Question 8 of 8: Question VIII — Phase Diagram (20 marks)

Question VIII — Phase Diagram (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

VIII.1 — 50 wt% Si alloy: first solid, last liquid

Given. Al-Si system; eutectic at 577°C / 12.6 wt% Si; $\alpha$ solvus (maximum Al-rich solid solubility) 1.65 wt% Si; $\beta$ solvus (maximum Si-rich solid solubility of Al) 99.8 wt% Si; alloy composition 50 wt% Si, cooled slowly from 1200°C.

Approach. A 50 wt% Si alloy lies on the Si-rich ($\beta+L$) side of the eutectic (between 12.6% and 100% Si), so on cooling from the liquid it first crosses the $\beta+L$ liquidus, precipitating Si-rich $\beta$ solid; the remaining liquid is depleted in Si and its composition tracks down the liquidus toward the eutectic point as cooling continues.

1. (a) Liquidus temperature at 50 wt% Si. Reading the liquidus curve of the printed diagram (see the callout below): $$T_{\text{liquidus}}(50\%\text{Si}) \approx \boxed{1000^\circ\text{C}}$$ This is the temperature at which the alloy first crosses from single-phase liquid ($L$) into the two-phase $\beta+L$ field on cooling from 1200°C.
2. (b) Composition of the first solid. The first solid to nucleate is $\beta$ (Si-rich solid solution); on this diagram the $\beta$ solidus/solvus sits close to the Si-rich edge across the whole $\beta+L$ field (maximum measured solubility of Al in $\beta$ is only $100-99.8=0.2$ wt%), so the first solid forms at essentially $$\boxed{\approx99.8\ \text{wt\% Si}}$$
3. (c) Composition of the last liquid. As cooling continues from 1000°C toward 577°C, the liquid composition follows the liquidus curve down toward the eutectic point, becoming progressively depleted in Si. The last liquid to exist, immediately above the eutectic isotherm, is at the eutectic composition itself: $$\boxed{12.6\ \text{wt\% Si}}$$
4. (d) Temperature at which the last liquid solidifies. The last liquid (eutectic composition) solidifies isothermally at the eutectic temperature: $$\boxed{577^\circ\text{C}}$$ (via the eutectic reaction $L\leftrightarrow\alpha+\beta$, converting the remaining 12.6%-Si liquid into a fine $\alpha+\beta$ mixture, ignoring supercooling as instructed).

VIII.2 — Age hardening on the Al-rich side

(a) Maximum age-hardenable composition. Precipitation (age) hardening on the Al-rich side requires a composition that is single-phase $\alpha$ at an elevated solutionizing temperature but falls inside the two-phase $\alpha+\beta$ field at room temperature, so that a supersaturated solid solution can be quenched in and then made to precipitate fine $\beta$ (Si) on reheating. That window exists only up to the maximum solid solubility of Si in $\alpha$, which this diagram places at the eutectic temperature: $$\boxed{1.65\ \text{wt\% Si}}$$ Above this composition, the alloy contains primary $\beta$ (or eutectic constituent) at every temperature and cannot be taken fully into single-phase $\alpha$ without partially melting it.

(b) Heat-treating schedule (illustrative alloy: Al–1.0 wt% Si, chosen safely below the 1.65% ceiling).

1. Solution treat. Heat to ≈555–565°C (within the single-phase $\alpha$ field for 1.0 wt% Si, but safely below the 577°C eutectic to avoid incipient melting) and hold ≈2–4 hours to fully dissolve any $\beta$ (Si) and homogenise the $\alpha$ solid solution.
2. Quench. Rapidly water-quench to room temperature, suppressing $\beta$ precipitation and freezing in a supersaturated $\alpha$ solid solution (metastable, single phase in appearance, but thermodynamically unstable since room-temperature Si solubility in $\alpha$ is far below 1.0%).
3. Age (reheat). Reheat to ≈150–200°C and hold several hours (artificial ageing) to precipitate a fine, closely-spaced dispersion of $\beta$ (Si) particles, which are the actual strengthening agent (analogous to Al–Cu, Al–Si-based casting alloys such as the 3xx.x series use exactly this GP-zone/precipitate sequence).

(c) Microstructures.

VIII.3 — General invariant-reaction formats

Following the given eutectic format $L\leftrightarrow S_1+S_2$:

Each is a three-phase invariant reaction (fixed T and composition, per the phase rule at $C=2$): the eutectoid is the eutectic's solid-state analogue, one solid decomposing into two new solids on cooling (e.g. $\gamma\leftrightarrow\alpha+\text{Fe}_3\text{C}$ in steel); the peritectic combines a liquid and an existing solid to form a single new solid on cooling (the reverse sense from eutectic/eutectoid, which each produce two phases); the monotectic is the eutectic's liquid-state analogue, one liquid splitting into a second, compositionally different liquid plus a solid on cooling (occurs in systems with a liquid miscibility gap, e.g. Cu-Pb).