Negative absolute pressures, though much investigated in liquids (see Physics Today, January 2011, page 14), have been thought to be impossible to sustain in solids. Informally, materials under negative pressure are said to be under tension. But more specifically, that tension must be isotropic; thin films produced by strain-engineering techniques that stretch them in just one or two dimensions, though useful, don’t qualify.
Now Nava Setter (Swiss Federal Institute of Technology, Lausanne), her former student Jin Wang (currently an assistant professor at the Tsinghua University Graduate School at Shenzhen, China), and their colleagues have developed a method to create freestanding crystalline nanomaterials stretched in all three dimensions.1 The researchers synthesized lead titanate nanowires in the material’s so-called PX phase—a low-density, metastable crystal structure shown in figure 1a—and induced them to transform into the denser, stable perovskite phase shown in figure 1b. Because of the dynamics of that transformation, the perovskite nanowires form with their surfaces under positive pressure and their cores under negative pressure. The pressures proved to be stable for more than two years.
Figure 1. Crystal structures of lead titanate.(a) The PX phase is metastable and low density. (b) The perovskite phase, the material’s ground-state structure, is 13% denser than the PX phase. Lead atoms are shown in red, oxygen in dark blue, and titanium inside the semitransparent light-blue octahedra. Unit cells are shown in black. (Adapted from ref. 1.)
Figure 1. Crystal structures of lead titanate.(a) The PX phase is metastable and low density. (b) The perovskite phase, the material’s ground-state structure, is 13% denser than the PX phase. Lead atoms are shown in red, oxygen in dark blue, and titanium inside the semitransparent light-blue octahedra. Unit cells are shown in black. (Adapted from ref. 1.)
“A clever trick”
The discovery was serendipitous. Setter’s research centers on ferroelectrics: materials that spontaneously acquire a bulk electric polarization when cooled below a certain critical temperature. All ferroelectrics are necessarily both piezoelectric and pyroelectric—that is, the polarization is responsive to both pressure and temperature—so their applications include ultrasound transducers, actuators, and temperature sensors.
Wang’s PhD work, conducted in the late 2000s, was on nanowires of lead zirconate titanate (Pb(ZrxTi1 − x)O3, or PZT), one of the most important classes of ferroelectrics, of which perovskite-phase PbTiO3 is a member. He wanted to investigate size effects: whether ferroelectric behavior differed in nanowires of different thicknesses. In the course of those experiments, he and Setter noticed some unusual phenomena, including spherical nanopores marring many of the wires. “At the time, we were disappointed,” says Wang, “because it seemed like an imperfection in the sample.” Amazingly, though, the “imperfect” wires showed enhanced ferroelectric properties: sharply higher transition temperatures and dramatically stronger spontaneous polarization.
Over the following years, the negative-pressure picture gradually emerged. The transformation from the PX phase to the perovskite phase is initiated by catalytic oxygen—O atoms absorbed from the environment and released when the transformation is complete—so it must begin at the wire’s surface. As the structural change works its way inward, the outer layer forms a rigid high-density shell around the remaining PX-phase nanowire. That shell encloses a volume 13% greater than the perovskite nanowire would normally fill.
Some of that excess volume is taken up by nanopores; the rest produces tensile stress of up to a few gigapascals. As the cross-sectional images in figure 2a show, the size and number of the pores depend on the wire’s diameter; as the numerical simulations in figure 2b show, so does the magnitude of the negative pressure at the wire’s center. For diameters greater than 500 nm, the tension becomes too strong for the material to accommodate and the wires crack.
Figure 2. Lead titanate nanowires with diameters of 50 nm, 100 nm, and 150 nm. (a) Experimental cross-sectional images show the spherical nanopores that take up some of the volume difference between the PX phase and the perovskite phase. (b) Numerical simulations show that as the wire diameter increases, so does the magnitude of the negative pressure at the wire’s center. (Adapted from ref. 1.)
Figure 2. Lead titanate nanowires with diameters of 50 nm, 100 nm, and 150 nm. (a) Experimental cross-sectional images show the spherical nanopores that take up some of the volume difference between the PX phase and the perovskite phase. (b) Numerical simulations show that as the wire diameter increases, so does the magnitude of the negative pressure at the wire’s center. (Adapted from ref. 1.)
The enhanced ferroelectric properties are consistent with a 2003 theoretical prediction.2 Spontaneous polarization arises when a ferroelectric’s metal ions break the lattice’s inversion symmetry by moving away from the centers of the O-ion cages that contain them. Stretching the material enlarges the cages and gives the ions more room to move. “In the theory community we’ve often joked about improving properties using negative pressure,” says Nicola Spaldin of ETH Zürich. “It’s easy for us to do on the computer, but we never imagined such a clever trick for achieving it in reality.”
The trick is not limited to PbTiO3. Setter, Wang, and colleagues have already found that it works for some other materials in the PZT family and are working to extend it to other ferroelectrics. Perovskite materials—anything with the chemical formula ABX3 and the ground-state crystal structure shown in figure 1b—are numerous and abundant, their applications are diverse, and many have low-density metastable phases similar to the PX structure. Setter speculates that many nonperovskite materials could also be made to undergo density-increasing transformations that start at the surface and proceed inward—and that extending the negative-pressure technique to different materials could enhance useful properties in ways theorists haven’t yet explored.
Indeed, a similar method is already widely used to make tempered glass. Rapidly cooling a piece of hot glass causes it to contract to produce a material whose surface is under compression and whose core is under tension. Those stresses are responsible for tempered glass’s advantageous mechanical properties, including fracture toughness and shattering behavior.
Although Setter, Wang, and company’s individual PbTiO3 nanowires are tiny, the total quantity of material can readily be upscaled. The PX-phase wires are easy to make, and the conversion to perovskite is as simple as heating the wires in air. “I foresee bulk applications” for negative-pressure nanomaterials, says Setter, “in powder form, as paints, or as composites.”
