Convex Hulls

Ternary Chemical Systems

3D ternary convex hulls show composition on an equilateral triangle base with formation energy as the z-axis. Convex hull faces are rendered between stable points.

Quaternary Chemical Systems

4D quaternary convex hulls project tetrahedral composition coordinates into 3D space. Each point represents a compound with its stability indicated by color.

Binary Chemical Systems

2D binary convex hulls show formation energy versus composition. Stable phases lie on the convex hull.

3D Convex Hull with Statistics

Example of a 3D ternary convex hull displayed alongside its computed statistics. The stats are bound to the diagram and update automatically when the data changes.

Highlighted Entries

Highlight specific entries with customizable visual effects. Hover over highlighted entries to see the "★ Highlighted" badge in the tooltip.

Marker Symbols

Customize marker shapes to distinguish different entry types. Click an entry to select it (shown as ★). Stable phases use ◆, high-energy phases use △, medium-energy use +.

Note: If pure element references are missing from the data, they are automatically added with formation energy = 0 eV/atom (the thermodynamic definition).

Temperature-Dependent Free Energies

When entries include temperatures and free_energies arrays, a temperature slider appears allowing dynamic visualization of G(T) at different temperatures. The hull is recomputed at each temperature, showing how phase stability changes.

Gas Atmosphere Control

For systems containing elements from gaseous species (O, N, H, etc.), the chemical potential depends on both temperature and partial pressure: μ(T, P) = μ°(T) + RT·ln(P). Use the gas pressure controls (left side) to simulate different atmospheric conditions.

Tip: Try setting pressure to very low values (10⁻⁶ bar) to simulate reducing conditions, or high values (1 bar) for oxidizing conditions. Observe how the relative stability of phases changes.