Scattering, from thin crystals

Scattering from Thin Crystals. The simple arguments given above hold only if samples are amorphous. Although some catalyst supports are non-crystalline, such as charcoal and silica, others such as alumina are not. Furthermore, the metal catalyst clusters themselves are generally crystalline and thus the above arguments must be modified to account for Bragg reflections from crystalline areas. 

Stoichiometric variations in compositions of a material and of surface layers can be revealed by AEM. Because a relatively small amount of scattering occurs through a thin HRTEM specimen, X-rays are generated from a volume that is considerably less than in the case of electron microprobe analysis (EPMA). For quantitative microanalysis, a ratio method for thin crystals (57) is used, given by the equation ... 

Structure refinement based on kinematical scattering was already applied by the Russian scientist 60 years ago. Weirich et al. (1996) first solved the structure of an unknown TinSe4by HREM combined with crystallographic image processing. Then they used intensities extracted from selected area electron diffraction patterns of a very thin crystal and refined the structure to a precision of 0.02 A for all the atoms. Wagner and Terasaki et al. (1999) determined the 3D structure of a new zeolite from selected area electron diffraction, based on kinematical approach. 

This is the most useful quantitative intensity formula that may be derived from kinematical theory, since it is applicable to thin layers and mosaic blocks. We add up the scattering from each unit cell in the same way that we added up the scattering from each atom to obtain the stractme factor, or the scattering power of the unit cell. That is, we make allowance for the phase difference r, . Q between waves scattered from unit cells located at different vectors ri from the origin. Quantitatively, this results in an interference function J, describing the interference of waves scattered from all the unit cells in the crystal, where... 

Figure 4.3 brings out the following features of the scattering from a thin (or small) crystal ... 

The scattered intensity is proportional to the volume of the crystal. This implies that the scattering from a thin epitaxial layer, large in area compared with the beam diameter, will be proportional to the layer thickness. 

In common with CdSe deposition from selenosulphate baths, cluster deposition of PbSe normally resulted in specular films, while ion-by-ion films were initially highly scattering as thin films but eventually (usually) became specularly reflecting with increase in thickness. As for CdSe, the development of specularity with thickness of ion-by-ion films could be explained by filling in of voids between the large crystals. 

A polycrystalline thin film does not have any preferred orientation (Figure 6.4 (c)). In such a case, the diffraction from the crystal is not a spot but a so-called Debye-Scherrer ring. Therefore, the sample does not have to be inclined to obtain the diffraction pattern. Conventional 2 0-6 scans move the scattering vector H in the radial direction along the film surface normal. Thus, these scans give sufficient information when the film is polycrystalline. The obtained diffracted intensity must be corrected in terms of the absorption and the Lorentz polarization. These two terms and the obtained diffracted intensity have the following relation ... 

The diffracted beam from a crystal is built up of rays scattered by all the atoms of the crystal which lie in the path of the incident beam. The reflection of visible light takes place in a thin surface layer only. 

Since the specimen is thin compared to the mean free path of the incident electrons, most will not interact at all with the constituent atoms of the sample but will simply pass undeflected through the material. However, provided the sample is crystalline, some fraction of the incident electrons will be scattered from crystal planes within the material by Bragg diffraction, and give rise to characteristic spots or rings in an electron diffraction pattern. These diffracted electrons lose little or none of their incident energy in such Bragg scattering events and are said to be elastically scattered. 

The propagation matrix F describes the modification of the wave field A upon propagation from coordinate z to coordinate z + dz. It is a multidimensional matrix with dimension given by the number of the open scattering channels. This formalism is successfully applied not only to describe the propagation of light in forward direction but also in case of X-ray diffraction from single crystals, and reflection from surfaces, thin films, and multilayers. 

Figure 26 Schematic illustration of the two possible models of the lamellar stack of semirigid chain polymers. Left, stacks with thin crystals and thicker interlamellar amorphous regions. Right stacks with thicker crystals and thinner interlamellar amorphous regions. The ambiguity of the microstructural model Is due to the Babinet principle, which makes the scattering from the two structures indistinguishable.

---