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A binary phase diagram is given below.

Isomorphous binary phase diagram: liquidus and solidus rise from the left melting point to the higher right melting point, with L above, S below and L+S between; a dashed line marks temperature T0 across the two-phase lens

Which one of the following figures qualitatively represents the G-X (Gibbs free energy - composition) plot at temperature T0 shown in the phase diagram?

  • A.G against X: liquid L curve with its minimum at the left and solid S curve with its minimum at the right, the two curves crossing
  • B.G against X: the solid S curve lies above the liquid L curve over the whole range
  • C.G against X: the solid S curve lies below the liquid L curve over most of the range
  • D.G against X: solid S curve with its minimum at the left and liquid L curve with its minimum at the right, the two curves crossing

Answer: A

The correct G-X plot is (A).

The diagram is an isomorphous system, with liquidus and solidus rising from the lower-melting component on the left to the higher-melting one on the right. At \(T_0\), alloys near the left are liquid and those near the right are solid, with a two-phase L+S range between.

So the liquid free-energy curve must be lower on the left and the solid curve lower on the right, the two curves crossing so that a common tangent spans the L+S range. Plot (A) shows exactly this: the L curve's minimum on the left, the S curve's minimum on the right, and the curves crossing between them.

In (B) the liquid is lower everywhere, which would make every composition liquid at \(T_0\). In (C) the solid is lower over nearly all compositions. In (D) the roles are reversed, putting the solid on the low-melting side.

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