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Update the textbooks: New research revises theory of how crystals form in everything from ice to metals

The most common scientific approach for thinking about how condensation, freezing, and other phase transitions begin is based in classical nucleation theory, which was developed about a century ago. Thousands of experiments have supported a key equation describing how initial ordered seeds, called nuclei, form within disordered matter.

Now, new UCLA-led research proposes a revision to classical nucleation theory.

The study, published in Nature Materials, used tiny spheres, or nanoparticles, made of complex materials with varying degrees of atomic order. The investigators devised a method for trapping crystal nuclei at various stages of development during a phase transition.

When the team examined the nanoparticles using an imaging method that maps individual atoms in 3D, what they saw differed from current explanations of the nucleation process.

"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."

The researchers introduced a more complex equation, which they call the gradient nucleation pathways model. It generalizes classical nucleation theory in line with the results of their rigorous experiments.

"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."

The findings represent a new understanding of a fundamental process of nature, and because nucleation is seen in so many different systems -- from droplets forming in clouds to industrial manufacturing -- the study could inform further discoveries and new technologies with broad societal impact.

Pausing crystal formation in search of new insights
The nanoparticles were made of high- and medium-entropy alloys, combinations of metallic elements in roughly equal proportions. In contrast, more familiar alloys such as steel are dominated by one principal element.

The researchers heated the nanoparticles then supercooled them, going from over 3,000 degrees Fahrenheit to room temperature within a few hundredths of a second. This process caused crystal nuclei to form but suspended them at various points in development.

"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."

Using a 3D imaging technique called atomic electron tomography, the team mapped the structure of each nanoparticle atom by atom. They conducted advanced statistical analyses to quantify how ordered or disordered various sections of the nanoparticles were. In all, the study examined a robust dataset of more than 8,000 nuclei, ranging in size from under 10 atoms to more than 1,000.

A new vista on the basics of phase transitions
In addition to the gradient from more order in the nuclei's cores to less at their surfaces, the results showed that as nuclei got larger, their cores grew more orderly in structure.

The findings provide a new view on the amount of energy needed for nuclei to form. In classical nucleation theory, the minimum amount required -- known as the energy barrier -- is as sharply drawn as the theory's conception of uniform nuclei. The complexity detailed in the researchers' extensive experimental data led to more of a sliding scale involving multiple steps.

"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."

For a full-on phase transition to occur, nuclei need to merge. The researchers observed something curious about that process: Even when separated by a small distance, the majority of crystals grew in the exact same orientation, making it easier for them to merge.

"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."

Potential impact on science, engineering, and society
High- and medium-entropy alloys, such as the ones used in the study, were first introduced about 20 years ago. Their disordered structure provides special properties, such that these alloys could make up materials that are uniquely strong and flexible, as well as more efficient and durable catalysts to drive 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."

The ubiquity of nucleation means that this research could foster innovation in scientific areas from physical science to climate modeling, and in industries from food and drugs to semiconductors and electronics. The new technique for studying nucleation with advanced imaging also may lead to further advances in understanding the process.

For Miao, there's great satisfaction in simply increasing the store of human knowledge.

"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."

Source: UCLA

Published September 2026

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