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Relaxors go critical

Naturevolume 441pages941942 (2006) | Download Citation


Relaxor ferroelectrics are fascinating and useful materials, but they seem to be heterogeneous, hopeless messes. Observing what they do under electric fields reveals critical behaviour that helps to make sense of them.

Piezoelectrics — materials that convert electrical energy into mechanical energy, and vice versa — form the alarms in our watches, the warning buzzers in our cars, and the transducers used in sonar and medical ultrasound. They are also being used for knifeless surgery and to build tiny pumps and motors for medical applications. On page 956 of this issue, Kutnjak and colleagues1 report investigations of the thermodynamic properties and phase diagram of relaxor ferroelectrics with giant piezoelectric effects. These materials offer a response that is up to ten times greater than that of standard piezoelectrics, and they are revolutionizing acoustic imaging and surgical applications.

Ferroelectrics have a spontaneous polarization (a dipole moment per unit volume, or net charge flow per unit volume from a nonpolar state) that can be switched in direction by applying an electric field. A prototypical ferroelectric is lead titanate (PbTiO3, or PT). Ferroelectric behaviour arises as a result of competition between long-range forces between ionic charges in the material, which act to destabilize the nonpolar structure, and short-range, repulsive forces, which have a stabilizing influence. Covalency softens this repulsion and allows the atoms to have average off-centre displacements2, and a net polarization. The piezoelectric behaviour of ferroelectrics arises from the coupling of strain and polarization when the polarization interacts with applied electric fields.

Relaxor ferroelectrics are solid solutions between a relaxor material and a ferroelectric such as PT. Relaxors do not have a polar ground state, and are heterogeneous3. They have disordered polarization, with small ordered ‘polar nanoregions’4,5 that individually polarize6 below a temperature known as the Burns temperature7.

Kutnjak and colleagues study the relaxor ferroelectric system PMN–PT (in full, PbMg1/3Nb2/3O3–PbTiO3), which is an exemplar of a new class of relaxor ferroelectric with pronounced piezoelectric properties. In the normal, collinear piezoelectric case, electric field is applied parallel to the polarization, and the resulting strain is small. But in high-coupling relaxor ferroelectrics, the energy barrier for polarization rotation is low, so even a field applied obliquely can easily rotate the polarization (Fig. 1). It is the polarization rotation effect that gives rise to very large electromechanical coupling8,9, with strains of up to 2% observed. Polarization rotations have been proved experimentally from X-ray diffraction and optical studies10,11.

Figure 1: The polarization rotation effect.
Figure 1

When an electric field E is applied along the cube axis (vertical), the polarization P rotates from the cube diagonal towards the cube axis. With the polarization along the cube diagonal, the lattice strain is small (the lattice is close to cubic), but with the polarization along the cube axis the strain is large — there is a large piezoelectric effect. Kutnjak et al.1 apply a field along the cube diagonal in a new-generation relaxor ferroelectric, and find that a first-order jump in polarization with temperature for small fields vanishes at a critical line that depends on temperature, electric field and the material's composition. The electromechanical coupling also peaks at this critical line.

Relaxor ferroelectrics are enormously useful because of their piezoelectric properties. But they also exhibit a cornucopia of mesoscopic and microscopic heterogeneities over a range of lengths and timescales. This diversity has so far made it difficult to systematize observations of them or even to determine their whole phase diagram — the jumping-off point for any materials study.

Kutnjak et al.1 measured properties of PMN–PT as functions of temperature, electric field and composition. In the resulting phase diagram, they found a critical line under applied electric field. For low fields, there is a first-order transition where local dipoles formed by atomic displacements are ordered at low temperatures, and rotate or become disordered, as in a paraelectric material, for temperatures above the transition point. At this transition, there is a discontinuity in the net polarization. As electric field is increased, the discontinuity in polarization decreases until it is zero at the critical line. This finding complements recent evidence for critical behaviour in PMN–PT at high pressures12. Unusual properties will emanate away from these bounding critical lines, giving rise to many of the strange and difficult-to-understand properties of these complex materials.

This critical behaviour can be better understood by analogy with the familiar pressure–temperature phase diagram of H2O. Heating water at 100 °C (373 K) under atmospheric pressure converts it to steam at a phase transition, and the jump in density between steam and water defines the transition as first order. As pressure is increased, the density difference between water and steam decreases, and goes to zero at a pressure of 22 megapascals (and a temperature of 647 K); above this critical point, there is no phase transition. Near the critical point, H2O has unusual properties, such as large density fluctuations and opalescence. Water would seem a strange substance if we lived at pressures near the critical point (it is anyway, but not because of this particular critical point).

To understand the importance of the critical lines in PMN–PT, even away from the actual critical values of applied field, one must understand that, whereas a fluid such as water cannot sustain large pressure gradients (it will simply flow to equalize the pressure), ferroelectrics can, by their nature as dielectrics, sustain large electric fields. These fields can be generated locally by chemical heterogeneities, domains and surfaces. Thus, even without an externally applied electric field, portions of the sample may be in the critical regime.

Near the critical line described by Kutnjak and colleagues, rotating the polarization becomes extremely easy, and in fact diverges at the critical point. This discovery helps to explain why PMN–PT has such a high coupling strength, and is likely to be a ubiquitous feature of these materials. It used to be thought that the complex chemistry of relaxor ferroelectrics was related to their large coupling; but the prediction that pure PT under pressure would show polarization rotation and a piezoelectric constant larger even than that of the high-strain piezoelectrics suggests otherwise13. Delineating these fundamental issues will make it easier to develop new materials and improve existing ones, as well as help to explain multitudes of experimental data.

This is an exciting and collegial field, in which theory, experiment and materials development work side by side. First-principles theory is being used for ‘materials by design’14,15. Basic physical ideas such as the nature of polarization16,17, molecular dynamic simulations4 and advanced experimentation3,5,10,11,12 have brought us to a point at which we not only have a greatly improved understanding of basic physical phenomena, but are also poised on the edge of hugely expanded applications of acoustic technologies.


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  1. Carnegie Institution of Washington, 5251 Broad Branch Road, NW, 20015, Washington DC, USA

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