Ferroelectric Relaxor Ceramics

The reason for these differences is attributed to the existence of nanosized domains (so-called polar regions ) in which indeed a hysteresis loop as well as symmetry changes can be observed. In perovskites of type ABO3, the substitution of ions of different valencies, sizes and polarizabilities at the A and B sites produces a variety of dipolar effects that are able to introduce a sufficiently high degree of disorder. This disorder breaks the transitional symmetry and thus prevents the formahon of long-range ordered domain states. 

For example, in the typical relaxor ceramic lead magnesium niobate (PMN Pb[Mgi/3Nb2/3]03), disorder is generated by the differences in valency, ionic radii, 

Likewise, in lead lanthanum zirconate titanate (PLZT) relaxors, the substitution of La for Pb at A sites produces randomly distributed Pb vacancies. In bismuth sodium titanate (BNT [BiNa]Ti206), the replacement of Bi by Na creates charge imbalances and vacancies. Ceramics with compositions Bai, jNaxTii Nbx03 are either classical ferroelectrics (for 0 x 0.075), ferroelectrics or antiferroelectrics (for 0.055 x 1) or relaxor ferroelectrics (for 0.075 x 0.055) with a diffuse transition temperature without any frequency dispersion. The relaxor behavior increases with increasing compositional deviation from both BaTi03 and NaNbOs (Khemahem et al., 2000). 

In conclusion, complex perovskite relaxor ceramics are characterized by a very diffuse range of the ferroelectric-paraelectric OD phase transition, owing to nano-scopic compositional fluctuations. The minimum domain size that stiU sustains cooperative phenomena leading to ferroelectric behavior is the so-called Kiinzig region (Kanzig, 1951), and is on the order of 10 to lOOnm in PMN. In contrast to normal ferroelectric ceramics, relaxor ceramics show a frequency dependence of the dielectric permittivity as well as the dielectric loss tangent, which presumably is caused by the locally disordered structure that creates shallow, multipotential wells. 

4(BiNa)Ti20s - BizTijOy -HBiNaTisOM -H3/2Na20T-tKBi203 T (8.7) 

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On the other hand, the A positions can be shared by dissimilar ions such as Na and Bi, yielding the complex ferroelectric relaxor ceramic BNT (bismuth sodium titanate) (Hosono et al., 2001 Pookmanee et al., 2001 Pookmanee et al, 2003 see Section 8.3.3). 

Figure 8.17 Temperature dependence of the polarization in classic ferroelectric (a) and ferroelectric relaxor ceramics (b). To Curie temperature Tr Burns temperature.

More detailed recent information on ferroelectric relaxor ceramics can be obtained from Ye (2008). Lead-free BaFeo.5Nbo.5O3 ceramics with multiferroic properties were developed by Bochenek et al. (2009). 

Shrout, T. R., and Halliyal, A., Preparation of lead-based ferroelectric relaxors for capacitors, Am. Ceram. Bull., 66, 704 (1987). 

The hysteresis loops studies appear to be very informative for nanograin ceramics also. In particular, above we have discussed above the relaxor state induced by the grain sizes. The studies of the relaxor state have been made on the basis of dielectric response analysis. In Ref. [27], the additional firm evidence of relaxor state has been obtained with the help of hysteresis loops measurements. In Fig. 2.16 we report the shape of hysteresis loops in ferroelectric relaxors at different temperatures. It is seen, that at r > (Tm = 363 K is the temperature of dielectric permittivity maximum for PbSci/2Nbi/202 (PSN)) there is no residual polarization, while it is nonzero at T< r. Similar behavior has been observed for 730 nm thick Pbo.76Cao.24Ti03 (PCT) film with average grain sizes 86 nm and Tm = 553 K. 

In contrast to classic ferroelectrics, with a sharp phase transition at Tc and along the MPB, respectively relaxor ceramics are characterized by a diffuse OD phase transition without any change in macroscopic symmetry, a slim hysteresis loop (as opposed to the wide hysteresis in classical ferroelectrics see Figures 8.5 and 8.10), and associated small coercive fields Eq as well as small remanent (Pr) and spontaneous polarizations (Ps). Most importantly, the polarization of relaxor ceramics does not vanish at Tc, but rather retains finite values up to a higher temperature, termed the Bums temperature (Tg), as shown schematically in Figure 8.17. The dielectric permittivity of relaxor ceramics attains a maximum value at a temperature for a particular frequency and, as this frequency increases, r, also increases. The temperature dependence of Er does not obey the Curie-Weiss law just above r ax, but only beyond Tr where Tr > Tm . In contrast to the displacive phase transformation in classical ferroelectrics, the difiuse transition in relaxor ceramics does not involve any change in macroscopic symmetry, and is of neither first nor second order. 

In this chapter, I will conduct a review on some of the fundamental material properties of relaxor ferroelectric PLZT ceramics, which include the dielectric, ferroelectric, electromechanical, electro-optical and thermo-optical behaviours. Further details on each section can be found in the references (Levesque and Sabat 2011 Sabat, Rochon, and Mukherjee 2008 Sabat and Rochon 2009b Sabat and Rochon 2009c Sabat and Rochon 2009a). 

Figures 1 and 2 respectively show the temperature dependence of the relative permittivity and loss tangent of relaxor ferroelectric PLZT (9.5/65/35). As the temperature increases from -60°C to 100°C, the relative permittivity generally increased due to the unfreezing of domains. Between 0°C and 10°C, a broad peak can be seen in the lower frequency curves. This peak corresponds to the diffuse phase transition in this relaxor ceramic from the ferroelectric to the paraelectric state (also called the relaxor phase). Further heating continued to increase the relative dielectric permittivity until a maximum was achieved, at which point, the crystal s structure became cubic. This maximum in the permittivity, which is frequency dependent, occurs at the Curie temperature. Evidence of these phase transitions can also be seen in the loss tangent graph in figure 2.

The increased strain with increasing dc bias in figure 7 can be explained by previous dielectric measurements of PLZT (9.0/65/35) ceramics as a function of both tempierature and dc bias (Bobnar et al. 1999) They have observed a sharp increase in the dielectric permittivity with increasing dc bias fields at temperatures dose to the ferroelectric-relaxor phase transition, indicating that the dc bias is inducing the creation of electric dipoles at this transition, and hence increasing the overall piezoelectric response. 

We have seen that relaxor ferroelectric PLZT ceramics, with compositions (a/65/35) with 7frequency-dependent paraelectric (or relaxor) to long-range ferroelectric phase transition. PLZT (9.5/65/35) ceramics undergo this phase change around 5°C. However, no evidence of this phase change is seen in figure 13. This is likely because the specific refractivity of materials R, which is a measure of the electronic polarization, is unaffected by this particular phase transition. This refractivity constant is defined by the Lorentz-Lorenz relation ... 

Finally we can note that the ferroelectric state of relaxors is characterised by an extremely narrow hysteresis loop with a low value for the remanent polarisation (Figure 6.19a). This sort of hysteresis loop can be considered to fall into the continuum described previously (Figure 6.9) and suggests that the microsttucture of the phases is at an even more reduced scale than the fine-grained ceramic samples. Indeed, the behaviour when the materials are either cooled in or without an external electric field (FC or ZFC) is also taken as indicative of a complex microstructure. The strain versus applied electric field loop has a U shape, rather like the central portion of the strain curve for an antiferroelectric (Figure 6.19b). 

As suggested, the defining characteristics of relaxor ferroelectrics are due to a complex microsttucture. In normal materials the ferroelectric domain size is large, often identical to the grain size in a ceramic sample, and each domain is uniform. In relaxor ferroelectrics the B-sites are occupied by two cations, B and B. These are not... 

Ceramic PLZT has a number of structures, depending upon composition, and can show both the Pockels (linear) electro-optic effect in the ferroelectric rhombohedral and tetragonal phases and the Kerr (quadratic) effect in the cubic paraelectric state. Because of the ceramic nature of the material, the non-cubic phases show no birefringence in the as-prepared state and must be poled to become useful electro-optically (Section 6.4.1). PMN-PT and PZN-PT are relaxor ferroelectrics. These have an isotropic structure in the absence of an electric field, but this is easily altered in an applied electric field to give a birefringent electro-optic material. All of these phases, with optimised compositions, have much higher electro-optic coefficients than LiNb03 and are actively studied for device application. 

Shvartsman VV, KhoUdn AL, Orlova A, Kiselev D, Bogomolov AA, Sternberg A (2005) Polar nanodomains and local ferroelectric phenomena in relaxor lead lanthanum zirconate titanate ceramics. Appl Phys Lett 86 202937... 

Mulvihill ML, Cross LE, Cao WW, Uchino K (1997) Domain-related phase transitionlike behavior in lead zinc niobate relaxor ferroelectric single crystals. J Am Ceram Soc 80 1462-1468... 

Finally, it is worth mentioning that a phenomenon analogous to the difference between the normal and giant flexoelectricity of calamitic and bent-core nematics, respectively, exists in crystals, ceramics and polymers too. The flexoelectric response (defined in Eq. (3.1)) of perovskite-type ferroelectrics, " of relaxor ferroelectric ceramics and polyvinylidene fluoride (PVDF) films are four orders of magnitude larger than the flexoelectricity of dielectric crystals. In those sohd ferroelectric materials the polarization induced by flexing is evidently of piezoelectric origin. 

Glinchuk, M.D. Relaxor ferroelectrics from cross superparaelectiic model to random field theory. Br. Ceram. Trans. 103(N2), 76-82 (2004)... 

The first area of ferroelectric ceramic application was that of capacitor engineering, where the dielectric effect is exploited. Most ceramic capacitors are, in reality, high-dielectric-constant ferroelectric compositions in which the ferroelectric properties (hysteresis loop) are suppressed with suitable chemical dopants while retaining a high dielectric constant over a broad temperature range. Historically, the first composition used for such capacitors was BaTi03 and its modifications, but today lead-containing relaxors and other compositions are also included. 

Lynch, C.S. (1998) Fracture of ferroelectric and relaxor electro-ceramics ... 

Shur, V. 1996. Switching kinetics in normal and relaxor ferroelectrics PZT thin films and PLZT ceramics. Proc. l(f ISAF, Piscataway, NJ IEEE, pp 233-240. 

More recently, because of their high dielectric constants k > 20 000), lead-based relaxor ferroelectrics have been used as capacitor materials. These ceramics have the general chemical formula Pb(5i, 2)03) vvhere Bi is typically a low-valence cation and B2 is a high-valence cation. Compositions used in capacitor applications are frequently based on lead magnesium niobate, Pb(Mgi/3,Nb2/3)03, and lead zinc niobate, Pb(Zni/3,Nb2/3)03. Other substituents and modifiers are added so that dielectric layers of these materials can be densified at relatively low temperatures ( 900 °C). The low firing temperatures permit the use of relatively inexpensive cofired electrode materials, such as silver. Typically, tape casting is used in the preparation of the dielectric layers. 

Relaxors. ferroelectric (q.v.) ceramics in which the ferroelectric-paraelectric phase transition takes place over a range, rather than at a well-defined curie temperature (q.v.). 

Khemahem, H., Simon, A., von der MUhll, R., and Ravez, J. (2000) Relaxor or classical ferroelectric behavior in ceramics with composition Bai NaxTii Nb Os. 

In most substances, the electrostrictive strain (M < 10 m A ) is too small to be used in practical applications. The first useful electrostrictive strain ( 0.1 %) was found in relaxor ferroelectric ceramics [3], while newly developed electrostrictive polymers exhibit an electrostrictive strain of more than 5 % [1]. It is experimentally and theoretically proven... 

A Sawyer-Tower circuit (Sawyer and Tower 1930), with a 9.8/jF series capacitance, was used to measure the ferroelectric hysteresis at room temperature. Figures 3 and 4 respectively show the electric displacement of PLZT (9.5/65/35) and PLZT (9.0/65/35) ceramics as a function of a dc bias electric field. The field was first increased from zero to +1.7 MV.m-i, back down to -1.7 MV.m-i, and finally up to zero. This cycle lasted 50 seconds and was repeated 3 consecutive times. Typical relaxor ferroelectric hysteretic curves were observed for these two compositions. 

If all the coefficients of equation (2) are known, one can accurately predict the longitudinal strain under a varying electric field for a given piezoelectric or electrostrictive material, and even for a material exhibiting both piezoelectric and electrostrictive effects, such as irreversible electrostrictive materials. For ideal reversible electrostrictive materials, which possess no remnant polarization at zero electric field, the odd power term of the electric field in equation (2) vanishes. However, we will consider the relaxor PLZT ceramics studied in this chapter as irreversible electrostrictives, to account for any ferroelectric behaviour under dc bias fields, and we will therefore include both terms of the electric field in equation (2). 

Figure 7 shows the ac strain amplitude versus dc bias fields, measured up to the fourth harmonic, with a driving 0.37 MV.m-i peak-to-peak ac field at 120 Hz for PLZT (9.5/65/35). In this case, the first harmonic piezoelectric strain is dominant and seems to increase with the dc bias field until a maximum is reached at 1.2 MV.m-i dc. The theoretical curve seen in this figure is the result of fitting the data collected at 120 Hz to the first harmonic term in equation (4), while fixing the ac field value. This general behaviour of relaxor ferroelectrics has been previously observed for PMN electrostrictive ceramics (Masys et al. 2003). 

Sabat, R. G., Rochon, P. (2009a). The dependence of the refractive index change of clamped relaxor ferroelectric lead lanthanum zirconate titanate (PLZT) ceramics on AC and DC electric fields measured using an interferometric method. Ferroelectrics, Vol. 386, No. 1, pp. 105. 

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