Physical Principles of Electron Microscopy by R.F. F. Egerton

Author:R.F. F. Egerton
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(4.11)

As expected, Eq. (4.11) specifies an inverse relation between b and θ; electrons with smaller impact parameter pass closer to the nucleus and experience a stronger attractive force. Because Eq. (4.11) is a general relationship, it must hold for θ = α, which corresponds to b = a. Therefore we can rewrite Eq. (4.11) for this particular case, giving:

(4.12)

As a result, the cross-section for elastic scattering of an electron through any angle greater than α can be written as:

(4.13)

Because σe has units of m2, it cannot directly represent scattering probability; we need an additional factor with units of m−2 to give the dimensionless number P e(>α). Also, our TEM specimen contains many atoms, each capable of scattering an incoming electron, whereas σe is the elastic cross-section for a single atom. Consequently, the total probability of elastic scattering in the specimen is:

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