Chapter 15, Problem 15A.11E

Interpretation Introduction

Interpretation:

The value of unit cell parameter, a has to be calculated.

Concept Introduction:

Bragg’s law:

The spacing between the layers of atoms is given by the formula,

  $\begin{array}{l}\text{nλ=2dsinθ}\\ \\ \text{d=}\frac{\text{nλ}}{\text{2sinθ}}\end{array}$

The separation of planes can be calculated using miller indices as,

    $\frac{\text{1}}{{\text{d}}^{\text{2}}}\text{=}\frac{{\text{h}}^{\text{2}}}{{\text{a}}^{\text{2}}}\text{+}\frac{{\text{k}}^{\text{2}}}{{\text{b}}^{\text{2}}}\text{+}\frac{{\text{l}}^{\text{2}}}{{\text{c}}^{\text{2}}}$

Where,

h, l, and k are miller indices which indicates each plane.

d is distance of separation of plane.

For a tetragonal primitive system, the relationship is given as below:

  $\frac{\text{1}}{{\text{d}}^{\text{2}}}\text{=}\frac{{\text{h}}^{\text{2}}+{\text{k}}^{\text{2}}}{{\text{a}}^{\text{2}}}\text{+}\frac{{\text{l}}^{\text{2}}}{{\text{c}}^{\text{2}}}$