Identifying independent components and internal process order parameters in nonequilibrium multicomponent nonstoichiometric compounds

In CALPHAD-type thermodynamic databases, nonstoichiometric compounds are typically described by sublattice models where the sublattice site fractions represent the occupation probability of different atomic, ionic or defect species on different sublattices. Here, we develop a general procedure and corresponding linear algebra tools for converting the sublattice site fractions to a combination of independent component compositions and internal process order parameters describing the extent of internal atomic exchange, electronic redox and defect generation reactions. We apply them to a number of nonstoichiometric phases in thermodynamic databases and literature. The general procedure can be applied to constructing thermodynamic databases in terms of internal process order parameters for nonstoichiometric phases in multicomponent systems such as high-entropy oxides and alloys, which can be utilized to model their kinetics of nonequilibrium processes and microstructure evolution.