Tunable chemical complexity to control atomic diffusion in alloys

The development of radiation-tolerant alloys is a significant challenge in materials science. Medium- and high-entropy alloys (HEAs), which are nearly equiatomic single-phase concentrated solid solution alloys (SP-CSAs), offer potential due to their tunable chemical complexity and lack of microstructural inhomogeneities. While HEAs exhibit promising properties like high fracture resistance, strength, and corrosion resistance, a comprehensive understanding of the relationship between their chemical complexity and diffusion behavior remains elusive. Previous research has investigated various factors influencing alloy properties, including mixing enthalpy, defect energetics, lattice distortions, stresses, and electronic and magnetic states. However, a clear predictive model connecting these properties to diffusion and radiation tolerance has been lacking. Recent progress has been made in understanding vacancy-based sluggish diffusion in CSAs, revealing its dependence on site percolation and composition-dependent vacancy migration energies. This study aims to develop a model incorporating the effect of chemical complexity on atomic transport and defect diffusion, specifically focusing on interstitial atom (IA) diffusion, a critical factor in radiation effects. The researchers propose a quantifiable measure of chemical complexity and use μs-scale molecular dynamics (MD) simulations to explore IA diffusion in Ni-Fe alloys, complemented by a mean field model and kinetic Monte Carlo (KMC) simulations. The goal is to establish a direct link between the distribution of local defect energies and the transport properties of concentrated alloys.

The literature review discusses existing research on high-entropy alloys (HEAs) and their properties. It highlights the challenges in understanding the relationship between chemical complexity and diffusion behavior in these alloys. Previous studies have investigated various factors influencing HEA properties, including mixing enthalpy, defect energetics, lattice distortions, and electronic and magnetic states. However, a clear predictive model linking these factors to diffusion and radiation tolerance has not yet emerged. The review specifically addresses the debate surrounding vacancy-based sluggish diffusion in HEAs, noting that it's not solely attributable to configurational entropy but also involves site percolation and composition-dependent vacancy migration energies. The authors cite studies supporting and opposing the concept of sluggish diffusion, laying the groundwork for their own investigation into interstitial atom diffusion and its connection to chemical complexity.

The research employed a multi-pronged approach combining microsecond-scale molecular dynamics (MD), a mean-field theoretical model, and kinetic Monte Carlo (KMC) simulations. The MD simulations, using empirical potentials consistent with density functional theory (DFT) calculations, investigated thermally activated IA diffusion in a range of Ni-Fe alloys with varying Fe concentrations (CFe = 0.025 to 0.975) and temperatures (500-1100 K). The simulations tracked interstitial atom trajectories over exceptionally long timescales (~106 jumps, ~5 μs), providing detailed data on diffusion coefficients, activation energies, and the chemical composition of migrating <100> interstitial dumbbells. Trajectory analysis techniques (TJD and TTD) were used to account for correlations in defect jumps. The mean-field model incorporates the effect of migrating defect energy properties on diffusion percolation, considering two ground states (Ni-Ni and Fe-Fe dumbbells) and the transitions between them. The model uses migration energies, formation energies, and Boltzmann factors to predict the diffusion coefficient. The KMC simulations provided a more detailed representation of IA migration, defining transition states 'on-the-fly' based on the local energies of different interstitial configurations. This model considers eight possible transition states resulting from the different combinations of Ni and Fe atoms in the <100> dumbbell. The formation energies of these dumbbells were calculated using static modeling over 700 different random distributions of atoms for each composition. A key parameter, α, was introduced to control the contribution of local energy differences to transition state energy, allowing the study of the effect of chemical complexity. By comparing results from MD, mean-field, and KMC models, the researchers aimed to identify the dominant factors governing IA diffusion in Ni-Fe alloys.

Molecular dynamics simulations revealed a non-monotonic composition dependence of the tracer diffusion coefficient in Ni-Fe alloys, with a minimum at CFe ≈ 0.50–0.65. This minimum corresponds to significantly slower diffusion compared to pure Ni and Fe, demonstrating the sluggish diffusion phenomenon. Analysis of partial diffusion coefficients and the chemical composition of migrating dumbbells indicated that percolation occurs near the minimum diffusion coefficient composition (pc ≈ 0.7 at 500 K). The mean-field model elucidated the underlying mechanism: the minimum in diffusion arises from the competition between faster Ni migration in Ni-rich alloys (due to higher Ni-Ni dumbbell stability) and faster Fe migration in Fe-rich alloys (due to lower migration energy). The KMC simulations, incorporating a tunable parameter α representing chemical complexity, confirmed the MD findings. Decreasing α, i.e., decreasing chemical complexity, reduced the sluggish diffusion and percolation effects, shifting the percolation threshold to lower Fe concentrations. At α = 0 (ideal solid solution), the diffusion coefficient became a linear function of composition. The researchers found that the distribution of local defect energies, rather than simple compositional factors, served as a key measure of chemical complexity, directly influencing atomic transport.

The findings challenge conventional models of diffusion in alloys, which often overlook the role of local energy variations. The study reveals that the interplay between the stability of different dumbbell configurations and migration energy differences drives the observed sluggish and chemically-biased diffusion. The distribution of local defect energies emerges as a crucial factor determining the transport properties, thus providing a novel measure of chemical complexity that can be used to predict and control diffusion in concentrated alloys. This insight has important implications for designing radiation-tolerant alloys and understanding the behavior of other concentrated solid solution alloys. The non-monotonic dependence of the diffusion coefficient on alloy composition suggests that optimizing radiation tolerance may not simply be a matter of maximizing compositional disorder but requires careful consideration of local energy landscapes.

This study successfully established a direct link between local defect energies and the transport properties of concentrated alloys. The researchers demonstrated that the distribution of local defect energies is a key measure of quantifiable chemical complexity for atomic diffusion, explaining the observed sluggish and chemically-biased diffusion. The combined use of MD, mean-field, and KMC modeling provides a robust and predictive framework for understanding and controlling atomic transport in concentrated alloys, enabling the design of improved materials with tailored properties. Future research could explore the influence of local chemical order and the implications of these findings for other concentrated solid solution alloys and defect types.

The study primarily focuses on interstitial atom diffusion in Ni-Fe alloys, and the generalizability of the findings to other alloy systems requires further investigation. The computational cost of the μs-scale MD simulations limited the exploration of a wider range of compositions and temperatures. The simplified mean-field model omits some complexities of real alloy behavior, such as local chemical ordering effects, which could be incorporated into future studies. Finally, the KMC model utilizes averaged local energies, rather than explicitly modeling all possible configurations, representing a simplification of the complex atomic interactions.