Lorentz-type relationship of the temperature dependent dielectric permittivity in ferroelectrics with diffuse phase transition

Abstract

The temperature dependence of the dielectric permittivity of perovskite Ba͑Zr x Ti 1−x ͒O 3 solid solutions, PbMg 1/3 Nb 2/3 O 3 relaxor, and BaTiO 3 ferroelectric ceramics was measured. It is found that a Lorentz-type law can be used to describe the dielectric permittivity of either the normal ferroelectrics with or without diffuse phase transitions ͑DPT͒ or the typical ferroelectric relaxors. The ferroelectric DPT can be well described by just one fitting process using the Lorentz-type law, while the relaxor ferroelectric transition needs two independent fitting processes. The Lorentz-type law fails at the low temperature side of the dielectric maximum of a first-order ferroelectric phase transition. Above the transition temperature, the dielectric curves of all the studied materials can be well described by a Lorentz-type law. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2987733͔A broad peak in the temperature dependence of dielectric permittivity is the main feature of ferroelectrics with a diffuse phase transition ͑DPT͒, especially for ferroelectric relaxors. [1][2][3][4] Actually, systems showing a broad dielectric peak at the frequency-independent peak temperature T m are different from the relaxor-type DPTs. 1,4 In typical relaxors, strong frequency dispersion in dielectric permittivity is observed at the low temperature side of the dielectric peak, while the high temperature permittivity is almost frequency independent. The temperature for maximum permittivity T m shifts to higher values with increasing frequencies following the Vogel-Fulcher law. 3 For a ferroelectric phase transition, the Curie-Weiss law 1 / = ͑T − T C ͒ / C is known to describe the high temperature side of the sharp permittivity peak in normal ferroelectrics. However, in ferroelectrics with DPT this law is observed only at temperatures significantly higher than T m ͓over 300 K for PbMg 1/3 Nb 2/3 O 3 ͑PMN͔͒. 1,2 When the temperature is decreased below the Burn's temperature T B , polar nanoregions ͑PNRs͒ appear and the displacive-type soft mode is overdamped. 5 The Curie-Weiss law becomes invalid within the temperature range of T m -T B .Since Smolenskii's 6 work, the temperature dependence of the dielectric permittivity above T m has been widely studied in order to find out the characteristic dielectric behavior of ferroelectrics with DFT. There are several models to quantitatively describe the temperature dependent dielectric permittivity of DPT. A brief review of these models has been given by Bokov and Ye. 7 Among these models, the following power law 8,9 is the most popular one:where the parameters ␥ and ␦ reflect the diffuseness of dielectric relaxation. Normally, ␥ = 1 describes a Curie-Weiss behavior of normal ferroelectrics, while ␥ = 2 is valid for a classical ferroelectric relaxor. 8 It should be mentioned that the maximum permittivity m and the temperature at maximum permittivity T m are frequency-dependent quantities for relaxors. So the parameters ␦ and ␥ also depend on frequency, and therefore Eq. ͑1͒ is not a...

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“…The relaxor dispersion degree around T m1 can be estimated by the Lorentz-type relation, [ 21 ] 2 , where T A ( T A ≠ T m1 ) and ε A are the temperature of the dielectric permittivity peak and the extrapolated value of ε at T = T A , respectively. The parameter δ A refl ects the relaxor diffuseness of the dielectric peak.…”

Dielectric Properties of Ba(Ti0.9Zr0.1)O3Ceramics Co-Doped with Bi and Cu

“…It is found that ε r (T) can be fitted quite well by Eq. Table 1 Curve fitting results at 10 kHz for BCTZ ceramics suggested there should be one polarization process for the fitting parameters δ being close in two temperature ranges T > T m and T < T m , and two polarization processes for the larger difference of δ in ceramics, one dominating in the high and the other in the low temperature range [14]. But the largest diffuseness (δ ≈ 100 • C) of the permittivity peak in x = 0.01 sample, which is in contradiction with the experiment shown in Fig.…”

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“…Besides, since e 0 m and T m used to determine the diffuseness parameter c using Eq. (7) are frequency dependent for relaxor materials, c is therefore not adequate to describe the frequency independent dielectric behavior at high temperatures (T > T m ) [33]. Hence the e 0 (T) data shown in Fig.…”

“…5 was further analyzed to understand the origin for the observed frequency dependent diffused phase transition. It has been emphasized in the reported literature that a description of the high temperature slope of the dielectric peak in ferroelectrics with or without diffused phase transition (DPT), and classical relaxor materials can be well described above and below T m with the Lorenz type empirical relation [29,33,34]:…”