Condition for constructive

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. 

Cold-weather conditions for construction is defined as a period when for more than 3 consecutive days, the following conditions exist [106, 107] the... 

Zachariasen Rules. In 1932, W. H. Zachariasen considered the conditions for constructing a random network like the one shown in Fignre 1.48 and proposed four rules for the formation of oxide glasses ... 

Fig. 21.5 Conditions for constructive of X-rays with a set of parallel planes of crystal.

A real two-dimensional crystal consists of a periodic structure in not only one, but in two directions. This second periodic structure in another direction also leads to a condition for constructive interference. The conditions for both directions have to be fulfilled at the same time. Both conditions are only fulfilled where the cones of both orientations intersect. As a result constructive interference occurs only on lines starting from the point of incidence. On a detector plate we would observe spots where these lines cross the plate. 

Figure 8.20 Condition for constructive interference for a one-dimensional array of scattering centers (top). Constructive interference occurs along the cones that reflect the rotational symmetry of the one-dimensional arrangement (middle). For a two-dimensional crystal, constructive interference is obtained along lines (bottom).

Equation (A.5) is known as the Laue2 condition for constructive interference. 

Consider the diffraction from a one-dimensional row of regularly spaced atoms. From Figure 5.19 it can be seen that the condition for constructive interference is... 

X-rays have wavelengths that are comparable to the spacing between atoms. Rows of atoms cause diffraction, so if the wavelength of the X-rays is known, the spacing between atoms can be determined. Figure 3.8 shows that the condition for constructive interference, hence strong scattered X-rays, is... 

Since, the scattered ray interfere subsequently, for rays reflected by two adjacent planes, the condition for constructive interference is given by (see Figure 1.22) [22]... 

One of the important featmes of Bragg scattering is that the strength of the scattered beam depends on how well the atoms are localized at their ideal lattice locations. If the atoms are all located very close to the lattice positions defined by the interference pattern, they will all nearly satisfy the conditions for constructive interference, and the scattering will be strong. 

The condition for constructive interference corresponds to that when the scattered waves are in phase. In Fig. 3.15a, the wavefront labeled 1 would have to travel a distance AB + BC farther than the wavefront labeled 2. Thus if and when AB + BC is a multiple of the wavelength of the incident X-ray A, that is,... 

The condition for constructive interference is simply that the path length difference for the two photons is an integer multiple of wavelengths (as shown in Fig. 2A), or... 

FIGURE 316. William H. Bragg and his son William L. Bragg reversed von Laue s experiment and used x-rays to measure the distances between ions or atoms in crystals (see text), (a) Depicts the conditions for constructive interference of x-rays termed Braggs Law (b) schematic of Braggs s x-ray apparatus (WH. Bragg and W.L. Bragg, X-Rays And Crystal Structure, 4th ed., London, 1924). 

FIGURE 7 12 (a) Schematic cross section oi an Interference filter. Note that the [Pg.176]

Yadav et al. reported a three-component coupling reaction under MW conditions for construction of a triazine system containing a thiazole core [85], In this reaction, a thiazole Schiff s base, an aldehyde, and NH4OAC react to yield thiazolo-s-triazine C-nucleosides 44 (Scheme 17.33). 

Diffraction is described by either Bragg or von Laue equations. The Bragg equation relates as a condition for constructive interference the wavelength of the electromagnetic radiation k to the interplanar distance a and the observation angle 0... 

The condition for constructive interference in all dimensions is a set of the common intersection of these cones, defined by the simultaneous solution of the respective equations. Thus, the equations represent one form of the scattering conditions required for diffraction to occur in three dimensions... 

The condition for constructive interference is that the waves should all be in phase with one another. Figure 1.15 gives examples of waves... 

Bragg condition A condition for constructive wave addition in a periodic lattice. 

The requirements for x-ray diffraction are (1) the atomic spacing in the solid must be comparable with the wavelength of the x-rays and (2) the scattaing centers must be spatially distributed in an ordered way (e.g, the environment present in crystals). The diffraction of x-rays by crystals (Fig. 3.17) was treated by Bragg in 1912. The condition for constructive interference, giving rise to intense diffraction maxima, is known as Bragg s law ... 

---