Crystallographic shear

Within the elastic range, loading applied along nonspecific crystallographic directions results in propagation of both longitudinal and shear waves which may be of considerable amplitude [80C01],... 

While the smooth substrate considered in the preceding section is sufficiently reahstic for many applications, the crystallographic structure of the substrate needs to be taken into account for more realistic models. The essential complications due to lack of transverse symmetry can be dehneated by the following two-dimensional structured-wall model an ideal gas confined in a periodic square-well potential field (see Fig. 3). The two-dimensional lamella remains rectangular with variable dimensions Sy. and Sy and is therefore not subject to shear stresses. The boundaries of the lamella coinciding with the x and y axes are anchored. From Eqs. (2) and (10) one has... 

The structural principles of Prl2 can be derived either from 4" nets (Prl2-I) or 3 nets (all other modifications) of iodine atoms that are stacked along a prominent crystallographic direction, in most cases the [001] direction. Between these layers, half of the respective interstices are filled with praseodymium atoms (but see Prl2-V below). Please note that 4" and 3 nets are closely related to each other, it only needs a shear procedure to transform one net to the other (Fig. 4.3). In the iodine layers I-I distances are even shorter in the 4" net (386 in Prl2-I [4]) than in the 3 net of Prl2-IV (426.5 pm [6, 9]). 

Fig. 13 87Rb NMR spectra of polycrystalline RbN03 (a) sheared z-filter 2D triple-quantum MQMAS spectrum, (b) MAS spectrum, (c) MQMAS isotropic projection, and (d-f) cross-sections of the 2D spectmm showing the three different crystallographic sites...

A crystallographic shear (CS) plane is a fault in which a plane of atoms has been (notionally) removed from the crystal. In oxides, this is frequently a plane of oxygen atoms, eliminated as a result of reduction. In the resulting structures, the slab types are all identical and the same as the parent phase. To illustrate this phenomenon, crystallographic shear in reduced tungsten trioxide will be described. 

The resonator is usually made of quartz and both longitudinal and shear modes can be used. As to the quartz, crystallographic cuts showing a highly stable temperature operation dependence are carefully selected in order to improve the possibility of obtaining satisfactory resolution values. 

Crystallographic shear plane. Series of discrete shear phases are observed among the oxides of several transition metals. By progressive reduction, series of Ti 02 i, V 02 i phases are obtained from the dioxides, as Me 03 i phases may be related to trioxides such as M0O3 or WO3. An example of a crystallographic shear plane formation is schematically shown in Fig. 7.54. 

Transition metal oxides attract great interests mainly due to their redox nature, which is thought to be related with their flexible stmcture modiflcation under reductive and oxidative conditions. Such stmcture modiflcation takes place by forming so called crystallographic shear (CS) stmctures to accommodate anion vacancies in speciflc crystallographic planes by simultaneous shear displacement and crystal stmctural collapse [30-32]. High-resolution transmission electron microscopy (HRTEM) is a... 

Role of Ciystallographic Shear Planes This area is tied to the subject of surface oxidation state. In redox kinetics it is believed that sites for hydrocarbon oxidation are different from that for reoxidation, and crystallographic shear planes (CSP) have been suggested to assist bulk oxygen movement between the sites 44,45,46,47), There have been a few studies of this phenomenon. In WO2.95 WO2.9 it has been shown CSPs are involved in oxygen transfer but... 

---