Modeling of In-Situ Nitrogen Alloying in SS316 during Laser Directed Energy Deposition

Laser directed energy deposition (LDED) can alloy AISI 316 with nitrogen in situ by replacing part of the argon shielding and carrier gas with N₂. Whether useful nitrogen levels can be reached depends on how fast molecular nitrogen is absorbed during the short life of the melt pool, so equilibrium thermodynamics alone is insufficient. This work develops a coupled thermal–thermodynamic–kinetic model and reduces it to a single dimensionless group. An Eagar–Tsai moving Gaussian heat source supplies the melt-pool free-surface area, volume, area-averaged surface temperature and lifetime. Sieverts' law with temperature-scaled Wagner interaction parameters sets the equilibrium solubility. Because LDED intensities do not produce a nitrogen-dissociating plasma, absorption is treated as reversible dissociative exchange at the free surface, second order in dissolved nitrogen. The rate law has an exact hyperbolic-tangent solution governed by a Damköhler number, Da = βN eq τ. Powder-in-flight absorption, layer-to-layer remelting and a Scheil-based N₂ porosity criterion complete the model. For 800 W, 10 mm s⁻¹ and 0.5 atm N₂, the model predicts a mean pool surface temperature of 2897 K, an equilibrium ceiling of 0.085 wt% and Da = 0.22. The steady-state deposit reaches 0.061 wt% N, i.e., 71% of the ceiling but only 42% of the gap between feedstock (0.043 wt%) and equilibrium, confirming kinetically limited operation for the uncalibrated rate constant. In this regime nitrogen pickup scales almost linearly with N₂ partial pressure rather than with its square root, rises with melt superheat (apparent activation energy 50.5 kJ mol⁻¹), and is strongly reduced by dissolved oxygen. Process maps over 600–1000 W, 5–15 mm s⁻¹ and 0.25–1 atm N₂ give 470–1000 ppm, below the 1410 ppm porosity threshold. Pure-argon deposition is predicted to lose nitrogen. The rate multiplier χ is the only adjustable kinetic parameter and requires experimental calibration.