Diffraction contrast diffracted beam intensity

In 1960, Hirsch, Howie, and Whelan developed the theory for diffraction contrast imaging [3]. In the case of two beam condition, the diffracted beam intensity Id for a perfect crystal is written as ... 

The essence of the topographic methods is that they map the interrsity of the diffracted beam over the surface of the crystal. Defects affect the diffracted intensity, so give contrast in the image. The methods are quite sertsitive enough to reveal individual dislocatiorrs, precipitates, magnetic domains and other long-range strain fields but cannot reveal point defects except in dense clusters. 

The image intensity /(x, y) at the image plane of the objective lens results from two-dimensional Fourier synthesis of the diffracted beams (the square of the FT of the waves at the exit face of the crystal), modified by a phase-contrast transfer function factor (CTF, sin /), given by Scherzer (1949), as... 

The most commonly employed imaging mode is bright field (BF), which uses only the central beam, usually called the transmitted beam. Image contrast is observed if, for whatever reason, the diffracted beams originating from different parts of the specimen vary in intensity. If a crystalline specimen is so oriented with respect to the incident beam that many strong diffracted beams are excited, then an extremely complex BF image... 

Now the form of R depends on the nature of the defect. To determine the contrast due to a particular kind of defect in BF and DF images, we must find the intensities Iq (=TT ) and 7g (=SS ) of the transmitted and diffracted beams as a function of position around the defect, using Eqs. (5.5) or Eqs. (5.8). In the following sections we discuss in detail the solutions of these equations for the various types of crystal defect already considered in general terms in Section 5.1. 

The reason we see a dislocation is that it bends a crystal plane near its core region. Indicate a case where we may not be able to see the dislocation in diffraction contrast under a two-beam condition (a two-beam condition refers to a crystal orientation in which the intensity of one diffraction spot is much higher than those of the other diffraction spots). Indicate the answer either graphically or using the relation of vectors g (the normal of planes which generate the diffraction beam) and b (Burgers vector of dislocation). 

Diffraction and mass-thickness contrast are both caused by an intensity change of a diffracted beam over the field of view. Since the intensity, specifically the amplitude, of a beam causes these types of image contrast, diffraction and mass-thickness contrast are referred to as amplitude contrast. ... 

Neutrons in thermal equilibrium at 298 K can be used for diffraction in a similar way to X-rays, since they also have wavelengths comparable to interatomic spacings. In contrast to X-ray diffraction, the powder neutron diffraction experiment is much more common than single crystal neutron diffraction, since the beam intensity tends to be 1000 times less than for X-ray diffraction, so that single crystals of a sufficient size to collect good data are difficult to grow. 

Diffraction intensities are shown in Fig. 34 with the notation [00], [10], and [20] indicating the specular, first- and second-order diffracted beams, respectively. It is immediately apparent from the contrast between the three figures that the availability of the PES sink has a marked effect on all the beams. The specular beam does not go through a minimum at 350 meV because as the energy is raised, dissociation becomes more probable, and thus more of the flux is channeled into this dissociation channel instead of into the reflected specular channel. Similarly, the peak values of the [10] and [20] beams are significantly reduced. In a nonreactive system, it is... 

---