Analyzing Crystal Fractionation

Le Castor

CuriosityGale Crater

PhoenixPolar Lander

One solution to this problem is the use of binary variation diagrams to study liquid lines of descent in volcanic suites.

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.

Mg variation diagrams (Bowen Diagrams):

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.

Vanuatu Arc

Epi

Appearance of Cpx

Appearance of Ulvo-spinel (Fe2TiO4)

Appearance of Apatite as a Liquidus PhaseIn Marquesa Archipelago

amphibolites

Analyzing Crystal Cumulates Using Pearce element Ratios

2:1

1:1

1:2

Olivine + Cpx 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 / Ci

liq

at equilibrium:

Cio = Fliq× Ci

liq + (1-Fliq) × Cisol

Cio = Fliq× Ciliq + (1-Fi

liq) × Ki × Ciliq

Cio = Fliq× Ci

liq if Ki = 0

Fliq = Cio / Ci

liq

or

Xxyl = 1- (Cio / Ci

liq)

Ciliq = Ci

o / ((F + Ki×(1-F)) for equilibrium crystallization

Ciliq = Ci

o × F(Ki -1) for fractional crystallization

Di = Xα× Kiα + Xβ × Ki

β + Xγ × Kiδ + …….. where ∑n Xn = 1

In the case of one crystallizing mineral:

In the case of 2 or more crystallizing minerals:

Ciliq = Ci

o / ((F + Di×(1-F)) for equilibrium crystallization

Ciliq = Ci

o × F(Di -1) for fractional crystallization

For Ki ≠ 0.0