IB Chemistry - Data Processing

IB Chemistry home > Syllabus 2016 > Data Processing > Single crystal X-ray crystallography

Syllabus ref: 21.1

X-ray crystallography is the oldest and most precise method crystallography in which a beam of X-rays strikes a single crystal, producing scattered beams.

When they land on a piece of film or other detector, these beams make a diffraction pattern of spots; the strengths and angles of these beams are recorded as the crystal is gradually rotated. Each spot is called a reflection, since it corresponds to the reflection of the X-rays from one set of evenly spaced planes within the crystal.


The theory

X-rays have just the right wavelength to undergo reflection when falling on regions of electron density. Some of the relected beams constructively interfere and the intensity increases, while others destructively interfere and the beam strength weakens.

The result is a series of spots that can be analysed to build up a picture of the regions of electron density within the crystal and hence the postions of the atoms.

The diffraction of light and other electromagnetic radiation was first studied by Bragg in the University of Leeds.



The technique of single-crystal X-ray crystallography has three basic steps.

  • Obtain a regular crystal
  • Mount the crystal and rotate in an X-ray beam
  • Analyse the data

Regular crystals

Many substances form crystallise materials, but it is often very difficult to make crystals that are sufficiently pure and large enough for analysis by X-ray.

The crystal should be sufficiently large (typically larger than 0.1 mm in all dimensions), pure in composition and regular in structure, with no significant internal imperfections such as cracks or twinning.

The X-ray beam

Thew source is usually monochromatic (one wavelength). The crystal is gradually rotated, previous reflections disappear and new ones appear; the intensity of every spot is recorded at every orientation of the crystal. Multiple data sets may have to be collected, with each set covering slightly more than half a full rotation of the crystal and typically containing tens of thousands of reflections.

Computational analysis

The data is analysised by computer and combined with other data to refine a model of the arrangement of atoms within the crystal. The final, refined model of the atomic arrangement - now called a crystal structure - is usually stored in a public database.


Information obtained

Single-crystal X-ray Diffraction is a non-destructive analytical technique which provides detailed information about the internal lattice of crystalline substances, including unit cell dimensions, bond-lengths, bond-angles, and details of site-ordering.

Directly related is single-crystal refinement, where the data generated from the X-ray analysis is interpreted and refined to obtain the crystal structure.

Crystallography is the most unambiguous method for determining structures of small molecules and macromolecules.



As the crystal's repeating unit, its unit cell, becomes larger and more complex, the atomic-level picture provided by X-ray crystallography becomes less well-resolved (more "fuzzy") for a given number of observed reflections.

Two limiting cases of X-ray crystallography- "small-molecule" and "macromolecular" crystallography - are often discerned.

Small-molecule crystallography typically involves crystals with fewer than 100 atoms in their asymmetric unit; such crystal structures are usually so well resolved that the atoms can be discerned as isolated "blobs" of electron density.

By contrast, macromolecular crystallography often involves tens of thousands of atoms in the unit cell.

Such crystal structures are generally less well-resolved (more "smeared out"); the atoms and chemical bonds appear as tubes of electron density, rather than as isolated atoms.

In general, small molecules are also easier to crystallize than macromolecules; however, X-ray crystallography has proven possible even for viruses with hundreds of thousands of atoms.


Summary of X-ray crystallography


  • No separate standards required
  • Non-destructive
  • Detailed crystal structure, including unit cell dimensions, bond-lengths, bond-angles and site-ordering information
  • Determination of crystal-chemical controls on mineral chemistry
  • With specialized chambers, structures of high pressure and/or temperature phases can be determined
  • Powder patterns can also be derived from single-crystals by use of specialized cameras (Gandolfi)


  • Must have a single, robust (stable) sample, generally between 50—250 microns in size
  • Optically clear sample
  • Twinned samples can be handled with difficulty
  • Data collection generally requires between 24 and 72 hours