Bragg reflection condition

The boundaries of the Brillouin zone can be constructed with the aid of the Bragg reflection conditions... 

The condition k — imja is nothing but the well-known Bragg reflection condition, n — lacosO, for = 0. See Chap. 3 for more details. 

Photon energies above 1500 eV are monochromatized using double crystal monochromators, which make use of the Bragg reflection condition ... 

Such off-zone-centre, soft-mode systems offer the most favourable conditions for a test of the hypothesis that the central peak is a precursor to a Bragg reflection in the transformation phase. Zone-centre softening, such as occurs in NbaSn, results in the central mode scattering emerging from an existing Bragg peak, which ultimately splits in the lower symmetry transformation structure, which presents a problem with resolution. 

To determine the expressions for the optimised counting times, we write the expressions (10) and (11) in terms of count-rates and times (count rates are constant quantities for each Bragg reflection). We assume that the incident neutron flux is constant during a flipping ratio measurement, and that no dead-time correction is needed. In these conditions, we have the relations ... 

To summarise, the first method involves a fixed wavelength and a variable 0 while the second involves a fixed 0 and a variable X. In either case the purpose is to find the conditions for Bragg reflection. The advantage of the second method is that higher neutron densities can be obtained and faster experiments and higher levels of resolution can be achieved. 

Equations (1) are the von Laue conditions, which apply to the reflection of a plane wave in a crystal. Because of eqs. (1), the momentum normal to the surface changes abruptly from hk to the negative of this value when k terminates on a face of the BZ (Bragg reflection). At a general point in the BZ the wave vector k + bm cannot be distinguished from the equivalent wave vector k, and consequently... 

How are the Laue condition and the Bragg condition connected In Fig. A.3 the wave vectors of the incident and outgoing radiation and the scattering vector are drawn for the Bragg reflection of Fig. A.l. We can conclude that for specular reflection, the scattering vector lattice plane. Its length is given by... 

Bragg Reflections. Let us now determine the geometric conditions under which diffraction of X rays by a crystal structure would take place. These are (except for intensity considerations) the same as the conditions for diffraction from the crystal lattice if a pointscattering center is placed at each point of the lattice. We shall accordingly examine the geometry of diffraction by such a crystal lattice. 

Condition for Bragg reflection from scattering centers conflned to a set of equidistant, parallel planes. (Planes are perpendicular to the page, their traces are indicated by the horizontal lines.)... 

The constant Ce = 7.29 10 is determined by the electron energy which was measured precisely for our electron microscope by convergent beam electron diffraction (Kmse et. al., 2003). Equation (2) only applies if kinematical diffraction conditions are chosen. To eliminate the influence of d5mamical electron diffraction, the sample was tilted out of the zone axis by minimizing the excitation of the Bragg reflections in the diffraction pattern. 

Fig. 10 Schematic representation of the reflection conditions according to Bragg s equation.

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