Nano-Calphad: extension of the Calphad method to systems with nano-phases and complexions

The abbreviation "nano-Calphad" stands for "Calculation of Phase Diagrams for nano-systems." Nano-systems contain at least one phase or at least one interface layer (film, complexion) with at least one of its dimensions being below 100 nm. The essential task of nano-Calphad is to introduce correctly the surface term into the equation for the Gibbs energy. In view of the controversy between the Kelvin and Gibbs equations, even this task does not have an obvious solution (in the present paper, the Gibbs method is preferred). However, there are many further questions to be addressed when the Calphad method is converted into the nano-Calphad method. This paper attempts to give an as full as possible list of all those problems, such as: (i) the definition of a new, independent thermodynamic variable, (ii) the extended phase rule, (iii) the curvature dependence of the interfacial energies, (iv) the dependence of interfacial energies on the separation between interfaces (including the problem of surface melting), (v) the role of the shapes and relative arrangement of phases, (vi) the role of the substrate (if such exists), and (vii) the role of segregation, taking into account its effect on the mass balance within multi-component nano-phases and its surface phase transition and complexion. It is also shown that the well-known meaning of the tie line in binary two-phase fields is lost in nano-systems. The issues related to the size limits of materials thermodynamics and the need for a more complete databanks on molar volumes and interfacial energies are discussed.