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Morphology and Dynamics of Self-interstitial Clusters in Irradiated Nickel

This study combines molecular dynamics simulations and high-speed in situ transmission electron microscopy to reveal that while self-interstitial clusters in irradiated nickel thermodynamically favor mobile perfect loops over sessile Frank loops for sizes N ≥ 14, their actual migration is governed by a non-rigid relay mechanism and hindered by kinetic barriers that create a heterogeneous energy landscape of mobile and pinned states.

Original authors: Ajay Annamareddy, Ibrahim Momohjimoh, Hangyu Li, Kevin G. Field, Paul M. Voyles, Dane Morgan

Published 2026-09-03

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CC BY 4.0

Original authors: Ajay Annamareddy, Ibrahim Momohjimoh, Hangyu Li, Kevin G. Field, Paul M. Voyles, Dane Morgan

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Inside the heart of a nuclear reactor, materials are constantly bombarded by high-energy particles. This invisible rain of radiation does not simply heat the metal; it physically knocks atoms out of their orderly places within the crystal structure. When an atom is knocked loose, it leaves behind a vacancy and becomes a wandering intruder, known as a self-interstitial atom. In the face-centered cubic metals used for critical reactor components, like nickel and certain steels, these intruders do not stay alone for long. They quickly gather into small clusters. How these clusters move, change shape, and interact with one another determines whether the reactor material will remain strong or eventually become brittle and fail. Understanding this microscopic traffic is essential for predicting the long-term safety and lifespan of nuclear energy systems.

A team of researchers has now peeled back the layers of this complex behavior by combining powerful computer simulations with a unique type of high-speed camera. They focused on nickel, a metal that serves as a model for many important nuclear alloys. Using molecular dynamics, a method that tracks the motion of every single atom in a virtual crystal, they watched how these clusters of extra atoms formed and evolved. They found that when these clusters first appear, they are messy and disordered. Over time, they settle into one of two distinct shapes. One shape is a stationary, faulted ring that gets stuck in place. The other is a perfect, smooth ring that can glide effortlessly through the metal. The researchers discovered that while the stationary rings can form easily, the smooth, moving rings are actually the more stable, lower-energy state for clusters of a certain size. However, the stationary rings often get stuck in a temporary state, unable to transform into the smoother shape because the energy required to make that switch is too high. This explains why both types of rings are seen in real materials, even though nature prefers the moving kind.

The study also revealed exactly how these moving rings travel. For a long time, scientists assumed that if a cluster of atoms moved, the entire group would slide forward together like a solid block. The new simulations show this is not the case. Instead, the cluster moves through a relay mechanism. Imagine a line of people passing a bucket down a line; only a few people move at any given moment to pass the load, while the rest stay put. In the metal, only a specific subset of the atoms in the ring shifts position at a time, passing the motion along the line. As the ring gets larger, more atoms are needed to participate in this relay, which makes the whole structure move slightly slower, even though the energy barrier to start moving remains incredibly low.

To test these computer predictions against reality, the researchers turned to a high-speed transmission electron microscope. This instrument acts like a movie camera for atoms, capable of capturing over a thousand frames per second. They examined thin slices of nickel that had been damaged by ion beams, creating the very defects they wanted to study. What they saw was a stark contrast to the smooth, continuous motion predicted by the simulations. In the real metal, the rings did not glide freely. Instead, they moved in a jerky, stop-and-go fashion. They would zip forward for a fraction of a second and then get pinned down, held in place by impurities or other defects in the material. When they finally broke free, they moved at speeds thousands of times faster than previously observed in older experiments, yet still far slower than the ideal speed predicted by the computer models.

The researchers calculated that the intrinsic speed of these rings in a perfect, defect-free crystal is about a billion times faster than what they measured in the real, imperfect samples. This massive gap suggests that the movement of these defects is not limited by how fast the atoms can move, but by how often they get caught. The rings are constantly being trapped and released by the messy environment of the irradiated metal. While the computer models successfully described how the rings want to move in an ideal world, the real-world observations showed that the material's own imperfections act as a brake, slowing the damage process down significantly. This finding is crucial because it tells engineers that the long-term behavior of reactor materials is governed less by the speed of the defects themselves and more by the complex landscape of obstacles they must navigate. By understanding both the ideal mechanics and the real-world traps, scientists can build better models to predict how nuclear materials will hold up under decades of stress.

Technical Summary: Morphology and Dynamics of Self-interstitial Clusters in Irradiated Nickel

Problem Statement
Self-interstitial atom (SIA) clustering is a critical early stage in radiation damage evolution within face-centered cubic (FCC) metals, such as nickel-based alloys and austenitic steels used in nuclear reactors. These clusters govern defect transport, recombination, and long-term microstructural stability. While it is established that interstitial clusters can reorganize into glissile perfect (prismatic) loops or sessile Frank loops, several fundamental aspects of their behavior remain poorly constrained. Specifically, the structural evolution of glissile loops during relaxation, the physical origin of the pronounced size dependence of loop diffusivity despite seemingly size-independent migration barriers, and the atomic-scale mechanisms of loop translation are not fully understood. Furthermore, a significant gap exists in connecting the high intrinsic mobilities predicted by atomistic simulations with experimentally observed motion, largely due to a lack of quantitative measurements at sufficiently high temporal resolution (millisecond scales) to resolve rapid fluctuations between mobile and pinned states.

Methodology
This study employs a dual approach combining molecular dynamics (MD) simulations and high-speed in situ transmission electron microscopy (TEM).

Molecular Dynamics: Simulations were conducted using the LAMMPS code with an embedded-atom method (EAM) potential for Ni. Perfect FCC Ni supercells (up to ~88,000 atoms) were used to generate SIA clusters. The study utilized a "minimize-anneal-minimize" procedure to relax defect configurations. To overcome kinetic limitations in spontaneous loop formation for larger cluster sizes ( $N$ ), the authors developed a direct construction method based on recurring structural motifs identified in MD: inserting aligned dumbbells for perfect loops and inserting faulted {111} planes for Frank loops. These constructed structures were validated against MD-relaxed loops at smaller sizes. Diffusion coefficients were calculated via mean-squared displacement (MSD) of the cluster center of mass, and migration mechanisms were analyzed by tracking individual dumbbell displacements over short time intervals.
Experimental: High-speed in situ TEM (>1000 frames/s) was performed on 4N pure Ni lamellae prepared by focused ion beam (FIB). The FIB process introduced nanoscale black-dot defect clusters (identified as interstitial/vacancy clusters). Specimens were heated to 500 °C, and defect trajectories were manually tracked to analyze motion dynamics.

Key Contributions and Results

Structural Evolution and Stability:
- MD simulations reveal that SIA clusters initially form disordered dumbbell arrangements which evolve into either sessile Frank loops ( $b = 1/3\langle111\rangle$ ) or glissile perfect loops ( $b = 1/2\langle110\rangle$ ).
- Perfect loops undergo substantial structural relaxation, reorganizing from noncompact configurations into compact, ordered arrays of aligned dumbbells. For cluster sizes corresponding to perfect squares (e.g., $N=25, 49$ ), the lowest-energy states are nearly square arrays.
- Energetics: Direct construction and relaxation across a wide size range ( $N \ge 14$ ) demonstrate that perfect loops are thermodynamically favored over Frank loops, with the energy advantage increasing with cluster size due to the stacking fault penalty in Frank loops. However, substantial kinetic barriers (0.7–2 eV) prevent the transformation of Frank loops to perfect loops at lower temperatures, explaining their persistence as metastable defects. This suggests the coexistence of both loop types is driven by kinetic trapping rather than thermodynamic stability.
Migration Dynamics of Perfect Loops:
- Activation Energy: For compact perfect loops ( $N = 16–400$ ), the migration activation energy is extremely low (~0.02 eV) and nearly independent of cluster size.
- Prefactor Scaling: The diffusion coefficient decreases with increasing cluster size, driven primarily by a decrease in the diffusion prefactor ( $D_0$ ), which scales approximately as $N^{-0.87}$ .
- Relay Mechanism: Trajectory analysis reveals that loops do not migrate via rigid-body translation. Instead, they move via a "row-wise relay" mechanism where only a subset of aligned dumbbell rows advances during each activation step. The number of participating atoms ( $\langle N_{move} \rangle$ ) scales as $N^{0.82}$ . This increase in the effective moving mass reduces the attempt frequency, accounting for the observed decrease in the diffusion prefactor.
Experimental Observations vs. MD Predictions:
- High-speed TEM revealed intermittent loop motion characterized by alternating "mobile" and "pinned" segments. Mobile segments exhibited velocities up to ~4000 nm/s for small clusters, significantly higher than previous TEM reports but still orders of magnitude below MD predictions.
- Discrepancy: Three analytical models (random-walk, driving-force, and confined-diffusion) applied to experimental trajectories yielded effective diffusivities in the range of $10^{-18}$ to $10^{-14}$ m²/s. This is 5 to 9 orders of magnitude lower than the intrinsic diffusivity predicted by MD ( $\sim 10^{-9}$ m²/s) for a perfect loop in an ideal crystal.
- The authors attribute this massive reduction to the heterogeneous energy landscape of the irradiated microstructure, including pinning by other defects, impurity drag (specifically Ga from FIB preparation), and unresolved trapping events occurring on timescales shorter than the experimental resolution.

Significance
The paper establishes a physically grounded understanding of the structural evolution, thermodynamic stability, and migration mechanisms of ideal interstitial loops in FCC Ni. By clarifying that perfect loops are thermodynamically favored but kinetically trapped in Frank configurations, and by elucidating the relay-based migration mechanism that dictates size-dependent mobility, the study provides essential inputs for mesoscale models of radiation-induced microstructural evolution.

Crucially, the work highlights a profound disconnect between intrinsic atomistic mobilities and experimental observations in real materials. The authors conclude that while MD accurately captures the intrinsic kinetics of loops in a perfect crystal, the actual transport of defects in irradiated alloys is dominated by extrinsic factors such as pinning and impurity drag. These findings underscore the necessity of incorporating such heterogeneous effects into models to accurately interpret experimental data and predict long-term material performance in nuclear environments.

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