An uncorrected transmission electron microscope operating at with spherical…

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 Seeing atoms: electron and scanning-probe microscopy

Problem

An uncorrected transmission electron microscope operating at

200\,\mathrm{kV}

with spherical aberration coefficient

C_s=1.2\,\mathrm{mm}

achieves a point resolution

d_{\min}=2.4\,\mathrm{\AA}

. A newer uncorrected instrument runs at

300\,\mathrm{kV}

with a smaller lens,

C_s=0.5\,\mathrm{mm}

. ((a)) Compute the relativistic de Broglie wavelength

\Lambda

of the electrons at

200\,\mathrm{kV}

and at

300\,\mathrm{kV}

. ((b)) Using the scaling law

d_{\min}\propto C_s^{1/4}\Lambda^{3/4}

, estimate the point resolution of the

300\,\mathrm{kV}

instrument, by scaling from the known

200\,\mathrm{kV}

figure rather than recomputing the prefactor.

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