Parameter-free prediction of irradiation defect structures in tungsten at room temperature using stochastic cluster dynamics

TL;DR

The paper addresses predicting irradiation defect microstructures in tungsten by linking atomistic defect physics to macroscopic measurements through a parameter‑free mesoscale framework. It introduces stochastic cluster dynamics (SCD), a stochastic MFRT approach, incorporating cascade‑produced defects, 1D SIA diffusion, and universal cluster‑size distributions, with large‑volume sampling to capture the high‑energy tail. Validated against room‑temperature self‑ion irradiation XRDS data, the model shows excellent agreement for defect densities and cluster sizes, especially for larger clusters ($n>30$), across irradiation and annealing states. The results provide a parameter‑free predictive capability for irradiation microstructures in tungsten, informing design considerations for plasma‑facing materials.

Abstract

The foundations of irradiation damage theory were laid in the 1950s and 60s within the framework of chemical reaction kinetics. While helpful to analyze qualitative aspects of irradiation damage, the theory contained gaps that delayed its implementation and applicability as a predictive tool. The advent of computer simulations with atomistic resolution in the 80s and 90s revealed a series of mechanisms that have proved essential to understand key aspects of irradiation damage in crystalline solids. However, we still lack a comprehensive model that can connect atomic-level defect physics with experimental measurements of quantitative features of the irradiated microstructure. In this work we present a mesoscale model that draws from our improved understanding of irradiation damage processes collected over the last few decades, bridging knowledge gained from our most sophisticated atomistic simulations with defect kinetics taking place over time scales many orders of magnitude larger than atomic interaction times. Importantly, the model contains no adjustable parameters, and combines several essential pieces of irradiation damage physics, each playing an irreplaceable role in the context of the full model, but of limited utility if considered in isolation. Crucially, we carry out a set of experiments carefully designed to isolate the key irradiation damage variables and facilitate validation. Using tungsten as a model material, we find exceptionally good agreement between our numerical predictions and experimental measurements of defect densities and defect cluster sizes.

Figures (5)

• Figure 1: Generalized mean-field cluster dynamics PDE based on classical nucleation theory. The right-hand side of the equation is broken down into separate contributions representing fundamentally different physical processes. These include diffusion, insertion of damage species, thermal evaporation of monomers from clusters, defect absorption at system sinks, and second-order cluster reaction kinetics. Each term is defined by specific material coefficients. (diffusivities, dissolution probabilities, sink strengths, reaction constants, etc.). All these coefficients encode the physics of the process, the host material, and the microstructure. The expression for the reaction coefficient $K_{ij}$ in the red box labeled Materias Physics represents the specific case of mutually-reacting 3D-moving objects.
• Figure 2: Cumulative PKA energy distribution function as a function of ion penetration depth due to 10.8-MeV W ion irradiation in W. The dashed black line represents the depth at which the maximum damage is attained ($x$=600 nm). The dashed red line indicates the depth damage profile at the point of saturation, which is seen to roughly follow a Bragg profile. The average PKA energy, obtained by integration of the two-dimensional surface in the entire $x$-$E$ space is 0.8 keV.
• Figure 3: Cluster size distributions for W from high-energy displacement cascade simulations by Byggmastar et al. byggmastar2025four. \ref{['vac-dist']} Vacancy clusters. \ref{['sia-dist']} SIA clusters. Inverse power law exponents are shown next to dashed segments, indicating the numerical scaling expected for cluster sizes above $n>4$. The correlations extracted from the work of Sand et al. sand2013high are shown as black dashed lines for comparison.
• Figure 4: Simulated cluster size distributions at end of irradiation (0.008 dpa) and after annealing for 24 hours at room temperature. \ref{['sia-scatter']} SIA clusters. \ref{['vac-scatter']} Vacancy clusters. The shaded region represents the range of visible clusters by conventional TEM. For loops, this limit ($n=30$) is obtained by setting the diameter of a circular disc to a minimum diameter of 1.5 nm.
• Figure 5: Evolution with time of the concentrations of \ref{['sia-concentration']} SIA ($I_n$) and \ref{['vac-concentration']} vacancy ($V_n$) clusters. Each plot tracks the evolution of single SIA and monovacancies (blue curves), clusters with more than two defects (red), and clusters beyond the TEM resolution limit (dashed green) for loops with lenticular shape ($n>30$) and voids with spherical shape ($n>110$). The TEM visible SIA cluster concentrations measured by Reza et al. using 20-MeV W ions at room temperature are shown in pane \ref{['sia-concentration']} for comparison reza2020thermal.