A thin foil of aluminium (fcc, ) is examined by transmission electron diffraction…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Crystal structure, bonding and diffraction

Solid State Physics, Ch Diffraction as measurement: form factors, thermal motion and refinement

Problem

A thin foil of aluminium (fcc,

a=4.050\,\mathrm{\AA}

) is examined by transmission electron diffraction with 200 kV electrons, wavelength

\lambda=0.0251\,\mathrm{\AA}

. ((a)) Find

k_{\rm in}=2\pi/\lambda

and the Ewald accessible-reflection limit

|\mathbf{G}|_{\max}=2k_{\rm in}

. ((b)) Using

|\mathbf{G}_{hkl}|=2\pi\sqrt{h^2+k^2+l^2}/a

, estimate the largest value of

N=h^2+k^2+l^2

geometrically allowed by the Ewald sphere, and state in one sentence what this implies about what actually limits the number of spots seen on an electron diffraction pattern.

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