Systematic thermodynamic analysis reveals that an essential condition for the thermodynamically valid chemographic projections proposed by Greenwood is completely excessive. In other words, the phases or components from which the projection is made need not be pure, nor have their chemical potentials fixed over the whole chemographic diagram. To facilitate the analysis of phase assemblages in multicomponent systems, all phases and components in the system are divided into internal and external ones in terms of their thermodynamic features and roles, where the external phases are those common to all assemblages in the system, and the external components include excess components and the components whose chemical potentials (or relevant intensive properties of components) are used to define the thermodynamic conditions of the system. This general classification overcomes the difficulties and defects in the previous classifications, and is easier to use than the previous ones. According to the above classification, the phase rule is transformed into a new form. This leads to two findings: (1) the degree of freedom of the system under the given conditions is only determined by the internal components and phases; (2) different external phases can be identified conveniently according to the conditions of the system before knowing the real phase relations. Based on the above results, a simple but general approach is proposed for the treatment of phases and components: all external phases and components can be eliminated from the system without affecting the phase relations, where the external components can be eliminated by appropriate chemographic projections. The projections have no restriction on the states of the phases or the chemical potentials of components from which the projections are made. The present work can give a unified explanation of the previous treatments of phases and components in the analysis of phase assemblages under various specific conditions. It helps to avoid potential misunderstandings or errors in the topological analysis of phase relations.
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