Phase Diagrams

· The Gibbs function for a substitutional solid solution of B-atoms in an A-atom matrix depends upon the number of B-atoms in solution and their enthalpy of solution. This is illustrated below.

· If H_B = Enthalpy of solution of B-atoms in an A-atom matrix, N = number of lattice sites, n = number of B-atoms, (N - n) = number of A-atoms, both the enthalpy and the entropy of the alloy depend upon n.
· The Gibbs function, G(n), is a minimum in thermodynamic equilibrium

· The B-atom equilibrium concentration, n₀, is then given by:
(n₀ /{N-n}) = (n₀ / N) = X_n = exp( - H_B / kT)