The diagram shows a T-X phase diagram (at one atmosphere pressure) for a system

Question

The diagram shows a T-X phase diagram (at one atmosphere pressure) for a system containing four different phases: liquid, forsteritic olivine (Mg2SiO4), enstatite (MgSiO3), and cristobalite (SiO2).

a) How many chemical components are there in this system? What chemical components would you choose to describe this system? Explain!

b) How many degrees of freedom are there are point "m" on the diagram? Show your work.

c) Consider a system with a bulk composition of X, as marked at top of phase diagram. What are the compositions and the proportions of all phases present in the system at temperatures of 1600oC? Be as quantitative as possible! (Hint-for this question you must name the phases present, give the compositions of each phase, and estimate the proportions of each phase)

d) Consider a system with a bulk compositions of Y. At what temperature does this system begin to crystallize the mineral enstatite? Explain!

Explanation / Answer

a) There are 3 chemical components, having chemical formula Mg2SiO4, MgSiO3 and SiO2. Two chemical components namely Mg2SiO4 and SiO2 are enough to describe the whole system as the MgSiO3 is a stoichiometric mixture is other two components.

b) F = C -P + 2, C-no. of components (2 in this case) and P-no. of phases in thermodynamic equilibrium (2 in this case).

Degree of freedom, F = 2-2+2= 2.

c) Composition  X has ~12.5% SiO2. At 1600C, the melt (~30% SiO2) and fosterite are in equilibrium. Applying the Lever rule, we can estimate the proportions of the phases.

Xfosterite = (12.5-30)/(0-30) = 0.583

XSiO2 = 0.417

d) composition Y has ~ 40% SiO2 corresponding to point e in the diagram. Enstatite will crystallize below 1543C as lamelle along with cristabolite.

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