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Evidence for a tricritical point coinciding with the triple point in (Pb0.94Sr0.06)(ZrxTi1−x)O3: A combined synchrotron x-ray diffraction, dielectric, and Landau theory study

Ravindra Singh Solanki, S. K. Mishra, Yoshihiro Kuroiwa, Chikako Moriyoshi, and Dhananjai Pandey
Phys. Rev. B 88, 184109 – Published 27 November 2013
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  • INTRODUCTION
  • EXPERIMENTS
  • RESULTS AND DISCUSSION
  • CONCLUSIONS
  • ACKNOWLEDGEMENTS
    • References

    Abstract

    We present here results of high-resolution synchrotron x-ray diffraction (SXRD) and dielectric studies in conjunction with Landau theory considerations on (Pb0.94Sr0.06)(ZrxTi1−x)O3 compositions in the vicinity of the morphotropic phase boundary (MPB) to find evidence for the flattening of the free-energy surface at the MPB proposed in recent ab initio studies on strongly piezoelectric ceramics. SXRD results reveal that the tetragonal and pseudorhombohedral monoclinic compositions with x = 0.515 and 0.550 transform directly into the cubic paraelectric phase, whereas for 0.520 ≤ x ≤ 0.545, the pseudotetragonal and pseudorhombohedral monoclinic compositions transform first to the tetragonal phase and then to the cubic phase. Our results reveal the existence of a triple point at x ≃ 0.550. It is shown that the tetragonal-to-cubic transition, irrespective of the composition, up to x ≃ 0.545 is accompanied with a discontinuous change in the unit cell volume and thermal hysteresis, confirming the first-order nature of this transition. However, the pseudorhombohedral monoclinic composition for x = 0.550 transforms directly into the cubic phase in a second-order manner. Our experimental results thus reveal a crossover from a first-order to a second-order phase transition through a tricritical point around x = 0.550. Landau theory calculations also confirm gradual flattening of the free-energy surface on approaching the tricritical composition x = 0.550. We conclude that the triple point in the Pb(ZrxTi1−x)O3 phase diagram is a tricritical point.

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    • Received 23 February 2013

    DOI:https://doi.org/10.1103/PhysRevB.88.184109

    ©2013 American Physical Society

    Authors & Affiliations

    Ravindra Singh Solanki1, S. K. Mishra2, Yoshihiro Kuroiwa3, Chikako Moriyoshi3, and Dhananjai Pandey1

    • 1School of Materials Science and Technology, Indian Institute of Technology (Banaras Hindu University), Varanasi-221005, India
    • 2Research and Technology Development Centre, Sharda University, Greater Noida-201306, India
    • 3Department of Physical Science, Graduate School of Science, Hiroshima University, Japan

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    Vol. 88, Iss. 18 — 1 November 2013

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    Images

    • Figure 1
      Figure 1
      Temperature dependence of dielectric permittivity (ɛ′) of PSZT at 100 kHz for the compositions with (a) x = 0.515, (b) x = 0.520, (c) x = 0.525, (d) x = 0.530, (e) x = 0.535, (f) x = 0.545, and (g) x = 0.550 during heating (filled circles) and cooling (open circles) cycles.Reuse & Permissions
    • Figure 2
      Figure 2
      (a) The cubic-to-tetragonal phase transition temperature (Tc) during heating and cooling cycles. (b) Discontinuous change (ΔV) in the unit cell volume at the transition temperature Tc during heating. (c) Landau free-energy barrier at Tc between the cubic and the tetragonal phases of PSZT for x = 0.515, 0.520, and 0.525 as calculated using Landau-Devonshire theory for which we used electrostrictive coupling coefficient (Q11) of PZT. (d) Landau free-energy barrier at Tc between the cubic and the tetragonal phases of PSZT for x = 0.515, 0.520, and 0.525 as calculated using Landau-Devonshire theory for which the value of electrostrictive coupling coefficient Q11 was obtained from the structural parameters of PSZT515.Reuse & Permissions
    • Figure 3
      Figure 3
      The evolution of synchrotron powder XRD profiles of the (111)pc, (200)pc, and (220)pc reflections of tetragonal PSZT515 with temperature.Reuse & Permissions
    • Figure 4
      Figure 4
      The evolution of synchrotron powder XRD profiles of the (111)pc, (200)pc, and (220)pc reflections of PSZT520 with temperature.Reuse & Permissions
    • Figure 5
      Figure 5
      The evolution of synchrotron powder XRD profiles of the (111)pc, (200)pc, and (220)pc reflections of PSZT525 with temperature.Reuse & Permissions
    • Figure 6
      Figure 6
      The variation of FWHM of the (a) (111)pc and (b) (200)pc reflections of PSZT520 with temperature.Reuse & Permissions
    • Figure 7
      Figure 7
      The variation of FWHM of the (a) (111)pc and (b) (200)pc reflections of PSZT525 with temperature.Reuse & Permissions
    • Figure 8
      Figure 8
      Observed (dots), calculated (central continuous line), and difference (bottom line) profiles of selected (111)pc, (200)pc, and (220)pc reflections for PSZT520 at various temperatures obtained after Rietveld refinement using plausible structural models. The vertical tick marks above the difference profiles give the positions of the Bragg reflections.Reuse & Permissions
    • Figure 9
      Figure 9
      The evolution of synchrotron powder XRD profiles of the (111)pc, (200)pc, and (220)pc reflections of PSZT530 with temperature.Reuse & Permissions
    • Figure 10
      Figure 10
      The evolution of synchrotron powder XRD profiles of the (111)pc, (200)pc, and (220)pc reflections of PSZT535 with temperature.Reuse & Permissions
    • Figure 11
      Figure 11
      The variation of FWHM of the (a) (111)pc and (b) (200)pc reflections of PSZT530 with temperature.Reuse & Permissions
    • Figure 12
      Figure 12
      The variation of FWHM of the (a) (111)pc and (b) (200)pc reflections of PSZT535 with temperature.Reuse & Permissions
    • Figure 13
      Figure 13
      The evolution of synchrotron powder XRD profiles of the (111)pc, (200)pc, and (220)pc reflections of PSZT545 with temperature.Reuse & Permissions
    • Figure 14
      Figure 14
      The variation of FWHM of the (a) (111)pc and (b) (200)pc reflections of PSZT545 with temperature.Reuse & Permissions
    • Figure 15
      Figure 15
      The evolution of synchrotron powder XRD profiles of the (111)pc, (200)pc, and (220)pc reflections of PSZT550 with temperature.Reuse & Permissions
    • Figure 16
      Figure 16
      The variation of FWHM of the (a) (111)pc and (b) (200)pc reflections of PSZT550 with temperature.Reuse & Permissions
    • Figure 17
      Figure 17
      Variation of (a) a and c lattice parameters and (b) unit cell volume of various PSZT compositions with temperature. Error bars are less than the size of the data points. Continuous lines are visual guides.Reuse & Permissions
    • Figure 18
      Figure 18
      Temperature dependence of (a) the a and c lattice parameters (open dots represent the extrapolated values of ac in the tetragonal region, and continuous lines are visual guides), (b) spontaneous strains x1 and x3 (continuous lines represent the least squares fit to the data points using a second-order polynomial), (c) dielectric stiffness (1ɛ′) (the continuous line gives the Curie-Weiss fit), and (d) P32 for PSZT515 (continuous lines are visual guides).Reuse & Permissions
    • Figure 19
      Figure 19
      (a) Temperature dependence of (a) the a and c lattice parameters (open dots represent the extrapolated values of ac in the tetragonal region, and continuous lines are visual guides), (b) spontaneous strains x1 and x3 (continuous lines represent the least squares fit to the data points using a second-order polynomial), (c) dielectric stiffness (1ɛ′) (the continuous line gives the Curie-Weiss fit), and (d) P32 for PSZT520 (continuous lines are visual guides).Reuse & Permissions
    • Figure 20
      Figure 20
      (a) Temperature dependence of (a) the a and c lattice parameters (open dots represent the extrapolated values of ac in the tetragonal region, and continuous lines are visual guides), (b) spontaneous strains x1 and x3 (continuous lines represent the least squares fit to the data points using a second-order polynomial), (c) dielectric stiffness (1ɛ′) (the continuous line gives the Curie-Weiss fit), and (d) P32 for PSZT525 (continuous lines are visual guides).Reuse & Permissions
    • Figure 21
      Figure 21
      Gibbs free-energy profiles of PSZT515 calculated at different temperatures using Landau-Devonshire theory (Ref. 22). T2 is the characteristic temperature at which the inflexion point in the free-energy profile develops, while for the temperature T1, a local minimum for the tetragonal phase appears well above the thermodynamic phase transition temperature Tc, at which the free-energy profile is triply degenerate on account of coexistence of the tetragonal and cubic phases. At a temperature well below Tc, the minima corresponding to the tetragonal phase become global minima.Reuse & Permissions
    • Figure 22
      Figure 22
      (a) Temperature dependence of P32 and (b) variation of spontaneous strains (x1, x3) with P32 for PSZT515. The continuous line gives the fit using the relation given in Eqs. (8) and (9). P32 has been calculated from Born effective charges and atomic coordinates using Eq. (14).Reuse & Permissions
    • Figure 23
      Figure 23
      Schematic phase diagram of PSZT around the MPB region constructed on the basis of present paper and earlier neutron and ultrasonic measurements (Refs. 6 and 7) on the same set of PSZT samples. Open circles in the phase diagram correspond to the high-temperature cubic (Pm3¯m) to tetragonal (P4mm) phase transition temperature during heating, obtained from dielectric measurements. The filled circles correspond to low-temperature AFD phase (space group Cc) transition temperatures (Refs. 6 and 7). The symbols PT and PR represent pseudotetragonal and pseudorhombohedral monoclinic phases, respectively. The vertical lines are first-order phase boundaries across which the two neighboring phases coexist. Also, the inclined P4mm-Cm(PT)/Cm(PR) phase boundary is a first-order phase boundary. The phase boundary marked with a filled circle is linked with the AFD transition whose order (first or second) is unsettled.Reuse & Permissions
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