The ternary diagram given below shows phase relations for the Anorthite-Diopside-Forsterite system at 1 bar pressure. Broken lines represent isotherms with temperature in °C. If 'P' is the initial melt composition, which one of the following is the CORRECT sequence of crystallization assuming equilibrium between crystal and melt?
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Trace the liquid path away from the Fo corner through P and note which cotectic and reaction point it crosses first.
Step 1: Locate point P.
P sits inside the corner of the triangle that belongs to forsterite, so forsterite is the first mineral the cooling liquid must throw out of solution.
Step 2: Follow the liquid, not the solid.
As forsterite crystals form and get removed, the liquid composition is pushed away from the forsterite corner, tracing a straight line that starts at Fo and passes through P. Only [Fo] is solid at this point.
Step 3: Watch for the first boundary crossing.
That straight liquid path eventually meets a cotectic curve, a curve where two minerals can grow side by side. Given the geometry of this particular system, the line from Fo through P lands on the Fo-An cotectic rather than the Fo-Di one, so anorthite joins the crystallising solids: [Fo + An].
Step 4: Watch for the reaction point.
Sliding along this cotectic as cooling continues, the liquid arrives at a special reaction (peritectic) point on the boundary. At this point forsterite reacts with the remaining liquid, and a new phase, spinel, appears alongside the anorthite that keeps growing. The three solids present just past this point are [Fo + An + Sp].
Step 5: Confirm against the answer choices.
Sequences that list diopside as the second mineral do not match this path, since the line from Fo through P never crosses the Fo-Di cotectic. Only the sequence ending in forsterite, anorthite and spinel fits.
\[
\boxed{[Fo] \to [Fo + An] \to [Fo + An + Sp]}
\]
