For more than a century, scientists have relied on classical nucleation theory to explain how matter begins to change phase. Whether water droplets condense from vapor, liquid freezes into ice, or a metal solidifies into a crystal, the theory describes the first ordered clusters—known as nuclei—that emerge inside otherwise disordered material. Its central idea is deceptively simple: a nucleus must grow beyond a critical size before it becomes stable, and the atoms inside it are expected to form a relatively uniform crystal surrounded by a sharp boundary separating order from disorder. Thousands of experiments have supported the theory’s central equation. But a new study led by researchers at UCLA suggests that this long-standing picture may be incomplete. Instead of forming as sharply defined miniature crystals, nuclei appear to develop through a gradual atomic-scale transition, with order increasing continuously toward their centers.
The research, published in Nature Materials, examined crystal formation in nanoparticles made from high- and medium-entropy alloys. These materials contain several metallic elements in roughly comparable proportions, unlike conventional alloys such as steel, which are dominated by one principal element. Their chemically complex and highly disordered atomic environments make them challenging systems for studying how crystals emerge. They also offer an unusually revealing setting because the atoms do not begin in a simple, uniform arrangement. By observing thousands of nuclei at different stages of development, the researchers were able to test whether the classical model’s assumption of a uniform crystal core and abrupt interface accurately reflects what happens in real materials.
The team developed a strategy for effectively freezing the nucleation process in place. The nanoparticles were heated to temperatures above 3,000 degrees Fahrenheit and then supercooled, dropping from extreme heat to room temperature within a few hundredths of a second. During this rapid thermal journey, crystal nuclei began to form, but the sudden cooling arrested them at different stages of growth. This created a collection of atomic snapshots representing early, intermediate and more advanced nuclei. Because the actual nucleation event occurs far faster than conventional data acquisition, directly watching a single nucleus form is extraordinarily difficult. By stopping many particles at different moments, however, the researchers transformed a fleeting process into a large statistical dataset.
They then used atomic electron tomography, an advanced three-dimensional imaging technique capable of mapping the positions of individual atoms within a nanoparticle. The method allowed the researchers to reconstruct each particle atom by atom and calculate how strongly ordered different regions were. In total, the study analyzed more than 8,000 nuclei, ranging from clusters containing fewer than 10 atoms to structures containing more than 1,000. Rather than finding a consistent crystalline region with a clean outer surface, the researchers observed a striking gradient. The innermost portion of each nucleus displayed the highest degree of crystallinity, while atomic order gradually declined with distance from the center. The transition into the surrounding disordered material was diffuse rather than sharply defined.
“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 at UCLA and a member of the California NanoSystems Institute. “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 observation challenges one of the most familiar visual images in materials science: a small, perfectly formed crystal embryo surrounded by atoms that have not yet joined it. In the new picture, the nucleus is more like a continuously evolving landscape, in which the distinction between crystal and non-crystal becomes progressively less certain as one moves outward.
To describe this behavior, the researchers introduced what they call the gradient nucleation pathways model. The model extends classical nucleation theory by allowing the degree of atomic order to vary throughout a nucleus. Classical theory remains within the new framework as a special limiting case: if the gradient is replaced by a perfectly uniform crystalline interior and a sharp interface, the classical results are recovered. Yet the experiments indicate that this idealized condition may rarely occur in the systems examined. The revised model therefore treats nucleation not as the sudden appearance of a finished miniature crystal, but as a multistep pathway through intermediate structures whose atomic order changes gradually.
This distinction also alters the way scientists think about the energy barrier involved in nucleation. In classical theory, forming a stable nucleus requires a system to overcome a sharply defined energetic obstacle. Small clusters are energetically unfavorable because creating an interface between ordered and disordered matter costs energy; only clusters that surpass a critical size can continue growing. The UCLA-led analysis suggests that the transition may instead involve a series of intermediate states. Miao compared the conventional energy barrier to a wall that must be climbed, while the gradient pathway resembles a ladder that allows matter to move upward through multiple smaller steps. If the system can pass through partially ordered configurations, nuclei may overcome the overall barrier more efficiently than the classical picture predicts.
The study also uncovered an unexpected pattern in how nuclei grow and eventually combine. As nuclei increased in size, their central regions became more highly ordered, indicating that crystallinity strengthens from the inside outward rather than appearing all at once. When separate nuclei approached one another, many were already oriented in nearly the same direction, even before they merged. Crystal orientation describes the alignment of atomic planes and axes, and matching orientations can make the final coalescence energetically easier. The observation suggests that neighboring nuclei may interact over short distances or follow correlated low-energy pathways during formation. Instead of growing independently and colliding randomly, they may become partially coordinated before joining into a larger crystal.
The implications extend well beyond the particular alloys used in the experiments. Nucleation is a universal step in processes ranging from cloud formation and ice growth to pharmaceutical crystallization, food production, semiconductor fabrication and the manufacture of structural metals. A more realistic description of how nuclei form could help scientists control when and where materials crystallize, as well as the size, orientation and properties of the resulting crystals. High- and medium-entropy alloys are especially attractive for engineering because their unusual compositions can produce combinations of strength, flexibility, thermal stability and catalytic activity. Understanding their earliest structural transformations could guide the design of more durable components, more efficient catalysts and advanced materials for demanding environments.
The researchers emphasize that their model is intended to apply broadly to nucleation systems, not only complex metallic nanoparticles. If gradients in order are common, they could influence models of freezing, condensation, precipitation and phase separation across physics, chemistry, Earth science and engineering. The ability to map atomic structures in three dimensions also opens a new experimental route for testing theories that previously relied heavily on indirect measurements. Classical nucleation theory is not discarded by the findings; rather, it is placed within a more general framework that recognizes the complexity of real atomic arrangements. “We believe this work will change how researchers think about nucleation,” Miao said, expressing hope that textbooks will eventually be revised. By revealing that crystals may begin not as sharply bounded objects but as smoothly evolving patterns of order, the study offers a fresh view of one of nature’s most fundamental transformations.
Subject of Research: Crystal nucleation and growth in high- and medium-entropy alloy nanoparticles; atomic-scale mechanisms of phase transitions.
Article Title: Crystal nucleation and growth in high-entropy alloys revealed by atomic electron tomography
News Publication Date: 25-Aug-2026
Web References: https://www.nature.com/articles/s41563-026-02727-y
References: Nature Materials; UCLA; California NanoSystems Institute; U.S. Department of Energy, Office of Science, Basic Energy Sciences program.
Image Credits: Miao Lab/UCLA
Keywords
Crystal nucleation, phase transitions, atomic electron tomography, high-entropy alloys, medium-entropy alloys, crystallography, materials science, nanotechnology, solid-state physics, UCLA, crystal growth, nucleation theory
