Background
Thermodynamics enables one to answer “Is corrosion possible?” before an experiment is run. Potential-pH diagrams are a graphical representation of the most stable thermodynamic reaction products as a function of the hydrogen ion activity and equilibrium potential, two variables important in most corrosion processes. All thermodynamic properties are functions of the state of the material (for example liquid, solid, gas, or ion) and the state of the system in which it resides (for example, the temperature, pressure, concentration, etc.). Changes in thermodynamic properties between initial and final states are not functions of the energy paths followed when moving from the initial state to final the state of the system. In that sense, these properties are called path independent.
Free energy is the maximum work that can be obtained theoretically if the energy released during the transformation is converted to work. The sign on the change in free energy between initial and final states determines if that final state can occur spontaneously. A free energy change between initial and final states that is negative implies that the final state is more favorable than the initial state under the defined conditions. A free energy change between initial and final states that is positive implies that the final state is less favorable than the initial state under the defined conditions. A system always tries to reside in a state in which its total free energy is a minimum. That property is the basis for the calculation of the potential-pH diagram.
In a series of reactions involving formation of a group of related compounds, for example, the compound form that has the lowest free energy of formation tends to be the most thermodynamically stable form of that compound. The potential-pH diagram is a pictorial representation that shows the state having the lowest free energy of the system as a function of the hydrogen ion activity (as represented by but not necessarily equal to the pH) and electrochemical potential (equilibrium potential) at a given temperature and pressure. The coordinates of pH (assumed to equal the hydrogen ion activity) and potential in which these diagrams are plotted are useful because pH as a measure of acidity and potential as a measure of oxidizing power are particularly important in the field of corrosion for which these diagrams were originally developed. These diagrams should be considered as analogous to road maps in which the towns and cities might represent the states of the system. The diagrams are silent with respect to the kinetics (rate) of moving between system states (between towns), or the actual reaction pathway (roads or paths between towns) that provide the highest reaction rate (shortest travel time). System states having corrosion mass (weight) loss rates of kilograms per second or micrograms per century would appear as regions of corrosion on the diagrams.
Potential-pH or Pourbaix diagrams were originally developed by Dr. Marcel Pourbaix, hence their alternative names. An atlas of diagrams of pure materials in water is available (M. Pourbaix, Atlas of Electrochemical Equilibria in Aqueous Solutions, NACE International, Houston, TX, 1974 available at http://www.nace.org). While the diagrams in this atlas were derived using sometimes inaccurate or obsolete thermodynamic free energy data, this reference is an excellent first source of information about these diagrams. The discussion in this reference provides insight on how these diagrams may be related to corrosion. More recent analyses of several metals have revealed that more recent thermodynamic tabulations sometimes disagree with the original data used by Pourbaix and diagrams calculated from these data. These discrepancies led to modifications for the diagrams for iron, nickel, and chromium See http://www.argentumsolutions.com/publications.html for details.
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Example
The potential-pH diagram usually reported is actually an overlay of two diagrams. One shows the form of the metal that has the lowest free energy in the environment as a function of pH and potential. This form can be metal, oxidized metal solid, or metal-containing ion. The other shows the form of the metal ion in the solution that has the lowest free energy state as a function of pH and potential. These two diagrams are calculated separately. The two diagrams are not in equilibrium with each other. For this reason, The potential-pH diagram is not analogous to a phase diagram. In fact, the only place where true equilibrium exists on each diagram is along the lines bordering the regions. The positions of those lines change with concentration, temperature, etc. Within the boundaries the form of the metal calculated is the form with the lowest free energy at that pH, potential, and temperature. If the most stable state of the solid is as an ion, that ion is identical on the two diagrams at the same potential and pH.
The diagrams were originally calculated and drawn by hand and a simplified method for doing so has been described elsewhere (E. D. Verink, Jr., "Simplified Procedure for Constructing Pourbaix Diagrams", in Uhlig’s Corrosion Handbook, 2nd ed., W. Revie, ed., ch 6, p. 111, 2000). But undertaking such calculations, while being useful from an educational standpoint, is not only tedious but is not necessary. Such diagrams are routinely calculated and plotted using a computer. Construction of potential-pH diagrams has been made internet accessible as a web application at http://www.argentumsolutions.com.
This figure shows the state of the nickel metal with lowest free energy as a function of hydrogen ion activity and equilibrium potential:
This figure shows the state of the nickel-containing ion with lowest free energy as a function of hydrogen ion activity and equilibrium potential:
The temperature is 25oC and ionic activities (concentrations) are 1x10-6. Very often in the literature these diagrams are shown superimposed on each other. This figure shows how superimposing these two diagrams might appear:
These diagrams can be interfaced with the real world (http://www.argentumsolutions.com/tutorials/thermexpert_tutorialpg1.html). A reasonable indication of corrosion may be obtained by placing the measured corrosion potential or controlled potential and measured or calculated pH both at steady state onto the theoretical diagram. The assumption is that the steady state corrosion or controlled potential can be used as a surrogate for the equilibrium potential and the measured or calculated pH can be used as a surrogate for the hydrogen ion activity. By placing the coordinates of (pH, corrosion or controlled potential) directly on the diagram, the practitioner may get a handle on the most thermodynamically stable state of the corroding system. These coordinates should lie in that portion of the diagram in which water is itself stable relative to oxygen or hydrogen.
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