How small is a small angle in the TEM and why are scattering angles in the TEM usually this small?
I can suggest you a book to find your answer. The book is "Transmission Electron Microscopy" by David B.Williams.
the scattering angle is about 0.1,I guess. I guess the reasons are as follow.
first, electrons have a high momentum and to have wide angle scattering severe interactions is required.
second,as far as severe interactions is required ,it only can happen when electron interacts with core of atoms,which only has small part of the atom.
you will find in the book that scatterings with higher degrees is possible but with less probability.And most of the scatterings with higher degrees are actually made by multiple scattering
The Born approximation (basic quantum mechanical model for scattering theory) as well as the more elementary Bragg picture of diffraction both tell you that a typical angle for a single scattering event is roughly equal to the wavelength (which is essentially the same thing as the inverse momentum) of the radiation divided by the length scale of the thing it's scattering off. So for a 100-300 kV electron with a wavelength of a few pm scattering off an atomic-scale thing with typical periodicity of a few hundred pm, a typical scattering angle ends up being ~0.01 radian.
The exception is when it scatters off something much smaller, such as an atomic nucleus, which means it has to get close enough to the nucleus for Rutherford scattering to be dominant. Then, in one of the more curious examples of the correspondence principle, the classical formula for the angular distribution applies. So this tells you that, mixed up with the ~0.01-radian scattering events that involve the atomic-scale structure, you'll have rare high-angle scattering events all the way up to 180 degrees.
Which is exactly what you observe. Multiple scattering and inelastic scattering complicate the story a bit, but this basic semiquantitative picture is still a good way of thinking about it.
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