X-ray Crystallography

In-depth explanation of X-ray Crystallography

X-ray crystallography determines the three-dimensional arrangement of atoms in a crystal by measuring how a beam of X-rays is diffracted by the regular array of atoms in a single crystal. The diffracted beams form a pattern of spots whose positions satisfy Bragg's law, n times lambda equals 2d sin theta, and whose intensities encode the electron density within the unit cell. A Fourier transform of the observed intensities gives an electron density map, from which atomic positions, bond lengths and bond angles are derived. Hydrogen atoms are hard to locate because they contribute few electrons. The technique has solved the structures of countless small molecules, proteins and DNA.

Going deeper: X-ray Crystallography

Key ideas: Bragg's law: n lambda = 2 d sin theta. Cu K-alpha radiation (0.1542 nm) and Mo K-alpha (0.0711 nm) are common sources. Systematic absences indicate lattice type, and the R factor (below about 5 percent for good small-molecule structures) measures agreement between model and data. Powder diffraction gives a fingerprint pattern for phase identification and lattice parameters.

Common mistakes and connections: The hardest part is growing a single crystal of sufficient size and quality, which is often the bottleneck. X-rays scatter from electrons, so heavy atoms dominate and hydrogens are poorly located. A crystal structure shows the solid state, which may differ from solution conformation. The phase problem means intensities alone do not give a map without extra methods. Links to unit cells, crystal systems and lattice planes.

Visualization of X-ray Crystallography

X-rays diffract from the ordered atomic planes of a crystal such as the NaCl lattice, and Bragg's law gives the plane spacing and unit-cell structure. The interactive lesson shows this as a live animation or chart.

Worked example and use case

Dorothy Hodgkin used X-ray crystallography to determine the structures of penicillin and vitamin B12.

Where X-ray Crystallography fits in Analytical, Lab & Spectroscopy

X-ray Crystallography is topic 54 of 99 in Analytical, Lab & Spectroscopy.

Related topics

• Atomic Absorption SpectroscopyAdvanced
• Flame PhotometryAdvanced
• ICP-MSAdvanced
• Electron MicroscopyAdvanced
• Scanning Tunneling MicroscopyAdvanced
• Gravimetric AnalysisIntermediate

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