Dielectric properties of (Pb,La)Zr0.55Ti0.45O3 ceramics have been investigated as functions of temperature and frequency. The dielectric constant as a function of temperature can be represented over a considerable temperature interval by a quadratic law of the type: ε−1=ε−1max + C(T−TC')2. The permittivity versus temperature curves are strongly broadened around TC' (where  is at a maximum) and the dielectric behaviour is at least partly of a relaxational nature. Interpretation of the dielectric behaviour (broadening, frequency dependence, quadratic law) seems possible by assuming a distribution of local Curie temperatures; the standard deviation of which can be correlated with the La concentration

Burggraaf, A.J.

Wolters, M.

English

Dielectric properties of (Pb,La)Zr0.55Ti0.45O3 ceramics have been investigated as functions of temperature and frequency. The dielectric constant as a function of temperature can be represented over a considerable temperature interval by a quadratic law of the type: ε−1=ε−1max + C(T−TC')2. The permittivity versus temperature curves are strongly broadened around TC' (where ϵ is at a maximum) and the dielectric behaviour is at least partly of a relaxational nature. Interpretation of the dielectric behaviour (broadening, frequency dependence, quadratic law) seems possible by assuming a distribution of local Curie temperatures; the standard deviation of which can be correlated with the La concentration

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Relaxational polarization and diffuse phase transitions of LA-substituted Pb (Zr,Ti)O3-ceramics

University of Twente Research Information

Mat. Res. Bull. Vol. i0, pp. 417-424, 1975. Pergamon Press, Inc. Printed in the United States. RELAXATIONAL POLARIZATION AND DIFFUSE PHASE TRANSITIONS OF LA-SUBSTITUTED Pb(Zr,Ti)O3-CER/~ICS M. Wolters and A.J. Burggraaf Twente University of Technology, Department of Chemical Engi- neering, Laboratory of Inorganic Chemistry and Materials Science P.O. Box 217, Enschede, the Netherlands (Received March Z5, 1975; Communicated by G. H. Jonker) ABSTRACT Dielectric properties of (Pb'La)Zr0.55Ti0.4503 ceramics have been investigated as functions of temperature and frequency. The dielectric constant as a function of tempe- rature can be represented over a considerable temperature interval by a quadratic law of the type: e-l=e -I + max C(T-Tc')2. The permittivity versus temperature curves are strongly broadened around T c' (where e is at a maximum) and the dielectric behaviour is at least partly of a re- laxational nature. Interpretation of the dielectric beha- viour (broadening, frequency dependence, quadratic law) seems possible by assuming a distribution of local Curie temperatures; the standard deviation of which can be cor- related with the La concentration. Introduction Lead-lanthanum zirconate-titanate ceramics (PLZT) are mate- rials with interesting electrical and optical properties (i). In a certain composition range a strong broadening of the e-T curve around the "Curie temperature" has been found, which is interes- ting from both scientific and application points of view. Recent- ly this composition range has been studied by Carl and Geisen (2) and Meitzler and O'Bryan (3) for PLZT compositions with a Zr/Ti ratio of 65/35. In this work special attention has been given to the depen- denc~ of the dielectric constant on temperature and frequency around the 'ferroelectric-paraelectric' phase transition. There have been investigated (Pb,La) (Zr,Ti)O 3 ceramics with a Zr/Ti ratio of 55/45 and variable La content~ (2-15 at.%). With this Zr/Ti ratio the phase diagram is somewhat simpler and the only ferroelectric phase occuring has tetragonal symmetry. Study of the dielectric properties of PLZT ceramics has ta- ken place in comparison with material systems with a comparable 417 418 Pb(Zr,Ti)O3-CERAMICS Vol. I0, No. 5 10- 1 "u % .5 5. 10 KHz ,,:,,, -10 1 ,o 10.0 E" o 5 0  100 1.~3 T("C) FIG. ] Dielectric properties (E', e", tan~) as functions of temperature for PLZT 11.|/55/45. 2 0  10 Kl.-Iz 15 w lO Y-X X = 8.1 X=IO2 5 0  10(3 150 T("C) - FIG. 2 Temperature dependence of the dielectric constant for. PLZT x/55/45. crystal structure and in which the same lattice position has been occu- pied by different ions. Experimental Procedures In (4) there has been given a general description of the used pro- cedures. Only some remarks will be made here. The following formulation is introduced for the description of the different compositions: PLZT x/55/45, in which x is the variable lanthanum concentration. All PLZT ceramics used here have been sintered at 1250°C during 16 hours to achieve coarse-grained cera- mics. The density of the sinteredqce- ramics varied from 7.60-7.72 g/cm ~, while the average grain size was lar- ger than 5 ~m. The dielectric measurements have been made with a Wayne Kerr Uni- versal Bridge B221 in the frequency range from 1-50 KHz and with a Wayne Kerr Radio Frequency Bridge B601 in the frequency range from 50-500 KHz. At room temperature some hyste- resis loops (P-E plot) have been mea- sured with an experimental set-up as used by Carl and Geisen (2). Results Dielectric Measurements The temperatures at which e' and tan6 are at a maximum are defined as respectively T c' and T t. It must be remarked that T c' is the tempera- ture where e' is at a maximum and needs not to be the Curie temperature, at which the phase transition ferro- electric (FE) - paraelectric (PE) oc- curs in classical ferroelectrics as e.g. coarse-grained BaTiO 3. The results, as partly repre- sented in Figs. 1 and 2, show that in the composition range 8-14 at.% La a relatively strong broadening of the e'-T and E"-T curves occur compared with the curves for coarse-grained BaTiO 3. This broadening increases with increasing La concentration, while at the same time the maximum value of e' (e'ma x) decreases. The values of T t and T c' decrease with increasing La concentration, while the difference Vol. I0, No. 5 pb(Zr,Ti)O3-CERAMICS 419 between T t and T c' increases)witn in- creasing La concentration (4 . The dielectric constant round T c' ~s frequency-dependent as can be seen in Fig. 3 for PLZT 12.0/55/45. In most cases Tc', T t and tan6ma x in- crease with increasing frequency, while e'ma x decreases. At temperatures far from Tc', in the FE and PE phases, frequency dependence almost vanishes The dielectric constant as a function of temperature for all com- positions and all measured frequen- cies can be described by a quadratic law of the type: -i -imax+C2 e =e (T_T c )2 (eq.l both above and below Tc', however with different values of C 2. In Fig. 4 this has been shown for two compo- sitions and with T>T c' The tempera- ture interval above T c' in which the dielectric behaviour can be described by the above mentioned quadratic law increased with increasing La concen- tration and reaches 50 degrees or more. Below T c' the dielectric con- stant can be described by this qua- dratic law in a relatively small tem- perature region, which almost coin- cides with the temperature region be- tween T c' and T t (4). X-r@~ diffraction measurements 70 In a former publication (4) there have been. given the unit cell I dimensions as function of the lantha- num concentration for annealed pow- s c ders (~ z 3 ~m) at 20°C. For x < ii.0 at.% La the material clearly shows tetragonal symmetry (at 20°C). A nota- ble change in unit cell dimensions 5c as function of La concentration takes place round x = 11.5 at.% La. For the c/a ratio especially this is very clear. For x > 12.0 at.% La the ma- terial still has a tegragonal symme- try with a very small distortion (c/a z 1.00). The c/a ratio in this case cannot be measured adequately from the X-ray ~eflection lines, but the asymmetric form of some reflec- tion lines indicates that the mate- I00001 i I00001 i i . . . .  6000 50 --- T (°C)1~ FIG. 3 Permittivity as a func- tion of temperature for PLZT 12,0/55/45 at three frequencies (I=|KHz; 2= 10KHz; 3=500KHz). m / /  /- jl~" / /  ~/'~'x = 111 - -  / 6 / /  . I~/'/ / S" / - -  @ 1C~0 . . . . . . .  1500 (T-T6)2 (o~) 900  850 ! w 800 FIG. 4 Dependence of I/g' on (T-Tc')2 for PLZT 8.1/55/45 and PLZT 11.|/55/45 at ,) 10KHz (T > T c . rial still has a tetragonal structure (for x = 12.0 at.% La the ratio c/a has been estimated as z 1.003 + 0.002, from the 002/ 200 reflection line, in which a small shoulder has been found, 4Z0 Pb(Zr, Ti)O 3-CERAM/CS Vol. I0, No. 5 ~:~ ...... .................... which has not been caused by the ..... ~ ~ ~  ~ CuKs 2 radiation. Measurements of hysteresis loops In Fig. Sb there have been . . . .  given hystere~l-s loops (at 20oc) for PLZT 10.2/55/45 and PLZT 12.8/55/45. For low La concentra- tions (x < ii.i at.% La) there have been found so-called square loops and for x > 12.0 at.% La FIG. 5a so-called 'slim' loops, the lat- ter occuring at temperatures lar- Hysteresis loop for PLZT ger than T t. 10.2/55/45 at 20°C Discussion .... , .... ~ Phase re!ations for PLZT x/55/45 ~ ~ i ~  ~ In classical ferroelectrics as e,g. BaTiO 3, one finds a phase transition between the ferroelec- tric (FE) and paraelectric (PE) ..... ,0m. phases at a distinct temperature~ At this Curie temperature diffe- rent properties show some remar- kable features, as for example the permittivity is at a maximum, FIG. 55 crystal symmetry becomes cubic, Hysteresis loop fDl PLZT changes in crystallographic pa- l2 0/55/45 at 20°C rameters occur and hysteresis loop • vanishes. However, in PLZT cera- mics a region between the FE and PE phase has been found which has not a true FE nor a true PE na- ture. In literature this region has been called quasi-ferroelec- tric (QFE) (2) or penferroelectric (3). This QFE region has been described as a 'phase' which has no or only weak measurable fer- roelectricity without applying an electric field. But on applying an electric field the material becomes real ferroelectric.. This raises the question if the ferroelectric behaviour exists already at zero field or is induced by the field. As a consequence the hysteresis loops in the QFE region show a so-called 'slim-loop' behaviour, as can be seen in Fig.5b. Moreover in this work it has been seen that there are some indications that the material is not entirely cubic in this QFE region, but still has a very little distortion which may be used as an indication for the occurrence of micro-regions. It must be remarked that the 'phase-transition' FE-QFE has been characterised (2,3,4,5) by many phenomena which also occur at the FE-PE phase transition in classical ferroelectrics (a change in crystallographic parameters, hysteresis loop changes in shape, dielectric losses are at a maximum). However the maximum value of the permittivity does not occur at the 'phase transition FE'QFE, but at a different temperature, called the apparent Curie temperature Tc'. Vol. i0, ]No. 5 Pb(Zr. Ti)O3-CERAk41CS 4Zl Dielectric.behaviour of PLZT x/55/45 A further discussion of the results shall have to treat at least the strong broadening of the e'-T curve and the frequency dependence of the dielectric properties. A broadening of the e'-T curve can be caused by four diffe- rent groups of causes: a) macroscopic inhomogeneities originating from the preparation procedure. b) internal stress effects caused by grain size (scale comparable with domain size). c) submicroscopic inhomogeneities (scale 50-i000~). d) relaxational polarization. As has been discussed in (4) macroscopic inhomogeneities and grain size don't play a major role with respect to:~the phenomena under discussion and in the materials which are reported here (mean grain size > 5 ~m). Microscopic inhomogeneities (50-i000~) within one phase remain as a possible cause of broadening. These inhomogeneities are in themodynamic equilibrium at high tempe- rature and may be frozen in at lower temperatures. They include e.g. compositional fluctuations (9-11). Thermal polarization fluctuations (6-8) may be another form of submicroscopic inhomo- geneities causing broadening of the e'-T curves. The frequency dependence of some properties round T ' points to the occurrence of a relaxational polarization mechanism. If this mechanism plays an important role the very large value of ~' can be explained by assuming a contribution of very large di~es probably of a ferroelectric nature and connected with the microregions mentioned before. So we can distinguish two contributions to the total pola- rization and e': a) relaxational polarization. This is caused by a reorientation of the electric moments of polar micro regions with respect to the weak, electric (alter- nating) field. b) induced (electron-ion) polarization. It includes the contribution of a ferroelectric phase transi- tion. This transition may be sharp (one single T ) or diffuse (distribution of Tc). c Both contributions may play a role. At high frequencies only the contribution under b remains, which will be called e'~. For the moment furhter analysis and interpretation will be given following a model proposed by Isupov et al. (9,10,11) for in- terpreting diffuse phase transitions in niobates. Essentially they assumed the existence of a m£xture of polar and non-polar micro-regions (having volumes of z 104 cells). It was presumed that the polar micro-regions had different local Curie temperatures For the distribution of numbers of micro-regions, n(Tc), a Gaussian distribution was assumed around a mean Curie temperature, e.g. Tc', with a standard deviation 6. Under the above mentioned assumptions Kirillov and Isupov (Ii) derived an expression for E' in the form: 2 I 1 1 (T-Tc) - + 2 + higher terms (eq. 2) e"-e' e' 2e' 6 max max 4ZZ Pb(Zr,Ti)O3-CERAMICS Vol. I0, No. 5 TABLE 1 Q u a d r a t i c  L a w  P a r a m e t e r s  f o r  PLZT x/55/45. (lOKHz) x (at.%) 10-3 ~'max C2 (108 °C-2) 2.0 19.2 i 4 . 2  2 3 . 8  2 1 . 7  28 21 19 16 1 3 . i  I 0 . 9  9 . 6  6 . 0  i 1 6.3 6.9 8.1 8.7 10.2 II.I 12.0 12.2 14.1 5.4 4.0 2.3 1.71 1.36 1.24 1.07 0.84 0.86 1.09 1.17 2223(°C] I32 33 42 46 54 69 74 69 84 If e'~and hiqher terms, invol- ving qT-Tc') 4, can be ignored (polarization is mainly relaxa- tional) eq. 2 is the same expres- sion as eq. 1 with: C 2 = (2e'max62)-1 (eq.3) In this work it has been shown (Fig. 4) that the dielec- tric behaviour of (Pb,La) (Zr,Ti) 03 ceramics over a considerable temperature interval can be des- cribed by a quadratic law. In Table 1 the values of C 2, e'ma x and 6 have been collected for all measured compositions above T c ' From Table 1 it can be con- cluded that C 2 passes through a minimum value as a function of the La concentration, while 6 increases continuously with increa- sing La concentration. Within the used model this implies that the fluctuations of local T c values become more intense the lar- ger the La concenbration and the wider (broader) the QFE region are. The occurrence of a distribution of local Curie temperatures may be caused by compositional fluctuations in the solid solution. Then it can be derived from statistical considerations that in a (pseudo) binary system and for a linear relationship between com- position and T c 6 reaches a maximum value as the ratio of the cation concentrations (here concentrations of different types of ions in the same sublattice) reaches the value one. Indeed 6 increases together with the ratioI~La ] + [Pb-vacancies])/ [Pb]. The value of 6 is frequency'dependent; for PLZT I~.0/55y45 the standard deviation 6 of the T c distribution function is 78°C at 1 KHz, 74oc at I0 KHz and 70°C at 500 KHz. So with increasing frequency 6 decreases. This follows from the model too (contri- bution- and fraction of dipoles taking part in the relaxational polarization process decreases with increasing frequency). At very high frequency the shape of the E'-T curve should reflect the contri bution of the induced polarization only and the remaining value of "6" would then be a measure for the diffuseness of the "true" phase transition. In preliminary results there has been found a strong effect of the grain size (1-8 ~m) of PLZT 8/55/45 on the broadening of the e'-T curves round T c' (12). However, grain size did not or only weakly influence the 'fluctuation parameter' 6. For a mean grain size of 8 ~m there has been found a 6 of 42 ~ 2.5°C and for 1.4 pm material 6 is 47 + 2.5°C. Dielectric behaviour of some other materialsystems The validity of eq. 1 in a number of other systems has been tested with the help of literature values. With 6 > 20 degrees and within a temperature interval of at least 30 degrees, eq. 1 was obeyed by: a) a limited number of (AI,A2)BO 3 perovskites. In most cases a Vol. i0, No. 5 Pb(Zr,Ti)O3-CERAMICS 4Z3 normal Curie-Weiss behaviour is followed~ b) a rather large number A(BI,B2)O 3 perovskites, e.g. Ba(TixSnl- x) 03 (13). c) a number of (AI,A2) !BI,B2!O q perovskites in which a very strong effect occurs e.g. (PD,Ba) (Ti,Zr)O 3 (14). d) a number of niobates with wolfram-bronze and other structures e.g. BaxSrl_xNb206 (15). Because :in most cases the dependence on frequency was not investi- gated, the meaning of 6 in these cases is merely that of a dis- tribution of Curietemperatures and does not imply a relaxator behaviour. The lack of X-ray and grain size data causes that at the moment nothing can be said on the physical background of the broadening in these cases. Acknowledgement The present investigations have been carried out partly under the auspices of the Netherlands Foundation for Chemical Research (S.O.N.). References i. G.H. Haertling and C.E. Land, J.Amer. Ceram. Soc. 54, 1 (1971). 2. K. Carl and K. Geisen, Proc. IEEE 61, 967 (1973). 3. A.H. Meitzler and H.M. O'Bryan Jr., Proc. IEEE 6-1, 959 (1973) 4. M. Wolters and A.J. Burggraaf, Phys. Stat. Sol. (a) 24, 341 (1974). 5. E.T. Keve and A.D. Annis, Ferroelectrics ~, 77 (1973). 6. B.N. Rolov, Proc. Int. Meeting on Ferroelectricity. Prague 1966, 154 (1966). 7. W.J. Fritsberg, ibid., 163 (1966) 8. W.J. Fritsberg, Sov. Phys. Solid State iO, 304 (1968). 9. V.A. Isupov, Sov. Phys.Tech. Phys. ~, 1846 (1956). i0. V.A. I supov, Sov. Phys. Solid State 5, 136 (1963). ii. V.V. Kirillov and V.A. Isupov, Ferroelectrics ~, 3 (1973). 12. K. Keizer and A.J. Burggraaf (to be published in Mat.Res. Bull.) 13. T. Nakamura et al., Jap. J.Appl.Phys. ~, 1191 (1966). 14. S.A. Fedulov et al., Sov. Phys. Cryst. ~, 547 (1962). 15. V.V. Voronov et al., Sov. Phys. Solid State 15, 1463 (1974). 

Relaxational polarization and diffuse phase transitions of LA-substituted Pb (Zr,Ti)O3-ceramics

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University of Twente Research Information