The thermodynamic factor in eqn [12] is propor­tional to the second derivative of the Gibbs free energy G of the alloy, with respect to the molar fraction of one of the components. It can be calcu­lated on the basis of thermodynamic data. A database such as CALPHAD61 builds free-energy composition functions of the alloy phases from thermodynamic measurements (specific heats, activities, etc.). When available, the phase diagrams are used to refine and/or to assess the thermodynamic model. Although the CALPHAD free-energy functions are sophisti­cated functions of temperature and composition, it is interesting to study the simple case of a regular solu­tion model. In the case of a binary alloy A1—CBC with a clustering tendency, the Gibbs free energy is equal to

G = 2kBTcC(1 — C) + kBTC ln(C)

+ kBT(1 — C) ln(1 — C) [15]

where Tc is the critical temperature and C is the alloy composition. The regular solution approximation leads to a concentration-dependent thermodynamic factor equal to

F = 1 — 4C(1 — C)T [16]

where concentration C now corresponds to a local concentration of B atoms, which varies in space and time.