Homogenous Solutions & Phase Diagrams

MATSCEN 3141

Heterogeneous equilibrium

Equality of chemical potential for all distributable components across coexisting phases (mu_alpha = mu_beta).

Common tangent construction

A geometric method on Gibbs’ curves that

1. Fulfill chemical potential equality

2. Reveal equilibrium phase compositions.

Lever rule

A mass-balance formula used to calculate the relative fraction of each phase in a two-phase region.

Overall composition (X_B^0)

Changes the relative amounts of each phase (PHASE FRACTIONS), but does not alter the individual phase compositions.

Miscibility gap

A two-phase region ($\alpha' + \alpha''$) where a single crystal structure separates into two compositionally distinct phases.

Phase diagram limitations

They map equilibrium states and compositions but do not show kinetics, diffusion speeds, nucleation barriers, or microstructure scale.

What does Common Tangent Do?

Sets the equilibrium compositions (Phase compositions)

where is the tangent line drawn?

drawing a straight line that is tangent to the lowest point of the Gibbs free-energy curves of both phases ( alpha and beta ).