Diffraction profiles, measurement

Fig. 5 Time dependence of X-ray diffraction profiles measured for the powder crystals of 1 at room temperature [51]...

Figure 1 shows full diffraction profiles measured at 300 and 11 K. All of the peaks at 300 K can be indexed as fee, with ao 14.17 0.01 A, as previously reported. Note that no hOO peaks are present in this profile, despite the fact that hOO is allowed for h even. At 11 K, 00 has decreased to 14.04 0.01 A and many new peaks have appeared. The new peaks can all be indexed as simple-cubic (sc) reflections with mixed odd and even indices (i.e., forbidden fee reflections). The crystal has therefore undergone a transition to a simple-cubic structure, but since the cube edge has not changed appreciably the basis must still consist of four molecules per unit cell, which were equivalent in the fee structure but which somehow become inequivalent at low temperature. 

We prepared samples by allowing an excess of TDAE to react with C60 This differs from previous work by the absence of any solvent. The sample used here had a low-temperature saturation moment of 0.33/ag per formula unit, and a critical temperature Tc=16.1K. Figure 1 shows the room-temperature diffraction profile measured at beamline X7A of the National Synchrotron Light Source. The pattern consists of a number of strong, sharp peaks from TDAE-C o, together with several significantly broader peaks from unreacted face-centred-cubic... 

In the example we have just described, the size of the crystals shows a rather wide distribution, which is why the diffraction profiles measured in the direction perpendicular to the interface or in the interface plane are bell curves, similar to those obtained for diffraction peaks measured with samples comprised of randomly oriented crystals. We will move on to a different case, in which virtually all of the crystals, or diffracting domains, are similar in size. 

Fig. 14.7 Comparison of the synchrotron x-ray diffraction profiles measured for stoichiometric LiFeP04 and the isolated solid solution of Lio.93peP04 with an identical particle size of 40 nm with magnified presentations of 301, 311, and 121 as the typical peaks...

This was first proved by the refinement of X-ray diffraction profiles measured for LixFeP04 (0 < x < 1) phases at room temperature. In the bi-phase reaction of LixFeP04 at room temperature, the orthorhombic lattice constants in each phase slightly deviate from those ofthe stoichiometric end components of LiFeP04 and FeP04. The deviation can be explained by assuming a model in which a most ofthe intermediate phase in the LixFeP04... 

In the simplest approach T is the full width of the peak (measured in radians) subtended by the half maximum intensity (FWHM) corrected for the instrumental broadening. The correction for instrumental broadening is very important and can be omitted only if the instrumental broadening is much less than the FWHM of the studied diffraction profile, which is always the case in presence of small nanoclusters. The integral breadth can be used in order to evaluate the crystallite size. In the case of Gaussian peak shape, it is ... 

We can learn the structural change in the crystals during topochemical polymerization by powder X-ray diffraction measurements. X-ray diffraction profiles continuously changed during the polymerization of 1 under the irradiation of an X-ray beam (Fig. 5) [51]. The reflections shifted and approached the reflection position of the polymer. This suggests that the polymerization... 

Figure 7.3. (a) In situ X-ray reflectivity vs. time (measured at the anti-Bragg condition, shown in inset at top) during dissolution of orthoclase feldspar, KAlSi308, (001) cleavage surface at extreme pH values. The removal of successive monolayers (ML) is noted for each set of data, (after [100]) (b) in situ crystal truncation rod diffraction profiles for a freshly cleaved orthoclase (001) surface (circles) and after reaction at pH = 2.0 (1 and 15 ML dissolved) (diamond and square) and pH = 12.9 (2 ML dissolved) (triangle) (after [103]). (Figures provided by P. Fenter.)... 

The golden-yellow nitrided surfaces were characterized by energy-dispersive x-ray and electron diffraction techniques. The results show that the nitrided surfaces contain mononitride phases. Depth-profile measurements were performed by argon-ion etching and surface analysis by means of x-ray photoelectron spectroscopy. 

This section would not be complete without giving some idea of the path that XDI has gone to become a modality of major importance in contemporary security screening. The first hard X-ray ( 100 keV) measurements of diffraction profiles of explosives in an XDI system that was in principle scalable in size to be able to analyse checked baggage were performed in the mid-1980s [14],... 

There are several ways of detecting peaks in such noisy signals. The Wiener-Hopf filter minimizes the expectation value of the noise power spectrum and may be used to optimally smooth the original noisy profile [19]. An alternative approach described by Hindeleh and Johnson employs knowledge of the peak shape. It synthesizes a simulated diffraction profile from peaks of known width and shape, for all possible peak amplitudes and positions, and selects that combination of peaks that minimizes the mean square error between the synthesized and measured profiles [20], This procedure is illustrated... 

Consider Fig. 9 showing the diffraction profile for the polymer Lucite (C5H802) taken from Tartari et al. [23], The dashed line represents the function F2 + S calculated from the mixture rule on the basis of the Independent Atom Model (IAM) using the tabulated atom form factors for H, C and O data presented in Fig. 8. The IAM curve is seen to approach the measured profile at high x values. 

Fig. 9. Diffraction profiles for Lucite (C5H802). Solid curve is measurement whereas dashed plot is fitted...

Knowledge of the effective atomic number allows the true width and height of the IAM curve to be determined and hence permits the molecular interference function, s(x), to be uniquely extracted on dividing the measured diffraction profile by the IAM function (cf. Eq. 7). 

The physical parameters whose measurement from diffraction profiles was considered above in Section 2.2. are directly applicable to the challenge of identifying and characterizing organic and other explosives in checked baggage. Table 1 summarizes the relationship between the diffraction profile analysis procedures described in Section 2.2. and physical parameters of significance for explosives detection discussed in this section. 

The reconstructed diffraction profiles are given in Fig. 20. There is broad agreement between the reconstructed profiles and those measured from small samples. All the plastics appear to have artefactual peaks at 2.3 and 2.7 nm 1. As explained by the authors, this results from the intense Al peak at 2.5 nm-1 that negatively affects the scatter signal from neighbouring materials and can be expected to diminish in importance as more projections are measured during the scan. 

Afterward, the x-ray diffraction profiles of the treated samples were obtained, by irradiating the side where the Ni was electrodeposited [34], and the intensity Aa of the (221) peak of the a-Fe, body-centered cubic phase, and the intensity A.( of the (220) peak corresponding to the y-FeNi, face-centered cubic alloy were measured [34,35],... 

In the substrate standard method the absorption effect is determined using the transmittance ratio (T =1. /I ), The determination of the transmittance involves additional measurements, i.e., step scanning over the silver profile, to obtain I. and I , IA is measured for each filter sample and if can be obtained several ways as discussed below, gThese additional measurements can be performed very quickly compared to the more lengthy measurements of the internal standard because the silver peak is quite intense, A step scan of the silver diffraction profile plus background counting time can be accomplished in about two minutes with better than 1% precision,... 

Figure 9.8 Powder X-ray diffraction profiles (in situ measurements) at (a) 76 and (b) 87 °C. These measurements were carried out under vacuum, Ref [20].

The evolution of US-induced crystallization around the glass transition temperature for metallic glass was monitored by electromagnetic acoustic resonance, which allowed resonance frequencies and internal frictions to be measured. In an as-cast glassy sample, such frequencies jumped up just above the glass temperature transition at the beginning of the process under ultrasonic vibration this was ascribed to nano-crystallization as confirmed by an X-ray diffraction profile, which was absent in the absence of US. Irregular A-shaped internal-friction peaks were also observed prior to abrupt crystallization [48]. 

A method for determining the particle size distribution from a single X-ray diffraction profile when strain is present was applied to co-precipitated nickel oxide on alumina and silica. Appreciable strain occurred in the NiO, possibly due to the pressure developed in the small particles to balance the surface tension forces and the distortion produced by the deformation of the f.c.c. structure into a rhombohedral form. Apart from errors in the size distribution created by neglected lattice strain, the measurement of strain itself is important because its correlation with catalytic activity has been suggested. 

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