For an equilibrium phase diagram of a binary A-B alloy at a constant pressure as shown in the figure, the degree of freedom at 'X' is (answer in integer) ______.
The figure shows a binary A-B alloy phase diagram with composition (wt.%B) on the x-axis and temperature on the y-axis. A liquidus curve runs from pure A down to pure B and a solidus curve runs below it; the region above the liquidus is labelled Liquid and the region below the solidus is labelled Solid. Point X lies inside the lens shaped region between the liquidus and the solidus curves, that is, in the two-phase (liquid + solid) region.
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Use the condensed Gibbs phase rule F = C - P + 1 for constant pressure, with C = 2 components and P = 2 phases in the two phase region.
Step 1: Think about which variables you are still free to choose at point X.
Instead of jumping straight to the phase rule formula, work out from physical reasoning how many independent variables can still be changed at X while both liquid and solid stay present.
Step 2: Pressure is already fixed.
The diagram is drawn at one constant pressure, so pressure is not a variable here at all, it is already used up.
Step 3: Look at what happens once you pick a temperature.
Once a temperature inside the two phase field is chosen, the liquidus curve fixes the composition of the liquid phase at that temperature, and the solidus curve fixes the composition of the solid phase at that same temperature. These are the two ends of the tie line through X. So the compositions of both phases are not free choices, they follow automatically once temperature is picked.
Step 4: Count the truly free choices.
The only quantity that can still be picked independently at X, given constant pressure and both phases present, is the temperature itself. Everything else, both phase compositions, follows from the tie line.
Step 5: Match this count to the phase rule.
This physical picture agrees with $F=C-P+1=2-2+1=1$: exactly one variable, temperature, is free.
