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Phase Diagrams
· Variables are associated with the composition, the number of phases, and the thermodynamic state of the system.
· There are CP variables due to composition and the number of phases.
· There are two thermodynamic variables, normally (T, p).
· The Total number of variables for the system:
Total Variables = {CP + 2}
· The number of degrees of freedom, F, for the system is the difference between the number of variables and the number of constraints: 
F = {CP + 2} - {C(P - 1) + P}, and collecting terms:

F = {C - P + 2} Gibbs Phase Rule
· The "normal" condition for making an alloy is one of constant pressure. For this condition the Gibbs phase rule becomes: 

Fp = [C - P + 1]p