Thin crystals, scattering

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 ... 

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. 

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. 

Kinematical theory is also called two-beam theory, as it includes consideration of only the incident and scattered X-ray beams. This is a very good approximation for thin crystals or for weakly scattering particles (e.g., most X-ray photons and neutrons), as rescattering of the initially scattered beam will be very weak. It is useful for calculating... 

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.

If the sample is crystalline, the scattered intensity depends very strongly on the orientation of the crystals and on their thickness. In bright field, a thin crystal will appear dark when it is correctly oriented for diffraction. If the crystal is not perfectly flat, the contours of correct orientation will appear as dark lines, called bend contours. Variation of intensity such as this in crystalline specimens is called crystallographic or diffraction contrast. Many types of defects in crystals cause localized distortion of the crystal lattice. These defects change the crystal orientation locally and so cause variations in the crystallographic contrast. Detailed information... 

Proper interpretation of the intensities of spots in a diffraction pattern gives the positions of the atoms in the crystal. Intensities are difficult to measure because of background from inelastic scattering of electrons. Electrons interact so strongly with matter that an electron can be scattered into one diffracted beam and then from that to another, even in a very thin crystal. This multiple scattering makes full theoretical treatment of electron diffraction complex [25]. It is not usual to determine atomic positions in a polymer crystal from an electron diffraction pattern, but it has been done by several groups [26-29]. 

X-ray scattering measures the crystallinity considering only crystals thicker than 2-3 nm. IR measures the total content of helix structures. The very thin crystals (< 2-3 nm) are included in the IR crystallinity assessment. It is also possible that the helices are present in the amorphous phase. 

The internal reference method has the following advantages 1) Samples do not need to contain heavy atoms for anomalous scattering effect. 2) The heavy atom method generally needs single crystals of high quality to secure the AC determination. On the other hand, the internal reference method is applicable even to crystals of low quality, e.g., extremely thin crystals, where the flnal R-value remains... 

Transmission electron microscopy (tern) is used to analyze the stmcture of crystals, such as distinguishing between amorphous siUcon dioxide and crystalline quartz. The technique is based on the phenomenon that crystalline materials are ordered arrays that scatter waves coherently. A crystalline material diffracts a beam in such a way that discrete spots can be detected on a photographic plate, whereas an amorphous substrate produces diffuse rings. Tern is also used in an imaging mode to produce images of substrate grain stmctures. Tern requires samples that are very thin (10—50 nm) sections, and is a destmctive as well as time-consuming method of analysis. 

X-ray diffraction consists of the measurement of the coherent scattering of x-rays (phenomenon 4 above). X-ray diffraction is used to determine the identity of crystalline phases in a multiphase powder sample and the atomic and molecular stmctures of single crystals. It can also be used to determine stmctural details of polymers, fibers, thin films, and amorphous soflds and to study stress, texture, and particle size. 

---