Incommensurate phase of Zr0.98Sn0.02TiO4 ceramics in an applied electric field

Solid

State Communications. Printed

Vol.

107. No. 9, pp. 459-462, 1998 Q 1998 Elsevier Science Ltd in Great Britain. All rights reserved 0038%1098/98 $19.00+.00

PII: SOO38-1098(98)00257-9

INCOMMENSURATE

PHASE OF Zro.u&o.02Ti04

CERAMICS

IN AN APPLIED ELECTRIC

FIELD

Yung Park* and Kevin M. Knowles University (Received

of Cambridge,

11 February

Department of Materials Science and Metallurgy, Cambridge CB2 3QZ, U.K.

1998; in revised form 15 May 1998; accepted

Pembroke

Street,

20 May 1998 by M.F. Collins)

The effect of a d.c. electric field on the dielectric constant and phase stability of Zr0.&n0.,uTi04 ceramics between 800°C and 1200°C has been investigated. The results show a non-linear variation of the transition temperature between the incommensurate and the commensurate phase and a decrease in the dielectric constant at this transition temperature as a function of the applied electric field. The incommensurate phase disappears in fields greater than the Lifshitz field EL of = 100 kV cm-‘. 0 1998 Elsevier Science Ltd. All rights reserved Keywords: transitions.

D. dielectric

response,

D. order-disorder

1. INTRODUCTION With advances in communication networks, communication at microwave frequencies is now required. A large number of dielectric materials have been developed for microwave applications [l-4]. Among these, Sn-doped zirconium titanate solid solutions, Zr I_,Sn,TiOa (x < 0.2), are known to have suitable dielectric constants (= 40), high quality factors (= 9000 at 7 GHz) and stable temperature coefficients of the resonance frecjuency (0 ppm K-l) [5, 61 for use in communication networks. At high temperatures ZrTi04 has the orthorhombic Pbcn structure of o-Pb02 with a random distribution of the zirconium and titanium ions on the available cation sites [7-91. On cooling from high temperature, ZrTi04 undergoes two successive phase transitions in the absence of an external field (either pressure or an applied electric field): (i) from a high temperature paraelectric or normal phase, N, to an incommensurate phase, I, at 1125 + 10°C (T,) [7-171 and (ii) from the incommensurate phase to a commensurate (C) phase at 845 + 5°C (T,) [ 14, 16, 171. The incommensurate phase stable between T, and Tc is modulated by a displacement wave with a wave vector q = (0.5 + &)a* along the

* Corresponding

author. E-mail: [email protected] 459

effects,

D. phase

u-axis of the high temperature orthorhombic unit cell [7], where 6 is the incommensurate displacement in terms of a*. It is interesting that ZrTiOd exhibits reconstructive phase transitions at both T, and Tc, in contrast to the displacive transitions seen in non-oxide materials such as RbzZnCld, NaNO* and SC(NH2)2 which also exhibit N-l and Z-C phase transitions. In ZrTiO+,, the distribution of Zr4+ and Ti4+ cations in the incommensurate and commensurate phases produces a chemical modulation of the density difference (pzp+ - ~r,4+), i.e. a composition wave [ 181. Christofferson and Davies analysed the modulated structure of the incommensurate phases for compositions between ZrTiO4 and Zr5Ti7024 by transmission electron microscopy and suggested that two types of structural units, ZrTi04 and ZrTi206, were mixed together in such a way as to produce incommensurate satellite reflections in electron diffraction patterns [ 191. Recently, one of the present authors has shown that the application of an external electric field E increases and both T, and Tc (dTi = 1.7KcmkV’ dTc = 1.5 K cm kV-‘) for fields up to 20 kV cm-] [ 171. Thus, electric fields up to 20 kV cm-’ stabilise the C phase relative to the I phase in ZrTi04. By comparison, high external electric fields have little influence on N-l phase transitions in KzSe04-like

INCOMMENSURATE

460

PHASE OF Zr0.9sSn0.02Ti04

crystals such as ZrTiO* [20]. The possibility arises that in a suitably large electric field the I phase will no longer be stable. Thus, a multicritical point (the Lifshitz point) could arise on an E - T phase diagram for ZrTi04 and solid solutions based on ZrTi04 where a line specifying the N-l phase transition temperature as a function of applied electric field merges with the line specifying the Z-C phase transition temperature as a function of applied electric field. Theoretical considerations of ferroelectric phase transitions using the Landau formalism for the free energy density as a function of order parameter 120-231 show that, for materials in which I phases arise where the low temperature C phase has a doubling of the unit cell relative to the high temperature N phase, as is the case for ZrTiOo [ 19]), it is perfectly feasible for a Lifshitz point to occur. The addition of SnOz to ZrTi04 is particularly useful for experimental studies of the I-C phase transition in ZrTi04-based solid solutions, as it enables materials to be sintered relatively easily for dielectric measurements and it increases the value of 6 and thus improves the resolution of the fundamental satellite reflections and their harmonics (1.5 1- n&O, 0), while also inhibiting the formation of secondary phases [24]. In this communication we report our experimental results on the effect of high d.c. electric fields on the dielectric constant and phase stability of Zr0.9sSn0.02Ti04 ceramics between 800°C and 1200°C and examine critically the evidence for the existence of a Lifshitz point in Zr0s8Sn0.a2Ti04. 2. EXPERIMENTAL

DETAILS

Zra.s8Sn0.02Ti04 ceramics were prepared by a conventional mixed oxide technique from individual powders of ZrOl (99.5% pure, low grade Hf), SnO? (99.9% pure) and TiOz (99.9% pure). The starting materials were mixed, calcined at 1050°C for 4 h, ground and dried, before being fabricated as multilayer ceramic capacitors. Pt paste was applied for the internal electrodes. The thickness of the ceramic between the electrodes was approximately 50 pm. The multilayer capacitors were sintered at 1300°C for 2 h to produce ceramics. Dielectric constants were measured at 1 kHz between 800°C and 1200°C in d.c. electric fields up to 150 kV cm-‘. Measurements were taken over an extended time period on specimens cooled slowly at 0.3”C h-’ in this temperature interval. 3. EXPERIMENTAL

301

’ 850

’ 900

Vol. 107, No. 9

B 950

I * ’ 9 1000 1050 1100 1150 V°C)

Fig. 1. Dielectric constant of Zr0,9sSn0.02Ti04 ceramics as a function of temperature for various d.c. electric fields up to 50 kV cm-‘. the peak at the higher temperature defining Tc. As the field strength increases, the magnitude of these two peaks both decrease. Furthermore, the temperature interval between the peaks can be seen to decrease as the field strength increases. For values of E greater than 50 kV cm-’ where measurements were taken, only a single peak in the dielectric constant could be distinguished. A plot of T, and Tc deduced from the dielectric measurements as a function of field strength is shown in Fig. 2, with best fit curves through the data obtained. The temperatures are specified relative to the value of Tc in zero field, TE.A plot of the difference, AK, between the peak dielectric constant at Tc and the background at the peak against E is shown in Fig. 3, in which the decrease in magnitude of the peak as E increases is evident. 4. DISCUSSION The experimental results presented in Figs l-3 are suggestive of the presence of a Lifshitz point in 400

, E‘ !

300-

a

-

d Y k I-

200 -

RESULTS

Plots of the variation of dielectric constant as a function of temperature for the Zr0.98Sn0.0~Ti04 ceramics are shown in Fig. 1 for field strengths E up to 50 kV cm-l. For each field strength two peaks can be seen, the peak at the lower temperature defining T,and

0,

0

40

80

120

E( kV/cm)

Fig. 2. E-T phase diagram for Zr0.9sSn0.02Ti04.

160

Vol. 107. No. 9

INCOMMENSURATE

PHASE OF Zro,ssSno,e2Ti04

the dependence of Tc on E at the Lifshitz point [21]. Equation (2) can be rearranged in the convenient form

1

Q

JTI-TC =

0

0

40

80

120

160

E (kV/c.m)

Fig. 3. The electric field dependence of AK,,, on cooling for Zra.asSn0.a2Ti04 ceramics.

measured

Zr0.98Sn0,02Ti04. The theory relevant for Zr0.98Sn0,32Ti04 has the same mathematical formalism as that devleloped for (NH4)*BeF4 by Preloviek et al. [21], because of the doubling of the unit cell when going from the paraelectric phase to the commensurate phase. This theory predicts that the dependence of T, on E’ takes the form T, - To = (T; - To)

(1)

where EL is the Lifshitz point, fi is the phase transition temperature in zero electric field and TOis a temperature which is introduced in the Landau formalism [213-231. Thus, T, is predicted to increase as E increases, in line with what we observe in Zr0.98Sn0.02Ti04. Furthermore, the difference T, - TO is predicted to be twice the zero field value at the Lifshitz point [21]. Our experimental data suggests that T, at the Lifshitz point is 114!i”C, in comparison with Tp of 1125°C. Thus, this st.ggests that TO= 1105°C for the theory to agree wirh our experimental data. As a result of the small width of the incommensurate phase the modulation can be taken to be of the planewave type, so that the I-C phase transition is of first order for all applied fields [21]. Under these circumsl:ances, Tl - TC is predicted to depend on E as T; - To T, - Tc = ~ 1-V

461

j/&EL

-

E)

(4)

and so the theory predicts that a plot of ,,/m against E should be a straight line passing through the point (0, EL). The data for E 5 50 kV cm-’ from Fig. 1 is plotted on Fig. 4 in this form. It is apparent that there is remarkably good agreement with theory, with the prediction that EL = 100 kV cm-‘, in agreement with the observation of just a single peak in the dielectric constant as a function of temperature at field strengths 5 90 kV cm-‘. Thus, both the experimental data and its analysis in terms of the relevant theory suggest the occurrence of a Lifshitz point for Zr0.~sSn~.0~Ti04. We note that with this value of EL, it follows from equations (2) and (4) that (Tp - Ta)/(l - 7) = 280 K for Zr0.98Sn0.02Ti04. The application of an external electric field E can be seen from Fig. 1 to cause two significant changes in the dielectric constant, K, as a function of temperature - the two maxima in K occurring at the I-C and N-l phase transition temperatures shift to higher temperatures and decrease in value as E increases. The diminution in the magnitude of K at the I-C phase transition temperature as E increases is consistent with the reported behaviour of the dielectric constant as a function of E at the I-C phase transitions in (NH&BeF4 [25] and Rb2ZnC14 [26]. The peak defining the N-Z phase transition temperature is always at a temperature higher than the peak defining the I-C phase transition temperature. Theory for the behaviour of the dielectric constant as a function of a dc. external bias has been developed for I-C phase transitions by Hudak [21] on the basis of the potential supplemented by a polarisation-electric field interaction term and PrelovSek [23] who used the model of a soliton lattice. They both predict that in an external

20. -o-

16

experimental

---... root mean

2

(2)

g+

square -7

12-

I

..

where

‘. .-.

E

.

..\L = 100 kV/cm ‘.

(3)

‘. ‘~

0 and where 0, y and [ are parameters in the Landau expansion of the free energy density of Zr0.98Sn0,02Ti04 and ~0 is the dielectric susceptibility of free space. From equation (2) it follows that the line describing the dependence of T, on E is tangential to the line describing

‘~

0

.I

100

50

150

E( kV/cm)

Fig. 4. A plot of ,/m against the d.c. electric field E. The extrapolated line indicates the Lifshitz point at the field for which dm = 0.

462

INCOMMENSURATE

PHASE OF Zr0.9sSn0.02Ti04

electric field, E, the dielectric constant retains its CurieWeiss divergence at the modified I-C phase transition temperature, T&E), but with the Curie constant decreasing as E increases, so that there is a sharpening of the dielectric peak at this transition temperature [21, 231. Comparison of theoretical predictions with experimental data however shows that there are discrepancies between theory and experiment [20, 21, 231. It is interesting to examine the behaviour of AK,,, = K,,, - &acksround shown in Fig. 3 in terms of a function of the form

A&m = B(E - EL)*

(5)

for suitable B and A, i.e. a function similar to that shown in equation (2). Fitting this empirical equation to the data shown in Fig. 3, we find that EL z 100 kV cm-’ and A = 2, so that the behaviour of AK,,, as a function of E is consistent with the behaviour of T, - Tc, in that both functions predict a similar value of the Lifshitz point for Zr0.9sSn0.02Ti04 within experimental uncertainty.

5. CONCLUSIONS By monitoring the dielectric constant as a function of temperature in Zr0.ssSn0.02Ti04 in high d.c. electric fields, we have mapped out the E-T phase diagram for this ceramic and have demonstrated the existence of a Lifshitz point in at a field of EL = 100 kV cm-‘. Agreement with theory developed for the phase transitions in (NH4)2BeF4 is remarkably good. REFERENCES 1. O’Bryan, H.M., Thomas, J. Jr. and Plourde, J.K., J. Am. Ceram. Sot., 57, 1974,450. 2. Wakino, K., Minai, K. and Tamura, H., J. Am. Ceram. Sot., 67, 1984, 278. 3. Kawashima, S., Nishida, M., Ueda, I. and Ouchi, H., J. Am. Ceram. Sot., 66, 1983, 42 1.

Vol. 107, No. 9

Nomura, S., Toyoma, K. and Kaneta, K., Jpn. J. Appl. Phys., 21, 1982, L624. 5. Higuchi, Y. and Katsube, H., U.S. Patent, 1987, No. 4665041. 6. Park, Y. and Kim, Y., U.S. Patent, 1996, No. 5 561 090. 7. Yamamoto, A., Yamada, T., lkawa, H., Fukunaga, O., Tanaka, K. and Marumo, F., Acra Crystallogr. Sec. C, 47, 1991, 1588. 8. Ikawa, H., Iwai, A., Hiruta, K., Shimojima, H., Urabe, K. and Udagawa, S., J. Am. Ceram. Sot., 71, 1988, 120. 9. McHale, A.E. and Roth, R.S., J. Am. Ceram. Sot., 69, 1986, 827. 10. Park, Y. and Kim, Y., J. Mater. Sci. Lett., 15, 1996, 853. 11. Park, Y., J. Mater. Sci. Let?., 14, 1995, 873. 12. Yamada, T., Urabe, K., Ikawa, H. and Shimojima, H., J. Ceram. Sot. Jpn., 99, 1991, 380. 13. Cocco, A. and Torriano, G., Ann. Chim. (Rome), 55, 1965, 153. 14. Park, Y., Kim, H.G. and Kim, Y.H., Jpn. J. Appl. Phys., 35, 1996, L1198. 15. McHale, A.E. and Roth, R.S., J. Am. Ceram. Sot., 66, 1983, C18. 16. Park, Y. and Kim, H.G., Appl. Phys. Lett., 70,1997, 1971. 17. Park, Y., Lee, H.M. and Kim, H.G., J. Appl. Phys., 82, 1997, 1491. 18. Cummins, H.Z., Phys. Reports, 185, 1990, 211. 19. Christofferson, R. and Davies, P.K., J. Am. Ceram. Sot., 75, 1992, 563. 20. Hud& O., J. Phys. C, 16, 1983, 2641. 21. PrelovSek, P., Levstik, A. and FilipiE, C., Phys. Rev., B28, 1983, 6610. 22. Michelson, A., Phys. Rev. L&t., 39, 1977, 464. 23. PrelovSek, P., J, Phys. C, 16, 1983, 3257. 24. Park, Y., Cho, K. and Kim, H.G., J. Appl. Phys., 83, 1998,4628. G., Freidank, W. and 25. Sorge, G., Schmidt, Klapperstiick, U., Phys. Status SoEidi (a), 19, 1973, K43. 26. Hamano, K., Ikeda, Y., Fujimoto, T., Ema, K. and Hirotsu, S., J. Phys. Sot. Japan, 49, 1980, 2278. 4.