Machine-learned interatomic potential for sputtering of tungsten-boron surfaces

Abstract: Boronization, where boron is deposited onto tungsten surfaces, is a key technique to reduce plasma contamination, such as oxygen in Tokamak fusion reactors. The exact interaction between the boron atoms and the tungsten surface, and the effect of the harsh environment on these surfaces are however not fully understood, partially due to the lack of accurate atomistic simulations and interatomic potentials. Here, we develop a machine-learned interatomic potential for sputtering studies of W-B structures and deposition of boron onto tungsten surfaces. The machine-learned potential is trained to density functional theory data and allows accurate large-scale molecular dynamics simulations. Our aim is to understand how boron behaves when deposited on tungsten and how tungsten and boron are sputtered under irradiation. We observe that both the surface configuration/orientation and the surface composition affect the sputtering, and that depositing boron onto tungsten surfaces produces a dense boron layer. The developed potential shows good accuracy for both surface and bulk properties and can be used for simulations of mixed W and B systems.

• The paper introduces the first tabulated Gaussian Approximation Potential for arbitrary W–B configurations under irradiation, reproducing bulk properties within a few percent and enabling large-scale molecular-dynamics simulations.
• The simulations show that self-sputtering exceeds cross-species sputtering, boron is preferentially removed from mixed WB surfaces, and prolonged irradiation can enrich surfaces in tungsten, although absolute yields differ from experiments.
• The paper finds that boron deposition evolves from orientation-dependent sticking to near-unity sticking after initial layer formation, producing a dense amorphous film with transient borophene-like structures and a 6–8 Å mixed interface.

Motivation and scope

Boronization—the deposition of a 10–100 nm boron layer on tungsten plasma-facing components—has been adopted by ITER to capture oxygen impurities, yet no interatomic potential existed for atomistic simulation of sputtering or deposition from mixed W–B surfaces. This paper fills that gap by constructing a tabulated Gaussian Approximation Potential (tabGAP) for the W–B system, trained on density functional theory (DFT) data, and applying it to large-scale molecular dynamics (MD) simulations of sputtering of pure B, pure W, and WB surfaces as well as boron deposition onto tungsten. The potential is the first capable of treating arbitrary W$_x$B$_y$ configurations under irradiation.

Potential construction

The model follows the tabGAP formalism, which restricts training to low-dimensional descriptors—a two-body distance descriptor (5 Å cutoff), a three-body angular descriptor (4.1 Å cutoff), and an EAM-density descriptor based on a generalized third-order Finnis–Sinclair density function—to enable fast tabulation for LAMMPS. A fixed screened Coulomb pair baseline handles short-range repulsion down to zero separation, calibrated against all-electron DFT dimer data. Training data were assembled iteratively from four groups: an inherited pure-W database, bulk B and tungsten-boride phases from the Materials Project (including $\alpha$-trigonal, $\beta$-trigonal, $\alpha$-orthorhombic B, WB, WB$_2$, W$_2$B, and a $\gamma$-plutonium-like phase) with elastic deformations and thermal displacements at 300–1000 K, liquids obtained by melt-quench cycles up to 5000 K, and surface configurations covering adsorption sites, vacancies, sputter-like upward displacements, and boron depositions at 5 eV onto all four relevant W surfaces. The iterative active-learning loop—generating candidate structures with intermediate potentials, computing DFT references, retraining—is standard but was applied consistently across melting, surface formation, and deposition stages.

Validation

The validation is thorough across dimer curves, energy–volume relations, lattice constants, cohesive and formation energies, adsorption energies, surface energies, quasi-static decohesion, and melting points.

Bulk properties are reproduced well: bulk moduli agree within roughly 5% of DFT (with B$_2$W overestimated by about 10%), lattice constants within 1.5% for pure elements (though BW shows a ~4% overestimation along one axis), and cohesive and formation energies within 0.02 eV/atom. The potential correctly captures phase ordering, including that $\alpha$-B is more stable than $_y$0-B at 0 K and that W-rich/equiatomic borides are thermodynamically favored over B-rich ones.

Surface properties show a systematic underestimation: adsorption energies of B on W surfaces are uniformly lower than DFT by 0.3–1.2 eV, and surface energies by 0.01–0.06 eV/Å$_y$1. Importantly, the stability ordering of sites and surfaces is preserved, so the bias is consistent rather than scattered—an acceptable defect for trend-level sputtering studies, though it implies the potential systematically underbinds surface species.

Decohesion reveals the most significant limitation. Quasi-static drag calculations show spurious local minima for pure boron that are absent in DFT, and adding these structures to the training set did not remove them. For tungsten, decohesion mismatches of ~3 eV arise from the spin-polarized isolated-atom reference used in training versus non-spin-polarized DFT drag curves, which the authors correctly argue is not a failure of the fit; for boron, where spin effects are small, the discrepancy remains unexplained. This caveat bears directly on the reliability of near-threshold sputtering predictions for boron targets.

Melting temperatures from liquid–solid coexistence simulations underestimate experiment by 100–150 K ($_y$25%), with both $_y$3- and $_y$4-B converging to the same melting point of 2250 ± 50 K, consistent with the known solid-state transition near 1000 K.

Sputtering results

Simulations used 1500 impacts per parameter set (250 per cell, six cells) with B and W projectiles at 200, 500, and 1000 eV, normal incidence, at 300 K, neglecting electronic stopping—a defensible choice below 1 keV but one that may contribute to quantitative disagreement with experiment.

Three regimes emerge: a threshold regime near 100–200 eV where yields approach zero, a transition regime at 500 eV, and a cascade-dominated regime at 1000 eV. Self-sputtering (W→W, B→B) consistently exceeds cross-species sputtering, attributed to mass-matched momentum transfer and low reflection; W→W produces the highest yields. Surface orientation matters strongly for tungsten targets under B bombardment—the close-packed (110) surface yields most because light ions cannot penetrate it efficiently, whereas open orientations allow deep penetration and bulk damage—and only weakly for boron targets, indicating that crystallographic effects are muted in covalent, low-mass systems.

For mixed WB surfaces, boron is preferentially sputtered in nearly all cases except the (010)W$_y$5 termination whose top layer is pure tungsten. The implication stated by the authors is that prolonged irradiation will enrich WB surfaces in tungsten. Boron projectiles exhibit high reflection yields on WB (up to the highest on (010)W$_y$6), while W projectiles have near-zero reflection, depositing their full energy in the lattice.

The comparison with experiment is candidly mixed: boron self-sputtering yields are underestimated by a factor of ~2, while tungsten self-sputtering is overestimated by ~50%, though trends match in both cases. The authors attribute this to ideal flat surfaces, absent electronic stopping, and missing surface roughness/amorphization effects. These are systematic offsets rather than random errors, so absolute yield predictions from this potential should be treated with caution even where relative trends are robust.

Boron deposition and film growth

Deposition of 2000 boron atoms at 5 eV onto each W surface reveals a two-stage growth mechanism. Initially, sticking probabilities differ by orientation—(111) highest, (100) and (112) lowest—but after a few tens of ions per nm$_y$7, once the first boron layer forms, sticking approaches unity on all surfaces and the substrate orientation becomes irrelevant. The deposited film is amorphous and dense, with a density of 2.42–2.44 g/cm$_y$8, between the computed $_y$9-B (2.32 g/cm$\alpha$0) and $\alpha$1-B (2.48 g/cm$\alpha$2) values, both of which agree well with experiment.

A notable observation is the transient appearance of an elevated, borophene-like layer at a fluence of ~50 nm$\alpha$3, consistent with experimental reports that boron favors 2D structures before bulk growth. The authors are appropriately cautious here: they state it is difficult to determine whether these layers are genuine borophene phases or merely planar voids within the growing film, since boron is intrinsically vacancy-rich. The layers vanish upon further deposition. A 6–8 Å interfacial mixing zone forms at the B/W boundary via ion-beam mixing, least pronounced on W(100).

Limitations and open questions

Several limitations constrain the interpretation of the results. All sputtering simulations use normal incidence and 300 K, whereas reactor-relevant fluxes involve oblique angles and elevated temperatures; the authors justify the temperature choice by the dominance of ballistic effects, but angular dependence—shown by prior SRIM work to be strong for boron—remains unexplored. Electronic stopping is neglected throughout. The spurious local minima in the boron drag curves persist despite additional training, leaving open whether the potential misdescribes some part of the B coordination landscape relevant to near-threshold sputtering. The identity of the borophene-like intermediate layer is unresolved. Finally, chemical sputtering by deuterium, identified elsewhere as potentially limiting boron coating lifetime, is outside the scope of this potential and dataset.

Conclusion

This work delivers the first validated machine-learned interatomic potential for W–B systems suitable for large-scale radiation-damage MD, with bulk, surface, and thermal properties reproduced at the few-percent level against DFT and experiment. Its application establishes that self-sputtering dominates over cross-species sputtering, that W surfaces will become tungsten-enriched under mixed bombardment due to preferential B removal, and that boronization proceeds via a two-stage sticking mechanism culminating in a dense amorphous film. Quantitative agreement with sputtering experiments is imperfect—factor-of-two and 50% deviations for B and W respectively—which the authors attribute to idealized simulation conditions. The potential enables future coupled deposition-erosion simulations of boronized tungsten walls, provided its surface-binding biases and the unexplained boron drag anomalies are kept in mind when interpreting absolute yields.