The interplay between vacancies ($V$) and interstitial solutes $X$ ($X=\text{C}$, N, and O) and its impact on thermodynamic properties of $\alpha \text{−}\mathrm{Fe}$ solid solutions are studied, starting from first principles calculations. A systematic comparison between the three solutes is performed, investigating $X–\mathrm{Fe}$, $X$–$X$, and $V$–$X$ interactions. In the $\alpha \text{−}\mathrm{Fe}$ lattice, the strength of $X–\mathrm{Fe}$ interactions is found to govern the dissolution properties. Next to vacancies, the competition between solute volume effects and $X–\mathrm{Fe}$ interactions results in the preference of all the solutes to occupy off-centered sites. Low-energy configurations of small $V_n{X}_m$ clusters are calculated for $n$ and $m$ up to 4. They are used to parametrize lattice interaction models at the atomic scale. A detailed analysis of the cluster properties suggests the relevance of many-body terms in these models. The accuracy of the resulting models is verified through their satisfactory prediction of vacancy-solute cluster properties beyond the fitting database. From these models, an entire set of $V_n{X}_m$ clusters is generated with a new configurational space exploration method. Statistical treatment of the solid solution including these clusters is then achieved by means of low-temperature expansions, checked against Monte Carlo simulations in some specific conditions. Based on the calculation of equilibrium cluster distributions, it is shown that the solubility limit of oxygen in Fe, hardly measurable experimentally, is largely affected by the presence of small $V_n{\mathrm{O}}_m$ clusters.

Combined density functional theory and empirical-potential calculations are performed to investigate the lowest-energy sites and migration mechanisms of He in various $$\alpha${}$-Fe grain boundaries (GBs). Before the defect calculations, we show that structural optimizations, including simulated annealing and atom removal, are crucial for locating the stable GB structure in a given temperature regime. Then, the He formation energies for all the substitutional and interstitial sites in two different GBs are evaluated, showing a strong He segregation tendency. At variance with the bulk Fe case, the formation energy of an interstitial He is either lower than or similar to that of a substitutional He in the GBs. Finally, both static and dynamic barriers for interstitial He diffusion in the GBs are determined. Although the diffusion details and precise paths are GB dependent, some common features are identified: (1) The He atom always remains confined to the GB region while diffusing; (2) the He diffusion is highly anisotropic along the GBs; (3) the GB diffusion of an interstitial He atom is found to be always slower than its bulk diffusion, but it can still be faster than the bulk diffusion of a substitutional He.

Based on a systematic first-principles study, the lowest-energy migration mechanisms and barriers for small vacancy-solute clusters $\left(V_n{X}_m\right)$ are determined in $\alpha$-Fe for carbon, nitrogen, and oxygen, which are the most frequent interstitial solutes in several transition metals. We show that the dominant clusters present at thermal equilibrium ($VX$ and $V{X}_2$) have very reduced mobility compared to isolated solutes, while clusters composed of a solute bound to a small vacancy cluster may be significantly more mobile. In particular, $V_{3}X$ is found to be the fastest cluster for all three solutes. This result relies on the large diffusivity of the most compact trivacancy in a bcc lattice. Therefore, it may also be expected for interstitial solutes in other bcc metals. In the case of iron, we find that $V_{3}X$ may be as fast as or even more mobile than an interstitial solute. At variance with common assumptions, the trapping of interstitial solutes by vacancies does not necessarily decrease the mobility of the solute. Additionally, cluster dynamics simulations are performed considering a simple iron system with supersaturation of vacancies, in order to investigate the impacts of small mobile vacancy-solute clusters on properties such as the transport of solute and the cluster size distributions.

Density functional theory (DFT) calculations have been performed to study the interaction of carbon with He-vacancy complexes in $\alpha \text{-Fe}$. Using the DFT predictions, a rate theory model that accounts for the evolution of carbon, helium, and defects created during irradiation has been developed to explore the influence of carbon on the kinetics of He diffusion and clustering after implantation in $\alpha \text{-Fe}$. This DFT-based rate theory model predicts that carbon not only influences vacancy $\left(V\right)$ migration but also He desorption, enhancing He mobility in particular for low $V/\text{C}$ ratios. The reason for this behavior is mainly the formation of $V\text{C}$ and $V{\text{C}}_2$ complexes, which significantly reduces the mobility of vacancies with respect to pure Fe, inhibiting the formation of higher order clusters, i.e., ${\text{He}}_n{V}_m$, and increasing thus the number of He at substitutional positions at room temperature. Assuming reasonable values of carbon concentration, we successfully reproduce and interpret existing desorption experimental results, where all the energetic parameters for the relevant reactions were obtained from first-principles calculations. In addition, our study provides a detailed explanation of the various He migration mechanisms that prevail under the considered experimental conditions.

An accurate prediction of atomic diffusion in Fe alloys is challenging due to thermal magnetic excitations and magnetic transitions. We propose an efficient approach to address these properties via a Monte Carlo simulation, using ab initio–based effective interaction models. The temperature evolution of self- and Cu diffusion coefficients in $\alpha$-iron are successfully predicted, particularly the diffusion acceleration around the Curie point, which requires a quantum treatment of spins. We point out a dominance of magnetic disorder over chemical effects on diffusion in the very dilute systems.

Body-centered cubic (bcc) Fe-Mn systems are known to exhibit a complex and atypical magnetic behavior from both experiments and 0 K electronic-structure calculations, which is due to the half-filled $3d$ band of Mn. We propose effective interaction models for these alloys, which contain both atomic-spin and chemical variables. They were parameterized on a set of key density functional theory (DFT) data, with the inclusion of noncollinear magnetic configurations being indispensable. Two distinct approaches, namely a knowledge-driven and a machine-learning approach have been employed for the fitting. Employing these models in atomic Monte Carlo simulations enables the prediction of magnetic and thermodynamic properties of the Fe-Mn alloys, and their coupling, as functions of temperature. This includes the decrease of Curie temperature with increasing Mn concentration, the temperature evolution of the mixing enthalpy, and its correlation with the alloy magnetization. Also, going beyond the defect-free systems, we determined the binding free energy between a vacancy and a Mn atom, which is a key parameter controlling the atomic transport in Fe-Mn alloys.