Numerical integration of the Gibbs–Thomson equation for multicomponent systems

 The differential form of the Gibbs–Thomson equation is derived for non-stoichiometric, partially stoichiometric and fully stoichiometric precipitates in a multicomponent system. This form can be readily used in a numerical integration scheme based on separation of variables. The validity of the proposed approach has been demonstrated with binary (Al–Sc) and ternary (Al–Mn–Si) systems. Good agreement with other approaches (e.g. analytical or Thermo-Calc) has been shown. The proposed approach aims at bridging the gap between open thermodynamic databases and precipitation models.