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

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.

💡 Research Summary

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This paper introduces a “spectral sampling” framework to quantify the full distribution of boron (B) interstitial diffusion barriers in nickel‑based alloys, focusing on the effects of substitutional Cr and Mo atoms both in the bulk and at a representative grain boundary (GB). Traditional diffusion studies often rely on a single average activation energy, which obscures the rich variability arising from local chemical environments in complex alloys. To overcome this limitation, the authors systematically vary the number (0–6) and arrangement of Cr or Mo atoms in the first‑nearest‑neighbor (1NN) octahedral cage surrounding a B interstitial. For each distinct local configuration they perform Nudged Elastic Band (NEB) calculations (six images, climbing‑image algorithm) using the universal neural‑network potential (PFP) validated against DFT.

In the bulk, the pristine Ni case (no solutes) exhibits a symmetric direct interstitial pathway with identical forward and reverse barriers. When Cr or Mo atoms occupy the cage, the octahedral site becomes distorted, leading to directionally biased (asymmetric) forward and reverse barriers. Cr tends to raise the barrier modestly while preserving low‑energy pathways in certain directions, whereas Mo produces a larger overall increase, especially when multiple Mo atoms are present. This asymmetry reflects a “chemical cushioning” effect: the interstitial experiences different forces depending on whether it moves into or out of a chemically decorated cage.

The study then extends the sampling to a Σ5⟨100⟩{210} symmetric tilt GB, a common low‑energy boundary in FCC metals. Because the GB lacks perfect periodicity, the authors employ a Voronoi‑based void‑finding algorithm to locate physically realistic interstitial sites within the GB region, then connect neighboring voids within 2.5 Å to construct a network of possible hops. NEB calculations are performed for each unique local coordination (including varying numbers of Cr or Mo atoms in the surrounding cage). The results reveal markedly different solute‑specific influences on GB transport. Cr preserves low‑energy in‑plane (within the (111) atomic plane) migration pathways while dramatically suppressing out‑of‑plane hops, effectively trapping B in the mid‑plane voids of the GB. This confinement explains the frequent observation of Cr‑rich borides (e.g., Cr₂B) at GBs, where B can rapidly redistribute and stabilize the interface. In contrast, Mo uniformly raises both in‑plane and out‑of‑plane barriers, reducing the overall GB diffusivity by roughly two orders of magnitude at 800 °C relative to Cr‑doped Ni, and by five orders of magnitude for out‑of‑plane transport. Consequently, Mo creates deep, uniform segregation wells that strongly anchor B, consistent with the formation of Mo‑rich borides (e.g., Mo₂B) that are thermodynamically stable and kinetically sluggish.

Segregation energies are computed as the difference between GB and bulk total energies for the same local solute coordination. Both Cr and Mo yield negative segregation energies, confirming that B preferentially partitions to the GB. However, the magnitude and distribution differ: Cr’s segregation wells are shallower and more heterogeneous, facilitating faster B migration along the GB, whereas Mo’s wells are deeper and more uniform, leading to strong B immobilization.

The authors argue that the spectral sampling approach is transferable to any interfacial geometry, including high‑angle random GBs, nanoparticle surfaces, or amorphous regions, because it relies only on systematic enumeration of local chemical environments and NEB barrier calculations. By providing a high‑resolution map of activation energies rather than a single average value, the method enables alloy designers to predict how specific dopants will reshape interstitial transport pathways, tailor segregation behavior, and ultimately control microstructural evolution (e.g., precipitation of borides, grain‑boundary strengthening, creep resistance).

In summary, the paper demonstrates that (i) Cr and Mo have complementary but distinct impacts on B diffusion: Cr maintains low‑energy in‑plane pathways while suppressing out‑of‑plane motion, leading to rapid B redistribution and Cr‑rich boride formation; Mo uniformly suppresses B mobility, creating deep segregation wells that stabilize Mo‑rich borides. (ii) The spectral sampling framework captures the full spectrum of migration barriers arising from local chemical disorder, revealing directionally biased diffusion and solute‑specific confinement effects. (iii) These insights reconcile long‑standing experimental observations of Cr‑ and Mo‑rich borides at grain boundaries and carbide interfaces in Ni‑based superalloys, and provide a quantitative tool for designing dopant strategies that engineer interstitial transport across complex interfaces.