Solid Solution Binary Diagrams
When two minerals form a complete solid solution - meaning that any mixture of their components is structurally permissible - the binary phase diagram takes on a different shape from the eutectic case. There is no single fixed eutectic point. Instead, crystallization proceeds over a range of temperatures, and the composition of both the growing crystals and the residual melt continuously shifts as cooling progresses. The critical complication is that earlier-formed crystals must exchange atoms with the melt throughout crystallization to remain in equilibrium with it - a process that makes the composition of the growing solid a moving target. [1]
The Olivine Binary Diagram
The olivine binary diagram plots temperature on the vertical axis and composition from 100% forsterite (Mg2SiO4) on the left to 100% fayalite (Fe2SiO4) on the right. Two curves define the diagram: the liquidus above which only melt exists, the solidus below which only olivine crystals exist, and the olivine + melt field between them. At any given temperature within this two-phase field, a horizontal tie-line from the solidus to the liquidus gives the composition of coexisting crystals (on the solidus) and melt (on the liquidus) simultaneously. [1]
Crystallization of a 70% Forsterite Melt
Consider an initial melt of composition 70% Fo and 30% Fa at 1900°C. Because this point lies above the liquidus, the system is entirely melt. The bulk composition is tracked by a vertical dotted line as cooling proceeds. [1]
Cooling brings the system to 1740°C, which is the liquidus temperature for a 70% Fo composition. At this point, the first minute crystals of olivine form. The tie-line at 1740°C shows that these first crystals have a composition of Fo91 - they are strongly enriched in Mg compared with the melt. Because the growing crystals preferentially incorporate Mg, the remaining melt becomes depleted in Mg and progressively richer in Fe. [1]
At 1600°C, the tie-line shows that the melt now has only 47% of the forsterite component, while the crystals have shifted to Fo79. This re-equilibration of the crystals - from Fo91 at the start to Fo79 now - is critically important. Under equilibrium crystallization, every increment of newly crystallized olivine, and all previously crystallized olivine, must exchange Fe and Mg with the melt by diffusion to acquire the new equilibrium composition. The lever rule at this temperature gives 71% crystals and 29% melt. [1]
Cooling continues to 1517°C, at which point all the olivine has the composition Fo70 - exactly the same as the original bulk composition of the starting melt. Crystallization is complete. The last drop of melt at this temperature has a composition of 36% Fo, as given by where the final tie-line intersects the liquidus. [1] Below 1517°C the system consists entirely of Fo70 olivine crystals.
Equilibrium Melting in Reverse
Equilibrium melting traces the same path in reverse. Heating Fo70 olivine, the first melt that forms has a composition of 36% Fo. As heating continues, olivine dissolves and the melt progressively acquires more Mg until, at 1740°C, the last crystal dissolves and the melt reaches 70% Fo - the original composition. [1]
Why the Crystals Must Re-Equilibrate
The requirement for continuous re-equilibration is what makes complete-solid-solution systems fundamentally different from eutectic systems. In the diopside-anorthite eutectic, each mineral crystallizes with a fixed composition and does not change. In olivine, every crystal that formed at any stage of cooling has the wrong composition for the new, lower temperature - it crystallised at Fo91 but needs to be Fo79 by 1600°C. It can only reach the correct composition if Fe and Mg diffuse between the crystal and the melt. If diffusion is too slow - for instance if cooling is rapid - the crystals cannot fully re-equilibrate and become zoned, with Mg-rich cores and Fe-richer rims recording the history of progressive crystallization.
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References & Citations
- 1.Introduction to Mineralogy Nesse, W. D.
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