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: Recall the Gibbs phase rule.
The general Gibbs phase rule for a system is
\[ F=C-P+2 \]
where \(F\) is the degree of freedom, \(C\) is the number of components, and \(P\) is the number of phases present. The "2" accounts for the two variables temperature and pressure.
Step 2: Apply the constant pressure condition.
The question fixes pressure as constant, so pressure is no longer a free variable. This removes one degree of freedom from the general rule, giving the condensed phase rule normally used for metallurgical phase diagrams:
\[ F=C-P+1 \]
Step 3: Identify the number of components at point X.
The system is a binary A-B alloy, so there are two components.
\[ C=2 \]
Step 4: Identify the number of phases at point X.
Point X lies inside the lens shaped region between the liquidus curve (top) and the solidus curve (bottom). In this region liquid and solid coexist together.
\[ P=2 \]
Step 5: Substitute into the condensed phase rule.
\[ F=C-P+1=2-2+1=1 \]
Step 6: Final answer.
The degree of freedom at point X is
\[ \boxed{1} \]
