Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

DoITPoMS Teaching & Learning Packages X-ray Diffraction Techniques Determining lattice parameters accurately
X-ray Diffraction Techniques AimsBefore you startIntroductionExperimental mattersBragg′s lawSingle crystal diffractionDetermining lattice parameters accuratelyRelationship between crystalline structure and X-ray dataPowder diffractionPhase identificationOriented (or textured) samplesSummaryQuestionsGoing further
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Determining lattice parameters accurately

When using diffraction data to obtain a lattice parameter, it is important to note the shape of the θ - sin θ curve:
Diagram of sin theta curve
The largest gradient on this curve is at low values of θ. This means that a small error in the recorded angle of the diffraction peak will cause a significant error in the calculated lattice parameter. At high values of θ the error in the calculated sin θ value will be reduced. This leads to a smaller error in the calculated value of the lattice parameter. The same conclusion can be drawn by differentiating the Bragg equation.

This implies that lattice parameters calculated from high angle diffraction peaks are more accurate than those taken from low angle peaks.

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