3D Mapping of Gibbs Energy Diagrams onto Phase Diagrams

Mats Hillert has shown [*] that what is called a Phase Diagram is derivable from a projection in a so-called Property Diagram. The (molar) Gibbs Energy as the property is plotted along the z-axis as a function of two other variables x and y. For binary systems, for example, T equals y and the mole fraction x equals x. It must be emphasized that the total pressure P must be kept constant for this representation. 

Our partners at Ex-Mente have developed a  tool that allows to visualize the above 3D-interrelationship between the molar Gibbs Energies of the phases occurring in a binary system and the corresponding phase diagram. The visualization shows, in a perspective view, the three-dimensional Gibbs energy vs Temperature vs molar fraction (G-T-x) relationship in cartesian representation. In the respective Gm vs x diagrams, i.e. for given values of T and P, the equilibrium condition Gm=min for a given value of x is used to establish the one- or two-phase regions. On the xy-plane, the phase diagram is depicted in  its usual Temperature vs molar fraction representation. By turning the mouse wheel, the temperature of the corresponding  G-x vertical graph is changed interactively.

Two interactive diagrams were generated, one for a metallic system and another one for a ceramic system:

  • Pb-Sn interactive diagram
  • Al2O3-CaO interactive diagram

Concerning the Al2O3-CaO interactive diagram, it should be born in mind that all Gibbs Energies must be given for one mole of total component oxides. Thus the composition of the compound CaO.Al2O3 corresponds to (CaO)0.5(Al2O3)0.5. Also the Gibbs Energy of CaO.Al2O3 has to be scaled down accordingly in order to be able to insert a correct data point in the Gm vs x diagram.

Please be aware that the behavior of the interactive diagram may be browser dependent.

[*] Mats Hillert, Phase Equilibria, Phase Diagrams and Phase Transformations – Their Thermodynamic Basis, Cambridge University Press, 2nd edition (2008), p. 158.

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