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

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Derivation of rhkldhkl = λL

Diagram of diffraction of electron beam

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