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 furtherTLP creditsTLP contentsShow all contentViewing and downloading resourcesAbout the TLPsTerms of useFeedbackCredits Print this page
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Derivation of rhkldhkl = λL
From the diagram,
\[\frac{r}{L} = \tan 2\theta \]
The Bragg condition (which is true for the sets of variables that produce diffraction spots) states that:
λ = 2dhkl sinθ
In electron diffraction, the angle θ is small so that we can make the following approximations:
tan2θ ≈ 2θ
sinθ ≈ θ
with θ in radians. Hence,
\[\frac{{{r_{hkl}}}}{L} = 2\theta = \frac{\lambda }{{{d_{hkl}}}}\]
and so it follows that
rhkldhkl = λ L