Grating, diffraction pattern

As one may infer from the quotation, W. L. Bragg realized that a crystal can act as an x-ray grating made up of equidistant parallel planes (Bragg planes) of atoms or ions from which unmodified scattering of x-rays can occur in such fashion that the waves from different planes are in phase and reinforce each other. When this happens, the x-rays are said to undergo Bragg reflection by the crystal and a diffraction pattern results. 

In the crystalline state of a substance, the molecules are arranged in a defined unit cell that is repeated in a three-dimensional lattice [1], Since the crystal lattice can act as a diffraction grating for X-rays, the X-ray diffraction pattern of a crystal consists of a number of sharp lines or peaks, often with baseline separation. Figure 1 shows the X-ray powder diffraction pattern of the crystalline and amorphous forms of nedocromil sodium trihydrate. 

It is readily apparent that a mask consisting of equal lines and spaces constitutes a diffraction grating and when uniformly illuminated will produce a diffraction pattern similar to that just discussed with an intensity profile depending on the grating period ( ), the wavelength (X) and the position of the image plane. This will be discussed in more detail later. 

The quality of the relief thus obtained can be determined directly in the course of etching because the light reflected from the etched grating produces a diffraction pattern that characterizes the depth and shape of the grating profile at any given moment. To this end, one has just to measure the intensity of the reflected light. The method possesses a high sensitivity the occurrence of the relief can be detected when its depth is only of the order of 0.01 /an. 

Diffraction of light by line gratings. Above grating of evenly spaced lines, with diffraction pattern. Below grating in which the unit of pattern is a pair of lines (repeat distance same as in the first), with diffraction pattern... 

This is a simple example of the synthesis of an image from a diffraction pattern by calculation. The synthesis of an image of a crystal structure from its X-ray diffraction pattern is more complex (because a three-dimensional diffraction grating is involved), but similar in principle, because the X-ray diffraction spots produced by an atomic pattern are absolutely analogous to the diffracted light beams formed by a pattern whose repeat distance is comparable with the wavelength of light. 

At low conversions the diffraction efficiency of the holographic grating can be monitored to determine the rate of photodimerization. Kohler et al. have measured an upper limit on the activation energy for photodimerization of 3.6 kcal/mol, which is very close to a value of about 3.1 kcal/mol determined by Nakanishi et al. for the dimerization of distyrylpyrazine [96]. Rates of disappearance of the diffraction pattern can be used to measure the rate of reversion to starting monomer which occurs upon thermal annealing above 100°C. Kohler et al. have measured the activation energy for this process to be 23.7 kcal/mol. 

The geometric structural information about the crystal can be extracted from the diffraction pattern by geometric analysis. The concept of a crystal as being a diffraction grating for X-radiation and the relationships between the geometry of the diffraction grating and the pattern of... 

Figure 3.1-6 The main components of a grating spectrometer N is the number of interfering rays, given by the number of rules so is the half width of the diffraction pattern of the collimator lens with the diameter D and the focal length /, it determines the optimal slit width (Laqua, 1980), h is the slit length.

As described above (Eq. 3.1-11), the collimator or camera lens or mirror of a grating spectrometer produces a diffraction pattern. A monochromatic beam produces a pattern of the width SqPi, which according to Fig. 3.1-8 is described by the equation ... 

Figure 1.11. A series of ten pmrs of photographs that show the effects of spatial filtering on the image of a two-dimensional grating. Each photograph shows (a) the diffraction pattern and (b) the resulting image. (Continued, pp. 24-27)...

So far we have only considered the diffraction pattern of a single slit and have shown that the intensity variation is bell shaped this is the envelope profile with a width inversely proportional to the width of the slit. Now we will consider what happens to the diffraction pattern when more slits are lined up parallel to the first to give the equivalent of a diffraction grating. This is a two-dimensional analogy to the buildup of a crystal... 

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