Pourbaix Diagram Explained: E-pH Diagrams for Corrosion Engineering

The Pourbaix diagram is the foundational thermodynamic tool for predicting which phase – dissolved metal ion, solid oxide, or metallic element – is stable for a given metal-water system at a chosen potential and pH. This article explains how E-pH diagrams are constructed from the Nernst equation, how to interpret the corrosion, passivation, and immunity domains, and how the iron, aluminum, and copper diagrams differ in ways that explain real-world corrosion behavior.

Thermodynamic Basis: The Nernst Equation

Every line on a Pourbaix diagram is the locus of potential and pH values at which two species – on either side of a specific half-reaction – have equal thermodynamic stability, i.e., equal Gibbs free energy. These equilibrium lines are calculated from the Nernst equation. For background on the free energy criterion underlying this approach, see our article on corrosion mechanisms.

General Nernst relation:
  E = E0 - (RT / nF) ln Q

At 25C, converting to base-10 log and grouping constants:
  E = E0 - (0.0592 / n) log Q

For a reaction releasing/consuming H+ ions, Q contains [H+],
so the line takes the form:
  E = E0 - (a) x pH       (sloped line, a = 0.0592 x m / n)
       where m = stoichiometric coefficient of H+ in the reaction

For reactions with NO H+ involvement (pure electron transfer):
  E = E0                  (horizontal line, independent of pH)

For reactions with H+ but NO electron transfer (pure acid-base
equilibria, e.g. solubility boundaries):
  pH = constant            (vertical line, independent of E)

This is why Pourbaix diagrams characteristically show three line types: horizontal lines for purely electrochemical (redox) equilibria, vertical lines for purely chemical (acid-base or solubility) equilibria, and sloped lines for reactions that involve both electron transfer and H+ or OH- exchange.

The Three Domains

Immunity

In the immunity domain, the metallic element itself is the thermodynamically stable form. No driving force exists for oxidation regardless of pH, so corrosion cannot occur thermodynamically. Cathodic protection systems are designed specifically to depress the metal’s potential into this domain.

Corrosion

In the corrosion domain, a soluble ionic species (Fe2+, Al3+, Cu2+, or similar) is the stable form, meaning the metal thermodynamically tends to dissolve. Whether this translates into a significant practical corrosion rate depends on the kinetics of the dissolution reaction, which the diagram itself does not address. This is directly relevant to localized attack discussed in our pitting corrosion coverage, since a metal can be in the corrosion domain globally while a stable passive film still locally protects most of the surface.

Passivation

In the passivation domain, a solid oxide or hydroxide compound is the thermodynamically stable phase. If this solid forms as a continuous, adherent, low-porosity film, it can dramatically reduce the practical corrosion rate even though the underlying driving force for oxidation remains present – this is the thermodynamic basis for the passive behavior of stainless steels, aluminum, and titanium. The diagram cannot tell you whether the film will actually be protective; that depends on film structure, chloride content, and mechanical integrity, topics covered further in our crevice vs pitting corrosion comparison.

Comparing Diagrams Across Metals

Practical Engineering Applications

Cathodic Protection Target Selection

Cathodic protection design uses the immunity domain boundary as the thermodynamic target potential; impressed current or sacrificial anode systems are sized to depress the structure’s potential below this line across the entire protected area, though practical protection criteria (such as the -850 mV CSE criterion for buried steel) include additional margin beyond the strict thermodynamic boundary.

Water Chemistry and pH Control

Boiler and cooling water treatment programs frequently target a pH range that places carbon steel comfortably within its passivation domain, which is the thermodynamic basis for the alkaline pH control commonly specified in closed-loop systems, complementing the inhibitor chemistries discussed in our corrosion inhibitors article.

Explaining Amphoteric Metal Behavior

The narrow passivation band for aluminum directly explains practical observations such as rapid attack of aluminum components by strongly alkaline cleaning solutions or concrete pore water (pH often above 12.5), even though the same aluminum performs well in neutral atmospheric exposure.

Industrial Significance

Pourbaix diagrams remain a first-pass screening tool in corrosion engineering curricula and failure analysis because they immediately reveal whether an observed corrosion mode is even thermodynamically plausible at the service pH and potential, narrowing the field of credible mechanisms before kinetic and microstructural factors such as those discussed in our HAZ microstructure article are brought in to explain the actual observed rate and morphology.

Frequently Asked Questions

Recommended Reference Materials

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