Convex Hulls

Ternary Chemical Systems

• Barycentric coordinates — composition mapped to an equilateral triangle base
• Formation energy on the z-axis, with convex hull faces between stable points

Quaternary Chemical Systems

• Tetrahedral projection — 4D composition coordinates mapped into 3D space
• Color-coded stability — each point colored by energy above hull
• Drag & drop — load your own JSON data onto any diagram

Binary Chemical Systems

• Formation energy vs. composition — stable phases lie on the lower convex hull

Statistics Panel

• Live-bound stats — phase counts, energy ranges, and hull distances update with the diagram
• Row highlighting — click a table row to highlight it (highlighted_entry_id + on_entry_click)
• Clickable IDs — entry_href callback turns the ID column into links
• Poly column — shows polymorph count per reduced formula
• Polymorphs filter — dropdown to isolate entries sharing a composition
• Subsystem coverage — grid of binary element pairs with entry counts
• CSV/JSON export — download table data

Side-by-Side Layout

• layout="side-by-side" — stats and table visible simultaneously, no toggle needed

Highlighted Entries

• Visual effects — pulse, glow, or size changes on selected entries
• Tooltip badge — hover to see "★ Highlighted" on marked entries
• Cross-dimensional — works on 2D, 3D, and 4D diagrams

Marker Symbols

• Custom shapes — assign per-entry marker symbols (★ ◆ △ + ■ ●)
• Click to select — selected entry shown as ★, updates dynamically

Note: Missing pure element references are automatically added with E_form = 0 eV/atom.

Temperature-Dependent Free Energies

• Temperature slider — appears when entries include temperatures + free_energies arrays
• Live hull recomputation — phase stability changes are visible as you drag the slider
• Order-disorder transitions — high-entropy polymorphs stabilize at elevated temperatures

Gas Atmosphere Control

• Chemical potential — μ(T, P) = μ°(T) + RT·ln(P) for gas-phase elements (O, N, H, ...)
• Pressure controls — adjust partial pressures to simulate reducing/oxidizing conditions
• Multi-gas support — O₂, N₂, H₂, CO, CO₂, H₂O, F₂

Tip: Try very low pressure (10⁻⁶ bar) for reducing or high (1 bar) for oxidizing conditions.

Standalone Stats for Quinary Systems

• Standalone stats — use ConvexHullStats without rendering a hull
• High-dimensional support — computed via process_hull_for_stats(), ideal for 5+ element systems