Ternary Composition–Temperature Phase Diagrams
The stability landscape of a ternary system as a function of temperature, computed from the
same convex-hull entries that feed the convex hull viewers. Every
phase gets a Gibbs energy of formation ΔGf(T) — from its own tabulated free_energies, or estimated with the Bartel et al. (2018) SISSO descriptor from
volume per atom and reduced mass with experimental elemental references — and the lower hull
is swept over temperature. Hull topology is piecewise constant, so the whole diagram is a
sequence of isothermal sections separated by exactly located transitions: decompositions,
polymorph changes and tie-line flips, each with its balanced reaction.
Pick a system below, drag one onto the viewer, or drop your own .json / .json.gz array of convex-hull entries. The Alexandria sets hold every binary and
ternary PBE entry within 0.3 eV/atom of the hull (fetch_alexandria_ternaries.py); the Materials Project sets are ternary slices of the quaternaries used on the convex-hull
page.
How to read it
- Isothermal section: tie-triangles are the three-phase regions at the current temperature; hovering any composition gives its equilibrium assemblage with atom fractions (the ternary lever rule). Unstable phases are coloured by their hull distance; orange rings mark the phases that change at the next transition on heating.
- 3D prism: the same data as a composition–temperature prism. Stable phases are vertical rods over their stability windows, tie-lines sweep out the vertical sheets that bound the three-phase volumes, and the isothermal cutting plane can be dragged up and down (or driven by the slider) to slice the prism at any temperature; everything above the plane is ghosted so the slice reads like a cut-away. Orbit with the mouse, toggle with the 2D/3D buttons.
- Stability map: one row per phase across temperature. Solid bars are the exact stability windows; the colour ramp is the energy above hull elsewhere. Drag to scrub the temperature, click a formula to select the phase.
- Transitions: every change of hull topology, bisected to 0.5 K, with a balanced reaction in the heating direction. ▼ decomposition, ▲ new phase, ⇅ polymorph change, ⤭ tie-line flip (four-phase reaction).
- Gas atmosphere: for systems with O, N, H or F the controls pane can treat the element as a gas at a chosen partial pressure; lower p(O₂) drives reductions to lower temperatures. Keyboard: ←/→ step T, shift+←/→ jump between transitions, space plays a heating ramp.
- Caveats: the SISSO descriptor is a ~50 meV/atom estimate for solids and ignores melting, solid solutions and configurational entropy; PBE overbinds O₂, which is why oxygen-rich phases such as LiO₈ sit on the 0 K hull. Read transition temperatures as trends, not measurements.