Physical Principles of Electron Microscopy: An Introduction to TEM ...

Chapter 6
ANALYTICAL ELECTRON MICROSCOPY
The TEM and SEM techniques described in earlier chapters yield valuable
information about the external or internal structure of a specimen, but little
about its chemical composition. Some of the phenomena involved (diffracted
electrons in TEM, BSE in the SEM) depend on the local atomic number Z,
but not to an extent that would enable us to distinguish between adjacent
elements in the periodic table. For that purpose, we need a signal that is
highly Z-specific; for example, an effect that involves the electron-shell
structure of an atom. Clearly, the latter is element-specific because it
determines the position of each element in the periodic table.
6.1 The Bohr Model of the Atom
A scientific model provides a means of accounting for the properties of an
object, preferably using familiar concepts. To understand the electron-shell
structure of an atom, we will use the semi-classical description of an atom
given by Niels Bohr in 1913. Bohr's concept resembles the Rutherford
planetary model insofar as it assumes the atom to consist of a central nucleus
(charge = +Ze) surrounded by electrons that behave as particles (charge �e
and mass m). The attractive Coulomb force exerted on an electron (by the
nucleus) supplies the centripetal force necessary to keep the electron in a
circular
orbit of radius r:
K (Ze)(e)/r 2 = mv 2 /r (6.1)
Here, K = 1/(4��0) is the Coulomb constant and v is the tangential speed of
the electron. The Bohr model differs from that of Rutherford by introducing
a requirement that the orbit is allowed only if it satisfies the condition:
(mv) r = n (h/2�) (6.2)