Single crystals diffraction theory

Nitromethane, CH -NOf. The equilibrium structure of singlet nitromethane has been studied at several levels of theory [3,60,64-71]. Two conformations are possible for nitromethane, staggered (Is) and eclipsed (le), but the eclipsed form has been characterized as a transition structure at MP2/6-31G with an imaginary frequency of 30 cm 1 [3]. Rotation around the H3C-NO2 bond occurs essentially without barrier the estimated value is only 0.01 kcal/mol. This is in accordance with a microwave study, which reports a C-N rotation barrier of only 6 cal/mol [72,73]. The C-N bond length of nitromethane has been estimated with X-ray single crystal diffraction [74], neutron diffraction [46,75], microwave spectroscopy [72,73], MP2/6-31G [3], and B3LYP/6-31+G [71] at respectively 1.449, 1.486, 1.489, 1.485, and 1.491 A, showing that the theoretical estimates compare very well with those determined by experimental methods. The experimentally reported vibrational frequencies of nitromethane... 

No matter how thorough, a kinetic study does not really determine a mechanism in the same sense that single-crystal X-ray diffraction measurements determine a structure. The reaction mechanism is but a scientific postulate that is open to revision when new data, new insights, or new theories of reactivity emerge. 

For readers learning electron diffraction, there are a number of books on electron diffraction for materials characterization [1,2,3,4]. Most of these books focus on crystals since many polycrystalline materials are perfect single crystals in an electron microscope because of the small electron probe. Full treatment of the dynamic theory of electron diffraction is given in several special topic books and reviews [5,6,7,8]. 

The. folded-chain lamella theory arose in the last 1950s when polymer single crystals in the form of thin platelets termed lamella, measuring about 10,000 A x 100 A, were grown from polymer solutions. Contrary to previous expectations, X-ray diffraction patterns showed the polymer chain axes to be parallel to the smaller dimension of the platelet. Since polymer molecules are much longer than 100 A, the polymer molecules are presumed to fold back and forth on themselves in an accordionlike manner in the process of crystallization. Chain... 

In conclusion, field dependent single-crystal magnetization, specific-heat and neutron diffraction results are presented. They are compared with theoretical calculations based on the use of symmetry analysis and a phenomenological thermodynamic potential. For the description of the incommensurate magnetic structure of copper metaborate we introduced the modified Lifshits invariant for the case of two two-component order parameters. This invariant is the antisymmetric product of the different order parameters and their spatial derivatives. Our theory describes satisfactorily the main features of the behavior of the copper metaborate spin system under applied external magnetic field for the temperature range 2+20 K. The definition of the nature of the low-temperature magnetic state anomalies observed at temperatures near 1.8 K and 1 K requires further consideration. 

For hydrogen bonds weaker than OH 0=C or NH 0=C, theory predicts smaller differences in the X-H bond lengths and negligible changes in the nonhydrogen bonds. TWo models have been studied theoretically with the ab-initio molecular orbital method at the HF/3-21G level of approximation. These are formaldehyde oxime cyclic dimer versus the monomer [378] and formaldehyde hydrazone cyclic dimer versus the monomer [379]. Except for the O-H and N-H bonds, these differences are too small to be detected by single crystal X-ray or neutron diffraction methods, as shown in Fig. 5.2. 

In theory single crystal methods can be effectively used for structure solution from powder diffraction X-ray data. However, in powder diffraction the number of peaks involved are limited, and hence the data-to-parameter ratio is very small, due to the transfer of the three-dimensional data to one dimension, namely, 29. In spite of the inherent shortcomings, conventional crystallographic methods such as Direct, Patterson and maximum entropy methods have been successfully applied to powder diffraction data. The most popular program, which uses reciprocal space methods for stmcture solution is EXPO. ... 

We now consider the diffraction of electrons by a single crystal in terms of the so-called kinematical theory. Although this theory has serious limitations, it is useful in practice under certain conditions, and it also provides an introduction to the more satisfactory dynamical theory, which we develop in Chapter 4. 

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