Section 7.4.3.1. Introduction

In many diffraction studies, it is necessary to correct the intensities of the Bragg peaks for a variety of inelastic scattering processes. Compton scattering is only one of the incoherent processes although the term is often used loosely to include plasmon, Raman, and resonant Raman scattering, all of which may occur in addition to the more familiar fluorescence radiation and thermal diffuse scattering. The various interactions are summarized schematically in Fig. 7.4.3.1, where the dominance of each interaction is characterized by the energy and momentum transfer and the relevant binding energy.

Figure 7.4.3.1| top | pdf | Schematic diagram of the inelastic scattering interactions, ΔE = E1 − E2 is the energy transferred from the photon and K the momentum transfer. The valence electrons are characterized by the Fermi energy, EF, and momentum, kF ( being taken as unity). The core electrons are characterized by their binding energy EB. The dipole approximation is valid when |K|a < 1, where a is the orbital radius of the scattering electron.

With the exception of thermal diffuse scattering, which is known to peak at the reciprocal-lattice points, the incoherent background varies smoothly through reciprocal space. It can be removed with a linear interpolation under the sharp Bragg peaks and without any energy analysis. On the other hand, in non-crystalline material, the elastic scattering is also diffused throughout reciprocal space; the point-by-point correction is consequently larger and without energy analysis it cannot be made empirically; it must be calculated. These calculations are imprecise except in the situations where Compton scattering is the dominant process. For this to be the case, there must be an encounter, conserving energy and momentum, between the incoming photon and an individual target electron. This in turn will occur if the energy lost by the photon, ΔE = E₁ − E₁, clearly exceeds the one-electron binding energy, , of the target electron. Eisenberger & Platzman (1970) have shown that this binary encounter model – alternatively known as the impulse approximation – fails as (E_B/ΔE)².

The likelihood of this failure can be predicted from the Compton shift formula, which for scattering through an angle can be written.

This energy transfer is given as a function of the scattering angle in Table 7.4.3.1 for a set of characteristic X-ray energies; it ranges from a few eV for Cr Kα X-radiation at small angles, up to ∼2 keV for backscattered Ag Kα X-radiation. Clearly, in the majority of typical experiments Compton scattering will be inhibited from all but the valence electrons.

Table 7.4.3.1| top | pdf | The energy transfer, in eV, in the Compton scattering process for selected X-ray energies Scattering angle φ (°) Cr Kα Cu Kα Mo Kα Ag Kα 5411 eV 8040 eV 17 443 eV 22 104 eV 0 0 0 0 0 30 8 17 79 127 60 29 63 292 467 90 57 124 575 915 120 85 185 849 1344 150 105 229 1043 1648 180 112 245 1113 1757 Data calculated from equation (7.4.3.1).