Incident angle transformations

The cross section of the collision region that the particle impacts with the Si surface with an incident angle of 45° at a speed of 2,100 m/s is shown in Fig. 16 [28]. As the particle impacts into the Si surface layer, the contact region of the Si surface layer transforms from crystal into amorphous phase immediately. The area of the depressed region and the thickness of the amorphous layer increase with the penetration depth of the particle (Figs. 16(a)-16(c)). After it reaches the deepest position, the particle then moves both upwards and rightwards, and some silicon atoms ahead of the particle are extruded out and result in a pileup of atoms. Then the released elastic deformation energy of the Si surface pushes... 

It is well known that the SPR may be registered as the sharp minimum of the reflection coefficient for the plane-parallel light which depends on the incidence angle. The position of the resonance angle and the minimum depth of the incidence are determined by the parameters of the metal layer, and the optical constants of the external medium. As molecules adsorb and interact at the gold surface, the dielectric properties of the formed layer change, which leads to the transformation of the resonance curve and to the displacement of the resonance angle [7, 9, 15]. 

Liquid samples do not require preparation before analysis. However, it is preferable to transform solid samples, especially if the matrix is not well known. In fact, depending on the incident angle of the primary X-ray radiation, the sample thickness can be variable from only a few angstroms (for a grazing angle of radiation) to half a millimetre (see Fig. 13.4). Thus any superficial heterogeneity will translate as variations in the results. 

A series of SAMs formed on Au from mono- and dithiol conjugated aromatic molecules was characterized by cyclic voltammetry, grazing incidence Fourier transform infrared spectroscopy, contact angle measurement, and ellipsometry.43 The analyses indicated that the molecular orientation of conjugated phenylene- and thophene-based dithiols became less tilted with respect to the surface normal as the chain length of the organic molecules increased. 

Solid samples and especially if the matrix is not known, need transformation prior to the measurement. In fact, the measured fluorescence of these materials only concerns a thickness of several micrometres beneath the surface. This thickness depends upon its composition and of the angle of incidence of the primary X-rays this can be from between several angstroms (if the incident angle is acute), up to half a millimetre. All superficial heterogeneity can have important consequences and cause variations in the result. This is the principal reason for surface treatment prior to analysis. 

The polarization factor, P, is usually known it depends on the radiation source and is closer to 1 for insertion devices such as wigglers or undulators as compared to bending magnets. The intensity, I, is measured as a function of 0 for many incident angles. Equation 4.2.1 can therefore be reduced to a linear fit of I vs. cos 0, where the slope and intercept can be transformed into the two remaining unknowns, A and a. 

Figure 28. Time-of-flight spectra for KMnFs transformed to energy transfer distributions for several temperatures at incident angles 35° and 36°. The low-energy mode (arrows) seen on the creation side (negative energy transfer) at 36° is very close to the zone boundary and appears to be associated with the surface phase transition that occurs at 191 K. At 35° the low-energy peak corresponds to a mode further removed fiom the zone boundary, which persists up to high temperatures. (Reproduced from Fig. 18 of Ref. 92, with permission.)...

Figure 43. TOP spectra transformed to energy transfer distributions for a Kr monolayer on Pt(lll) at four different angles. With decreasing incident angle, larger phonon wavevectors are probed. One can see that the two phonons which lie very close in energy in panel a merge together in panels b and c with increasing wavevector, and that only one phonon remains in the spec-tmm after a certain wavevector is reached (panel d). (This figure has been reproduced from Fig. 2 of Ref. 129, with permission.)...

In Fig. 5, a spectrum is plotted, which exhibits the oscillatory features of the symmetric stretch motion of Naa in its electronically excited B-state, indicating the well-known oscillation time of 320 fe. The pump-probe spectnun was obtained with transform-limited pulses of 80 fs duration at a center wavelength of 620 nm. Then the experiment was repeated by changing one experimental parameter only the duration of the pump pulse. This was accomplished — as indicated in Fig. 11 — by passing the pump beam across a set of two parallel gratings. The assembly creates a linear frequency chirp. Its duration and spectral sequence depends only on the incidence angle... 

LSM, SEKZ and LSCF powders were characterized by XRD using a Shimadzu XDR-7000 diffractometer and scanning electron microscopy (SEM-SSX 550, Shimadzu). Infrared spectra were also recorded with FTIR (IR Prestige-21, Shimadzu) in the 400 - 4600 cm"i spectral range. Specific surface area measurements were performed only for the LSM powders. An infrared reflectance spectrum of a LSM pellet prepared from a powder calcined at 900 °C was recorded with a Fourier-transform spectrometer (Bomem DA 8-02) equipped with a fixed-angle specular reflectance accessory (external incidence angle of 11.5°). 

Figure 3.1 Spectra from thick anode x-ray tubes, (a) The energy spectrum from a molybdenum anode x-ray tube measured with a Si(Li) detector (40 kV tube voltage, 39-/Lim-thick beryllium x-ray tube window, 90° electron beam incidence angle, 32° x-ray takeoff angle). Although the low spectral intensity near 40 keV makes accurate measurement of Emax difficult, the spectrum approaches zero intensity near 40 keV. The Mo K lines occur at 17.4 keV and 19.8 keV, and the L lines are visible at 2.4 keV. (b) The spectrum from (a) transformed into the wavelength coordinate system. The Mo L line at 5.3 A is broad due to the Si(Li) detector energy resolution. The value of Xmin is readily apparent at 0.31 A. (c) The spectrum from (a) on a linear vertical scale, (d) Spectra from tungsten, molybdenum, and chromium anode x-ray tubes. The positions of characteristic lines are marked by vertical lines of arbitrary height. (Adapted from R. Tertian, Fluorence X, Theorie et Pratique de VAnalyse, Thesis, Universite de Paris, and reprinted by courtesy ofEG G ORTEC.)...

Fig. 3. Schematic diagram of (a) the recording and (b) the reconstruction schemes in the PCR method, ft, is the internal half crossing angle of eso and e ft is the internal incident angle of ef, and/s and are the focal lengths of the Fourier transform lenses in the recording and...

The surface PSD function can be calculated from the BRDF through a scatter model. For example, the grating equation model discussed in Section 2.3.2 shows that high-frequency surface perturbations will scatter light far from specular and low-frequency perturbations will scatter close to specular. The PSD shows the amount of modulation versus / that is, the square of the Fourier transform of the surface profile. Because it is a sample property, the same PSD should be obtained regardless of wavelength- and incident angle-dependent differences in the BRDF data. 

The Fourier transform infrared (FT-IR) spectra were recorded on a Spectrum One KY (Perkin Elmer, Inc., Waltham, MA) system coupled with a mercury-cadmium-tellurium (MCT) detector. The incident angle of the p-polarized infrared... 

A R A ) is nothing but the Laplace transform of 4>(2). In principle, it is possible to extract (2) by performing measurements at various A (or equivalently at various incidence angles) and then by taking the inverse laplace transform of A -R(A ). This procedure however, does not converge easily and requires extreme data accuracy over the complete A range (0 to ). Moreover, the A range experimentally accessible has a natural cut-off at... 

Experimentally, the absorbance A(5) of a band is measured as a function of the angle of incidence B and thus of S. Two techniques can be used to determine a(z). A functional form can be assumed for a(z) and Eqs. 2 and 3 used to calculate the Laplace transform A(5) as a function of 8 [4]. Variable parameters in the assumed form of a(z) are adjusted to obtain the best fit of A(5) to the experimental data. Another approach is to directly compute the inverse Laplace transform of A(5) [3,5]. Programs to compute inverse Laplace transforms are available [6]. 

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