Displacive reconstruction

Buerger [11] has classified transitions as either reconstructive or displacive. Reconstructive transitions involve a major reorganization of the crystal structure... 

A. Wander, M.A. Van Hove, and G.A. Somoijai. Molecule-Induced Displacive Reconstruction in a Substrate Surface Ethylidyne Adsorbed on Rh(l 11) Studied by Low-Energy-Electron Diffraction. Phys. Rev. Lett. 67 626 (1991). 

Figure 2.18 reveals that the threefold adsorption sites are not yet completely occupied, suggesting the possibility to increase the coverage even beyond 0 = 1. This is indeed the case and saturation is reached only at0 = 1.5,forwhichtheassociatedl x 2structureis reproduced in Fig. 2.19. The H atoms are no longer adsorbed in identical sites, and rows of Ni atoms in the topmost layer have been shifted together by 0.6 A to allow occupation of opposite threefold adsorption sites. As a consequence, the structures of even deeper layers are affected. This is a case of displacive reconstruction in which the symmetry of the surface unit cell is affected without a change in the atomic density.

In particular, the decoupling of both sensor and actuator operation for force and displacement reconstruction according to Fig. 6.8 is the main difference in the intelligent actuator concepts depicted in Fig. 6.7. In the case of self-sensing actuators the output y of the sensory path is strongly influenced by the driving quantity X of the solid-state transducer and must be... 

Figure 4.30 Displacive reconstruction of the W(IOO) surface. In panel (a), the bulklike terminated surface is shown with arrows indicating the zigzag displacements (0.21 A) that the top-layer atoms undergo.

Another important application area is the non-destructive defectoscopy of electronic components. Fig.2a shows an X-ray shadow image of a SMC LED. The 3-dimensional displacement of internal parts can only be visualized non-destructively in the tomographic reconstmction. Reconstructed cross sections through this LED are shown in Fig.2b. In the same way most electronic components in plastic and thin metal cases can be visualized. Even small electronic assemblies like hybrid ICs, magnetic heads, microphones, ABS-sensors can be tested by microtomograpical methods. 

One more application area is composite materials where one wants to investigate the 3D structure and/or reaction to external influences. Fig.3a shows a shadow image of a block of composite material. It consists of an epoxy matrix with glass fibers. The reconstructed cross-sections, shown in Fig.3b, clearly show the fiber displacement inside the matrix. The sample can be loaded in situ to investigate the reaction of matrix and fibers to external strain. Also absorption and transmission by liquids can be visualized directly in three-dimensions. This method has been applied to the study of oil absorption in plastic granules and water collection inside artificial plant grounds. 

Although it sounds reasonable to use the maximum likelihood to define our esfimafe of the displacement, there are two questions that remain. Firstly, what is the variance of the error associated with this estimate This defines N which was used in Eq. 22 fo defermine fhe error in fhe wavefront reconstruction. Secondly, is it possible to do better than the centroid In other words is it optimal ... 

Fig.2. Density of states in a five-layer W(OOl) slab, projected on the surface atomic layer. The upper panel shows the results for the unreconstructed and the lower panel for the reconstructed Qateral displacements) surface (after Ref. 26).

Assuming that a number of NMR data sets (e.g., 2-D or 3-D maps of displacement vectors resulting from an external periodic excitation) from an object are acquired, the remaining difficulty is their reconstruction into viscoelastic parameters. As written in Section 2 the basic physical equation is a partial differential equation (PDE, Eq. (3)) relating the displacement vector to the density, the attenuation, Young s modulus and Poisson s ratio of the medium. The reconstruction problem is indeed two-fold ... 

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