# Pourbaix diagram A **Pourbaix diagram**, also called a potential–pH or E–pH diagram, maps which species of an element is thermodynamically stable in water as a function of the electrode potential *E* and the [[PH|pH]]. For a metal the map divides into three kinds of territory that a corrosion engineer reads directly: *immunity*, where the metal itself is stable and cannot corrode; *corrosion*, where a soluble ion is stable and the metal dissolves; and *passivation*, where a solid oxide or hydroxide is stable and may protect the metal beneath it.[^pourbaix1966] In the microsim below the reader drags a single point around the E–pH plane of [[Iron|iron]] and the verdict changes with it. Immunity belongs to metallic Fe at low potential; corrosion belongs to Fe²⁺ in acid, Fe³⁺ at high potential and low pH, and the ferrite ion HFeO₂⁻ in strong alkali; [[Passivation_(chemistry)|passivation]] belongs to the oxides Fe₃O₄ and Fe₂O₃ over a broad band of near-neutral and alkaline water. The boundaries are [[Nernst_equation|Nernst]] lines of the form `E = E0 - (0.0592·m/n)·pH`, and two dashed lines *a* and *b* mark where water itself is reduced to hydrogen and oxidized to [[Oxygen|oxygen]]. A [[Stainless_steel|stainless]] variant overlays the Cr₂O₃ field that widens the passive band. On the [[Materials_science|Materials science]] flagship this article serves the *Passivation and the Pourbaix diagram* section of Part VIII, Industry, and answers the question the [[Galvanic_corrosion|galvanic corrosion]] sim leaves open: why some metals survive in a couple that thermodynamics says should eat them. ## Naming The diagram is named for Marcel Pourbaix, the Belgian chemist who systematized the construction and published equilibrium diagrams for most of the elements in his *Atlas of Electrochemical Equilibria in Aqueous Solutions*.[^pourbaix1966] The form was not entirely new — plotting redox equilibria against pH is an obvious consequence of the [[Nernst_equation|Nernst equation]] — but the Atlas turned it into a reference work, with a consistent set of conventions for the activity of dissolved species and a uniform layout that made diagrams for different elements comparable. Several other names are in use for the same construction. *E–pH diagram* and *potential–pH diagram* are the neutral descriptive terms. In geology and [[Geochemistry|geochemistry]] the vertical axis is usually labelled Eh, the redox potential measured against the standard hydrogen electrode, and the plot is called an Eh–pH diagram. In aquatic and environmental chemistry the axis is often converted to the dimensionless pe, discussed below. All four are the same plot with different axis labels. ## Diagram The axes are potential on the vertical and pH on the horizontal, conventionally covering −1 to +2 V and pH 0 to 14 at 25 °C. Each field is labelled with the species that is thermodynamically stable there, and each boundary is the locus where two neighbouring species are in equilibrium — not a physical barrier, but the line at which the more stable species changes. For iron, the field structure is the one the sim animates. At low potential, metallic Fe is stable at all pH: this is the immunity region, and it is what [[Cathodic_protection|cathodic protection]] is designed to reach by pushing the metal's potential down into it. Raise the potential in acid and Fe²⁺ becomes stable — the metal corrodes. Raise it further and Fe³⁺ takes over at low pH. Move to the right instead, into near-neutral and alkaline water, and solid magnetite Fe₃O₄ and then haematite Fe₂O₃ become stable: these are the passive fields, and a metal there is covered by an oxide it grew itself. At very high pH the oxide dissolves again as the ferrite ion HFeO₂⁻, which is why iron corrodes in strong alkali as well as in acid. Because the position of a boundary between a solid and a dissolved species depends on how much dissolved species counts as "dissolved", every diagram states an assumed activity. The usual convention, and the sim's, is 10⁻⁶ molar: below that concentration the metal is declared not to be corroding. That choice moves the horizontal Fe²⁺/Fe boundary from its standard value of −0.44 V down to −0.62 V (derived from the Nernst equation below and the standard potential of −0.44 V for Fe²⁺/Fe).[^os-appl] ## Applicable chemical systems Pourbaix's Atlas covers most of the elements, and the same construction applies to any system whose species can be listed with known free energies. Beyond the pure metal–water systems it is routinely extended in two directions. Other ligands can be added: chloride, carbonate, sulfide, phosphate and ammonia each introduce their own solid and dissolved species, and the resulting diagram is conditional on a stated concentration of that ligand as well as on the metal's activity. And alloys can be treated approximately by superposing the diagrams of their components, which is how the chromium field is read onto the iron diagram for [[Stainless_steel|stainless steel]]. Systems far from the metal–water case use the same axes. Aquatic chemists plot the stability of nitrogen, sulfur, carbon, manganese and uranium species to interpret [[Groundwater|groundwater]] and sediment chemistry; hydrometallurgists plot leaching and precipitation fields to choose a process route; and the diagrams are computed at temperatures and pressures far from ambient for reactor water chemistry and for hydrothermal geology. The construction is indifferent to the chemistry: it needs only a list of candidate species and their free energies of formation. ## Limitations The single most important limitation is that a Pourbaix diagram is a statement about [[Thermodynamics|thermodynamics]] and says nothing about rate. It identifies the stable species, not how quickly the system reaches it. A point deep in a corrosion field may correspond to attack of a micrometre a year or a millimetre a day, and the diagram cannot tell the difference; [[Chemical_kinetics|kinetics]] is a separate calculation. The electrochemical form of the same caution is familiar from cell measurements: a measured open-circuit voltage can differ from the equilibrium value when side reactions occur, potentials do not add whereas free energies do, and the standard hydrogen electrode is itself an idealization.[^haverkort-caution] The passivation fields carry a second, subtler caveat. The diagram says an oxide is stable there; it does not say the oxide is protective. Protection requires a film that is thin, adherent, continuous and slow to dissolve, and thermodynamics is silent on all four. [[Aluminium|Aluminium]] and [[Chromium|chromium]] owe their usefulness to films that happen to be excellent; iron's oxide in most conditions is not, which is why [[Rust|rust]] flakes off and exposes fresh metal while the diagram serenely reports a passive field.[^callister-passive] Third, the diagram is built for pure water at one temperature, usually 25 °C, with one assumed activity for dissolved species, usually 10⁻⁶ M. Changing any of those moves the boundaries. Fourth, and the most damaging in service, it ignores localized attack. Chloride ions break passive films at defects and cause pitting and crevice corrosion in conditions the diagram places safely in a passive field; that is why marine service requires molybdenum-bearing grades and [[Duplex_stainless_steel|duplex stainless steels]] rather than simply a metal whose diagram looks favourable.[^callister-passive] Real surfaces also depart from equilibrium through mixed potentials, non-equilibrium films and slow solid-state transformations. ## Expression of the Nernst equation as a function of pH The Nernst equation gives the potential of a half-reaction away from standard conditions. In the single-electron form used in the Portal Book electrochemistry manual it reads `E_eq = E0' + (RT/nF)·ln(c_O/c_R)`, with *n* the number of electrons and *F* the [[Faraday's_laws_of_electrolysis|Faraday constant]] of about 96,485 C per mole of electrons.[^haverkort-nernst] Converting the natural logarithm to base 10 collects the constants into one number: at 298.15 K, `R·T·ln(10)/F = 0.0592 V` (derived), so the equation becomes `E = E0 - (0.0592/n)·log10(Q)` with *Q* the reaction quotient.[^os-ch16] Now let the half-reaction consume *m* protons along with its *n* electrons, which every metal-oxide reduction does. Writing the reaction in the reduction direction, the proton activity appears in *Q* raised to the power −*m*, and `-log10([H+]) = pH` by definition, so at unit activity of the other species the potential becomes `E = E0 - (0.0592·m/n)·pH`. That is the equation the sim draws, and it explains the whole geometry of the plot at a glance. A boundary between species that differ by electrons but not by protons has *m* = 0 and is horizontal. A boundary between species that differ by protons but not by electrons has *n* = 0, the potential drops out, and the boundary is vertical. Every other boundary is a straight line of slope `-0.0592·m/n` volts per pH unit: −0.0592 V/pH when the ratio is one, −0.1775 V/pH for a reaction such as `Fe₂O₃ + 6H⁺ + 2e⁻ -> 2Fe²⁺ + 3H₂O` in which six protons accompany two electrons (derived). ## Calculation of a Pourbaix diagram Building a diagram is a matter of listing the candidate species, writing every pairwise equilibrium between them, reducing each to a line by the rule above, and keeping only the segments that bound the region where each species is actually the most stable. The three line types are the whole construction. ### Vertical boundary line A vertical line separates two species that differ in protons but not in oxidation state, so no electrons are exchanged and the equilibrium is a pure acid–base or solubility equilibrium. Its position is a pH, obtained from the equilibrium constant — a [[Solubility_equilibrium|solubility product]] or an acid dissociation constant — and the assumed activity of the dissolved species.[^os-ch17] The Fe²⁺/Fe(OH)₂ and the oxide/ferrite boundaries of the iron diagram are of this kind, and they move when the assumed activity is changed — one decade in activity shifts such a boundary by `1/m` of a pH unit for each proton in the reaction. ### Horizontal boundary line A horizontal line separates two species of different oxidation state that do not differ in protons, so the equilibrium potential does not depend on pH. Fe³⁺/Fe²⁺ at +0.77 V and Fe²⁺/Fe at −0.44 V under standard conditions are the two textbook cases,[^os-appl] and the second is the one the sim shifts to −0.62 V when the 10⁻⁶ M convention is applied, since the Nernst term `(0.0592/2)·log10(10⁻⁶)` contributes −0.178 V (derived). Horizontal lines are the boundaries of the immunity region, which is why cathodic protection is described as a potential to be reached rather than a chemistry to be arranged. ### Sloped boundary line A sloped line separates species differing in both protons and electrons, and its slope is `-0.0592·m/n` volts per pH unit. Most of the interesting boundaries of a metal diagram are of this kind, because an oxide formed from a metal or an ion almost always releases protons: `2Fe²⁺ + 3H₂O -> Fe₂O₃ + 6H⁺ + 2e⁻` is the passivation boundary of iron and slopes at −0.178 V/pH. Boundaries with *m* = *n* slope at exactly −0.0592 V/pH, parallel to the water lines below, which is why so much of a typical diagram consists of parallel lines. ## The stability region of water Two dashed lines cross every Pourbaix diagram and belong to the solvent rather than to the element being plotted. Line *a*, the lower one, is the reduction of water to hydrogen, `2H⁺ + 2e⁻ -> H₂` at 1 bar, whose standard potential is 0.000 V by definition; with *m* = *n* = 2 the line is `E = -0.0592·pH`.[^haverkort-nernst][^os-appl] Line *b*, the upper one, is the oxidation of water to oxygen, `O₂ + 4H⁺ + 4e⁻ -> 2H₂O`, whose standard potential is +1.229 V; with *m*/*n* = 1 the line is `E = 1.229 - 0.0592·pH`.[^haverkort-nernst] The two lines are parallel and 1.229 V apart at every pH, which is exactly the thermodynamic voltage of water [[Electrolysis|electrolysis]].[^haverkort-nernst] Between them water is stable; below *a* it is reduced and hydrogen is evolved; above *b* it is oxidized and oxygen is evolved. At pH 0 the band runs from 0.000 to 1.229 V, at pH 7 from −0.414 to 0.815 V, and at pH 14 from −0.828 to 0.401 V (derived). The band is where aqueous chemistry actually happens, so a field of the diagram that lies entirely outside it is a thermodynamic curiosity rather than a service condition. It also sets the limits of cathodic protection: driving a structure far below line *a* protects it but wastes current on hydrogen evolution, and in high-strength steels the hydrogen produced there causes embrittlement, so protection criteria specify a potential window rather than "as negative as possible". ## Applications The diagram's main industrial use is corrosion engineering, where it answers three questions in order: can this metal corrode here at all, can it be moved into immunity by changing its potential, and can it be moved into passivation by changing the pH or the potential. Water treatment for boilers and heating circuits is the everyday application of the third: raising the pH of the circuit moves iron into its passive field, which is why closed systems are dosed alkaline. Beyond corrosion, the same maps are used to plan hydrometallurgical leaching and precipitation, to interpret the mobility of metals in [[Groundwater|groundwater]] and sediments, to predict the speciation of contaminants in soils and mine drainage, and to screen candidate electrode materials for stability in aqueous electrolytes. ### Concept of <span>pe</span> in environmental chemistry Environmental chemists often replace the potential axis with pe, defined as the negative base-10 logarithm of the activity of a hypothetical free electron, by analogy with pH.[^stumm-pe] The two axes carry the same information and convert through the same constant as above: `pe = E/0.0592` at 25 °C, so `pe = 16.90·E` with *E* in volts (derived). The stability band of water then runs from `pe = -0.0592·pH/0.0592 = -pH` along line *a* to `pe = 20.8 - pH` along line *b* (derived), which is a tidier statement than its voltage equivalent. The reason for the substitution is symmetry of bookkeeping. With both axes as logarithms of activities, an equilibrium between two species becomes a linear relation between pe and pH with integer coefficients read straight off the balanced equation, and mass-action calculations for natural waters can be carried out entirely in logarithmic units. The usage is standard in aquatic chemistry and rare in corrosion engineering, where the measured quantity is a voltage. ## Gallery A Pourbaix atlas is read as a set. Placing the diagrams of iron, [[Aluminium|aluminium]], [[Zinc|zinc]], [[Copper|copper]], chromium and [[Titanium|titanium]] side by side shows at once why the engineering metals behave so differently: zinc's immunity region sits well below iron's, which is what makes it a sacrificial anode; aluminium and chromium have wide passive fields bounded by dissolution at both low and high pH; and titanium's passive field covers nearly the whole plot within the water band, which is why it is used where nothing else survives. Wikitube's version of that comparison is the interactive sim above with its element presets rather than a fixed plate; for the static diagrams themselves, see the pair's own gallery at the pinned revision below. ## See also - [[Passivation_(chemistry)]] - [[Stainless_steel]] - [[Chromium]] - [[Duplex_stainless_steel]] - [[Nernst_equation]] - [[Galvanic_corrosion]] - [[Corrosion]] - [[Electrochemistry]] ## Notes All explanatory notes and source citations for this page are collected as numbered footnotes under References, immediately below. Values marked "(derived)" in the body are computed on this page from the cited constants and standard potentials and are not quoted from a source. ## References [^pourbaix1966]: Pourbaix, Marcel (1966). *Atlas of Electrochemical Equilibria in Aqueous Solutions*. Oxford: Pergamon Press. (Originally published in French; edition details, the iron plate and the pages defining the immunity, corrosion and passivation conventions and the 10⁻⁶ M activity convention are all to pin. Not a Portal Book; no DOI or URL asserted.) [^os-appl]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First*, 2nd ed. OpenStax (Portal Book 051). Appendix L, Standard Electrode (Half-Cell) Potentials, pp. 1125–1130 — the standard potentials for Fe²⁺/Fe, Fe³⁺/Fe²⁺ and 2H⁺/H₂ quoted here, rounded to two decimals; exact tabulated values to pin. https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first [^os-ch16]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First*, 2nd ed. OpenStax (Portal Book 051). Chapter 16, Electrochemistry, pp. 753–790 — the Nernst equation, cell and electrode potentials, and the relation between potential, free energy and equilibrium (section pages to pin within the chapter range). https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first [^haverkort-nernst]: Haverkort, Willem (2024). *Electrolysers, Fuel Cells and Batteries: Analytical Modelling* (Portal Book 053). Chapter 1, Electrochemistry, pp. 20–41. The Nernst equation in its single-electron form `E_eq = E0' + (RT/nF)·ln(c_O/c_R)` at p. 32; the Faraday constant F ≈ 96,485 C/mol at p. 25; the standard potentials 2H⁺/H₂ = 0 V and O₂/H₂O = 1.229 V at p. 28; and the 1.23 V equilibrium voltage of water electrolysis at p. 26. https://open.umn.edu/opentextbooks/textbooks/electrolysers-fuel-cells-and-batteries-analytical-modelling [^haverkort-caution]: Haverkort, Willem (2024). *Electrolysers, Fuel Cells and Batteries: Analytical Modelling* (Portal Book 053), p. 25 and p. 27 — the cautions that a measured open-circuit voltage can differ from the equilibrium voltage when side reactions occur, that potentials do not add whereas free energies do, and that the standard hydrogen electrode is an idealization. These are the electrochemical form of the equilibrium-versus-reality caveat in the Limitations section. https://open.umn.edu/opentextbooks/textbooks/electrolysers-fuel-cells-and-batteries-analytical-modelling [^callister-passive]: Callister, W. D.; Rethwisch, D. G. (2010). *Materials Science and Engineering: An Introduction*, 8th ed. Hoboken: Wiley. Chapter 17, Corrosion and Degradation of Materials — passivity, the protective oxide films of aluminium, chromium and the stainless steels, and the role of chloride in pitting and crevice corrosion. Not a Portal Book; pages to pin. [^stumm-pe]: The pe convention and its use in aquatic and environmental chemistry. Standard aquatic-chemistry texts introduce pe as the negative logarithm of electron activity and give the 25 °C conversion used here; the specific text, edition and pages are to pin. No DOI or URL asserted. [^os-ch17]: Flowers, Paul; Neth, Edward; Robinson, William; et al. (2019). *Chemistry: Atoms First*, 2nd ed. OpenStax (Portal Book 051). Chapter 15, Equilibria of Other Reaction Classes, pp. 719–752 — solubility products and complex-ion equilibria, which fix the position of the vertical (pH-only) boundaries of a Pourbaix diagram (section pages to pin). https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first ## External links - [*Chemistry: Atoms First*, 2nd ed.](https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first), Open Textbook Library — Portal Book 051, open access; Chapter 16 is the electrochemistry this article rests on - [*Electrolysers, Fuel Cells and Batteries: Analytical Modelling*](https://open.umn.edu/opentextbooks/textbooks/electrolysers-fuel-cells-and-batteries-analytical-modelling), Open Textbook Library — Portal Book 053, open access; the Nernst form used here is at p. 32 - For atlases, plotting services and agency datasets, see the external links of the Wikipedia pair at the pinned revision below; none is reproduced here unverified. ### Software Pourbaix diagrams are today computed rather than drawn by hand, from assessed databases of free energies of formation. Three families of tool are in use: commercial thermochemical packages built on assessed CALPHAD-type databases, which compute E–pH sections alongside phase diagrams and can extend them to elevated temperature and to multi-ligand solutions; open, web-hosted aqueous-stability applications published alongside computational materials databases, which generate a diagram for an arbitrary composition from first-principles formation energies; and general equilibrium solvers into which a user enters a species list and free energies directly. Because the tools' addresses change, the current URLs are not reproduced here; the pair's External links section at the pinned revision lists them. <!-- MATTERSIM:BEGIN g33 — Matter & Energy Cluster microsim (framework build, specs/sims/Pourbaix_diagram.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Pourbaix diagram* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Pourbaix_diagram.html" data-title="Pourbaix diagram"></div> *Built from `MICROSIM_GUIDE/specs/sims/Pourbaix_diagram.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).* <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Pourbaix_diagram) : [Wikitube](https://en.wikitube.io/wiki/Pourbaix_diagram) · pinned revision [1361942991](https://en.wikipedia.org/w/index.php?oldid=1361942991) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Materials_science]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Materials_science row M56 · sim pending (matter/Pourbaix_diagram).*