Radiation diffraction

Studies of black-body radiation led to Planck s hypothesis of the quantization of electromagnetic radiation. The photoelectric effect provided evidence of the particulate nature of electromagnetic radiation diffraction provided evidence of its wave nature. 

Figure 3.6. Phase diagram for behenic acid at the air/water interface. The symbol x denotes the points at which synchrotron radiation diffraction experiments were carried out. For the notation and acknowledgements see Figure 3.5.

XRD and grazing-incidence synchrotron radiation diffraction (GISRD) plots of a hybrid sample at different depths from the surface showed the abundance of a-Al203, AT and mullite to vary with depth (Fig. 5.13). As the depth increased, the abundance of both mullite and AT decreased, but that of aAl203 increased. The composition depth profiles as determined from the Rietveld analysis are shown in Fig. 5.13(a). From the results it can be seen... 

Depth profiling of phase compositions in a hybrid LGM as revealed by (a) X-ray diffraction and (b) grazing-incidence synchrotron radiation diffraction. 

Singh, M. Low, I.M. (2002a) Depth-profiling of phase composition and preferred orientation in a graded alumina/mullite/aluminium-titanate hybrid using x-ray and synchrotron radiation diffraction. Mater Res. Bull. 37, 1279-1291. 

Remember from Chapter 4 that the periods and frequencies of waves are reciprocally related.) Exactly those properties are expressed by their reciprocal lattice vectors h. The amplitudes of these electron density waves vary according to the distribution of atoms about the planes. Although the electron density waves in the crystal cannot be observed directly, radiation diffracted by the planes (the Fourier transforms of the electron density waves) can. Thus, while we cannot recombine directly the spectral components of the electron density in real space, the Bragg planes, we can Fourier transform the scattering functions of the planes, the Fhki, and simultaneously combine them in such a way that the end result is the same, the electron density in the unit cell. In other words, each Fhki in reciprocal, or diffraction space is the Fourier transform of one family of planes, hkl. With the electron density equation, we both add these individual Fourier transforms together in reciprocal space, and simultaneously Fourier transform the result of that summation back into real space to create the electron density. 

Steiner, B. Dobbyn, R.C. Black, D. Burdette, H. Kuriyama, M. Spal, R. van den Berg, L. Fripp, A. Simcheck, R. Lai, R.B. Batra, A.K. Matthiesen, D. Ditchek, B. High resolution synchrotron X-radiation diffraction imaging of crystals grown in microgravity and closely related terrestrial crystals. J. Res. National Inst. Standards Technol. 1991, 96, 305. 

Due to the extremely short wavelengths of the accelerated electrons, the resolution of the instrument is not due to the radiation diffraction limits but to other effects such as multiple scattering of the electrons in the resist layer and substrate surface, and secondary electron emission [73,75,78]. These, mainly resist dependent, effects are hard to identify in detail but can be controlled to some extent during the exposure. However, it is not just the resolution of the resist which is the controlling factor in the ultimate particle size reached, rather it depends on exposure conditions (dose, beam intensity, etc.), the type of developer and processing technique used, and the way in which the hnal pattern is transferred to the substrate [79]. 

The microstructures of the consolidated and deformed samples were characterized by X-ray diffraction, optical and electron microscopy (SEM and TEM). The samples for mechanical testing have been prepared by spark erosion. The linear thermal expansion was determined by using a thermomechanical system (TMA). The temperature-dependent elastic moduli have been measured by the resonance frequency and the pulse-echo method. The bulk moduli were determined by synchrotron radiation diffraction using a high-pressure diamond-die cell at HASYLAB. The compression and creep tests were performed with computer-controlled tensile testing and creep machines. 

The resonance frequency technique has been used for determining the adiabatic Young s moduli in dependence on test temperatures up to 1000 °C. The shear moduli were measured by the pulse-echo ultrasonic technique. The bulk moduli were determined by synchrotron radiation diffraction. The temperature-dependent Young s and shear moduli are plotted in fig. 7. 

Some examples of applications of neutron and synchrotron radiation diffraction applied to the determination of residual stresses in various industrial and technological components have been presented. The reliability of the technique has been shown, being able to determine residual stresses induced by various thermomechanical treatments, such as shrink-fit joints, welds and surface treatments in automotive and aerospace materials. It has been shown how, by this method, it is possible to determine stresses both in the coating and in the substrate of plasma-spray deposed hydroxyapatite layers on Ti alloy for biomedical applications. 

Adsorption of radiation Scattering of radiation Refraction of radiation Diffraction of radiation Rotation of radiation Electrical potential Electrical current Electrical resistance Mass to charge ratio Rate of reaction Thermal properties Mass Volume... 

Many of the physical properties of crystals, as well as the geometry of the three-dimensional patterns of radiation diffracted by crystals, (see Chapter 6) are most easily described by using the reciprocal lattice. The two-dimensional (plane) lattices, sometimes called the direct lattices, are said to occupy real space, and the reciprocal lattice occupies reciprocal space. The concept of the reciprocal lattice is straightforward. (Remember, the reciprocal lattice is simply another lattice.) It is defined in terms of two basis vectors labelled a and b. ... 

The intensity of a beam of radiation diffracted by a set of (hkl) planes does NOT depend upon ... 

Figure 6.12 Scattering vector Q = 4rtsin0/2 of synchrotron radiation diffraction profiles of three as-sprayed hydroxyapatite coatings showing the vicinities of the (002) and (004) interplanar spacings of hydroxyapatite and oxyapatite (Heimann, 2009).

Most of the current optics using Synchrotron Radiation diffracts in the vertical plane and thus is sensitive to vertical bouncing of the beam. The horizontal optical plane of the dispersive scheme combines this extra advantage which helps to keep superior energy resolution since the orbit seems to show a better stability in the horizontal direction. Owing to the horizontal polarization of S.R., one must consider the cos (20) attenuation factor which reduces the Darwin width of the crystal. This results in a lower reflectivity and an improved energy resolution as well. 

The intensity of radiation diffracted from a set of hkl planes depends on the relative phases of the waves from adjacent planes, which in turn depends on the symmetry of the structure and the types of atoms that are in the unit cell. When these waves are completely in step the diffracted beam is intense. When they are completely out of step, the diffracted intensity is zero (see also Section 14.7). The relative intensity of the diffracted radiation from a set of planes is portrayed by the weighted reciprocal lattice. 

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