Metallurgical Surface Heat Treatment, AMS 2759/10 Controlled Gas Nitriding & KN Potential
Gas Nitriding Potential KN & Case Depth Formula
Calculate Retort Ammonia Partial Pressure p_NH3 (atm), Hydrogen Partial Pressure p_H2 (atm), Lehrer Nitriding Potential KN (atm^-0.5), and Parabolic Nitrided Case Depth (mm).
Why AMS 2759/10 precision gear nitriding controls Lehrer Potential KN = p_NH3 / p_H2^(1.5) instead of archaic burette % dissociation!
At `510–530 °C` (below steel’s `A_1` transformation so precision aerospace gears suffer near-zero quench distortion!), catalytic cracking of pure `1`-atm inlet ammonia (`NH_3 -> (1/2) N_2 + (3/2) H_2`) by reacted fraction `alpha` (`0 < alpha < 1`) expands `1` mole of inlet gas to **`1 + alpha` total exhaust moles**—giving **Residual Ammonia Partial Pressure `p_{NH3} = (1 - alpha) / (1 + alpha)`** (atm) and **Hydrogen Partial Pressure `p_{H2} = (1.5 * alpha) / (1 + alpha)`** (atm)! E. Lehrer’s phase diagram proves surface iron-nitride phase formation (`alpha-Fe` diffusion zone vs tough `gamma’-Fe_4N` vs brittle spalling `epsilon-Fe_2N_{1-x}` "white compound layer") is governed strictly by **Thermodynamic Nitriding Potential `K_N = p_{NH3} / (p_{H2}^{1.5})`** (`atm^{-0.5}`), while interstitial nitrogen diffusion drives **Effective Nitriding Case Depth `NHD = k_N * SQRT(t_{hr})`** (`mm`)!
Verify on an AMS 2759/10 Two-Stage (`Floe` Process) 4140/4340 Gear Retort—Stage-1_Reacted_Ammonia_Fraction `alpha` = 0.34 (B2), Isothermal_Hold_Time `t` = 24.0 h (B3), and `520 °C` Alloy_Diffusion_Constant `k_N` = 0.085 mm/h^0.5 (B4): `p_{NH3}` equals `0.4925` atm (E2), `p_{H2}` equals `0.3806` atm (E3), Nitriding Potential `K_N` hits `2.098` atm^-0.5 (nucleating an active nitrogen supply in Stage 1, E4), and `24`-hour Case Depth reaches `0.416` mm (E5)!
| AMS 2759/10 Gas Nitriding KPI (1 atm NH3 Feed, t=24 h, kN=0.085, alpha=0.34 vs 0.55) | Formula | Verified Output |
|---|---|---|
| Ammonia Partial Pressure p_NH3 (atm) | (1 - alpha) / (1 + alpha) | 0.4925 atm (0.2903 atm @ Stage-2 0.55) |
| Hydrogen Partial Pressure p_H2 (atm) | (1.5 * alpha) / (1 + alpha) | 0.3806 atm (0.5323 atm @ Stage-2 0.55) |
| Lehrer Nitriding Potential KN (atm^-0.5) | p_NH3 / (p_H2 ^ 1.5) | 2.098 (0.748 white-layer suppression!) |
| Effective Case Depth NHD (mm) | Diffusion_k_mm_sqrth * SQRT(Time_hr) | 0.416 mm (~0.0164 in) |
Stoichiometric NH3 Cracking Partial Pressures, Lehrer KN & Root-Time Depth Formula
Validate `Reacted_Fraction alpha` in `(0.05, 0.95)`, `Hold_Time t > 0.5` h, and `Diffusion_Constant k_N` in `(0.02, 0.25]` mm/h^0.5! Notice the common stoichiometry trap: `1` mole of `NH_3` reacting by fraction `alpha` yields `1 + alpha` total moles—forgetting the `(1 + alpha)` denominator overestimates both `p_{NH3}` and `p_{H2}`.
=LET(al_f, B2, th_r, B3, kn_d, B4, IF(OR(al_f <= 0.05, al_f >= 0.95, th_r <= 0.5, kn_d <= 0.02, kn_d > 0.25), "Invalid Nitriding Input", ROUND(kn_d * SQRT(th_r), 3)))Floe-Process Stage-2 High Dissociation (alpha = 0.55) White-Layer Reduction Check (Set B2 = 0.55)
Raise Stage-2 ammonia cracking to `alpha` B2 = 0.55 (or bleed dissociated `H_2`/`N_2` gas): `p_{NH3}` E2 drops to `0.2903` atm, `p_{H2}` E3 climbs to `0.5323` atm, and Lehrer Potential `K_N` E4 plunges nearly `3x` from `2.098` down to **`0.748` atm^-0.5**—dropping into the `alpha-Fe` / low-`gamma’` region so brittle `epsilon` white layer dissolves inward without sacrificing `0.416` mm case depth!
=IF(ISTEXT(E5), E5, LET(pn_a, (1 - B2) / (1 + B2), ph_a, (1.5 * B2) / (1 + B2), ROUND(pn_a / (ph_a ^ 1.5), 3)))Try the example
Use the original values or change them to test your understanding.