Cross-sectioning techniques transform

Traditionally, production of metallic glasses requites rapid heat removal from the material (Fig. 2) which normally involves a combination of a cooling process that has a high heat-transfer coefficient at the interface of the Hquid and quenching medium, and a thin cross section in at least one-dimension. Besides rapid cooling, a variety of techniques are available to produce metallic glasses. Processes not dependent on rapid solidification include plastic deformation (38), mechanical alloying (7,8), and diffusional transformations (10). 

To sum up, the basic idea of the Doppler-selected TOF technique is to cast the differential cross-section S ajdv3 in a Cartesian coordinate, and to combine three dispersion techniques with each independently applied along one of the three Cartesian axes. As both the Doppler-shift (vz) and ion velocity (vy) measurements are essentially in the center-of-mass frame, and the (i j-componcnl, associated with the center-of-mass velocity vector can be made small and be largely compensated for by a slight shift in the location of the slit, the measured quantity in the Doppler-selected TOF approach represents directly the center-of-mass differential cross-section in terms of per velocity volume element in a Cartesian coordinate, d3a/dvxdvydvz. As such, the transformation of the raw data to the desired doubly differential cross-section becomes exceedingly simple and direct, Eq. (11). 

The analytical techniques proposed in the literature generally give reliable information on lipids present in the paint layer. However, the presence of lipid mixtures and of particular environmental conservation conditions may affect the lipid pattern to such an extent that their identification may be very difficult and sometimes erroneous. Thus, a multianalytical approach is recommended which integrates chromatographic data with techniques such as mapping based on Fourier transform infrared spectroscopy or SIM on cross-sections, in order to better understand the distribution of lipids in the various paint layers. 

The H2 molecule is a system for which quite recently it has been possible to measure in unprecedented detail state-selected vibrationally and rotation-ally resolved photoionization cross sections in the presence of autoionization [27-29]. The technique employed has been resonantly enhanced multiphoton ionization. The theoretical approach sketched above has been used to calculate these experiments from first principles [30], and it has thus been possible to give a purely theoretical account of a process involving a chemical transformation in a situation where a considerable number of bound levels is embedded in an ensemble of continua that are also coupled to one another. The agreement between experiment and theory is quite good, with regard to both the relative magnitudes of the partial cross sections and the spectral profiles, which are quite different depending on the final vibrational rotational state of the ion. 

In the time-independent approach one has to calculate all partial cross sections before the total cross section can be evaluated. The partial photodissociation cross sections contain all the desired information and the total cross section can be considered as a less interesting by-product. In the time-dependent approach, on the other hand, one usually first calculates the absorption spectrum by means of the Fourier transformation of the autocorrelation function. The final state distributions for any energy are, in principle, contained in the wavepacket and can be extracted if desired. The time-independent theory favors the state-resolved partial cross sections whereas the time-dependent theory emphasizes the spectrum, i.e., the total absorption cross section. If the spectrum is the main observable, the time-dependent technique is certainly the method of choice. 

The Raman spectrum of hydrogen sulfide H2S has been investigated at medium resolution in connection with the measurement of Raman scattering cross sections (Schrdtter and Kldckner, 1979). Later the g-branch of the v band was resolved using the cw CARS technique (Frunder et ah, 1985) and analysed by comparison with data from Fourier transform IR spectra (Lechuga-Fossat et ah, 1984). 

The stretching and bending modes of zeolite lattices have weak Raman cross sections, which makes measuring high quality Raman spectra difficult. Laser induced fluorescence is also a common problem with dehydrated zeolites, although this can be overcome with the Fourier transform technique. As with the corresponding infrared spectra, the frequencies of the Raman active lattice modes depend on both the local structure and the composition of the zeolite lattice. 

The direct reconstruction of a disordered system by EELS is an important technique by virtue of its wide applicability. The theory for this problem requires only simple expressions that connect the inelastic cross section with the structural characteristics of the system. The second goal of this chapter will be to develop this theory. Note that the modern source of information about distribution functions is the Fourier transform of the static structure factors for a system. 

Different approaches can be taken to obtain radial images. Radial field gradients can be applied by the use of dedicated hardware [Hakl, Leel, Lee2]. Alternatively, a 2D image can be reconstructed from one projection by the backprojection technique, and a radial cross-section can be taken through it. The most direct way to access the radial image from a projection consists in computing the inverse Hankel transformation (cf. Section 4.4.2) of the FID measured in Cartesian k space (cf. Fig. 4.4.1) [Majl]. But in practice, the equivalent route via Fourier transformation of the FID and subsequent inverse Abel transformation (cf. Section 4.4.3) is preferred because established phase and baseline correction routines can be used in the calculation of the projection as an intermediate result. 

To obtain further insight into the meaning of the inelastic neutron spectra, it is necessary to have specific theoretical models with which to compare the experimental results. In the harmonic approximation it is possible to calculate the incoherent inelastic neutron spectrum i.e., the neutron scattering cross section for the absorption or emission of a specific number of phonons can be obtained with the exact formulation of Zemach and Glauber.481 A full multiphonon inelastic spectrum can be evaluated by use of Fourier transform techniques.482 The availability of the normal-mode analysis for the BPTI136 has made possible detailed one-phonon calculations483 for this system the one-phonon spectrum arises from transitions between adjacent vibrational levels and is the dominant contribution to the scattering at low frequencies for typical experimental conditions.483 The calculated one-phonon neutron en-... 

The detection technique can also have an effect upon the angle- and velocity-dependent intensities. Cross sections refer to fluxes of molecules into a given range of velocities and angles. The commonly employed technique of mass spectrometric detection provides a measure of the density in the ionization region. Since density and flux are related by the velocity, we must include a factor of 1/v in making the transformation indicated in equation (B2.3.10) from the CM cross sections to the measured laboratory intensities. 

Nowadays, sophisticated cooling techniques have been available to ensure the laser materials to be operated at cryogenic temperatures, in which the costs can be weU compensated by the advantages that can be gained in laser performances. Spectroscopic advantages include increased emission cross section and reduced population of the terminal level that transforms the 1030 nm emission of the strong transition of F5/2(l) into a four-level scheme, while material properties... 

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