Calculating Nickel Concentration in Olivine
Understanding Partition Coefficient ($K_D$)
The partition coefficient ($K_D$) describes how a specific element distributes between two immiscible phases (in this case, solid olivine and liquid magma) at equilibrium.
The formula is:
$ K_D = \frac{\text{Concentration in Solid}}{\text{Concentration in Liquid}} $
For Nickel (Ni) between olivine and basaltic magma, this is:
$ K_{D(\text{Ni, olivine/melt})} = \frac{C_{\text{Ni, olivine}}}{C_{\text{Ni, melt}}} $
Applying the Formula to Find Ni Concentration
We are given:
- Partition coefficient for Ni, $K_{D(\text{Ni, olivine/melt})} = 5$
- Concentration of Ni in the basaltic magma (melt), $C_{\text{Ni, melt}} = 20$ ppm
We need to calculate the concentration of Ni in the crystallizing olivine ($C_{\text{Ni, olivine}}$).
Rearranging the formula to solve for $C_{\text{Ni, olivine}}$:
$ C_{\text{Ni, olivine}} = K_{D(\text{Ni, olivine/melt})} \times C_{\text{Ni, melt}} $
Substituting the given values:
$ C_{\text{Ni, olivine}} = 5 \times 20 \, \text{ppm} $
$ C_{\text{Ni, olivine}} = 100 \, \text{ppm} $
Therefore, the concentration of Ni in the olivine that crystallizes from this magma is 100 ppm.
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)
