A hypothetical garnet peridotite composed of 60% olivine, 25% orthopyroxene, 10% clinopyroxene and 5% garnet undergoes 10% batch melting described by $\frac{C_L}{C_o} = \frac{1}{F+D-F*D}$ where F is degree of melting and D is bulk partition coefficient. The ratio of Ce in the melt to the original rock will be ___________ (round off to 2 decimal places). (The $K_D$ values of Ce for olivine, orthopyroxene, clinopyroxene and garnet are 0.001, 0.003, 0.10 and 0.02, respectively)
This solution explains how to calculate the ratio of Cerium (Ce) concentration in the melt to the original rock concentration during partial melting of a garnet peridotite.
Peridotite Composition and KD Values
The garnet peridotite has the following modal composition and known partition coefficients ($K_D$) for Cerium (Ce):
- Olivine (Ol): 60% (XOl = 0.60), KD,Ol = 0.001
- Orthopyroxene (Opx): 25% (XOpx = 0.25), KD,Opx = 0.003
- Clinopyroxene (Cpx): 10% (XCpx = 0.10), KD,Cpx = 0.10
- Garnet (Grt): 5% (XGrt = 0.05), KD,Grt = 0.02
The degree of melting is given as 10% (F = 0.10).
Calculating Bulk Partition Coefficient (D)
The bulk partition coefficient (D) represents the overall partitioning of Ce between the solid and the melt, considering the proportions of each mineral phase. It is calculated as the weighted average of the individual mineral partition coefficients:
D = $\sum (X_i \times K_{D,i})$
Substituting the given values:
D = (0.60 $\times$ 0.001) + (0.25 $\times$ 0.003) + (0.10 $\times$ 0.10) + (0.05 $\times$ 0.02)
D = 0.0006 + 0.00075 + 0.0100 + 0.0010
D = 0.01235
Determining Ce Ratio in Melt (CL/C0)
The question provides the formula for batch melting relating the concentration in the melt (CL) to the original concentration in the rock (C0):
$\frac{C_L}{C_0} = \frac{1}{F + D - F \times D}$
This formula can also be written as:
$\frac{C_L}{C_0} = \frac{1}{D + F(1-D)}$
Now, we substitute the calculated value of D and the given value of F:
$\frac{C_L}{C_0} = \frac{1}{0.01235 + 0.10 \times (1 - 0.01235)}$
$\frac{C_L}{C_0} = \frac{1}{0.01235 + 0.10 \times (0.98765)}$
$\frac{C_L}{C_0} = \frac{1}{0.01235 + 0.098765}$
$\frac{C_L}{C_0} = \frac{1}{0.111115}$
$\frac{C_L}{C_0} \approx 9.00072
Final Ratio Determination
The calculated ratio of Ce in the melt to the original rock is approximately 9.00072. Rounding this to two decimal places gives 9.00.
This value falls within the specified range of 8.9 to 9.1.
Important Questions from Igneous Petrology (Trace Elements/Melting/Evolution)
- Choose the explanation(s) for negative Eu anomalies in upper crustal rocks like granite and granodiorite.
- A source rock undergoes melting. Assuming batch melting, $5\%$ partial melting and bulk distribution coefficient of $0.045$, the enrichment factor ($C_L/C_o$) of Rb in the melt will be ________. (Round off to $2$ decimal places)
- A basaltic magma has an initial nickel concentration of 300 ppm. Olivine crystallizes from this magma by equilibrium crystallization (Case I) or fractional crystallization (Case II). Then, the absolute value of the difference between the nickel concentrations of the liquids remaining after 25% crystallization in these two cases is ________.
(Use $K_{D,Ni}$ olivine/melt = 10). - The modal abundance in an ultramafic rock and the partition coefficients of lutetium (Lu) in clinopyroxene, orthopyroxene, olivine and plagioclase are tabulated below. The bulk distribution coefficient of lutetium ($D_{Lu}$) in the ultramafic rock is ________.
Mineral Modal abundance (%) Partition coefficient Clinopyroxene 45 0.506 Orthopyroxene 40 0.42 Olivine 10 0.045 Plagioclase 05 0.019 Choose the CORRECT combination for the following four statements.
Statement I: Anhydrous partial melting of peridotites produces basaltic magma.
Statement II: Hydrous melting of peridotites produces andesitic magma.
Statement III: Congruent melting of minerals produces liquids of compositions identical to the minerals.
Statement IV: Incongruent melting of minerals produces liquids of different compositions and new solids.
