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?
Show Hint
Trace the liquid path away from the Fo corner through P and note which cotectic and reaction point it crosses first.
Step 1: Read the ternary diagram.
The diagram has three liquidus fields, one each for the primary crystallisation of forsterite (Fo), anorthite (An) and diopside (Di), separated by cotectic boundary curves. Isotherms drawn on the diagram show falling temperature as the melt cools and moves across these fields. Point P is the starting melt composition and it plots inside the forsterite field.
Step 2: Track the first stage of cooling.
Since P lies in the forsterite field, forsterite alone starts crystallising as the melt cools. As solid Fo is removed from the liquid, the remaining liquid composition moves directly away from the Fo corner of the triangle, in a straight line away from Fo through P. The solid assemblage at this stage is just [Fo].
Step 3: Track the second stage.
The liquid path eventually reaches the boundary curve that separates the forsterite field from the anorthite field. Once on this cotectic, both forsterite and anorthite crystallise together, and the liquid composition now runs along the boundary curve. The solid assemblage becomes [Fo + An].
Step 4: Track the third stage.
Following the boundary curve further, the liquid reaches a reaction point on the Fo-An boundary where a peritectic type reaction sets in between forsterite and the liquid, generating spinel (Sp) while anorthite continues to crystallise. Forsterite is partly resorbed in this reaction, but is not used up, so the assemblage now carries three phases: [Fo + An + Sp].
Step 5: Match to the options.
This sequence, [Fo] then [Fo + An] then [Fo + An + Sp], matches option (D) exactly, and rules out the other sequences that either keep diopside as the second phase or invent a wrong boundary path.
Final Answer:
\[
\boxed{[Fo] \to [Fo + An] \to [Fo + An + Sp]}
\]
