Scientists Just Challenged a Century-Old Theory of How Crystals Form

3D atomic imaging of advanced materials provides new insights into transitions such as liquids freezing into solids.

For nearly a century, scientists have relied on classical nucleation theory to explain how phase transitions such as freezing and condensation get started. The theory describes how small, ordered regions called nuclei emerge within disordered matter, and a central equation behind that picture has been supported by thousands of experiments.

But when UCLA-led researchers examined crystal formation atom by atom in three dimensions, the nuclei did not look the way the classical model predicts.

Their study, published in Nature Materials, used nanoparticles made from complex alloys with different levels of atomic order. The researchers developed a way to freeze crystal nuclei at different stages of formation, allowing them to inspect a process that normally happens too quickly to capture directly.

The resulting 3D atomic maps revealed that the transition from ordered crystal to surrounding disordered material was gradual rather than abrupt.

“The crystals were not uniform with a sharp boundary from the disordered atoms around them, as predicted by classical nucleation theory,” said corresponding author Jianwei “John” Miao, a professor of physics and astronomy in the UCLA College and member of the California NanoSystems Institute at UCLA. “Instead, we saw a gradient. Every nucleus had a core of highest crystallinity and then became more disordered as you go from that core to the boundary.”

Crystal boundaries were not sharp

To account for what they observed, the researchers developed a more complex equation called the gradient nucleation pathways model. The new framework expands classical nucleation theory rather than discarding it.

“It seems that the classical theory is actually a special case,” Miao said. “If you substitute that case into our equation, then you get exactly the same results as classical nucleation theory. But experimentally, we never observed a sharp boundary. Instead, we observed this gradient at the atomic scale.”

Because nucleation underlies processes ranging from cloud droplet formation to industrial manufacturing, revising how it is understood could influence research across many fields and potentially inform new technologies.

Atomic maps captured nucleation in progress

The nanoparticles consisted of high- and medium-entropy alloys, which combine several metallic elements in roughly equal amounts. More conventional alloys, including steel, are instead dominated by a single main element.

To capture nucleation at different moments, the researchers first heated the nanoparticles and then supercooled them from more than 3,000 degrees Fahrenheit to room temperature within a few hundredths of a second. The rapid cooling initiated crystal formation while leaving nuclei suspended at different developmental stages.

“The data acquisition process takes much longer than nucleation does,” Miao said. “Trapping the crystals as they form allowed us to study nucleation at different stages.”

The researchers then used atomic electron tomography, a 3D imaging technique that maps individual atoms, to reconstruct each nanoparticle atom by atom. Advanced statistical analysis quantified how ordered or disordered different regions were.

Altogether, the dataset contained more than 8,000 nuclei, ranging from fewer than 10 atoms to more than 1,000.

Across the nuclei, the same pattern appeared repeatedly: atomic order was greatest in the core and gradually decreased toward the surface. The larger the nucleus became, the more ordered its central region also became.

Nucleation may proceed in smaller steps

Those gradients also changed how the researchers interpreted the energy required for a nucleus to form.

Classical nucleation theory describes a distinct minimum energy requirement, known as the energy barrier, that a nucleus must overcome. The experimental results instead suggested a more gradual process involving several intermediate stages rather than one sharply defined threshold.

“The energy barrier is like a wall that must be climbed, and in classical nucleation theory, only a small fraction of nuclei with enough energy can get over that wall,” Miao said. “However, our results show that nature adopts a more effective strategy, like using a ladder to climb over the wall through multiple intermediate states. Our gradient nucleation pathways model captures this process and explains how nuclei can overcome the energy barrier more efficiently.”

A complete phase transition also requires separate nuclei to join together. Here, the team found another unexpected pattern: most nearby crystals developed in exactly the same orientation even before they merged, making their eventual combination easier.

“I found it amazing that many nuclei were already nearly aligned before they merged,” Miao said. “This likely reflects a lower-energy pathway, but it also shows there’s always more to learn about how nature organizes matter.”

The model could guide material design

The high- and medium-entropy alloys used in the experiments were first introduced about two decades ago. Their highly mixed atomic structures can produce unusual combinations of properties, including strength and flexibility, and may also enable more-efficient and durable catalysts for chemical reactions.

“These are important materials, and understanding nucleation can help us find better ways to design them,” Miao said. “At the same time, our model can be broadly applied to all nucleation systems.”

Because nucleation occurs across so many natural and engineered systems, the findings could influence areas ranging from physical science and climate modeling to food, pharmaceuticals, semiconductors, and electronics. The atomic imaging approach itself may also give researchers a new way to investigate how nucleation unfolds.

For Miao, the broader significance lies in revising a basic understanding of how matter organizes itself during phase transitions.

“We believe this work will change how researchers think about nucleation,” he said. “I hope textbooks will eventually be revised to reflect this new understanding.”

Reference: “Crystal nucleation and growth in high-entropy alloys revealed by atomic electron tomography” by Yakun Yuan, Saman Moniri, Yao Yang, Jihan Zhou, Andrew Yuan, Dennis S. Kim, Yongsoo Yang, Chenyang Li, Kun Luo, Qi An, Wei Chen, Peter Ercius and Jianwei Miao, 25 August 2026, Nature Materials.
DOI: 10.1038/s41563-026-02727-y

The research was primarily supported by the Basic Energy Sciences program’s Materials Sciences and Engineering Division within the U.S. Department of Energy’s Office of Science.

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