On a binary eutectic phase diagram, an alloy of composition X is cooled to a temperature where the liquidus and solidus lines bracket it in a two-phase (liquid + solid) region. What does the lever rule tell you?
AThe total composition of each phase present
BThe relative amounts (mass fractions) of the two phases present
CThe temperature at which solidification will complete
DWhether the microstructure is proeutectoid or hypereutectoid
The lever rule uses the distances between the alloy composition and the two phase-boundary compositions at a given temperature to compute the fraction of each phase. It does not give phase compositions (those are read directly from the diagram boundaries) nor transformation temperatures.
Question 2 True / False
A binary phase diagram generally represents the equilibrium state, so real alloys cooled at normal rates will match it exactly.
TTrue
FFalse
Answer: False
Phase diagrams show equilibrium, which requires infinitely slow cooling so diffusion can fully homogenize each phase. At practical cooling rates, diffusion is incomplete, producing cored (compositionally graded) microstructures whose compositions deviate from equilibrium predictions.
Question 3 Short Answer
What distinguishes the eutectic point on a binary phase diagram from other points in the two-phase liquid+solid region?
Think about your answer, then reveal below.
Model answer: The eutectic point is an invariant point — a unique composition and temperature at which a single liquid phase transforms simultaneously into two distinct solid phases. No other composition melts or solidifies at a single fixed temperature; instead, they pass through a temperature range with coexisting liquid and solid.
At the eutectic, the Gibbs phase rule gives zero degrees of freedom (for a binary system at fixed pressure): F = C − P + 1 = 2 − 3 + 1 = 0. This means composition and temperature are both fixed, so the transformation occurs at one sharp temperature — the eutectic temperature.