Engineering & Science
Sieverts' Law: Diatomic Gas Solubility (H2, N2, O2) in Molten Metals & Vacuum Degassing
Calculate dissolved atomic hydrogen or nitrogen concentration [X] = K_S * SQRT(P_X2) in ppm for steelmaking, aluminum foundry degassing, and TIG/MIG welding, plus target vacuum degassing pressure.
Why diatomic gases obey a SQUARE-ROOT pressure law instead of Henry's linear law!
When diatomic hydrogen gas H2(g) dissolves into molten steel, titanium, or aluminum during arc welding or ladle refining, the molecule MUST dissociate into two monatomic interstitial atoms: 0.5 H2(g) <-> [H]_metal! Applying chemical equilibrium K_S = [H] / (P_H2^0.5) yields Adolf Sieverts' 1929 square-root solubility law: [H] = K_S * SQRT(P_H2), where K_S is Sieverts' constant (e.g., 24.5 ppm/atm^0.5 for hydrogen in liquid iron at 1,600 °C) and P_H2 is diatomic partial pressure in atmospheres!
Notice the crucial vacuum-degassing consequence of the square-root exponent: to cut dissolved hydrogen in liquid steel in HALF (from 4.90 ppm down to 2.45 ppm), you must reduce H2 partial pressure FOUR-FOLD (from 0.04 atm down to 0.01 atm)! Conversely, hitting ultra-clean aerospace rotor steel spec [H]_max = 2.0 ppm requires pulling vacuum partial pressure down to P_max = ([H]_max / K_S)^2 = (2.0 / 24.5)^2 = 0.00666 atm (~5.1 Torr)!
| Ladle / Weld Atmosphere (Fe at 1600 °C, KS = 24.5) | Partial Pressure P_H2 (atm) | Dissolved Hydrogen [H] (ppm) | Degassing Scaling |
|---|---|---|---|
| Humid Slag / Damp Flux | 0.04000 atm | 4.90 ppm (Hydrogen flake risk!) | Baseline melt pickup |
| 4x Lower Partial Pressure | 0.01000 atm | 2.45 ppm (0.5x concentration!) | SQRT(1/4) = 1/2 dissolved gas |
| RH Vacuum Degasser Target <= 2.0 ppm | P_max = (2 / 24.5)^2 | 0.00666 atm (6.75 mbar) | Quadratic vacuum requirement |
Dissolved Atomic Gas Concentration [X] = K_S * SQRT(P_X2) (ppm by Weight)
Evaluates Sieverts' square-root equilibrium solubility for K_S > 0 and P_X2 >= 0.
=IF(OR(B2 <= 0, B3 < 0), "Invalid Sieverts Inputs", ROUND(B2 * SQRT(B3), 2))Maximum Allowable Vacuum Partial Pressure P_max = ([X]_target / K_S)^2 (atm)
Solves Sieverts' law in reverse for the vacuum degasser partial pressure needed to meet target ppm B4.
=IF(OR(B2 <= 0, B4 < 0), "Invalid Sieverts Inputs", ROUND((B4 / B2) ^ 2, 5))Try the example
Use the original values or change them to test your understanding.