Multiple diffraction spots

Fig. 3.5. Real space (left) and reciprocal space (right) applicable to Pd(lOO) + (2>/2 X yj2) R45° 2C0. Substrate (overlayer) atoms and diffraction spots are indicated by crosses (circles). Large filled circles represent kinematically produced spots, small filled circles represent multiple-diffraction spots...

These reciprocal lattice vectors, which have units of and are also parallel to the surface, define the LEED pattern in k-space. Each diffraction spot corresponds to the sum of integer multiples of at and at-... 

There are only three equatorial spots. Each of the three can be accounted for by double diffraction (of 330, 5 50, and 880, with the factor for R of 1.9021 —2sin72°). By vector addition it is seen that the other spots can be accounted for by multiple diffraction of hh 0. 

The intensities of the diffraction lines depend upon the factors already mentioned, but further corrections must be included if the calculated intensities are to correspond accurately with the observed intensities. An important factor is the multiplicity of the reflections in the powder pattern, p. This correction term can be easily understood by deriving the powder pattern from the diffraction spot pattern of a single crystal (Figure 6.18a). The intensity of each spot is well defined, and the intensity of say, the 200 spot, 7(200), can be measured independently of all other reflections. If an X-ray beam is incident upon a random array of crystals, instead of a single crystal, each diffraction spot will lie at a... 

Spots to be expected on the basis of an unmodified kinematic theory (no attenuation) are shown as small full dots. Those that can arise only from multiple diffraction or from a periodic modulation of the atomic... 

According to kinematic theory the intensity of diffraction spots is proportional to the square of the structure factor (Eq. 4). This simple proportionality is lost in reality because of multiple diffraction effects, which are taken into account adequately in dynamic theory [149]. 

In this section, we show how multiple scattering can be considered in intensity calculations. It also shows that multiple scattering allows for diffraction spots, which are systematically cancelled in the (invalid) kinematic calculation of the structure factor. 

Joyce-Loebel MK III C flat-bed microdensitometer. The structure factor magnitudes were derived from the integrated intensities according to F(hk ) 2 = I(hk ). The largest errors in the intensity measurements were for the darkest spots. The scattering factors of C, 0 H for the diffraction of electrons were taken from the International Tables for X-Ray Crystallography, vol. IV (7). No correction for multiple scattering and n-beam dynamical interactions were applied because the thickness of the crystals was of the order of 100 X (6). 

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