Anisotropic Lattice Distortion

A-plane GaN films with different thickness between 1 [im and 67 [im were grown on r-plane sapphire by metal-organic vapor phase epitaxy (MOVPE) and HVPE. The a-plane MOVPE films were grown at University of Stuttgart and University of Bremen at 1030-1050 °G using a conventional two-step process employing GaN or AlN buffer layers [45, 46]. The a-plane HVPE films were grown at University of California, Santa Barbara, directly on sapphire in a three-zone horizon reactor at 1040-1070 °C [47]. 

GaN films versus the strain components, and according to Equation 7 and using the stiffness constants from [44]. The squares show the calculated values of Syy using the measured and and the 

Further details about the data and measurement, and calculation procedures of the anisotropic strain components in both a- and c-plane GaN films can be found in [17-19, 29, 30, 41]. 

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In further work the same team [82] used angle-dispersive X-ray diffraction in the pressure range 2-6 GPa to study crystalline GeSc2. This confirmed the transition to a three-dimensional crystalline structure above 2 GPa at 698 K. This transition was explained by an anisotropic lattice distortion due to the cooperative tilting of rigid Ge(Sc4) tetrahedra. The authors claimed that a similar transition, including anomalous compressibility and thermal expansion phenomena, could be observed in... 

This property is readily established from the definition of Fourier transform and convolution. In scattering theory this theorem is the basis of methods for the separation of (particle) size from distortions (Stokes [27], Warren-Averbach [28,29] lattice distortion, Ruland [30-34] misorientation of anisotropic structural entities) of the scattering pattern. 

The spin density wave (SDW) is a 2kF instability due to spin-spin interactions and the ground state has no lattice distortion. s is typical of an antiferromagnetic ground state and therefore anisotropic below the transition temperature, Tc. Antiferromagnetic resonance (AFMR) may be a good technique to characterize this transition. A particular characteristic is that the Tf1 NMR relaxation rate diverges at Tc. 

Dq anisotropic Gaussian contribution from lattice distortions ... 

From the width of the reflections of the wide-angle X-ray scattering (WAXS) fiber pattern the apparent size and the degree of perfection of the crystalline domains can be determined. In PpPTA the size and disorder parameters are strongly anisotropic. Normal to the chain axis the dimensions of the domains are 4-6 nm. Analysis of the meridional reflections shows that these fibers apparently have a paracrystalline structure with a longitudinal crystallite size of at least 25 nm and a lattice distortion parameter gu of 2-3%. Annealing at temperatures up to 600°C increases the lateral size to about 10 nm and the longitudinal size to about 80 nm, while gn decreases to about... 

Choice of lattice linear dimensions Lx, Ly (usually Lx = Ly = L, apart from physically anisotropic situations, such as the ANWII model ). Only finite lattices can be simulated. Usually boundary effects are diminished by the choice of periodic boundary conditions, but occasionally studies with free boundaries are made. Note that Lx, Ly must be chosen such that there is no distortion of the expected orderings in the system e.g. for the model of where due to a third nearest neighbor interaction superstructures with unit cells as large as 4 x 4 did occur, L must be a multiple of 4. 

Some examples of direct measurement of the crystal distortion during the reaction by optical and electron microscopy, IR absorption, and x-ray diffraction have been reported (see references in Ref. 311). The observed (anisotropic) changes in lattice parameters have been used for calculating the kinetic parameters of the transformations. For some reactions, it was possible to follow by x-ray diffraction the change in lattice parameters and also in atomic coordinates, so the relaxation could be observed at atomic level. 

When mechanical stress is exerted on molecular crystalline solids of coordination compounds, not only crystalline lattice but also the constituent molecules are subjected to distortion. The type and extent of distortion of each molecule is inevitably different due to the anisotropic nature of mechanical stressing. This, in turn, causes disproportionation of then-ligand fields to decrease their symmetry. 

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