Question

The olivine series of minerals consists of crystal in which $F{e}^{2+}$ and $M{g}^{2+}$ ions may substitute for each-other causing substitutional impurity defect without changing the volume of the unit cell. In olivine series of mineral, oxide ion exists as fcc with $S{i}^{4+}$ occupying ${\frac{1}{4}}^{th}$ of the octahedral void and divalent ion occupying ${\frac{1}{4}}^{th}$ th of the tetrahedral void. The density of forsterite (Magnesium silicate) is $3.0\text{g/cc}$ and that of fayalite (Ferrous silicate) is $4.0\text{g/cc}$. If density of olivine is $3.53\text{g/cc}$, then which of the following statement is INCORRECT.

• A. Forsterite = $M{g}_{2}Si{O}_4$ ; Fayalite = $F{e}_{2}Si{O}_4$
• B. An olivine contains $40\%$ Forsterite and $60\%$ Fayalite
• C. Forsterite $M{g}_{2}Si{O}_4$ with $60\%$ percentage
• D. Both (A) and (B)

Answer 1

The correct option is C Forsterite $M{g}_{2}Si{O}_4$ with $60\%$ percentage

According to given data
$O^{2-}=8\times \frac{1}{8}+6\times \frac{1}{2}=4$
$S{i}^{4+}=\frac{1}{4}\times \text{octahedral void}=\frac{1}{4}\times 4=1$
$M{g}^{2+}=\frac{1}{4}\times \text{tetrahedral void}=\frac{1}{4}\times 8=2$
$\because$ Forsterite = $M{g}_{2}Si{O}_4$, Fayalite = $F{e}_{2}Si{O}_4$
Let the forsterite be $x\%$ and fayalite be $(100-x)\%$ then


average density = $\frac{\text{total mass}}{Totalvolume}$

$3.53=\frac{100}{\frac{x}{3}+\frac{100-x}{4}}$
$x=40$




$x=40\%$ (Forsterite) and $60\%$ (Fayalite).