Shapes of phases in isothermal phase diagrams: what is wrong with the Thermo-Calc logo

The solubility of defects is essential to control the mechanical, electrical and thermal properties of engineering materials. The concentration of defects can be visualized on a phase diagram as providing the width to single-phase regions of compounds. Although the shape of these regions can have a tremendous impact on the maximum defect solubility achievable and guides the engineering of materials, little attention has been paid to the shape of the phase boundaries surrounding these single-phase regions. Here we examine the shape of single-phase boundaries that can be expected for dominating neutral substitutional defects. Single-phase regions in an isothermal phase diagram should be expected to be concave or star-shaped, or at least straight polygonal sides rather than be convex-like droplets. A thermodynamic justification is used to show the concave (hyperbolic cosine) shape depends on the thermodynamic stability of the compound when various substitutional defects dominate. More stable compounds have star-like phase regions, while barely stable compounds should be more polygonal shaped. The Thermo-Calc logo for example would be more physical if it contained a star-like central compound and pointed elemental regions.