Crystal symmetry mismatch

A way to stretch or compress metal surface atoms in a controlled way is to deposit them on top of a substrate with similar crystal symmetry, yet with different atomic diameter and lattice constant. Such a single monolayer of a metal supported on another is called an overlayer. Metal overlayers strive to approach the lattice constant of their substrate without fully attaining it hence, they are strained compared to their own bulk state [24, 25]. The choice of suitable metal substrates enables tuning of the strain in the overlayer and of the chemisorption energy of adsorbates. A Pt monolayer on a Cu substrate, for instance, was shown to bind adsorbates much weaker than bulk platinum due to compressive strain induced by the lattice mismatch between Pt and Cu, with Cu being smaller [26]. 

Traditional zeolite-based molecular sieves most commonly exhibit incommensurate adsorption. This can be attributed to two main criteria (1) the dimensions of their channels or cages are, on average, much larger than that of the adsorbate molecules and (2) symmetry mismatches are often present. For example, zeolite-Y exhibits incommensurate adsorption for benzene and toluene molecules adsorbed within its super cage (Figure 4). The incommensurate adsorption type depends also on external parameters such as temperature. Single crystal and PXRD studies on the -hexane-loaded silicate-I MFI-type zeolite shows that at room temperature the adsorbed molecules are dynamically disordered and distributed over the entire channel, whereas at sufficiently low temperature, the adsorbate becomes well ordered within the channel, which is commensurate with the framework type. ... 

Internal Loops in RNA Oligomer Crystals. The first crystal structure of an RNA internal loop was solved in 1991(8). The dodecamer rGGACUUCGGUCC (internal loop underlined) forms a duplex in the crystal with an internal loop of consecutive U-G, U-C, C-U and G-U mismatches as shown in Figure 2. The chains of the double helix show two-fold symmetry in the crystal, thus the U-G and U-C pairs are identical to the C-U and G-U pairs. As can be seen, the internal loop generally continues the double helices which surround it by formation of non-Watson-Crick base pairs. The major groove of the A-form helix is opened with respect to a canonical RNA helix. 

The chapter begins with an overview of elastic anisotropy in crystalline materials. Anisotropy of elastic properties in materials with cubic symmetry, as well as other classes of material symmetry, are described first. Also included here are tabulated values of typical elastic properties for a variety of useful crystals. Examples of stress measurements in anisotropic thin films of different crystallographic orientation and texture by recourse to x-ray diffraction measurements are then considered. Next, the evolution of internal stress as a consequence of epitaxial mismatch in thin films and periodic multilayers is discussed. Attention is then directed to deformation of anisotropic film-substrate systems where connections among film stress, mismatch strain and substrate curvature are presented. A Stoney-type formula is derived for an anisotropic thin film on an isotropic substrate. Anisotropic curvature due to mismatch strain induced by a piezoelectric film on a substrate is also analyzed. 

It is obvious by now that the mismatch of symmetry between the Knoop indenter and 111 planes is a weakness when exploring hardness anisotropy of such planes. However, since scratch hardness does not suffer from such a mismatch, the resolved shear stress curves for the (111) plane in cubic crystals with the three commonly found slip systems shown in Figure 3.29 may be useful in anisotropy and slip system investigations. Clearly more detailed anisotropy is predicted but the small anisotropy factors implied in the scale-of Figure 3.29 must be remembered. Generally speaking, only the main features of the predicted curves have ever been established and experimental uncertainty makes it unlikely that the fine detail will be found. 

Fig. 30.14. Schematic representation of the p -Gd2(Mo04)3 structure. Diamonds drawn with so id and broken lines represent M0O4 tetrahedra at two different levels in space. The axis system A, B and B show the crystal in three different orientation states. States B and B are parallel (their axis systems are drawn antiparallel in the x and y directions, however, they are parallel through the internal symmetry of the structure) but have a translational mismatch at the antiphase boundary. State A is of opposite polarity. (From Barkley and Jeitschko (1973) by courtesy of J. Appl. Phys.)...

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