What does CALPHAD stand for?

CALculation of PHAse Diagrams. It is a method that models the Gibbs free energy of every phase in a system as a function of composition and temperature, then finds the phase assemblage that minimizes the total energy — reproducing the phase diagram and much more.

How is a phase diagram actually computed?

At a chosen temperature and overall composition, the solver minimizes the total Gibbs energy over all candidate phases subject to mass balance. Geometrically that is the common-tangent (binary) or convex-hull (multicomponent) construction on the Gibbs-energy surfaces. Sweeping temperature and composition traces the phase boundaries.

Why do two CALPHAD databases disagree?

The model parameters are assessed by fitting experimental and first-principles data, and different assessments weight that data differently — especially for metastable phases and sparsely measured corners. The phase models and even which phases are included can differ, so always state the database behind a result.

Thermodynamics · guide

How CALPHAD computes a phase diagram

CALPHAD turned phase diagrams from hand-drawn experimental maps into something you can compute for any composition and temperature. The idea is simple to state and powerful in practice: write down the free energy of every phase, then let the lowest energy win.

Energy, not geometry

A phase diagram is the visible shadow of an energy competition. CALPHAD works directly on that energy: each phase gets a model for its molar Gibbs free energy as a function of composition and temperature, and the equilibrium state is whichever combination of phases minimizes the total. The diagram is then just a map of which assemblage wins where.

Modelling one phase

For a simple solution phase the molar Gibbs energy is built from three physically distinct parts:

G = Σ xᵢ·°Gᵢ + RT·Σ xᵢ·ln xᵢ + G^excess

The first term is the mechanical mixture of the pure components (°G_i, the SGTE lattice-stability data). The second is ideal mixing entropy. The third — the excess energy — carries all the non-ideal interaction and is usually a Redlich–Kister polynomial:

G^excess = xₐ·x_b · Σₖ Lₖ · (xₐ − x_b)^k

The L_k are the interaction parameters that get fitted. Magnetic ordering adds a further Inden–Hillert–Jarl term for phases like bcc iron.

Ordered phases and the compound-energy formalism

Intermetallics and interstitial solutions are not random mixtures, so they are described with sublattices. The compound-energy formalism assigns species to each sublattice and writes the energy in terms of the end-member compounds plus mixing on each sublattice — the standard way to model carbides, σ-phase, ordered B2/L1₂ phases and the like.

Finding equilibrium

With every phase's energy defined, equilibrium at a fixed temperature and overall composition is a constrained minimization:

minimize G_total = Σ_phases n^φ · G^φ subject to mass balance

Geometrically this is the common-tangent construction in a binary and the lower convex hull of the Gibbs surfaces in higher order systems. A robust solver grids the surfaces, takes the hull, then polishes locally — which is exactly how austenite's in-browser engine works.

Open the calculatorCALPHAD equilibrium calculator →Compute the equilibrium phase assemblage and fractions from composition and temperature, with SGTE lattice stabilities and Redlich–Kister excess terms — in the browser.

What you get beyond the diagram

Because the method is energy-based, the same calculation yields phase fractions, phase compositions, activities, driving forces for precipitation, and the inputs that downstream kinetics models (precipitation, solidification, diffusion) need. The phase diagram is the headline; the thermodynamic detail underneath is what makes CALPHAD useful for real alloy design.

Frequently asked

What does CALPHAD stand for?: CALculation of PHAse Diagrams. It is a method that models the Gibbs free energy of every phase in a system as a function of composition and temperature, then finds the phase assemblage that minimizes the total energy — reproducing the phase diagram and much more.
How is a phase diagram actually computed?: At a chosen temperature and overall composition, the solver minimizes the total Gibbs energy over all candidate phases subject to mass balance. Geometrically that is the common-tangent (binary) or convex-hull (multicomponent) construction on the Gibbs-energy surfaces. Sweeping temperature and composition traces the phase boundaries.
Why do two CALPHAD databases disagree?: The model parameters are assessed by fitting experimental and first-principles data, and different assessments weight that data differently — especially for metastable phases and sparsely measured corners. The phase models and even which phases are included can differ, so always state the database behind a result.

References

N. Saunders, A.P. Miodownik, "CALPHAD: A Comprehensive Guide," Pergamon, 1998.
H.L. Lukas, S.G. Fries, B. Sundman, "Computational Thermodynamics: The Calphad Method," Cambridge University Press, 2007.
A.T. Dinsdale, "SGTE data for pure elements," CALPHAD 15(4), 1991.
M. Hillert, "The compound energy formalism," Journal of Alloys and Compounds 320, 2001.

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