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BaZr0.5Ti0.5O3: Lead-free relaxor ferroelectric or dipolar glass

C. Filipič, Z. Kutnjak, R. Pirc, G. Canu, and J. Petzelt
Phys. Rev. B 93, 224105 – Published 15 June 2016
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  • INTRODUCTION
  • EXPERIMENTAL DETAILS
  • DATA ANALYSIS AND DISCUSSION
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    Glassy freezing dynamics was investigated in BaZr0.5Ti0.5O3 (BZT50) ceramic samples by means of dielectric spectroscopy in the frequency range 0.001 Hz–1 MHz at temperatures 10<T<300 K. From measurements of the quasistatic dielectric polarization in bias electric fields up to ∼28 kV/cm it has been found that a ferroelectric state cannot be induced, in contrast to the case of typical relaxors. This suggests that—at least for the above field amplitudes—BZT50 effectively behaves as a dipolar glass, which can be characterized by a negative value of the static third order nonlinear permittivity. The relaxation spectrum has been analyzed by means of the frequency-temperature plot, which shows that the longest relaxation time obeys the Vogel-Fulcher relation τ=τ0exp[E0/(T−T0)] with the freezing temperature of 48.1 K, whereas the corresponding value for the shortest relaxation time is ∼0 K, implying an Arrhenius type behavior. By applying a standard expression for the static linear permittivity of dipolar glasses and/or relaxors the value of the Edwards-Anderson order parameter q(T) has been evaluated. It is further shown that q(T) can be described by the spherical random bond-random field model of relaxors.

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    • Received 1 April 2016

    DOI:https://doi.org/10.1103/PhysRevB.93.224105

    ©2016 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Relaxor ferroelectrics
    1. Physical Systems
    Glassy systems
    1. Techniques
    Dielectric spectroscopy
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    C. Filipič, Z. Kutnjak, and R. Pirc

    • Jožef Stefan Institute, Jamova cesta 39, 1000 Ljubljana, Slovenia

    G. Canu

    • Institute for Energetics and Interphases, National Research Council, via De Marini 6, I-16149 Genoa, Italy

    J. Petzelt

    • Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Praha 8, Czech Republic

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    Vol. 93, Iss. 22 — 1 June 2016

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    Images

    • Figure 1
      Figure 1

      Temperature dependence of the real part of the complex dielectric constant ɛ′ in BZT50 at various frequencies, showing a typical relaxor behavior.

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    • Figure 2
      Figure 2

      Temperature dependence of the imaginary part of the complex dielectric constant ɛ′′ in BZT50 at various frequencies, where the peak positions of ɛ′′(f,T) differ from the peak positions of ɛ′(f,T) (see Fig. 1).

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    • Figure 3
      Figure 3

      The temperature Tmax(f), at which the maxima of ɛ′′(f,T) occur, is found empirically to scale with f according to the Vogel-Fulcher (VF) relation f=f0exp[−E0/(Tmax−T0)] with a VF freezing temperature T0=9.5±1.2 K, attempt frequency f0=4.08×1013 Hz, and activation energy E0=2225 K.

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    • Figure 4
      Figure 4

      Cole-Cole diagram: Measured values of ɛ′′ plotted vs ɛ′ in BZT50 at various temperatures between 50 and 95 K. Solid lines between experimental points measured at the same temperature serve as guide to the eye.

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    • Figure 5
      Figure 5

      Temperature dependence of the parameters ɛs and ɛ∞ in BZT50. The parameters were obtained by fitting experimental data with the Havriliak-Negami (HN) function.

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    • Figure 6
      Figure 6

      Temperature-frequency plots for several fixed values of the reduced dielectric constant δ, top to bottom, 0.05, 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 0.95, 0.98. Solid lines are fits obtained with a generic VF type ansatz, providing a freezing temperature T0(δ) for each value of the parameter δ.

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    • Figure 7
      Figure 7

      Freezing temperature T0 vs δ. The limiting cases δ→1 and δ→0 yield the freezing temperatures T02=48.1 K and T01≈0 K, respectively. Solid line is extrapolation to δ→1. The value T0=9.5 K determined from the maxima of ɛ′′(f,T) (see Fig. 3) approximately corresponds to δ≈0.6.

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    • Figure 8
      Figure 8

      Temperature dependence of the FC and ZFH (after field-cooled) quasistatic dielectric polarization in high electric field (28 kV/cm). There is no sign of an induced ferroelectric phase. The ZFH polarization represents the remanent polarization Pr. As indicated, the steepest slope in Pr(T) variation, at TF∼50 K, yields an estimate for the freezing temperature.

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    • Figure 9
      Figure 9

      Relation between the induced polarization and the applied quasistatic electric field P(E) at several temperatures above TF. Note the nonlinear relation P(E) with zero remanent polarization at all temperatures. With decreasing temperature the nonlinearity increases.

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    • Figure 10
      Figure 10

      Temperature dependence of the first (a), third (b), and fifth (c) order dielectric constants obtained by fitting of the nonlinear P(E) data with the function P(E)=ɛ0ɛ1E+ɛ3E3+ɛ5E5.

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    • Figure 11
      Figure 11

      Temperature dependence of the dielectric constant ɛFC≅P(E)FC/(ɛ0E) obtained by a field-cooled experiment in low electric field (10 kV/cm). ɛFC values (diamonds) agree well with the values of ɛ1 shown in Fig. 10. Also presented (open circles) is the temperature and frequency dependence (1 Hz–1 MHz) of the real part of dielectric constant ɛ′(f,T) measured in a low electric field (1 V/mm).

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    • Figure 12
      Figure 12

      Temperature dependence of the spin-glass or Edwards-Anderson (EA) order parameter q(T) derived from Eq. (7), where the linear susceptibility has been determined from the field-cooled polarization measured in low electric field (Fig. 11). Also displayed are the values of the fit parameters J0, J, and Δ̃=Δ/J2 obtained by fitting Eq. (8) to q(T).

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