Higher order reflections

Several peaks of interest (ideally higher order reflections of the same type hkl, 2h, 2k, 21, 3h, 3k, 31,. .., nh, nk, nl) are fitted by Fourier series the same procedure is applied to the diffraction lines of a reference sample, in which size and strain effects are negligible, in order to determine the instrumental line broadening. Such information is used in order to deconvolute instrumental broadening from sample effects (Stokes-Fourier deconvolution [36]). 

X-ray diffraction from cast films provide useful information of bilayer structure. Periodic peaks in small and middle-angle diffraction from cast films on glass plates are attributed to the reflections from (h, 0,0) planes of the multiple lamella structure. The spacing of higher order reflections (h > 1) satisfies with numerical relation of 1 / h of the long period calculated from the first order reflection =1), which is equivalent to the bilayer thickness. Every cast film measured in this experiment showed more than 6 reflection peaks. 

The multipole model reduces the crystal electron density to a number of parameters, which can be fitted to experimental structure factors. For CU2O, structure factors for the (531) and higher-order reflections out to (14,4,2) were taken from X-ray measurements. Weak (ooe) (with o for odd and e for even) and very weak (eeo) reflections were also taken from X-ray work. Fig. 6 shows a three-dimensional plot of the difference between the static crystal charge density obtained from the multipole fitting to... 

Figure 2. Formation of nanocrystals with bcc-Fe(Co) lattice from amorphous (Fe3Co2)73Nb7Si5B15 annealed at 840K/800min with the corresponding XRD and electron diffraction patterns (right). Vertical hues and indices indicate the positions of the bcc-Fe(Co) peaks higher order reflections not measured by XRD are easily identifiable on the electron diffraction pattern with sufficient intensity.

The period of the plane wave with amplitude F(H), in the direction of the wavevector H, equals l/H. The period is therefore shorter for higher-order reflections, which thus add resolution to the image. As more higher-order reflections are included in the summation, the resolution of the image improves, as illustrated in Fig. 5.1. The improvement is analogous to the increase in resolution in an optical image obtained with shorter-wavelength radiation. 

In eke attempt to obtain correct calculated intensities the following problem arises gup-pose a particular set of atomic coordinates gives some measure of agreement of calculated with observed intensities for one projection, but nevertheless there are still considerable discrepancies, especially among the higher order reflections—a situation which probably means that the postulated atomic coordinates are roughly correct, but need adjustment. Which atoms should be moved, and by how much ... 

The d-spacings of the 211 (d = 33.1 A) and 220 (d = 28.6 A) reflections of the pristine MCM-48 silica are observable in the host/guest compounds whereas the higher order reflections (20 4-6°) disappear. In addition, the 113/021 (d = 2.53 A 1=100%) and 208/220 (d = 1.48 A 1=36%) reflections of the inverse cobalt iron structure appear in sample A and B. In contrast to the bulk material of CoFe24 (figure 2) synthesized under exact the same conditions as the phases A and B, the reflections of the host/guest compounds are much broader and weaker in intensity, indicating the occurrence of very small particles. 

Figure 1. XRD pattern of the material depicted in Fig. 2, showing higher-order reflections.

By drawing similar diagrams for higher-order reflections (3g, 4g, etc.) satisfying the Bragg condition, we can easily see that if a reciprocal lattice point G of the systematic row lies on the Ewald sphere (i.e., s g = 0), then the magnitude of the diffraction error Sg of the first-order reflection will be given by... 

With these materials of Scheme 3 the deformed helix B from Fig. 18 was realized. A spectrum of an IR reflecting cholesteric siloxane in the non-irradiated and irradiated states is shown in Fig. 24. The portrait shown on the right is a result of the higher order reflection. 

Make a diffractometer scan to find the angle 26 at which diffraction occurs from the (hkl) planes. [Higher-order reflections may also be observed, i.e., reflections from (nh, nk, nl) planes.]... 

The zero-order term of this expansion, which is independent of x, just redefines the zero-order Hamiltonian. Disiegarding higher order reflects the expectation that in condensed phases the deviations x from the minimum energy configuration are small. 

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