Analyzing Crystal Fractionation. Phoenix Polar Lander. Le Castor. Curiosity Gale Crater.
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Four component systems are insufficient to accurately portray the phase relations of primary magmas as they evolve due to processes such as crystal fractionation. For example, we cannot determine when an oxide mineral will crystallize in the olivine liquidus projection to the left.
One solution to this problem is the use of binary variation diagrams to study liquid lines of descent in volcanic suites.
Mg is an analogue for temperature, so that plotting other elements against Mg, gives one an idea of how these elements change as temperature drops during crystal fractionation. This type of diagram is most commonly used in suites with relatively primitive Mg-rich lavas, and is less useful for volcanic suites dominated by relatively felsic lavas.
In Marquesa Archipelago
XCpx versus Yolivine
Estimating degree of crystallization using highly incompatible elements:
Incompatible elements are those that preferentially partition into a liquid phase coexisting with solid phases. They tend to be elements whose high charge (HFSE, high field strength elements such as: Zr, Nb, Hf) or large ionic radii (LIL, large ion lithophile elements such as: Rb, Ba, La), prevent them from substituting for the common major elements. For any trace element i:
Ki = Cisolid / Ciliq
Cio = Fliq× Ciliq + (1-Fliq) × Cisol
Cio = Fliq× Ciliq + (1-Filiq) × Ki × Ciliq
Cio = Fliq× Ciliq if Ki = 0
Fliq = Cio / Ciliq
Xxyl = 1- (Cio / Ciliq)
In the case of one crystallizing mineral:
Ciliq = Cio / ((F + Ki×(1-F)) for equilibrium crystallization
Ciliq = Cio × F(Ki -1) for fractional crystallization
In the case of 2 or more crystallizing minerals:
Ciliq = Cio / ((F + Di×(1-F)) for equilibrium crystallization
Ciliq = Cio × F(Di -1) for fractional crystallization
Di = Xα× Kiα + Xβ × Kiβ + Xγ × Kiδ+ …….. where ∑n Xn = 1