A team of researchers has observed early-stage crystal nucleation in four dimensions (4D)—space (3D) plus time. Led by Jianwei (John) Miao, a professor at the University of California, Los Angeles (UCLA) and deputy director of the STROBE NSF Science and Technology Center based in Boulder, Colo., the team reports in a recent issue of Nature that their observations contradict classical nucleation theory and highlight the need for a more comprehensive atomic-scale nucleation model. The work also suggests that the imaging technique utilized, 4D atomic electron tomography (AET), could offer insights into fundamental questions related to phase transitions, defect dynamics, and other atomic-level materials processes.

“Nucleation is a ubiquitous phenomenon in many physical, chemical, and biological processes. However, early stage nucleation is an extremely challenging process to study,” says Miao. The main difficulties are identifying nucleation sites early and tracking their individual development as the whole system undergoes a phase transition.

To overcome these challenges, Miao led an interdisciplinary team of researchers from UCLA, Lawrence Berkeley National Laboratory, University at Buffalo, University of Colorado at Boulder, and the University of Nevada–Reno. The team studied nucleation in iron–platinum (FePt) nanoparticles, an alloy commonly used in phase transition experiments. As synthesized, the nanoparticles have a chemically disordered face-centered cubic (fcc) structure, but annealing causes a solid–solid transition to one of two ordered phases.

To observe nucleation, the researchers synthesized FePt nanoparticles around 5 nm in diameter and deposited them onto silicon nitride membranes. The nanoparticles were annealed in vacuum for 9 minutes and then imaged with a scanning transmission electron microscope (STEM) at multiple orientations. The same nanoparticles were annealed for another 7 minutes, imaged again, annealed for 10 more minutes, and imaged a final time. From the series of STEM images corresponding to each accumulated annealing time, the team reconstructed 3D atomic models of the nanoparticles for analysis.

The researchers identified nucleation sites on the reconstructed models of the nanoparticles annealed for 9 minutes. For each possible lattice structure, they calculated the short-range bond order parameters—a measure of the order in an emerging crystal structure. Then they iterated through atomic sites, identifying the locations of the highest order parameter atoms and classifying them by phase.

Next, the researchers tracked the nuclei of the most common and technologically useful phase, an ordered face-centered tetragonal structure, across the other annealing times to observe their behavior. The fact that the team could precisely track individual atoms over repeat imaging is remarkable, according to Margaret Murnane, the director of STROBE. “[This] is much needed as we try to make more and more precise structures,” she says.

The work yielded three experimental observations inconsistent with classical nucleation theory, which were further supported by molecular dynamics simulations of nucleation in liquid–solid phase transitions of Pt. First, the early-stage nuclei were irregularly shaped, not spherical as classical theory predicts. Second, with time, nuclei fluctuated in size, dissolved, merged, and divided even at sizes where classical theory predicts steady growth. And finally, no clear boundary separated the parent phase from the nuclei. Instead, order gradually diffused outward from the core of a nucleation site. Given the agreement of experimental observations and simulations, Miao concludes that “a theory beyond classical nucleation theory is needed to describe early-stage nucleation at the atomic scale.” 

Ilke Arslan leads the Electron and X-ray Microscopy Group at Argonne National Laboratory. “This meticulous work by Miao and his colleagues shows the scientific value of a very detailed set of analyses to understand the progression of particle growth with atomic resolution in three dimensions,” she says. “It brings us further toward the goal of 3D, atomic resolution, and (close to) in situ imaging, that will have implications for understanding a broad range of materials systems in ways we have never been able to before,” she adds.

Read the abstract in Nature.