Bragg relationship

The underlying principle of X-ray diffraction is as follows. When a beam of X-rays passes through a crystalline solid it meet various sets of parallel planes of atoms. The diffracted beams cancel out unless they happen to be in phase, the condition for which is described in the Bragg relationship ... 

XRD on battery materials can be classified as powder dififaction, a technique developed by Peter Debye and Paul Scherrer. In powder dififaction the material consists of microscopic crystals oriented at random in all directions. If one passes a monochromatic beam of X-rays through a fiat thin powder electrode, a fraction of the particles will be oriented to satisfy the Bragg relation for a given set of planes. Another group will be oriented so that the Bragg relationship is satisfied for another set of planes, and so on. In this method, cones of reflected and transmitted radiation are produced (Fig. 27.2). X-ray diffraction patterns can be recorded by intercepting a... 

Ziman model. This model is based on a consideration of Bragg reflection for electron waves (Fig. 3.8). When the individual reflections add in phase, the Bragg relationship... 

X-ray diffraction is the elastic scattering of X-ray photons by atoms in a periodic lattice. The scattered monochromatic X-rays that are in phase produce constructive interference. Figure 6.1 illustrates how diffraction of X-rays by crystal planes allows one to derive lattice spacings by using the Bragg relationship ... 

If one measures the angles, 26, under which constructively interfering X-rays leave the crystal, the Bragg relationship [Eq. (6-1)] gives the corresponding lattice spacings, which are characteristic for a certain compound. 

In a three-dimensional crystal, the Bragg relationship must be satisfied simultaneously in all three dimensions... 

The diffraction of X-rays by crystalline matter is described by the Bragg relationship... 

When a crystalline polymer is oriented, the random circular film pattern (random orientation) transforms to a collection of defined reflection arcs that are correlated with particular (hkl) planes that can be identified based on the crystal structure and Bragg relationship (see Fig. 12a-b). It follows that the magnitude of the azimuthal spread (x/2) of these reflections is indicative of the degree of orientation. (The breadth, k, of the reflection is related to crystal size and imperfection—see Ref. 32.) Also, the location of the reflection with respect to the sample axes indicates the orientation of the crystallographic planes. For example Fig. 5(a) and (b) show two X-ray photographs of polyethylene that had been cold rolled. From the (200) reflection in sample (a) one sees that the a-axis is aligned preferentially normal to Z whereas in (b) there are two distinct orientations of the a-axis—one along Z and one normal to this. 

The spacing between two adjacent planes may be obtained from the Bragg relationship. 

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