Mineral Modal abundance (%) Partition coefficient Clinopyroxene 45 0.506 Orthopyroxene 40 0.42 Olivine 10 0.045 Plagioclase 05 0.019
Calculating Bulk Distribution Coefficient for Lu in Ultramafic Rock
The bulk distribution coefficient ($D_{bulk}$) represents the average partitioning of an element between a rock and a melt, considering the modal abundance of each mineral and its individual partition coefficient.
The formula used is:
$D_{bulk} = \sum_{i} (X_i \times D_i)$Where:
- $X_i$ is the modal abundance of mineral $i$ (as a fraction).
- $D_i$ is the partition coefficient of the element (Lutecium, Lu) in mineral $i$.
Mineral Data for Calculation
| Mineral | Modal Abundance (%) | Partition Coefficient (DLu) |
|---|---|---|
| Clinopyroxene | 45 | 0.506 |
| Orthopyroxene | 40 | 0.42 |
| Olivine | 10 | 0.045 |
| Plagioclase | 5 | 0.019 |
Step-by-Step Calculation of DLu
- Convert Modal Abundances to Fractions:
- Clinopyroxene: $45\% = 0.45$
- Orthopyroxene: $40\% = 0.40$
- Olivine: $10\% = 0.10$
- Plagioclase: $5\% = 0.05$
- Calculate the Contribution of Each Mineral to DLu:
- Clinopyroxene: $0.45 \times 0.506 = 0.2277$
- Orthopyroxene: $0.40 \times 0.42 = 0.1680$
- Olivine: $0.10 \times 0.045 = 0.0045$
- Plagioclase: $0.05 \times 0.019 = 0.00095$
- Sum the Contributions to Find DLu: $D_{Lu} = 0.2277 + 0.1680 + 0.0045 + 0.00095$ $D_{Lu} = 0.40115$
Final Result
The calculated bulk distribution coefficient ($D_{Lu}$) for lutetium in the ultramafic rock is 0.40115.
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). 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)
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.
