Solution (source code)

= Solution

The cooling curve first falls in the entirely liquid field. On crossing the <liquidus>, primary Ag-rich $\alpha$ begins to grow. <Latent heat> release makes the descent shallower; the remaining liquid becomes richer in <copper> and approaches the <eutectic composition>.

At $779^\circ\mathrm C$, the remaining liquid solidifies as $\alpha+\beta$, giving an \b[isothermal arrest] under the ideal equilibrium, heat-extraction model. After the liquid is exhausted, <temperature> falls through the two-solid field. Continued loss of solid solubility causes additional redistribution and precipitation; it does not require another invariant liquid-freezing plateau.

\Image[/past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2016/paper-1-ag-cu-cooling.png]
{title=Original schematic cooling curve for Ag-20 wt% Cu, with an unspecified liquidus kink and a labelled eutectic arrest}

Immediately before the eutectic reaction, the remaining liquid fraction is
$$
w_L=\frac{20-9}{28-9}=\frac{11}{19}=0.5789;
\qquad w_{\alpha,\rm primary}=\frac8{19}=0.4211.
$$
The arrest represents freezing of roughly $58\%$ of the sample by <mass>. Its duration cannot be calculated without the heat-extraction rate and <latent heat>, and the onset <temperature> cannot be calculated exactly from the supplied phase-diagram points alone.