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

DoITPoMS Teaching & Learning Packages Indexing Electron Diffraction Patterns Indexing with the orientation of the electron beam known
Indexing Electron Diffraction Patterns AimsBefore you startIntroductionMathematics relating the real space to the electron diffraction patternLaue zonesKikuchi linesUsing polycrystalline materials in the TEMConvergent beam electron diffraction (CBED)Using other methods in conjunction with electron diffractionSummaryQuestionsGoing further
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Indexing with the orientation of the electron beam known

Diagram showing real space plane and reciprocal lattice plane

From the Ewald sphere diagram, we know that the zero order Laue zone (ZOLZ) contains reflections hkl where hu + kv + lw = 0 (the Weiss zone law). This ZOLZ can be identified by finding two reciprocal lattice vectors in the ZOLZ. Suppose these two reciprocal lattice vectors are h1a* + k1b* + l1c* and h2a* + k2b* + l2c*. Then we know

h1u + k1v + l1w = 0

and

h2u + k2v + l2w = 0

and that the angle between these reciprocal lattice vectors is the angle between the h1k1l1 and h2k2l2 planes.

Other reflections in the electron diffraction pattern can then be deduced from simple vector addition, with the proviso that the indices of the reciprocal lattice vectors are integers and that they are not forbidden by the lattice. The pattern can then be built up manually or by computer.

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