On “Lattice Image” in Electron Micrographs

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Abstract
Assuming a plate-shaped crystal in which a lattice plane with the spacing d is perpendicular to the crystal surfaces and the potential varies according to the harmonic form V(x)=2V 1cos (2πx/d) in direction x perpendicular to the lattice plane, the lattice image of electrons on the exit surface was calculated by using the exact solution of Schrödinger equation for electron waves in the crystal. The values of d and V 1 were assumed to be 13.0 Å and 2.14 volts, respectively. These values are those approximately appropriate to (001) of Pt-Phthalocyanine. Calculation was made both for the case of normal incidence of primary electrons and the case in which Bragg condition is satisfied. Wavelength of electrons was assumed to be 0.0603 Å corresponding to the accelerating voltage 41.5 kV. A number of aspects of the lattice image which take place by the participation of higher order reflections were revealed. By the effect of higher order reflections, the peaks in the lattice image become much pronounced for the crystal thicker than about 300 Å, while, on the contrary, the intensity profile turns out to be rather flat for the crystal thinner than about 150 Å, in accordance with the trend expected from the phase grating theory.

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