🔬 materials science

A model of grain growth in UN integrating molecular dynamics, phase-field modeling, and uncertainty quantification

This study establishes the first quantitative grain growth framework for uranium mononitride (UN) by integrating molecular dynamics, phase-field modeling, and uncertainty quantification to determine that intrinsic grain boundary mobility is the dominant factor governing growth kinetics, while pore drag is negligible and grain boundary energy has minimal influence.

Original authors: Mohamed AbdulHameed, Fadel M. Nasr, Wen Jiang, Mahmoud Yaseen, Benjamin Beeler

Published 2026-09-11

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CC BY 4.0

Original authors: Mohamed AbdulHameed, Fadel M. Nasr, Wen Jiang, Mahmoud Yaseen, Benjamin Beeler

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, fuel does not remain static. Even as it burns, the tiny crystals that make up the fuel pellets are constantly shifting, merging, and growing larger. This process, known as grain growth, is a fundamental dance of atoms that dictates how long a fuel can last and how safely it can operate. For decades, scientists have understood this behavior well in common nuclear fuels like uranium dioxide, but a promising alternative called uranium mononitride has remained a mystery. This material, a hard ceramic made of uranium and nitrogen, offers superior heat conductivity and density, making it a top candidate for next-generation reactors. Yet, without knowing exactly how its internal crystals grow and interact, engineers cannot fully trust it to power a reactor for years. The missing piece of the puzzle was a clear map of how the boundaries between these crystals move and how the material's internal energy drives that motion.

A team of researchers has now built that map, creating a comprehensive digital model that connects the movement of individual atoms to the behavior of the entire fuel pellet. They did not rely on a single method but instead wove together three distinct approaches to simulate the life of the material. First, they used powerful computer simulations to watch how atoms arrange themselves at the boundaries between crystals at temperatures ranging from absolute zero up to 2000 degrees Celsius. This allowed them to calculate the energy stored in these boundaries, a key driver of growth. Next, they turned to a real-world experiment conducted years ago on a similar fuel, using a clever mathematical approach to strip away the effects of tiny pores and extract the true speed at which the crystal boundaries move. Finally, they combined these findings into a large-scale simulation that watched thousands of virtual grains grow over time, testing how sensitive the results were to small changes in the input data.

The results revealed a surprisingly simple story about what drives this growth. The researchers found that the energy stored in the boundaries between crystals is nearly constant at lower temperatures but begins to rise as the heat increases. More importantly, they discovered that tiny pockets of empty space, or pores, which often get in the way of moving boundaries in other materials, are essentially harmless in this specific fuel under the conditions they studied. By analyzing the only available experimental data on this material, they proved that these pores do not significantly slow down the growth process. This allowed them to calculate the intrinsic speed of the crystal boundaries, a number that had never been precisely known before. They determined that the boundaries move with a specific speed factor and an energy barrier that must be overcome for the movement to happen, providing the first quantitative rules for how uranium mononitride evolves over time.

To ensure these rules were robust, the team ran thousands of simulations, slightly varying the numbers they had calculated to see how much the final grain size would change. They found that the speed at which the boundaries move is the single most important factor. If the speed is slightly off, the predicted size of the crystals changes dramatically. The energy required to move the boundaries is the second most important factor, while the energy stored in the boundaries themselves has a very minor effect. This hierarchy tells future scientists exactly where to focus their efforts: to predict the life of this fuel with high confidence, they must measure the speed of the crystal boundaries more precisely. The study confirms that the material follows a predictable pattern of growth, where the distribution of grain sizes eventually settles into a stable, self-similar shape, regardless of how the fuel started.

This work provides the first complete framework for understanding how uranium mononitride ages under heat. By combining atomic-level calculations with large-scale simulations and rigorous testing of uncertainty, the researchers have turned a vague understanding of the material into a precise, predictive tool. They have shown that the material behaves in a straightforward, predictable manner, driven by the movement of its internal boundaries rather than being hindered by internal defects. While the study was conducted on a specific type of fuel and under specific conditions, the methods they developed can be applied to other advanced nuclear materials. The path forward is now clear: with the rules of the game finally written down, the next step is to refine the measurements of the most critical numbers, ensuring that when this fuel is used in the future, its performance can be trusted with absolute certainty.

Technical Summary: A Multiscale Framework for Grain Growth in Uranium Mononitride

Problem Statement
Uranium mononitride (UN) is a promising advanced nuclear fuel due to its high fissile density and thermal conductivity. However, its widespread adoption is hindered by a lack of fundamental understanding regarding its microstructural evolution, specifically grain growth kinetics. While grain growth in other actinide fuels like UO₂ and U₃Si₂ has been studied, the kinetics and mechanisms in UN remain unexplored. A critical gap exists in the quantitative parameters required for mesoscale simulations: specifically, the grain boundary (GB) energy as a function of temperature and misorientation, and the intrinsic GB mobility free from experimental artifacts such as pore drag. Furthermore, the sensitivity of grain growth predictions to uncertainties in these parameters has not been systematically quantified.

Methodology
The authors developed an integrated multiscale framework combining molecular dynamics (MD), phase-field modeling, and surrogate-assisted uncertainty quantification (UQ).

Molecular Dynamics (MD): To determine GB energies, the study utilized the Tseplyaev and Kocevski interatomic potentials within the LAMMPS software. The researchers constructed 27 symmetric tilt bicrystal models with misorientation angles between 0° and 90° around the [001] axis. For each boundary, a rigorous search for the minimum energy structure was performed using rigid-body translations and atom deletion iterations (the $\gamma$ -surface method). MD simulations were conducted from 0 K to 2000 K to evaluate temperature dependence.
Mobility Extraction: The study addressed the scarcity of UN-specific grain growth data by analyzing the only available dataset for actinide nitrides (Ronchi and Sari, 1983), which involved (U,Pu)N pellets. A mechanistic pore-drag model, incorporating partial pore-GB coupling, was applied to extract the intrinsic (drag-free) GB mobility from the experimental cubic growth kinetics ( $n=3$ ). This involved regressing the effective mobility against a model accounting for pore drag forces to determine if drag effects were significant.
Phase-Field Modeling: Isothermal grain growth simulations were performed using the MOOSE framework. The model employed the Allen-Cahn equation with non-conserved order parameters to represent grains. Simulations were conducted in 2D domains (2500 nm) over temperatures of 1500–2000 K, utilizing the GB energies from MD and the extracted mobility parameters.
Uncertainty Quantification and Sensitivity Analysis: A surrogate-assisted approach was employed to analyze the impact of input uncertainties (GB mobility prefactor $M_0$ $M_{0}$ , activation energy $Q_M$ $Q_{M}$ , and GB energy $\gamma$ $γ$ ) on the output (average grain size). This involved:
- Generating 330 parameter samples via Latin Hypercube Sampling.
- Reducing the dimensionality of the time-dependent grain size outputs using Principal Component Analysis (PCA).
- Training Gaussian Process (GP) regression models on the principal components.
- Computing time-resolved Sobol sensitivity indices to quantify the contribution of each parameter to the output variance.

Key Results

Grain Boundary Energy: The Tseplyaev potential yielded GB energies consistent with Density Functional Theory (DFT) values, whereas the Kocevski potential systematically underestimated energies due to anomalous U-U repulsion preventing GB closure. The average GB energy is nearly temperature-independent below 1000 K but increases at higher temperatures. A polynomial correlation was established: $\gamma(T) = 1.382 + 3.279 \times 10^{-6} T + 5.748 \times 10^{-18} T^5$ (J/m²), with a standard deviation of approximately 30% across the 27 boundaries.
Grain Boundary Mobility: The mechanistic pore-drag analysis revealed that pore drag is negligible under the experimental conditions of the reference dataset, with mobility reduction factors $s \approx 0.93–0.99$ . Consequently, the effective mobility derived from the experimental data was adopted as the intrinsic mobility. The resulting Arrhenius parameters are $M_0 = 2.05 \times 10^{-15}$ m⁴/(J·s) and $Q_M = 0.89$ eV.
Phase-Field Simulations: Simulations confirmed normal curvature-driven grain growth, characterized by a linear evolution of $(D^2 - D_0^2)$ with time. The grain size distributions converged to a Hillert-like form, independent of the initial microstructure. The coefficient of variation (CV) of grain sizes across different initial conditions saturated exponentially, with higher temperatures accelerating the approach to self-similarity but resulting in broader steady-state distributions.
Sensitivity Analysis: The global sensitivity analysis demonstrated a clear hierarchy of influence. The mobility prefactor $M_0$ dominates the output variance at all times (contributing ~~48% of first-order variance at $t=5000$ s), followed by the activation energy $Q_M$ (~~28%). The GB energy $\gamma$ contributes minimally (~7%). The analysis also revealed that while parameter interactions are significant at early times, they diminish as the system approaches the asymptotic parabolic growth regime.

Significance and Claims
The paper claims to establish the first quantitative grain growth framework for UN. Its primary contributions are:

Providing temperature-dependent GB energies for 27 symmetric tilt boundaries, validated against DFT.
Developing a rigorous procedure to extract drag-free GB mobility from limited experimental data by explicitly modeling and ruling out pore drag effects.
Delivering the first intrinsic GB mobility parameters ( $M_0$ and $Q_M$ ) for UN.
Identifying, through time-resolved sensitivity analysis, that reducing uncertainty in the mobility prefactor $M_0$ and activation energy $Q_M$ is the highest-priority target for future experimental efforts, as these parameters dominate predictive uncertainty.

The authors note that while the current mobility parameters are treated as order-of-magnitude estimates due to the use of (U,Pu)N data and approximations in surface diffusivity, the framework provides a transferable, physics-informed, and uncertainty-aware methodology applicable to fuel performance codes and extensible to other advanced nuclear fuel systems. The study explicitly states that the 2D nature of the simulations results in growth rates half those expected in 3D bulk pellets, but the qualitative behaviors and sensitivity rankings remain valid.

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