Reflection geometry

There are two prineipal types of instrument geometry for laboratory powder diffractometers refleetion and transmission. In reflection geometry, the sample is in the form of a flat plate, while in transmission geometry a glass capillary or thin foil is used. 

The Bragg angle for the monochromator, 20m, is set to satisfy Bragg s law for the diffracting planes of the monochromator crystal. 

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Fig. 25. Reflection geometry for irras showing the s andp components of the electric fields of the incident (U ) and reflected (S ) beams (41).

For the reflection geometry shown in Figure 6b, the diffraction efficiency is given by equation 13. 

NIR images are taken exclusively in reflection geometry. Therefore, the method is mainly surface-sensitive with a limited penetration depth. 

Guinier [6], p. 181), with the cross-section, F0, of the incident X-ray beam, the angle of incidence on the sample surface, a, and the angle of exit with respect to the sample surface being ae. For symmetrical-reflection geometry (a = Ofe = 6) the irradiated volume becomes Fq/ (2id), and 1 /2fi is the penetration depth into the sample. We thus have... 

When reflection geometries are set up in modern scattering applications to study the structure of thin layers, the simplifying assumption of infinite sample thickness is not allowed, and the absorption correction becomes more difficult. Moreover, symmetrical-reflection geometry is utilized less frequently than asymmetrical-reflection geometry with fixed incident angle. Thus both cases are of practical interest. 

Figure 7.4. Sketch for the deduction of the intensity, It, transmitted into the detector for symmetrical-reflection geometry. The photon is scattered in a depth of x. Integration direction is indicated by a straight dashed arrow... 

Figure 7.4 presents a sketch for the deduction of the intensity in symmetrical-reflection geometry. F is the footprint area of an incident microbeam on the sample surface, and dlt is the related contribution to intensity. Again utilizing the absorption law Eq. (7.1) we have... 

Figure 7.5. Relationship between symmetrical (

scattered beam are shown by dashed-dotted arrows, the incident angle is a = 0 + scattering vector s. For the tilted sample the sample-fixed scattering vector S3 is indicated (after [84])... 

For very thin sample thickness t and a scattering angle 29 that is well above the critical angle of total reflection, the exponential factor is approximately unity and a simple background subtraction without consideration of absorption is allowed. Symmetrical-reflection geometry is only a special case of asymmetrical-reflection geometry. 

On the other hand, if the primary beam is illuminating the complete sample surface (case 2), the absorption factor for symmetrical-reflection geometry becomes... 

For symmetrical-reflection geometry the modulus of the true scattering vector is... 

For asymmetrical-reflection geometry the relation is more complicated. Considering the geometry sketched in Fig. 7.5, the true tilt angle is... 

Figure 8.2. WAXS curves from semicrystalline and amorphous poly(ethylene terephthalate) (PET). Separation of the observed intensity into crystalline, amorphous, and machine background (laboratory goniometer Philips PW 1078, symmetrical-reflection geometry)... 

Let us consider a nanostructured thin film built from lamellar particles [84], If the principal axis of layer stacks is oriented normal to the film surface, the scattered intensity measured in symmetrical-reflection geometry (SRSAXS) is... 

A special O-ring cell design is needed for in situ infrared (IR) vibrational characterization of an electrochemical interface. The absorption of one monolayer (i.e. <1015 cm 2 vibrators) can be measured if the silicon electrode is shaped as an attenuated total reflection (ATR) prism, which allows for working in a multiple-in-ternal-reflection geometry. A set-up as shown in Fig. 1.9 enhances the vibrational signal proportional to the number of reflections and restricts the equivalent path in the electrolyte to a value close to the product of the number of reflections by the penetration depth of the IR radiation in the electrolyte, which is typically a tenth of the wavelength. The best compromise in terms of sensitivity often leads to about ten reflections [Oz2]. 

Figure 1. X-ray patterns of calcined MSU-1 and -4 Silica obtained with Tergitol 15S12 and Tween 20 as templating agents. The patterns were recorded with a Bruker D5000 diffractometer in Bragg-Brentano reflection geometry. Cu-L radiation was employed that was monochromatized by a graphite single crystal in the diffracted beam.

In vitro measurements of native chemical concentrations in whole blood were first reported for a 69-sample data set by Berger et al. using the same Cassegrain-based reflective geometry that was designed originally for serum [1], Enejder et al. subsequently optimized the collection optics for whole blood... 

Fig. 4.1. Schematic diagram of the second harmonic generation experimental apparatus with the sample in the reflection geometry. The polarization analyzers are set to transmit p-polarized light at the frequency labeled in the figure. The (co/2co) filters transmit the (fundamental/harmonic) light while blocking the (harmonic/fundamental) light. For phase measurements, a quartz plate is mounted on a translation stage for movement towards the sample at a distance L.

A complementary approach to the standard reflection geometry described above uses the attenuated total reflection (ATR) geometry which couples surface plasmon waves to the incident electric field and enhances the SH production. Two configura-... 

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