Researchers at the University of Chicago’s Pritzker School of Molecular Engineering and Delft University of Technology have developed a new method for watching ions move through solid materials, revealing that diffusion can be far more complex than the familiar picture of particles wandering randomly from regions of high concentration to low concentration. The technique, known as “tracer exchange,” allowed the team to distinguish several forms of ionic motion—including ordinary diffusion, accelerated transport and unusually slow movement—in lithium iron phosphate, a material widely used in rechargeable batteries and increasingly investigated for lithium extraction. The findings, published in Nature Communications, could reshape how scientists understand transport in batteries, electronic materials, catalysts and selective membranes.
Diffusion is one of the most familiar processes in science. Drop ink into water and its molecules gradually spread, driven by countless random collisions. This behavior is generally described by Fick’s laws of diffusion, a mathematical framework developed in the nineteenth century that connects particle movement with concentration gradients. In a liquid, molecules have room to move around one another, making the statistical behavior relatively straightforward. In a solid, however, atoms and ions must navigate a rigid crystal lattice, often through narrow pathways and energetically difficult sites. The lattice can also bend, expand, soften or react chemically as ions move, creating a dynamic environment that cannot always be represented by a simple diffusion coefficient.
“People sometimes would just take Brownian motion as the default movement for ions in solid, and sometimes it’s still true, but not necessarily true,” said Chong Liu, an associate professor at the University of Chicago’s Pritzker School of Molecular Engineering and one of the study’s corresponding authors. “In this paper, we discovered anomalous diffusion,” Liu said, referring to movement that departs from the standard Brownian model. “We actually saw both” subdiffusion, in which particles spread more slowly than expected, and superdiffusion, in which they spread more rapidly. These behaviors emerged as the researchers tracked how different ions exchanged positions inside lithium iron phosphate, or LFP, a cathode material used in many lithium-ion batteries.
The study was led by researchers at UChicago PME and TU Delft, with contributions from scientists at the Massachusetts Institute of Technology and the University of Illinois Urbana-Champaign. Its central innovation was to adapt the logic of isotope tracing—a method often used to follow atoms through chemical reactions, biological pathways and geological processes—to the study of ion transport in a solid. In a tracer exchange experiment, chemically distinguishable versions of ions are introduced or monitored as they move through the material. By measuring where the tracer ions appear over time, scientists can reconstruct how rapidly they travel, which pathways they use and whether their movement remains consistent throughout the process.
That information is difficult to obtain from conventional electrochemical measurements alone. When a battery electrode charges or discharges, several processes can occur simultaneously: ions may move across a surface, electrons may travel through the electrode, chemical reactions may alter the crystal and ions may diffuse into or out of the solid. A measurement of the overall current can show that transport is taking place, but it may not reveal which step is limiting the process. Tracer exchange offers a way to separate these contributions by following the ions themselves. The researchers used sodium and lithium as tracers while examining their movement through LFP, allowing them to identify multiple transport regimes that would otherwise appear to be a single averaged process.
The resulting picture was a nanoscale landscape filled with obstacles, shortcuts and changing rules. Some ions moved in a manner consistent with traditional Fickian diffusion, spreading through the solid with behavior that could be described by established models. Elsewhere, the geometry of the crystal confined ions to effectively one-dimensional channels. In such pathways, ions could be forced to move in single file, meaning that one ion’s progress depended strongly on the positions and movements of those ahead of it. This self-exclusion effect can slow transport and produce subdiffusion. At other locations, structural changes or chemical reactions appeared to open faster routes, producing superdiffusive behavior in which ions moved farther or more rapidly than a conventional random-walk model would predict.
“These assumptions break because the self-exclusion and the cross-channel hopping are different for highly confined materials,” said Gangbin Yan, a UChicago PME graduate and co-first author of the study. “You cannot describe this just using the traditional diffusion model.” In a conventional model, particles are often treated as if each step is independent and statistically similar to the one before it. In a crystal containing narrow channels and interacting ions, that assumption can fail. An ion may be blocked by another ion, pushed along by local rearrangements, or redirected when the lattice changes around it. The motion of one species can also influence the movement of another, creating coupled ion-ion and ion-electron transport rather than isolated diffusion.
The discovery matters because the performance of a battery depends not only on how much energy its materials can store, but also on how efficiently ions and electrons move during operation. If ions become trapped, forced into bottlenecks or slowed by structural changes, a battery may charge more slowly, deliver less power or suffer greater degradation. Conversely, identifying fast pathways could help engineers design particles and electrode architectures that reduce resistance. The same principles apply beyond batteries. In electrochemical lithium extraction, for example, researchers must distinguish the movement of lithium through a solid from surface reactions and electronic limitations. Understanding each contribution could improve systems designed to recover lithium from dilute sources such as brines or industrial water.
The implications extend to materials that transport hydrogen, remove pollutants or separate valuable chemicals. Membranes and catalysts often depend on ions entering, leaving or migrating through confined structures. Hydrogen moving through metals, reactants traveling through catalytic materials and charged species crossing selective membranes may all display transport behaviors that differ from simple Brownian motion. “The developed methodology could distinguish between surface ionic reactions, electronic limitations and solid diffusion,” said Pierfrancesco Ombrini, a co-first author and PhD candidate at TU Delft. Because tracer exchange can be adapted to different materials and chemical species, it may become a general platform for examining exchange processes across a broad range of solid-state systems.
The researchers describe their results as a foundation for future work rather than a final explanation of every transport process in solids. The next challenge is to determine precisely how crystal structure, ion concentration, temperature, particle size and electrochemical conditions control the transitions between subdiffusion, superdiffusion and normal diffusion. The team also hopes to use the method to guide the design of improved batteries and electrochemical extraction technologies. “This work demonstrates that something as apparently well-known and described as diffusion of ions is much more intricate and can transition between different modes,” said Marnix Wagemaker of TU Delft, the study’s other corresponding author. By making those hidden modes visible, tracer exchange could help turn the complicated inner life of solid materials into a measurable design tool.
Subject of Research: Coupled multi-ion and electron transport in solid materials, including anomalous ionic diffusion in lithium iron phosphate.
Article Title: Crossover dynamics of non-Fickian ionic diffusion in solids
News Publication Date: 30-May-2026
Web References:
https://pme.uchicago.edu/
https://www.tudelft.nl/en/
https://www.nature.com/articles/s41467-026-73937-w
References:
Yan et al., “Crossover dynamics of non-Fickian ionic diffusion in solids,” Nature Communications, 30 May 2026. DOI: 10.1038/s41467-026-73937-w
Image Credits: UChicago Pritzker School of Molecular Engineering / John Zich
Keywords
Ion diffusion, anomalous diffusion, lithium-ion batteries, lithium iron phosphate, tracer exchange, solid-state transport, ion exchange, electrochemical energy storage, lithium extraction, materials science, nanoconfinement, superdiffusion, subdiffusion
Tags: advanced materials for energy storagecomplex ion migration in solidsdiffusion in crystalline latticesimpact on battery efficiencyion transport analysis methodsion transport in solid materialsionic diffusion mechanismslithium iron phosphate battery materialsmolecular engineering of solid electrolytesnanoscale ion dynamicssolid-state ionic mobilitytracer exchange technique
