4: X-ray Crystallography

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4.1: Background
4.2: Unit Cells
The construction of a simple powder diffractometer was first described by Hull in 19171 which was shortly after the discovery of X-rays by Wilhelm Conrad Röntgen in 18952. Diffractometer measures the angles at which X-rays get reflected and thus get the structural information they contains. Nowadays resolution of this technique get significant improvement and it is widely used as a tool to analyze the phase information and solve crystal structures of solid-state materials.
4.3: Miller Indices (hkl)
The orientation of a surface or a crystal plane may be defined by considering how the plane (or indeed any parallel plane) intersects the main crystallographic axes of the solid. The application of a set of rules leads to the assignment of the Miller Indices (hkl), which are a set of numbers which quantify the intercepts and thus may be used to uniquely identify the plane or surface.
4.4: Sample and data collection
X-ray Crystallography is a scientific method used to determine the arrangement of atoms of a crystalline solid in three dimensional space. This technique takes advantage of the interatomic spacing of most crystalline solids by employing them as a diffraction gradient for x-ray light, which has wavelengths on the order of 1 angstrom (10-8 cm).
4.5: Crystallography quick reference
The branch of science devoted to the study of molecular and crystalline structure and properties, with far-reaching applications in mineralogy, chemistry, physics, mathematics, biology and materials science.

Thumbnail: 3D depiction of electron density (blue) of a ligand (orange) bound to a binding site in a protein (yellow).[131] The electron density is obtained from experimental data, and the ligand is modeled into this electron density. (CC BY-SA 4.0; Theislikerice via Wikipedia)