explanation about ellingham diagram
Since any explanation of how to calculate and plot an Ellingham diagram is more about the mechanics of the derivation process and less about how to use the tool, which is the intent of this article, the concept is covered very briefly here.
Enthalpy (DH) and entropy (DS) are essentially constant with temperature. Unless a phase change occurs, the free energy (DG) versus temperature plot can be drawn as a series of straight lines, where DS is the slope and DH is the y-intercept.
DG = DH T DS
The slopes of those plotted lines change when any of the materials involved melt (M) or vaporize/boil (B). In a heat-treat system this is (for the most part) irrelevant, except in the brazing and sintering processes where those phase changes (melting) can indeed occur.