MSE 27-676 Interactive Applet Lecture 12 Companion

Free Energy Curves & Phase Diagram Explorer

Visualize how Gibbs free energy curves (g vs. x), chemical bonding (Δh_mix), and thermal disorder (−TΔs_mix) construct binary T–x phase diagrams via common tangents.

Presets:

Prototype Example

e.g. Ge–Si, Cu–Ni Isostructural single solid solution (continuous lattice across full composition range; complete liquid and solid miscibility).

Qualitative topological model • Not calibrated CALPHAD data

Interactive Sliders & Thermodynamic Parameters

Adjust temperature or tune mixing energetics to witness how phase stability shifts live.

Show Δh & −TΔs breakdown Show Common Tangent

Temperature (T) 1200 K

600 K (∂g/∂T = −s) 1550 K

Solid Mixing Enthalpy (Ω_S) 0.0 kJ/mol

< 0 (Ordering) > 0 (Clustering / Immiscible)

Liquid Mixing Enthalpy (Ω_L) 0.0 kJ/mol

Negative (Attract) Positive (Repel)

Pure Melting Points

T_m,A (Pure A) 1000 K

600 K 1800 K

T_m,B (Pure B) 1500 K

600 K 1800 K

Landmarks & Invariants: (Click to jump directly to invariant F=0 or pure melting points)

Free Energy Landscape: g(x)

Isothermal slice at 1200 K. Common tangents determine phase equilibria.

Liquid (L) Solid (S)

Phase Diagram: T–x

Constructed by sweeping T and tracking common tangent boundaries. Click or drag to set T.

Free Energy μ Intercepts

Species A μ_A (x_B=0):

-14.2 kJ/mol

Species B μ_B (x_B=1):

-18.6 kJ/mol

Active State (Both Plots) cursor x_B • T

Selected Comp. (x_B): x_B = 0.40

Equilibrium Phases:

Liquid + Solid

Phase Diagram & Equilibria (T–x)

Boundary Limits: x_L = 0.31 | x_S = 0.62

Phase Fractions: f_L = 71%, f_S = 29%

Phase Rule (F):

F = 1 (Tie-line)