Stationary Points of Phase Diagrams Gibbs-Konowalow Laws

5 STATIONARY POINTS OF PHASE DIAGRAMS GIBBS-KONOWALOW LAWS 

Equations (12.68) establish how any /+ 1 intensive vectors must be related to one another in the heterogeneous equilibrium of p phases. Let us now assume for definiteness that these are labeled 

This permits us to write each of (12.68) in the more symmetrical form 

According to (12.82), 771 must vanish whenever the determinantal row or column vectors become linearly dependent, i.e., when there exists some linear combination Y of the variables Xf+ 2, Xf+ 3. Xc+2 such that F(A) = -A) for every phase A. For example, when p = 2, 771 must vanish when values of and c+2 are proportional in the two phases. The vanishing of 77 signals a type of redundancy of the extensive variable Xb as though the system could be prepared from one fewer chemical component than had been supposed. However, the vanishing of an 77 could arise from other special linear relationships connecting entropies or volumes, as well as composition variables. 

To see the consequences of some vanishing 7]h let us introduce a new basis set of /vectors R ) that is identical to the starting set, except for the final member Z)  

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