X-rays reveal co-existing cubic and tetragonal phases in perovskite material

The perovskite-based PMN-PT ((1-x)Pb(Mg_1/3Nb_2/3)O₃-xPbTiO₃) family of materials is known for its outstanding ability to convert mechanical energy into electrical energy and vice versa, a property known as piezoelectricity that has applications in technologies such as sensors and actuators. PMN-PT has been widely studied to understand why it has such strong electromechanical properties [1]. 

Like many other perovskite oxides, PMN-PT changes its internal structure (and thus its properties) when cooled, transitioning from a cubic phase (where it does not have a permanent polarization) to either a tetragonal or rhombohedral phase (where it does). All such phase transitions result in the formation of complex patterns of ferroelectric and ferroelastic domains. However, the mechanisms governing the phase transitions, and the resulting formation of ferroic domains, are still not completely understood.

This work studied the phase transition from cubic to tetragonal phase in a 0.65PMN-0.35PT crystal using high-resolution single-crystal multi-temperature X-ray diffraction. Initial tests at Tel-Aviv University [2] revealed an ‘intermediate’ state near the temperature where the phase transition occurs.

More detailed experiments were conducted at the ESRF’s ID28 beamline, where X-ray diffraction measurements were taken at 25 different temperatures ranging from 403 to 458 K, focusing closely on the range of 424 to 442 K. The crystal’s structure was examined at 32 specific Bragg peaks, to better understand the transition process. 

During the transition from cubic (C) to tetragonal (T) phases in the crystal, a Bragg peak can split into components, which are linked to the corresponding ferroelastic domains within the crystal. When the crystal transitions back to the cubic phase, these sub-peaks merge back into one.

Figure 1b-d shows Bragg peaks around 426, 437 and 440 K, corresponding to the tetragonal, intermediate and cubic phases. In the intermediate state, both cubic and tetragonal phases exist together. Figure 1c illustrates that this ‘intermediate’ region is characterized by C-T phase-coexistence, with sub-peaks corresponding to both the tetragonal domains (T₁ and T₂) and the cubic phase (C). By measuring the intensity of the C peaks, it was possible to determine how much of the material is in the cubic phase at different temperatures.

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Fig. 1: a) The temperature dependence of the C-phase fraction, η_c (T), during heating and cooling through the phase transition of 0.65PMN-0.35PT. b) - d) Projection of the diffraction intensity distribution around 7 1 ̅  2 Bragg peak at different temperatures corresponding to the tetragonal phase (b), intermediate state (c) and cubic phase (d). The labels "C", "T₁" and "T₂" show the assignment of the sub-peaks to the cubic phase or the corresponding tetragonal domains.

Figure 1a presents this temperature dependence and illustrates the range (about 4 K wide) where both phases co-exist. This co-existence shows a delay, or hysteresis, of about 1.8 K during heating and cooling. The researchers also looked at how the crystal’s lattice parameters change with temperature (Figure 2). They found that the lattice parameters of the cubic phase closely match an average of those of the tetragonal phase.

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Fig. 2: Temperature dependence of the T (⁠a_T, c_T⁠) and C (⁠a_c) lattice parameters during a) heating and b) cooling. The dashed lines represent the dependence of the orientational average (a_CT =2/3 a_T + 1/3 c_T) on temperature⁠.

The matching of certain lattice parameters between the C and a specific form of the T phase (adaptive tetragonal phase, or ATP) suggests that these phases can connect smoothly without creating strain. This connection happens along a specific plane in the crystal, known as a low-index habit plane (HP), where both phases share the same 2D lattice parameters [3].

The ATP consists of alternating tetragonal domains, where the longer axis of these domains changes direction. This alternating structure, when miniaturized, averages out to form a larger structure with monoclinic symmetry. When the proportions of these domains are 2/3 and 1/3, it is possible to find a low-indexed {110}-type HP whose two-dimensional lattice parameters of the cubic phase align perfectly with those of the ATP. 

In summary, this work observed that within a narrow temperature range of 4 K, both cubic and tetragonal phases co-exist in a 0.65PMN-0.35PT single crystal. This phase coexistence shows a hysteresis of 1.8 K when heating and cooling the crystal. The cubic and tetragonal phases have structural dimensions, which allows them to connect smoothly along a specific plane, known as the {110}-type habit plane. Overall, the study provides insights into the structural behaviour of PMN-PT during phase transitions, which could help improve its use in various applications.

Principal publication and authors
Lattice match between coexisting cubic and tetragonal phases in PMN-PT at the phase transition, I. Biran (a), A. Bosak (b), Z.-G. Ye (C), I. Levin (d), S. Gorfman (a), Appl. Phys. Lett. 124, 242901 (2024); https://doi.org/10.1063/5.0202576
(a) Department of Materials Science and Engineering, Tel Aviv University, Tel Aviv (Israel)
(b) ESRF
(c) Department of Chemistry and 4D LABS, Simon Fraser University, Burnaby, British Columbia (Canada)
(d) Materials Measurement Science Division, National Institute of Standards and Technology, Gaithersburg, Maryland (USA)

References
[1] A.A. Bokov & Z-G. Ye, J. Mater. Sci. 41, 31-52 (2006).
[2] S. Gorfman et al., J. Appl. Cryst. 54, 914-923 (2021).
[3] J.S. Bowles & J.K. Mackenzie, Acta Metall. 2, 129-137 (1954).