Interface plane

X yxzx — x s xxzx s zxx x s zzz l l e normal to the interface being taken along the Z axis with the X axis in the interface plane. The surface nonlinear polarization Ps (2co) is localized at the interface and is usually described as a nonlinear polarization sheet. This approximation holds because the thickness corresponding to the physical region of the... 

Calculate the strains and that would be applied if the lattice parameters in the interface plane of the layer were forced to conform to the substrate (full coherent epitaxy). Multiply these by (1-i ) where R is the (fractional) relaxation of the layer. (See the discussion of measurement of relaxation in Chapters.)... 

One SEXAFS specific feature is the polarisation dependence of the amplitude. This derives from the high anisotropy of the surface and of ultrathin interfaces, that we may consider as quasi two dimensional systems. The relative orientation of the X-ray electric vector with respect to the surface (interface) normal does represent a preferential excitation for those atom pairs aligned along the electric vector e.g. with the electric vector perpendicular to the surface (interface) plane the EXAFS amplitude will be maximum for the atom pairs aligned normal, or almost normal to the surface (interface). The electric vector can be also aligned, within the surface plane, along different crystallographic directions. 

AB can then grow either by nucleation in the supersaturated segment, by continuous addition at sites of repeatable growth on the boundary, or by recurring AB nucleation on the interface plane. In view of the commonly occurring misfit at most boundaries, it is probable that sufficient growth sites are normally available. 

In this process, the net flux of substitutional atoms across the interface plane results in local volume changes (i.e., as a crystal plane is removed by climb, the crystal contracts in a direction normal to the plane). However, free expansion in directions parallel to the interface plane is constrained by the specimen ends, where significant diffusion has not occurred, and by the coherence of the interface between the expanding and contracting regions. Therefore, dimensional changes parallel to the interface (i.e., normal to the diffusion direction) are restricted, and in-plane compatibility stresses are generated. No out-of-plane compatibility stresses develop because the diffusion couple can expand freely in the diffusion direction. 

For tilt boundaries, the value of E can also be calculated if the plane of the boundary is specified in the coordinate systems for both adjoining grains. This method is called the interface-plane scheme (Wolfe and Lutsko, 1989). In a crystal, lattice planes are imaginary sets of planes that intersect the unit cell edges. The tilt and twist boundaries can be defined in terms of the Miller indices for each of the adjoining lattices and the twist angle, , of both plane stacks normal to the boundary plane, as follows ... 

Figure 5 shows schematically the misfit dislocation orientation and possible Burgers vectors (grey vectors). The electron-beam direction and dislocation lines are aligned parallel to the [11-20] direction. 60° or 120° misfit dislocations are characterized by ba = 1/3 [-12-10] and 1/3 [-2110]. The edge component be = Vi [1-100] is compatible with an inserted (1-100) plane as observed in Fig.4(b). It can assumed that three set of misfit dislocations along the three directions are present in the (0001) interface plane. 

Figure 5. Schematic representation of the orientation of a misfit dislocation (bold black hne) and possible Burgers vectors (grey vectors) in the (0001) interface plane...

This vast number of possibilities calls for a systematic procedure to identify a subset of the most likely interface matchings of the parent crystals. This subset will then be the starting point for atomistic modeling. The question about unit cell size and shape is relatively simple to address. Many related procedures based on linear elasticity theory and lattice strain estimates may be adopted. The basic situation is sketched in Fig. 4 an overlayer unit cell A needs to be matched together with a substrate unit cell B. Matching pairs of unit cells are, in general, multiples of primitive cells in the interface plane for the metal and ceramic, respectively. 

It is instructive to compare this model to that of Bolding and Carter discussed above, for the case where both substrate and overlayer have orthogonal lattices (in the interface plane). If we multiply the overlayer unit... 

Panels a and c of Figure 6 demonstrate that water molecules on the bulk side of the Gibbs surface (solid lines) lie parallel to the interface. The water molecules on the vapor side of the liquid/vapor interface, as well as those on the CCI4 side of the water/CCU interface (dashed lines), have a very slight tilt away from bulk water. The molecules on the vapor side and on the CCI4 side of the interface have their planes perpendicular to the interface, so one OH bond points away from the bulk, and the other one is nearly parallel, with a slight tendency to point towards the bulk. The plane of the water molecules on the bulk side, on the other hand, is parallel to the interface, so both OH bonds are in the interface plane... 

Flux is a somewhat abstract entity and does not relate this information directly. It quantifies the chemical movement rate across an interface plane into a receiving media such as the air boundary layer (BL) in the above example. Only when it is coupled with an air dispersion model does it produce concentrations in air. In the case of a large soil surface area source, a simple relationship exists between flux and concentration. For neutral air stability conditions in the atmospheric BL with steady-state wind speed v (m/sec), the concentration in air, c (mg/m ), can be approximated by... 

Copper NMR was used to gauge the quality of [Ni/Cu] " and [Co/Cu] superlattices synthesized by the ion sputtering method. The authors noted that the shapes of the spectra vary noticeably with the change in angle between the interface planes and the external field. This is a unique feature of superlattice systems, not observed in bulk metals, and which can offer information on the electronic states in the copper layers. A study of CUAI2 by A1 and Cu NMR investigated quadrupole and anisotropic shift interactions between 3 and 40 MHz. 

We have just described the effect of the intensity distribution on the structural defects in the direction perpendicular to the interface. Naturally, the size of the crystals can also have a finite dimension in the interface plane. This leads to wider lattice points in the direction defined by q (Figure 7.18e). Likewise, the microstrains in the interface plane may lead to an increased width along q. ... 

In the example we have just described, the size of the crystals shows a rather wide distribution, which is why the diffraction profiles measured in the direction perpendicular to the interface or in the interface plane are bell curves, similar to those obtained for diffraction peaks measured with samples comprised of randomly oriented crystals. We will move on to a different case, in which virtually all of the crystals, or diffracting domains, are similar in size. 

An observation by in plane-view optical microscopy is shown in Figure 7.34. The dark areas correspond to the substrate and the lighter ones to the islands. At this scale, the film shows a very peculiar microstracture that indicates a non-random distribution of matter. In other words, the relative distances between the islands are not random, something which is described as an organized microstmcture in the interface plane. The fringes shown by X-ray diffiaction, in the profile from Figure... 

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