Chapter 15, Problem 15A.5ST

Interpretation Introduction

Interpretation:

From the given structure factors, the electron density along the corresponding direction has to be constructed.

Concept Introduction:

Fourier synthesis of the electron density:

Electron density $\text{ρ(x)}$ can be calculated as:

    $\text{ρ(x) = }\frac{\text{1}}{\text{V}}{\text{{F}}_{\text{0}}\text{+2}{\displaystyle \sum _{\text{h=1}}^{\text{¥}}{\text{F}}_{\text{h}}}\text{cos(2hπx)}}\underset{}{\to }(1)$

    ${\text{F}}_{\text{h}}$ is known as structure factor. It can be either + or -.

    ${\text{F}}_{\text{h}}{\text{= I}}_{\text{h}}{}^{\text{1/2}}$, ${\text{I}}_{\text{h}}$ is the intensity.

Low values of h will give major features of the structure and high values of h gives fine detail.

The above equation is known as Fourier synthesis of electron density.

It helps to reconstruct the varying electron density in a unit cell by superimposing cosine waves of different wavelengths.