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The metallurgy you actually need — Fe-N phase diagram in plain English
Epsilon vs gamma-prime, the 590°C ceiling, and what Kn = 2.5 on a vendor quote actually constrains.
Step 1 of 4The Fe-N system in one paragraph
Nitrogen diffuses into iron at roughly 350-590°C and forms several distinct phases depending on how much nitrogen ends up in the lattice and how hot the steel is. Two phases matter for tool and die work: γ' (gamma-prime, Fe₄N) and ε (epsilon, Fe₂₋₃N). Below both sits the diffusion zone: the original steel matrix with nitrogen dissolved interstitially and, in alloy tool steels, very fine alloy-nitride precipitates (CrN, VN, MoN, AlN) pinning the matrix. The compound layer is the outer crystalline iron-nitride zone of γ' and/or ε. The diffusion zone is the load-carrying case beneath it.
Quick check
A microsection shows a 6 µm crystalline layer at the surface and a hardness gradient extending another 250 µm into the substrate. What are you looking at?