Question

The substance called olivine may have any composition between Mg2SiO4 and Fe2SiO4, i.e. the Mg atoms can be replaced by Fe atoms in any proportion without altering the crystal structure except by expanding it slightly: this is an example of a binary solid solution series. For different compositions, the lines in the powder diffraction patterns are in slightly different positions, because of the cell expansion, but the overall pattern remains basically the same. The spacing of the lattice planes varies linearly with composition, and this can be used in a rapid and non- destructive method of analysis. a. The (062) reflection from olivine is strong and well resolved from other lines. Calculate d062 for an olivine that displays its (062) reflection at a Bragg angle of 37.21° (i.e., a diffraction angle of 74.42°) when x-rays with a wavelength of 0.1790 nm are used. b. The d062 spacing as measured accurately for synthetic materials is 0.14774 nm for Mg2SiO4 and 0.15153 nm for Fe2SiO4. What would be the approximate composition, expressed in mol.% Mg2SiO4, of an olivine material for which do62 has the value obtained in part 2.1 above?

Answer 1

Answer:

The answer is "0.147 nm and  99.63 mol %"

Explanation:

In point (a):

$\to nk1 = 062$

$\to \text{Bragg angle}$ $\theta =37.21^{\circ}$

$\to \text{diffraction angle}$ $2 \theta = 74.42^{\circ}$

$\to \lambda = 0.1790 nm$

find:

d(062)=?

formula:

$\to nx = 2d \sin \theta$

$\to d(062) = \frac{1 \times 0.1790^{\circ}}{2 \times \sin 37.21^{\circ}}$

               $= \frac{0.1790^{\circ}}{2 \times 0.604738126}\\\\= \frac{0.29599589}{2}\\\\= 0.147$

In point (b):

$\to Mg_2SiO_4\longleftrightarrow Fe_2SiO_4$

$d= 0.14774 \ \ \ \ \ olivine = 0.147 \ \ \ \ \ 0.15153$

formula:

$\to d=\frac{a}{\sqrt{n^2+k^2+i^2}}$

that's why the composition value equal to 99.63 %