Piezoelectric crystals respond mechanically to an applied electric field and vice versa. They are commonly used as transducers in microphones, ultrasound systems, and other applications. Among piezoelectric crystals, the so-called relaxor-ferroelectric single crystals have the highest capacity for transforming voltage into displacement. Despite decades of study, the reason for their high strong piezoelectric response has remained unclear.

In research recently published in Nature Communications, an international team of scientists led by researchers at Pennsylvania State University (Penn State) has now shown that small, polarized regions within the relaxor-ferroelectric crystals contribute 50–80% of the room-temperature piezoelectricity of these crystals. The team used simulations to elucidate the mechanism behind this contribution.

In regular ferroelectric crystals, the electric domains align in the presence of an electric field, resulting in polarization. This is also true of relaxor-ferroelectric crystals; however, relaxor-ferroelectric crystals also contain tiny spatial regions (5–10 nm) with net electric polarizations. These polar nanoregions are randomly distributed within the crystal.

Major changes in the dielectric and piezoelectric properties of crystals usually occur around phase transitions. In a series of cryogenic experiments, the team studied the long-range crystal structure, domain patterns, polarization, and dielectric relaxation frequency of relaxor-PbTiO₃ (PT) solid solution crystals. Their results verified that there were no phase transitions below 200 K. However, there is a significant difference in the piezoelectricity between regular ferroelectric crystals and relaxor-ferroelectric crystals within that temperature range.

Next, the team studied the interactions of the polar nanoregions with long-range ferroelectric domains by simulations. “The simulation uncovered how polar nanoregions help generate ultrahigh piezoelectricity—by aligning with the polar direction of the ferroelectric domains and by facilitating polarization rotation,” says Fei Li, a research associate at Penn State and first author of the paper.

The simulations showed that at ~150 K, the polar nanoregions become unstable. In order to minimize the free energy of the system, some nanoregions change orientation so that their polar direction is collinear with that of the ferroelectric matrix. As the temperature rises, a larger percent of the nanoregions become collinear. At ~350 K, all of the polar nanoregions are aligned with the ferroelectric matrix.

In the presence of a perpendicular electric field, the simulation shows that it is much easier to rotate the polarization of collinear nanoregions than it is to rotate the polarization of the matrix. This, in turn, facilitates the rotation of nearby polarized regions in order to minimize energy at the interfaces.

Together, these effects increase the shear piezoelectric response of relaxor-ferroelectric crystals, but their contributions are temperature-dependent. At 50 K, the nanoregions are essentially frozen; there is no piezoelectric increase over regular ferroelectric crystals. At ~150 K, the polarization of the nanoregions begins to change, causing an increase in piezoelectricity. As the temperature increases so does the impact of rotation facilitation, which gradually overtakes the impact of the orientation changes. At 350 K, all of the nanoregions are aligned, so their contribution to piezoelectricity is only in the form of facilitating rotation.

Combining the results of experiments and simulations, the team showed that the polar nanoregions lead to an increase in piezoelectricity of 50–80% at room temperature when compared to a crystal without polar nanoregions.

“These results demonstrate that the local structure of polar nanoregions plays a dominant role in controlling the macroscopic properties, where modest changes in local structure impact the macroscopic properties greatly,” says Shujun Zhang, who co-led the project with Li, Thomas Shrout, and Long-Qing Chen from Penn State.

Zhang continues, “Ferroelectric materials have been the mainstay for piezoelectric applications, from medical imaging ultrasound to piezoelectric sensors and actuators. This research gives a paradigm and opens a new direction for designing high performance ferroic functional materials.”

The team’s demonstration that the dielectric and piezoelectric properties of relaxor-PT crystals freeze abruptly at low temperatures is impressive, according to Dragan Damjanovic, an expert in piezoelectric, dielectric, and ferroelectric materials at the Swiss Federal Institute of Technology in Lausanne.

“This strongly points to significant contributions to the dielectric and piezoelectric properties coming from polar nanoregions that partly freeze and change their interaction with ferroelectric matrix at low temperatures. This is for me the main value of this paper, which I see as a landmark in the field of relaxor-ferroelectrics,” Damjanovic says.

The mechanism proposed in this paper matches experimental results well, but there is more work to be done. The atomistic origin of polar nanoregions is still an open question, say the researchers, and in-situ follow-up experiments would provide further support for their mesoscale conclusions. Although questions remain, this work underscores the importance of local structural engineering on the quest for new materials with high-performance properties.

Read the article in Nature Communications.