Question 8 of 8: Question VIII: Phase Diagram

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.

Part 1 — Given. Al-Si eutectic phase diagram (from the exam appendix): eutectic at 577°C, 12.6 wt% Si; maximum solubility of Si in $\alpha$ (Al-rich solid solution) at the eutectic temperature, 1.65 wt% Si; $\beta$ (Si-rich solid solution) essentially pure, solidus at 99.8 wt% Si; alloy composition 50 wt% Si, cooled slowly from 1200°C.

Find. (a) first-solid temperature, (b) first-solid composition, (c) last-liquid composition, (d) last-liquid solidification temperature.

Approach. The 50 wt% Si alloy is Si-rich of the eutectic (12.6 wt%), so on cooling from an all-liquid state it enters the $\beta+L$ two-phase field first; the liquidus temperature at 50 wt% Si (read from the printed curve, calibrated against the diagram's own labelled points) fixes (a), and the tie-line end-points there and at the eutectic isotherm answer (b)–(d) directly from the printed diagram values.

[Figure not reproduced: Al-Si eutectic phase diagram, redrawn from the exam figure, with the tie-line construction for the 50 wt% Si alloy at its liquidus (blue) and the eutectic isotherm (red) marked. See the official exam paper.]

1. (a) First-solid temperature. A 50 wt% Si alloy cooling from 1200°C crosses into the $\beta+L$ two-phase field where the liquidus curve reaches 50 wt% Si. Reading the liquidus at that composition gives $$\boxed{T\approx971^{\circ}\text{C}}.$$
2. (b) Composition of the first solid. At the liquidus, the tie line runs from the liquid composition (50 wt% Si) across to the solidus of the phase that is nucleating. Since the alloy sits on the Si-rich side of the eutectic, the first solid to form is primary $\beta$, whose solidus the diagram fixes at essentially pure silicon: $$\boxed{\approx99.8\ \text{wt\% Si}}.$$
3. (c) Composition of the last liquid. As cooling continues through $\beta+L$, the liquid composition tracks down the liquidus curve toward the eutectic point; the last liquid remaining just above the eutectic isotherm is therefore at the eutectic composition itself, $$\boxed{12.6\ \text{wt\%\ Si}}.$$
4. (d) Temperature at which the last liquid solidifies. That last liquid solidifies via the eutectic reaction, at the eutectic (invariant) temperature printed on the diagram: $$\boxed{577^{\circ}\text{C}}.$$

Part 2(a) — Given. The Al-rich $\alpha$ solvus meets the eutectic isotherm at 1.65 wt% Si (577°C), and the solubility of Si in $\alpha$ falls with decreasing temperature (the solvus line drawn sloping toward the Al axis).

Find. The maximum Si content for which an Al-Si alloy is age-hardenable.

Precipitation (age) hardening needs a solvus whose solubility decreases with falling temperature, so that a composition solutionized as single-phase $\alpha$ at high temperature can be quenched into a supersaturated solid solution and then aged to precipitate a fine, hardening dispersion of $\beta$. That mechanism is only available up to the composition where the alloy is still single-phase $\alpha$ just below the eutectic temperature — i.e. up to the maximum solid solubility itself, $$\boxed{1.65\ \text{wt\%\ Si}}.$$ Beyond this composition, the alloy enters the $\alpha+\beta$ two-phase field immediately below the eutectic isotherm with no single-phase $\alpha$ solutionizing window available.

Part 2(b). Choosing an Al–1.0 wt%Si alloy (comfortably inside the 1.65 wt% age-hardenable limit) as a concrete example, a standard three-stage schedule is: (i) solutionize at a temperature just below the solvus/eutectic line, e.g. ≈550–560°C, held long enough (several hours) to dissolve all $\beta$ into a homogeneous single-phase $\alpha$; (ii) quench rapidly (water quench) to room temperature, suppressing diffusion so the alloy is trapped as a supersaturated solid solution (SSSS) — still single-phase $\alpha$, but now carrying far more Si than room-temperature equilibrium solubility allows; (iii) age (reheat) at an intermediate temperature, e.g. ≈170–180°C for several hours, to let fine $\beta$ (Si-rich) precipitates nucleate and grow throughout the $\alpha$ matrix, which is what produces the hardening — overaging past the optimum time coarsens the precipitates and softens the alloy again.

Part 2(c). The three microstructures below correspond to the same three stages: solutionized (uniform single-phase $\alpha$ grains, no visible second phase); quenched (still visually single-phase $\alpha$ — the supersaturation is not resolvable optically, only by the elevated hardness/lattice strain it carries); reheated/aged (a fine, dispersed population of $\beta$ precipitates throughout each $\alpha$ grain, which is what pins dislocations and raises the strength).

Part 3. Following the same Liquid $\leftrightarrow$ Solid 1  + Solid 2 pattern given for the eutectic reaction, the three related invariant reactions are written:

The eutectoid reaction is the solid-state analogue of the eutectic: one solid phase transforms isothermally, on cooling, into two different solid phases (e.g. the classic $\gamma\leftrightarrow\alpha+\text{Fe}_3\text{C}$ reaction in the Fe-C system). The peritectic reaction runs the eutectic pattern with one fewer degree of freedom on the liquid side: an existing solid combines with the remaining liquid, on cooling, to form a single new solid phase. The monotectic reaction is the odd one out, involving two liquids: one liquid phase separates, on cooling, into a solid phase and a second, compositionally distinct liquid phase.