Stern-Geary Corrosion Current

Before 1957, measuring a corrosion rate meant waiting. You hung a coupon, left it for ninety days, cleaned it and weighed it. Milton Stern and Al Geary's paper changed that by showing that a very small polarization about the corrosion potential — small enough to leave the surface undisturbed — carries the corrosion current in its slope. The measurement takes minutes and does no damage, which is why linear polarization resistance instruments now sit permanently in cooling towers, pipelines and concrete structures.

The derivation combines the two Tafel branches. At the corrosion potential the anodic and cathodic currents are equal and opposite, and their sum is zero; push the potential slightly away and the imbalance that appears is proportional to the corrosion current itself. Linearising both exponentials about that point and taking the slope gives $I_{corr} = B / R_p$, where $B = \beta_a \beta_c / [2.303(\beta_a + \beta_c)]$. The 2.303 is $\ln 10$, left over from writing the Tafel slopes per decade rather than per e-fold.

What makes this a field technique rather than a laboratory one is how forgiving $B$ turns out to be. It is a kind of harmonic mean of the two Tafel slopes, and across the entire plausible range of slopes it varies only between roughly 13 and 52 mV. The 26 mV that both slopes at 120 mV produce is therefore rarely wrong by more than a factor of two, while $R_p$ itself ranges over four or more orders of magnitude between a passive stainless and actively corroding steel. Assuming $B$ and measuring $R_p$ gets you most of the way, which is a rare and lucky arrangement.

It is not unconditional. Where the cathodic reaction is under diffusion control — oxygen reduction in still water is the standard example — $\beta_c$ effectively goes to infinity, $B$ collapses to $\beta_a/2.303$, and the conventional 26 mV overestimates the corrosion rate, sometimes badly. On a passive surface the measured resistance is dominated by the film rather than by charge transfer, and calling the result a corrosion current is a category error. And on a rebar in concrete or an anode in dry soil, the uncompensated solution resistance can be most of what the instrument reads, which makes the metal look far healthier than it is.

The last point is bookkeeping and it costs people a factor of ten thousand. This equation as written returns a current when $R_p$ is a plain resistance in ohms, and a current density when $R_p$ has been normalised to the exposed area in Ω·cm². Corrosion instruments almost always do the normalisation internally and report µA/cm², but a bench measurement on an unfamiliar probe usually has not. Before this number goes into a penetration rate, establish which one you are holding — and remember that a probe's nominal area is its geometric area, which for a rough or fouled surface is not the area that is corroding.