In TEM, the sample is bombarded by an electron beam. The resolution is deter­mined by the wavelength of the electron and the numerical aperture of the electron optical lens. Similar to the wavelength of neutrons, the wavelength of the electrons is calculated by Eq. (4.93). The energy of the electrons in TEM microscopes is typ­ically 100—300 keV. At 100 keV electron energy, and taking into consideration the mass of the electron, the wavelength of the electron is about 4 X 1012 m. The res­olution (d) is quantitatively expressed as follows:

d = _A_

2n sin a 2NA

where A is the wavelength of the electron, n is the refractive index of the medium of the lens, a is the half-angle of the maximum cone of radiation that can enter or exit the lens, and NA is the numerical aperture. This means that theoretically the maximum resolution of the electron microscope is about 2 pm. Practically, the best resolution is in the order of tenths of a nanometer.

Since the electron is a charged particle with a relatively short range, the sample must be thin to transmit the electrons. Therefore, the method requires special prepa­ration of the samples. The thin samples are placed on gold sample holders, as illus­trated in Figure 10.21.

As mentioned previously, the imaging is possible using the elastically scattered electrons. Inelastic electron scattering has a positive and a negative effect. Although it disturbs the imaging because the change of the wavelength changes the focal length (chromatic error), it allows chemical analysis via the emission of the characteristic photons (electron microprobe).

Figure 10.21 A gold sample holder for TEM. The diameter is about 3 mm.

The irradiating electrons are scattered on the electrons of the irradiated atoms. Thus, the light elements have a smaller degree of scattering than the heavier ones. For this reason, the compounds consisting of light elements, such as organic sub­stances, are covered by contrast material with a high atomic number (e. g., osmium, lead, gold, silver, etc.). These metals are evaporated or adsorbed onto the surface of the sample.