Spectral Sampling of Boron Diffusion in Ni Alloys: Cr and Mo Effects on Bulk and Grain Boundary Transport

Abstract

Understanding how light interstitials migrate in chemically complex alloys is essential for predicting defect dynamics and long-term stability. Here, we introduce a spectral sampling framework to quantify boron diffusion activation energies in Ni and demonstrate how substitutional solutes (Cr, Mo) reshape interstitial point defect transport in both the bulk and along crystallographic defects. In the bulk, boron migration energy distributions exhibit distinct modality tied to solute identity and spatial arrangement: both Cr and Mo raise barriers in symmetric cages but induce directional asymmetry in partially decorated environments. Extending this framework to a $\Sigma5\langle100\rangle{210}$ symmetric tilt grain boundary reveals solute-specific confinement effects. Cr preserves low-barrier in-plane mobility while suppressing out-of-plane transport, guiding boron into favorable midplane voids. Mo, by contrast, imposes an across-the-board reduction in boron mobility, suppressing average diffusivity by two additional orders of magnitude at 800 $^\circ$C and reducing out-of-plane transport by five orders of magnitude relative to Cr. Both elements promote segregation by producing negative segregation energies, but their roles diverge: Cr facilitates rapid redistribution and stabilization at interfacial sites, consistent with Cr-rich boride formation, while Mo creates deeper and more uniform segregation wells that strongly anchor boron. Together, these complementary behaviors explain the experimental prevalence of Cr- and Mo-rich borides at grain boundaries and carbide interfaces in Ni-based superalloys. More broadly, we establish spectral sampling as a transferable framework for interpreting diffusion in disordered alloys and for designing dopant strategies that control transport across complex interfaces.

Figures (8)

• Figure 1: Visualization of the simulation cell used for grain boundary (GB) diffusion analysis, rendered in OVITO stukowskiVisualizationAnalysisAtomistic2009a. (a) The pure Ni $\Sigma5\,\langle100\rangle\,\{210\}$ symmetric tilt GB cell (S5) containing 4,800 atoms. The out-of-plane dimension ($\hat{z}$) measures 17.62 Å. (b) Detailed view of the S5 interface structure with common neighbor analysis coloring. Predetermined interstitial voids are marked by the smaller atomic species. Green denotes "fcc" coordination, while white indicates "other."
• Figure 2: Schematic of the face-centered cubic octahedral cage with a boron atom positioned at the pristine octahedral interstitial site. In contrast to the conventional octahedral--tetrahedral--octahedral (O--T--O) diffusion pathway, boron migrates via one of twelve available exits leading to neighboring octahedral sites by passing near, but not through, the tetrahedral site. Instead, boron "squeezes" between two lattice atoms (through the edge of the tetrahedral cage) following what is commonly referred to as the direct interstitial pathway. Depending on the direction of migration, boron can either "glide" (remaining within the same (111) atomic plane) or "climb" (moving into an adjacent (111) plane above or below the original site).
• Figure 3: Schematics and corresponding minimum energy pathways for a boron bulk diffusion event. (a) illustrates the event in the pure Ni system ($n=0$ Cr), where the minimum energy pathway is symmetric ($E_{\mathrm{forward}} = E_{\mathrm{reverse}}$). (b) shows the geometric distortion and boron occupancy for the same event in the alloy at $n=3$ Cr, where the chemical decoration induces an asymmetric (or directionally biased) minimum energy pathway ($E_{\mathrm{forward}} \neq E_{\mathrm{reverse}}$).
• Figure 4: Activation energy spectra for boron diffusion via the direct interstitial pathway in bulk face-centered cubic Ni. The top panel shows the forward activation energy barriers as a function of Cr and Mo coordination in the octahedral cage, while the bottom panel presents the corresponding reverse barrier distribution. The colors correspond to the number of Cr or Mo neighbors in the final state octahedral cage.
• Figure 5: Displacement vector map of forward energy barriers for boron diffusion events at the $\Sigma5\,\langle100\rangle\,\{210\}$ (S5) grain boundary (GB), compiled from the same dataset used to generate the spectra in Fig. \ref{['fig:gb_spectra']}. The GB midplane is indicated by the dashed black line. From left to right, the panels show boron diffusion in pure Ni ($n=0$), with six Cr atoms decorating the gaining cage ($n=6$), and with six Mo atoms decorating the gaining cage ($n=6$). Directional markers are overlaid to aid interpretation: diamonds represent in-plane diffusion along the GB midplane, circles denote diffusion toward the midplane, and "x" markers indicate diffusion away from the midplane.