Question 8
In the lead–tin thermal equilibrium phase diagram, a liquidus line is represented by the letter
Not quite. E is the solidus on the lead-rich side. It starts at the melting point of lead, like H, which is why it tempts you. Below and to the left of E the alloy is solid $\alpha$, so no liquid is left on that side. In 2021, 4.1% of Queensland students chose (A).
Not quite. F is the solvus. It sits below the eutectic temperature, between solid $\alpha$ and solid $\alpha+\beta$, so there is solid on both sides and no liquid anywhere near it. In 2021, 2.1% of Queensland students chose (B).
Not quite. G is the horizontal eutectic line at about 183 °C. It is where the last liquid disappears, so it belongs to the solidus. Everything below it is solid $\alpha+\beta$. In 2021, 7.1% of Queensland students chose (C).
That is it. Step through the hints below to see why. In 2021, 86.6% of Queensland students chose (D).
Redrawn from QCAA’s 2021 diagram with its own values. Shading: blue is all liquid, pale orange is solid plus liquid, grey is all solid.
Read the axis first. It counts % Tin, so pure lead is the left edge and pure tin is the right edge.
The two top corners where the curves start are the melting points of the two pure metals. Lead is the higher one, at the top left.
Find the field that is nothing but liquid. It is the large open region across the top, above every curve.
A liquidus is a boundary of that field. Cross it on the way down and the first solid appears.
Only one lettered line touches the all-liquid field. H runs from the melting point of lead down to the eutectic point at about 60% Sn.
E and G both have solid on one side and solid plus liquid on the other, so they are parts of the solidus. F has solid on both sides, so it is the solvus.
$$L\ \big|\ \alpha+L\quad\Rightarrow\quad H\text{ is the liquidus}$$
H is the upper boundary of the lead-rich side, with everything liquid above it and solid $\alpha$ plus liquid below it. The other liquidus is the unlettered line from the eutectic point up to the melting point of tin.
The most common wrong answer was (C), the horizontal eutectic line. It is the line where the last liquid freezes, so it belongs to the solidus. The liquidus is where the first solid appears.
Only mark this done when you could do it without help. Reading the solution does not count.
Question wording and any figures are from the 2021 QCAA Engineering external assessment, © State of Queensland (QCAA) 2021, licensed under CC BY 4.0, and have been adapted, except where a third-party source is named. Tangent Tuition is not affiliated with the QCAA.
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