A garnet peridotite contains 2400 ppm of nickel. After 20% partial melting, a basaltic melt is generated, leaving a residue comprising 60% olivine, 30% orthopyroxene and 10% clinopyroxene. Given the $K_D^{Ni}$ (olivine) = 10, $K_D^{Ni}$ (orthopyroxene) = 4 and $K_D^{Ni}$ (clinopyroxene) = 2, the nickel concentration in the melt, assuming equilibrium batch melting, is ___________ ppm.
Nickel Concentration Calculation in Partial Melting
This solution calculates the nickel concentration in a basaltic melt generated from the partial melting of garnet peridotite. We use the principles of equilibrium batch melting and distribution coefficients ($K_D$) to determine the final melt composition.
Understanding Equilibrium Batch Melting
Equilibrium batch melting assumes that the melt generated at each stage remains in equilibrium with the remaining solid residue. The concentration of a trace element (like nickel) in the melt ($C_L$) is governed by the initial concentration in the source ($C_O$), the fraction of melt produced ($F$), and the bulk distribution coefficient ($D$) between the solid residue and the melt.
Calculating the Bulk Distribution Coefficient (D)
The bulk distribution coefficient ($D$) represents the average partitioning of nickel between the solid residue and the melt. It is calculated based on the mineralogy of the residue and their respective nickel distribution coefficients.
- Residue composition: 60% Olivine, 30% Orthopyroxene, 10% Clinopyroxene.
- Distribution coefficients ($K_D^{Ni}$): Olivine = 10, Orthopyroxene = 4, Clinopyroxene = 2.
The formula for the bulk distribution coefficient is:
$ D = \sum (X_i \times K_{D,i}) $Where $X_i$ is the weight fraction of mineral $i$ in the residue and $K_{D,i}$ is the distribution coefficient for mineral $i$.
Substituting the given values:
$ D = (0.60 \times 10) + (0.30 \times 4) + (0.10 \times 2) $ $ D = 6.0 + 1.2 + 0.2 $ $ D = 7.4 $Applying the Batch Melting Equation
The concentration of nickel in the melt ($C_L$) is calculated using the batch melting equation:
$ C_L = \frac{C_O}{F + D(1-F)} $Given:
- Initial nickel concentration ($C_O$) = 2400 ppm
- Melt fraction ($F$) = 20% = 0.20
- Bulk distribution coefficient ($D$) = 7.4
Now, substitute these values into the equation:
$ C_L = \frac{2400 \text{ ppm}}{0.20 + 7.4 \times (1 - 0.20)} $ $ C_L = \frac{2400}{0.20 + 7.4 \times 0.80} $ $ C_L = \frac{2400}{0.20 + 5.92} $ $ C_L = \frac{2400}{6.12} $ $ C_L \approx 392.16 \text{ ppm} $Final Nickel Concentration
The calculated nickel concentration in the basaltic melt is approximately 392.16 ppm. This value falls within the range specified.
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 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)
