Diffraction peak

Furthennore, the magnetic diffraction and the nuclear diffraction do not interfere with one another, and the nuclear and magnetic intensities simply add together, although in many cases the magnetic unit cell is larger than the nuclear unit cell, which produces additional diffraction peaks. 

Figure C2.17.9. Size-dependent changes in PXRD linewidtlis. PXRD can be used to evaluate tire average size of a sample. In tliese cases, different samples of nanocrystalline titania were analysed for tlieir grain size using tire Debye-Scherr fonnula. As tire domain size increases, tire widtlis of tire diffraction peaks decrease.

Crystallite Size. From the width of the peaks the computer can determine the size of the crystaUites in the sample. The smaller the crystaUite size, the broader are the diffraction peaks. This kind of analysis is important for determining particulate size of certain materials (eg, sUica) where a range of crystaUite size may be a health hazard if inhaled into the lungs. 

When there is constructive interference from X rays scattered by the atomic planes in a crystal, a diffraction peak is observed. The condition for constructive interference from planes with spacing dhkl is given by Bragg s law. 

In the concepts developed above, we have used the kinematic approximation, which is valid for weak diffraction intensities arising from imperfect crystals. For perfect crystals (available thanks to the semiconductor industry), the diffraction intensities are large, and this approximation becomes inadequate. Thus, the dynamical theory must be used. In perfect crystals the incident X rays undergo multiple reflections from atomic planes and the dynamical theory accounts for the interference between these reflections. The attenuation in the crystal is no longer given by absorption (e.g., p) but is determined by the way in which the multiple reflections interfere. When the diffraction conditions are satisfied, the diffracted intensity ft-om perfect crystals is essentially the same as the incident intensity. The diffraction peak widths depend on 26 m and Fjjj and are extremely small (less than... 

Figure 5 Bragg>Brentano diffraction pattern for magnetic media used in a demonstration of 1-Gb/in magnetic recording. The iines show a deconvoiution of the data into individual diffraction peaks, which are identified.

Rgure 3 Experimental and calculated results (a) for epitaxial Cu on Ni (001). The solid lines represent experimental data at the Cu coverage indicated and the dashed lines represent single-scattering cluster calculations assuming a plane wave final state for the Cu IMM Auger electron A schematic representation lb) of the Ni (010) plane with 1-5 monolayers of Cu on top. The arrows indicate directions in which forward scattering events should produce diffraction peaks in (a). 

The analogy of a crystal surface as a diffraction grating also suggests how surface defects can be probed. Recall that for a diffraction grating the width of a diffracted peak will decrease as the number of lines in the grating is increased. This observation can be used in interpreting the shape of RHEED spots. Defects on a crystal surfr.ee can limit the number of atomic rows that scatter coherendy, thereby broadening RHEED features. 

Macrostrain is often observed in modified surfaces such as deposited thin films or corrosion layers. This results from compressive or tensile stress in the plane of the sample surface and causes shifts in diffraction peak positions. Such stresses can easily be analyzed by standard techniques if the surface layer is thick enough to detect a few diffraction peaks at high angles of incidence. If the film is too thin these techniques cannot be used and analysis can only be performed by assuming an un-... 

X-ray diffraction peaks were rather broad with coherence lengths as low as 20 nm and this was attributed to rapid quenching. It was proposed that the carbon atoms are arranged in polyyne chains (n = 4) along the c-axis. The density of Carbolite (1.46 g-cm ) is lower than values for other carbynes and for diamond and graphite - hence the name - and this was attributed to a rapid quenching process. 

The x-ray diffractograms of those three samples are shown in Fig. 12. The lower pattern corresponds to the quenched sample where only the mesophase is present (the layer line, appearing at lower angles is not shown). The other two diagrams corresponding to the annealed samples present several sharp diffraction peaks, which... 

Fig. 6—1. Diagram of Beeghly s experiment. Note the attenuation of both the primary and secondary x-rays by the tin plate. The position of the detector is so chosen as to avoid diffraction peaks resulting from the interaction of the primary beam and metal crystals.

The use of an analyzing crystal in Method I will eliminate possible interference by diffraction peaks or b characteristic lines of the film. This method, called Method III to preserve the numbering ift the literature,9,10 is well adapted to a spectrograph (4.15) and may thus... 

Fig. 11. X-ray diffraction pattern of a Ni99Cul alloy partially transformed into its (3-hydride (0 NiCuH) before (a) and after (b) hydride decomposition. Arrows point to the diffraction peaks representing the rich in copper alloy phsae desegregated from the initial alloy after a multiple hydrogen absorption-desorption treatment. After Palczew-ska and Majchrzak (48).

Grating spectroscopy makes use of the strong wavelength dependence (or dispersion) in the positions of the diffraction peaks. The width of the diffraction peak will give the resolution for a grating with N rulings, the closest minimum occurs at angle AO from a diffraction maximum. 

In this section we will discuss in some detail the application of X-ray diffraction and IR dichroism for the structure determination and identification of diverse LC phases. The general feature, revealed by X-ray diffraction (XRD), of all smectic phases is the set of sharp (OOn) Bragg peaks due to the periodicity of the layers [43]. The in-plane order is determined from the half-width of the inplane (hkO) peaks and varies from 2 to 3 intermolecular distances in smectics A and C to 6-30 intermolecular distances in the hexatic phase, which is characterized by six-fold symmetry in location of the in-plane diffuse maxima. The lamellar crystalline phases (smectics B, E, G, I) possess sharp in-plane diffraction peaks, indicating long-range periodicity within the layers. 

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