DFT and MLIP study of solute segregation to coherent and semi-coherent α-Fe/Fe$_3$C interfaces

TL;DR

Aiming to quantify how alloying solutes segregate to pearlite interfaces by merging DFT with uMLIPs to cover complex, multi-element environments. The authors benchmark seven uMLIPs against DFT and then study coherent and semi-coherent α-Fe/Fe3C interfaces, selecting GRACE-2L-OAM for the semi-coherent model. They find weak segregation at the coherent interface (Cu about $-0.3\,\text{eV}$) and deep traps near the misfit dislocation at the semi-coherent interface with $E_{seg}< -1.5\,\text{eV}$, leading to pronounced embrittlement in most solutes. The work demonstrates a robust workflow for extending ab initio insights to defect-rich, multiphase interfaces with implications for precipitation and dislocation dynamics in recycled steels.

Abstract

Solute segregation to interfaces significantly impacts material behavior. A large majority of theoretical works focus on grain boundaries and coherent interfaces. Studies on semi-coherent interfaces are usually prohibited by the structural complexity, yielding models beyond the practical capability of density functional theory (DFT), or chemical complexity, restricted by the availability of (classical) interatomic potentials. This work investigates solute segregation to the coherent and semi-coherent $α$-Fe/Fe$_3$C interface in pearlite and its effect on mechanical properties using novel universal machine learning interatomic potentials (uMLIPs). DFT calculated solution enthalpies, segregation energetics, and changes in cohesion at the coherent interface are used to benchmark several state-of-the-art uMLIPs. We find that the GRACE-2L-OAM and GRACE-2L-OMAT models most accurately reproduce the quantum-mechanical predictions. While Cu has the strongest segregation energy of $\approx$ -0.3 eV to the coherent interface among the investigated tramp and trace elements, all of them, As, Cr, Cu, Mo, Ni, P, Sb, and Sn, exhibit significantly more negative segregation values reaching below $\approx$ -1.5 eV in the presence of the misfit dislocation at the semi-coherent interface. The deepest traps are identified in the vicinity of the dislocation core, although the spatial distribution of segregation energies differs markedly among the solute species. The cohesion of the coherent interface is strongly reduced by Sb, Sn, P, and As, and only mildly by Cu, whereas Ni shows a negligible effect, and Cr and Mo slightly enhance cohesion. In contrast, all investigated solutes (except for P) tend to embrittle the semi-coherent interface, with Sn and, especially, Sb having the strongest impact in tensile tests performed in the out-of-plane direction. Abstract shortened for ArXiv.

Figures (7)

• Figure 1: Coherent $\alpha$-Fe/Fe3C interface structure with the Bagaryatsky OR. (a) Front view of the interface, including the bulk Fe3C unit cell (left) and the bulk $\alpha$-Fe unit cell (right). (b) Side view of the interface.
• Figure 2: Solution enthalpies, $\Delta H_\text{sol}$, in bcc $\alpha$-Fe and Fe3C. The three inequivalent substitutional sites in Fe3C are marked in the structural model. The partitioning energy, $E_\text{part}$, quantifies the thermodynamic preference of the solute for the ferrite or cementite phase and is indicated by the black arrow. The green background highlights situations of favorable dissolution.
• Figure 3: Impact of solute segregation on $\alpha$-Fe/Fe3C interface cohesion, $\eta$ (J/m$^2$). For clarity, results are shown only for scenarios with segregation tendency, i.e., $E_\text{seg}(X)\leq 0$ (or minimum $E_\text{seg}(X)$ in case of anti-segregating behavior of Cr and Mo). The explored sites are indicated in the structural model (right). The symbol style for each data point directly corresponds to the highlighted atom position in the displayed model: full symbols (without outline) are Fe sites on the ferrite side of the interface, while the open symbol corresponds to the C site in cementite.
• Figure 4: Comparison between VASP and uMLIP predictions. Solute solution enthalpies ($\Delta H_\text{sol}$) in (a) $\alpha$-Fe and (b) Fe3C. (c--f) Segregation energies ($E_\text{seg}$) at distinct interfacial sites, as highlighted in the structural models. (g) Cohesion change ($\eta$) corresponding to the $\min(E_\text{seg})$ site, evaluated for different cutting planes. (h) Overall model RMSE against the number of cases where the predicted solute trend (i.e., the sign of the quantity) deviates from DFT (e.g., VASP predicts a favorable solid solution or strengthening effect while uMLIP predicts the opposite). Performance metrics are shown for the best three models.
• Figure 5: Relaxed semi-coherent $\alpha$-Fe/Fe3C interface following the Bagaryatsky OR.