Metal Oxidation Thermodynamics and Richardson Ellingham Diagrams

Overview

This lecture develops a general framework for reactions between gases and condensed phases and then specializes to metal oxidation. The instructor derives how Gibbs free energy changes with reaction extent and shows how equilibrium constants arise from the chemical potentials of each species, treating the reference state and activities in a simplified, yet powerful way.

"The activity of a material in its reference state is 1." - MIT OpenCourseWare

• General reaction form and the role of chemical potentials
• Equilibrium condition and the simplifications used for metal-oxygen systems
• How approximations lead to a simple PO2–based coexistence line between metal and oxide

Introduction to gas condensed-phase reactions

The lecture begins by reminding us of a general reaction AA + BB → CC + dd and extends beyond ideal gases to a more general setting. It shows how the change in Gibbs free energy D G can be expressed in terms of the reaction extent, mu I, the chemical potential, and activities A I. At equilibrium, D G = 0, which yields the equilibrium constant K in terms of activities.

"The activity of a material in its reference state is 1." - MIT OpenCourseWare

When specializing to metal oxidation, the reaction is typically written as M Z + O2(g) ⇌ M Z O2, with Z indicating the metal oxidation state. The equilibrium constant then involves the activities of the oxide, the metal, and O2 gas. The key simplifications come from treating O2 as an ideal gas (activity = partial pressure over 1 atm) and assuming the condensed phases are pure. Under these assumptions, the oxide is a line compound with fixed stoichiometry, and the metal is assumed not to dissolve oxygen appreciably. This reduces the equilibrium condition to a simple relationship between oxygen partial pressure and standard Gibbs energy of formation.

"This simplified quite a lot." - MIT OpenCourseWare

Thermodynamics of metal oxidation: Enthalpy and entropy approximations

The enthalpy of formation ΔH° for many metal oxides is negative and large in magnitude, reflecting the exothermic nature of metal–oxygen bond formation. Temperature dependence of ΔH° is often small enough to neglect in standard conditions, so ΔH° is treated as effectively constant. The entropy change ΔS° is dominated by the removal of an O2 molecule from the gas phase, which has a large entropy. In oxidation, the gas entropy decrease dominates the reaction entropy, justifying the approximation that the temperature dependence of ΔS° can be neglected for many practical calculations. This leads to a simple expression for the equilibrium PO2: PO2 = exp(−ΔG°/(R T)) with ΔG° ≈ ΔH° − T ΔS°. The dominant entropy contribution comes from the condensation of O2 gas.

"The reaction entropy is dominated by condens[ation] of O2 from the gas." - MIT OpenCourseWare

Le Chatelier and oxide passivation

With the thermodynamics in hand, the lecture discusses how the oxygen partial pressure controls the direction of the reaction. If the ambient PO2 is higher than the equilibrium value, metal oxidizes spontaneously; if PO2 is lower, oxide decomposes back to metal and O2 gas. Titanium is used as a vivid example: at room temperature, the equilibrium PO2 is extraordinarily small, so titanium readily forms a native oxide layer that passivates the surface. This passivation is crucial for applications in stainless steel and microelectronics and explains why certain metals resist corrosion in air while others oxidize aggressively.

"The oxide will decompose into more oxygen gas and more metal." - MIT OpenCourseWare

Richardson Ellingham diagrams and their use

The course then introduces Richardson Ellingham diagrams: plots of ΔG° versus temperature for metal oxidation reactions. Since PO2 is related to ΔG° by PO2 = atmosphere × exp(−ΔG°/(R T)), lines of constant PO2 emerge as contours on a ΔG°–T plot. An oxidation reaction appears as a straight line with slope −ΔS° and intercept ΔH°. Contours of constant PO2 are lines through the origin with zero intercept, whose slope encodes the desired oxygen partial pressure for coexistence at a given temperature. This visualization helps explain which metal will preferentially oxidize in the presence of competing oxides and how processing decisions should be made in metallurgy and materials science.

As an illustration, the diagram shows Mn and Sn oxides with their respective intercepts and slopes, indicating that at a given temperature the PO2 contour for Mn oxidation is lower than that for Sn, meaning manganese has a higher affinity for oxygen and can reduce tin oxide under appropriate conditions.

"Manganese metal will reduce tin oxide. So if you were to put tin oxide … in a furnace in the presence of manganese metal and heat it up, the manganese will convert to manganese oxide and the tin oxide will convert to tin metal." - MIT OpenCourseWare

Phase diagrams and real materials

The lecture provides phase-diagram evidence that many oxides form line compounds and that solid phases tend not to dissolve oxygen, whereas liquids can incorporate dissolved oxygen. Tin, copper, and titanium are discussed to illustrate how solid oxides coexist with a metal; in contrast, liquid metal can dissolve more oxygen, showing how phase state affects oxidation thermodynamics. The diagrams help identify when passivation layers form and how they can be engineered for corrosion resistance or intentional oxide growth in manufacturing processes.

"Spontaneous oxide formation process is really important for a lot of reasons." - MIT OpenCourseWare

Beyond the basics: Allingham diagrams and learning resources

Finally, the Ellingham framework is connected to Allingham diagrams, which extend the interpretation by marking effective phase transitions like melting points and boiling points, revealing how temperature-driven changes shift enthalpy and entropy contributions. The lecturer invites students to explore Do It Do‑It‑POMS resources for interactive Ellingham diagrams, data, and exercises, highlighting the value of these diagrams as a learning tool and a practical guide for materials processing and alloy design.

"go to the Do It POMS page for Ellingham diagrams, and let me share that just to show you where you might go to play with this a little more" - MIT OpenCourseWare