X-ray diffraction intensity

Fig. 3.3. Time-dependent change in the 006 X-ray diffraction intensity of LiTaC>3. From [10]...

Fig. 3.4. X-ray diffraction intensity of the (111) reflection of CdTe at pump pulse density 0.6mJ/cm2. Filled circles and solid curve indicate the experimental data and the fit with an oscillation at 5.3 THz, respectively. From [4]...

Fig. 6. X-ray diffraction intensity (arbitrary units) as a function of reciprocal coordinate for prion peptides. 106-122 meridional scan of the pattern of SHal06-122 dried from 50% AcN H1(S/D) meridional scan of the pattern of SHal09-122 dried from 50% AcN H1(L) lyophilized HI A8A SHall3-120 dried from 50% AcN. SHal06-122 is from Fig. 2A in Inouye et al (2000). Diffraction patterns of A8A, HI (L), and HI (S/D) were previously reported (Nguyen et al., 1995). The strongest reflections (with Miller indices) are 4.56 A (201) in SHal06-122, 4.77 A (200) in HI (S/D), 4.44 A (201) in HI (L), and 4.33 A (201) in A8A. Low-angle reflections arising from the stacking of slabs are indicated by. ...

The IAM model further assumes the atoms in a crystal to be neutral. This assumption is contradicted by the fact that molecules have dipole and higher electrostatic moments, which can indeed be derived from the X-ray diffraction intensities, as further discussed in chapter 7. The molecular dipole moment results, in part, from the nonspherical distribution of the atomic densities, but a large component is due to charge transfer between atoms of different electronegativity. A population analysis of an extended basis-set SCF wave function of HF, for example, gives a net charge q of +0.4 electron units (e) on the H atom in HF for CH4 the value is +0.12 e (Szabo and Ostlund 1989). 

As anticipated, the multipolar model is not the only technique available to refine electron density from a set of measured X-ray diffracted intensities. Alternative methods are possible, for example the direct refinement of reduced density matrix elements [73, 74] or even a wave function constrained to X-ray structure factor (XRCW) [75, 76]. Of course, in all these models an increasing amount of physical information is used from theoretical chemistry methods and of course one should carefully consider how experimental is the information obtained. 

Pei et al. looked at the structure of the orthorhombic phase of Ba1 xKxBiOs powders by time of flight powder neutron diffraction (59). Neutron diffraction intensities should be considerably more sensitive to oxygen atom positions than are X-ray diffraction intensities for compounds such as this. The structural parameters at 300K for x=0.1 and x=0.2 are presented in Table 5. The crystal structure is the same as that of BaPbOs (Table 2) with small differences in cell parameters and atomic coordinates. The refinements show that the atoms are displaced from the ideal positions by many standard deviations, and the thermal parameters for the oxygen atoms make physical sense. The crystal structure is one in which relatively regular Bi-O octahedra (Bi-O distances... 

Figure 4.26 Temperature dependence of (a) the relative X-ray diffraction intensity of high-spin ( TJ and low-spin (Mj) phases of [Fe(4, 7-(CH3)2 phen) (NCSlj] and (b) the high-spin fraction estimated from Mossbauer spectra. In (a) the ordinate represents relative diffraction intensity of lines at 6 = 4.92° and 0...

As an example of this technique we can compare the computed and the experimental X-ray diffraction intensity for liquid water at T=298°K (see, for example, E, Clementi, Lecture Notes in Chemistry, Vol, 2, Springer Verlag, 1976), In the same way we can consider water around amino acids. For example, in Fig, 1 we present the isoenergy contour... 

Clementi, J. Chem. Phys., 64, 1351 (1976) the full details of the computed X-ray diffraction intensity are available in G. C. Lie, M. Yoshimine, and E. Clementi, J. Chem. Phys., 64, 2314 (1976). The previous computations by Stillinger and Rahman did not use a quantum-mechanically derived potential, but an empirical potential. Present quantum-mechanical techniques, if properly used, can yield remarkably accurate potentials. This fact is not fully appreciated by a large number of chemists, possibly discouraged by the rather large amount of poor theoretical chemistry computations currently in the literature. It is notable that the repulsive part of a potential can be inferred from experiments, in general, with poor accuracy. 

Table 1. Observed (obs) and Calculated (cal) X-Ray Diffraction Intensities of KBr-Amylose 00...

The first belongs to space group Fm3m, and the latter to I 43m, and these two possibilities can be distinguished by comparing the X-ray diffraction intensities expected from the two structure types with those actually observed. This type of deduction is based on consideration of the roles of the individual atoms in a crystal structure, which usually finds application in compounds of inorganic composition such as binary and ternary compounds, alloys, and minerals. 

Besides the formation of an elastic network, amylose gelation is also characterized by the development of opacity, which is generally attributed to chain aggregation.197,400 401 For a polydisperse amylose preparation (DP 3080, 2.4% solution, quenched to 32°C), the increase in turbidity slightly preceded the onset of G development.197 Crystallization, as detected by x-ray diffraction (intensity of the 100 diffraction peak),... 

Sorum [12] to a final R of 0.10. Thus, the reinvestigation of the structure of acetylcholine bromide, [C7H1602N] + Br, with X-ray diffraction intensities collected from two untwinned crystals showed that the crystals are monoclinic, and are characterized by a space group of P21/ra, with a = 10.966 (4), b = 13.729 (7), c = 7.159 (4) A, p = 108.18 (7)°, and Z = 4. The structure was refined by full-matrix least squares calculations using 1730 observed reflections, and anisotropic temperature factors for all non-hydrogen atoms. The final R was found to be 0.041. Atomic coordinates, thermal parameters, bond lengths, and angles were compared with those from a previous work on acetylcholine derivatives. 

For many years it was believed that hydrogen atoms could not be seen" in the electron density maps produced by X-ray diffraction. The reason for this is that the atomic X-ray scattering power is proportional to the square of the atomic number. This statement was generally, but not invariably, true until the demise of film-recording methods in the mid-1960 s and the advent of the computer-controlled X-ray diffractometers which could provide very accurate X-ray diffraction intensities. 

Although several standard test methods have been developed for the chemical analysis of catalysts only small samples of supported platinum and palladium reference materials are available. Zeolites have been characterized for zeolite area, unit cell dimensions, and relative x-ray diffraction intensity. The crush strength of alumina pellets has also been determined. As the needs of catalyst users and producers change so will the materials characterized. To the extent that adequate amounts of material can be donated, standard test methods developed, and round robin tests performed Committee D-32 on catalysts will continue to make them available through NIST as reference materials. 

In our studies, the model substance (montmorillonite) was a calcium bentonite (Istenmezeje, Hungary), the characteristic features of which are given here. X-ray diffraction (intensity of the basal reflection) and thermoanalytical (weight loss upon heating) data show 91% montmorillonite content. The other constituents are 5% calcite, 3% kaolinite, 1% x-ray amorphous silicates, and a trace of quartz. The amorphous phase is silicate particles, which are not crystalline for... 

Use of the reciprocal lattice unites and simplifies crystallographic calcnlations. The motivation for the reciprocal lattice is that the x-ray pattern can be interpreted as the reciprocal lattice with the x-ray diffraction intensities superimposed on it. See Section 14.2 for the definition of the reciprocal lattice vectors a b and c in terms of the direct basis vectors a, b, and c. Table 14.2 shows the parallel between the properties of the direct lattice and the reciprocal lattice, and Table 14.3 relates the direct and reciprocal lattices. 

Figure 10.6 X-Ray Diffraction Intensities of an As-Sputtered Molybdenum Disulphide Film and a Wear Track Showing Re-Orientation of the Crystal Structure (Ref. 294)...

Figures 16 and 17 show some of the important results that Corradini obtained. Figure 16 plots the computed X-ray-diffracted intensity versus (47t sin 9)/. The predicted intensities agree well with the experimental results of molten polyethylene. Figure 17 plots the correlation parameter t versus the distance r, where T(r) is given by...

Figure 16 X-ray-diffracted intensity 1 versus g.. i is equal to 4tt (sin 0)/. (From Ref. 99.)...

A second and more subtle area of difference is in the crystallography of the erionite phase itself (10). Table I compares x-ray diffraction intensities of low angle lines for a natural erionite (Jersey Valley, Nev.) and a synthetic erionite prepared at Esso Research Laboratories. The agreement is quite good except for those lines which have been marked by an astrisk indicating an intensity of less than half of that for natural erionite. Without exception, the designated lines (101, 201, 103, 211, 213, 311, and 401) have odd values for the 1 index. Further, their intensities are substantially less than the reference. 

Small samples (spheres or cubes with size of about 0.5 mm) of diaplectic feldspar glasses (Table 3.1) were used for X-ray diffraction experiments [25,30,33]. The measurements of X-ray diffraction intensities were made using a four-circle... 

FIGURE 1.5. The experimental setup used by Friedrich and Knipping to measure X-ray diffraction intensities. The important components consisted of an X-ray source to provide a finely collimated X-ray beam, a crystal to scatter X rays, and a detection system, such as photographic film, to measure the directions and intensities of the diffracted beams. The intensities so measured are related to the squares of the amplitudes of the scattered beams, but information on the relative phases of these scattered beams is lost. This same general experimental setup is currently used, although the source of X rays and the detection system are now much more sophisticated-... 

Measure the unit-celt dimensions and X-ray diffraction intensity data for crystals of the native protein. 

Any reasonably heavy atom can serve as an anomalous scatterer if the appropriate wavelength of X rays is used. For neutrons, however, there are fewer atoms that scatter anomalously (for example, Li, B, Cd, Sm, Eu, Gd) and their high absorption may limit their use. If X-ray diffraction intensity data are sufficiently carefully measured, it is possible to determine absolute configurations even if there are no heavy atoms in the structure, although values of A/" are very small for the light elements. Results of determinations of absolute structure must come from laboratories with an excellent reputation for careful intensity measurement. For example, Hakon Hope has been able to assign absolute... 

Figure 3. Temperature dependence of x-ray diffraction intensity for equatorial and meridional arcs (BP6L). Heating rate = 10 K/min.

Because part of the anomalous dispersion component is jt/2 out of phase with the isomorphous, real component, the net observable effect is a breakdown of Friedel s law regarding the perfect equality of the magnitudes of and If-h-k-i- That is, the two need not be absolutely equivalent but can demonstrate some slight difference A I anom = fhki — f-h-k-i- This difference will normally be imperceptible and within the expected statistical error of most X-ray diffraction intensity measurements, but with care in data collection, and judicious choice of X-ray wavelength, it can be measured and used to obtain phase information in conjunction with isomorphous replacement phase determination, or even independently, as described in Chapter 8. 

Fig. 15. X-ray diffraction intensity curves normalized to the same total intensity (a) sample I (b) sample II with different draw ratios (Z). (Figure 4 in the original literature Q. Chen, H. Kurosu, L. Ma and M. Matsuo, Polymer, 2002, 43, 1203.)...

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