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Phase diagrams and the lever rule

At constant pressure, how many degrees of freedom are there at the eutectic point of a binary system (where a liquid and two solid phases coexist)?

  1. A0
  2. B1
  3. C2
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Answer: A. 0

Gibbs' phase rule is F = C − P + 2, but for condensed systems at constant pressure we use F = C − P + 1. At the eutectic point of a binary system (C = 2), three phases, liquid L, α and β, coexist (P = 3), so F = 2 − 3 + 1 = 0: an invariant point at which the temperature and the composition of every phase are fixed. That is why an alloy of eutectic composition solidifies at a single temperature and its cooling curve shows a thermal arrest. One results from applying F = C − P + 2, which includes pressure as a variable, to a constant-pressure phase diagram. Two is the number of degrees of freedom in a single-phase region (P = 1), where temperature and composition can be varied independently.

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