Fundamentals of Inelastic Electron Scattering by P. Schattschneider

By P. Schattschneider

Electron power loss spectroscopy (ELS) is an unlimited topic with a protracted and honorable heritage. the matter of forestalling strength for prime power debris the earliest pioneers of quantum mechanics equivalent to Bohr and Bethe, who laid the theoretical foun­ dations of the topic. The experimental origins may possibly might be be traced to the unique Franck-Hertz test. the fashionable box contains subject matters as varied as low power mirrored image electron power loss experiences of floor vibrational modes, the spectroscopy of gases and the trendy thought of plasmon excitation in crystals. For the learn of ELS in electron microscopy, numerous traditionally unique parts of physics are suitable, together with the idea of the Debye­ Waller issue for digital inelastic scattering, using advanced optical potentials, lattice dynamics for crystalline specimens and the speculation of atomic ionisation for remoted atoms. but the box of electron strength loss spectroscopy comprises few important texts which are advised for college students. With the new visual appeal of Raether's and Egerton's hooks (see textual content for references), we've got for the 1st time either a finished assessment text-due to Raether-and a lucid introductory textual content which emphasizes experimental aspects-due to Egerton. Raether's textual content has a tendency to stress the hot paintings on floor plasmons, whereas the power of Egerton's publication is its remedy of internal shell excitations for microanalysis, in line with using atomic wavefunctions for crystal electrons.

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Example text

A) The minimum detectable number of ;ltoms of various elements from Li to Fe in a 50 nm thick iron foil, and the equivalent data plotted as an atomic percentage. J i =10- 10 A at 100 kY. 9J. b) The minimum mass fraction (MMF) of various elements in a 20 nm thick carbon matrix. The vertical scales correspond to beam currents of J i = 10- 8 A (left scale) and J i =10- 6 A (right scale), both at 25 kY. The shqrt-dashed curve corresponds to a variable spectrometer aperture which is large enough so that Tl ~1.

In this approach, the initial and final wave functions of the atom are assumed to be solutions of the Schrodinger Eq. for hydrogen, scaled to take into account the effective potential of the nucleus and the screening from the outer shells. This widely used concept is called hydrogenic model. 10]. See Fig. 5 . gM d(EIRI L Fig. 3. Photographs of a plastic model of the Bethe surface for atomic hydrogen. The horizontal axes for E / R and In (q aO) 2 define the base plane. The vertical axis represents Rdf( q , E)/dE.

18) + r')n(r'). The rightermost integral is the density autocorrelation function. 17) yields the ever-cited theorem that the dynamical structure factor 18(q,w)1 2 is the space-time Fourier transform of the density autocorrelation. 5]. 21 As will be shown in Sect. 14) and the dielectric permittivity c of a medium. Hence, there is a relation between c and the structure factor 8. Since the former describes dissipation of energy and the latter expresses charge-density fluctuations in space and time, this relation is known as fluctuation-dissipation theorem.

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