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

DoITPoMS Teaching & Learning Packages Indexing Electron Diffraction Patterns Example of indexing with a known electron beam orientation
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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Example of indexing with a known electron beam orientation

Suppose the material under examination is copper, and suppose the electron beam direction is [211]. Copper has a cubic close packed structure with a lattice parameter, a, of 0.361 nm. Allowed reflections must have h,k,l either all even or all odd. Thus the planes with the highest interplanar spacings (and hence those that give rise to reflections with the smallest rhkl values) are {111}, {200}, {220}, {311}, {222}, etc.

Looking at the {111} planes, it is apparent that the Weiss zone law is obeyed for (111) when [uvw] = [211]. Hence 111 is a possible reciprocal lattice vector.

No {200} plane will obey the Weiss zone law for [uvw] = [211], but of the {220} planes it is apparent that (022) will. Hence 022 is a second possible reciprocal lattice vector.

The angle between the 111 and 022 reciprocal lattice vectors is 90° - the dot product of these two reciprocal lattice vectors is zero. The ratio of the lengths of these two reciprocal lattice vectors is √3 : √8. These are the two shortest reciprocal lattice vectors in the [211] electron diffraction pattern. Thus the pattern looks like:

Electron diffraction pattern

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