How does x-ray crystallography reveal the three-dimensional arrangement of atoms in a solid?
Describe how x-ray crystallography uses the diffraction of x-rays by a crystal to determine three-dimensional structure
A focused answer to the WACE Year 12 Chemistry dot point on x-ray crystallography, how the diffraction of x-rays by the regular array of atoms in a crystal is used to determine bond lengths, bond angles and three-dimensional structure, with a worked example and common exam mistakes.
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What this dot point is asking
X-ray crystallography is the technique that reveals the actual three-dimensional arrangement of atoms in a crystalline solid. Unlike mass spectrometry, infrared and NMR, which give pieces of evidence about molar mass, functional groups and connectivity, x-ray crystallography can deliver the complete structure including bond lengths and angles.
Why x-rays and crystals
X-rays are used because their wavelength (around m) is comparable to the spacing between atoms in a crystal. When a wave meets a regularly repeating array with a similar spacing, it diffracts. The ordered, repeating arrangement of atoms in a crystal lattice acts as a three-dimensional diffraction grating for the x-rays.
How the structure is found
The x-rays scattered by the atoms interfere with one another, reinforcing in some directions and cancelling in others, producing a pattern of spots whose angles and intensities depend on the spacing and arrangement of the atoms. By measuring this pattern from many orientations and applying mathematical analysis, the positions of the atoms (and therefore bond lengths and bond angles) can be reconstructed.
Strengths and limitations
The great strength is that the technique gives the full three-dimensional structure, including precise bond lengths and angles, which the spectroscopic methods cannot. Its main limitation is that the substance must form a suitable single crystal; many compounds (and most liquids) cannot be crystallised easily, so the method is not always applicable. Growing a good crystal can be the hardest step.
Why this matters
X-ray crystallography has determined the structures of countless molecules, from simple salts to DNA and proteins, and it underpins drug design and materials science. In the context of Unit 4 it completes the toolkit of instrumental analysis: it is the technique to reach for when a complete three-dimensional structure of a crystalline solid is needed.