. 8.
SHIRANE G., AXE J.D. and HARADA J.,Phys. Rev. 2, 155 (1970). BURNS G. and SCOTT B.A., Solid State Commun. 13,417(1973).
An PbTi1_~Zr~O3 wurden Ramanstreuexperimente durchgefuhrt. Die Substitution von Ti durch Zr führt zu einem Erweichen der niedrigsten E(TO) Schwingung in PbTIO3. DarUber hinaus tritt in den Ramanspektren eine Schwingungsbande auf, deren Intensitat mit wachsender Zr Konzentration zunimmt. Es gibt Anzeichen für eine Wechselwirkung der Schwingungen.