The chemical reactions occurring in metallurgical processes such as the reduction of iron ore and the decarburization of molten iron can be explained in terms of the free energy in thermodynamics. When the free energy of reactants is different from that of products, a reaction will occur. If it leads to a decrease in free energy, it will reach equilibrium when the free energy of the reactants and products becomes equal. For an explanation of the smelting and refining reaction, Gibb's energy (free energy at constant pressure) is used, which is calculated by using temperature, pressure, and concentration as independent variables. The reactions for smelting and refining are based on those of reduction and oxidation.

The figure shows the changes in the standard Gibb's energy which occur when oxides of elements are formed by the chemical reactions for producing iron and steel. This figure is called the Ellingham diagram. In general, the reaction in which an element reacts with 1 mole of oxygen to form an oxide is given by Eq. 1, and the change in the standard Gibb's energy of this reaction is given by Eq. 2, where G0 is called the oxygen potential.

Taking an example of the reaction in which magnetite (Fe3O4) combines with oxygen to form hematite (Fe2O3), the Gibb's energy change at 1,000K during this reaction is about 200 kilojoules per 1 mole from the value at point A. When the straight line that connects point A with point Q is extrapolated to the line outside the right-hand margin, these two lines cross at a point where the partial pressure of oxygen (Po2) is about 10-6 Pascals (Pa). This shows that the reaction reaches equilibrium with a gas under an oxygen partial pressure of 10-6 Pascals (Pa) at 1,000K. In a gas with an oxygen partial pressure of higher than 10-6 Pascals (Pa), the reaction proceeds to form hematite. However, when the partial pressure of oxygen is lower than this level, hematite is decomposed and magnetite is formed; in other words, hematite is reduced to magnetite.

Generally, with metal oxides, when the temperature increases, the negative absolute value of the Gibb's energy of formation will be smaller, which makes the oxides unstable and easy to reduce. Similarly, the degree of stability of various oxides can be compared by this figure. For example, the oxides of iron are progressively less likely to be thermodynamically reduced in the order of hematite, magnetite, wustite (FeO). Under the conditions for wustite to be reduced, neither alumina nor the oxides of titania are reduced, while the oxides of copper and nickel are reduced.

The conditions for the formation of sulfides can also be discussed by using diagrams for the Gibb's energy of formation, temperature, and sulfur gas partial pressure of each reaction. When considering the desulfurization in iron and steel making, it is necessary to examine the Ellingham diagram in this manner.