Displaced distorted

Apart from the heat bath mode, the harmonic potential surface model has been used for the molecular vibrations. It is possible to include the generalized harmonic potential surfaces, i.e., displaced-distorted-rotated surfaces. In this case, the mode coupling can be treated within this model. Beyond the generalized harmonic potential surface model, there is no systematic approach in constructing the generalized (multi-mode coupled) master equation that can be numerically solved. The first step to attack this problem would start with anharmonicity corrections to the harmonic potential surface model. Since anharmonicity has been recognized as an important mechanism in the vibrational dynamics in the electronically excited states, urgent realization of this work is needed. 

In some crystalline materials a phase transition on lowering the temperature may produce a modulated structure. This is characterized by the appearance of satellite or superstructure reflections that are adjacent reflections (called fundamental reflections) already observed for the high temperature phase. The superstructure reflections, usually much weaker than fundamental reflections, can in some cases be indexed by a unit cell that is a multiple of the high temperature cell. In such a case the term commensurate modulated structure is commonly used. However, the most general case arises when the additional reflections appear in incommensurate positions in reciprocal space. This diffraction effect is due to a distortion of the high temperature phase normally due to cooperative displacements of atoms, ordering of mixed occupied sites, or both. Let us consider the case of a displacive distortion. 

Typical crystalline macromolecular substance lattice defects result from end groups, kinks, jogs, Reneker defects, and chain displacements. Distortion of the whole crystal lattice can be conceived in terms of the paracrystal. The defects can be classified in terms of point, line, and network defects. 

It is important to evaluate the surface distortion associated with the assymetric field at the surface, a difficult task often simplified by assuming that distortion is limited to the direction normal to the plane [64, 6S]. Benson and co-workers [6S] calculated displacements for the first five planes in the (100) face of sodium chloride and found the distortion correction to of about 100 ergs/cm or about half of itself The displacements show a tendency toward ion pair formation, suggesting that lateral displacements to produce ion doublets should be considered [66] however, other calculations yielded much smaller displacements [67]. 

As for crystals, tire elasticity of smectic and columnar phases is analysed in tenns of displacements of tire lattice witli respect to the undistorted state, described by tire field u(r). This represents tire distortion of tire layers in a smectic phase and, tluis, u(r) is a one-dimensional vector (conventionally defined along z), whereas tire columnar phase is two dimensional, so tliat u(r) is also. The symmetry of a smectic A phase leads to an elastic free energy density of tire fonn [86]... 

In thermoplastics and some thermosetting resins, displacement strains are not likely to produce immediate failure of the piping but may result in detrimental distortion. Especially in thermoplastics, progressive deformation may occur upon repeated thermal cycling or on prolonged exposure to elevated temperature. 

It is known that a metallic ID system is unstable against lattice distortion and turns into an insulator. In CNTs instabilities associated two kinds of distortions are possible, in-plane and out-of-plane distortions as shown in Fig. 8. The inplane or Kekuld distortion has the form that the hexagon network has alternating short and long bonds (-u and 2u, respectively) like in the classical benzene molecule [8,9,10]. Due to the distortion the first Brillouin zone reduees to one-third of the original one and both K and K points are folded onto the F point in a new Brillouin zone. For an out-of-plane distortion the sites A and B are displaced up and down ( 2) with respect to the cylindrical surface [11]. Because of a finite curvature of a CNT the mirror symmetry about its surface are broken and thus the energy of sites A and B shift in the opposite direction. 

The other tetrahalides can all readily be made by direct reactions of the elements. Crystalline SeCU, TeCU and -SeBr4 are isotypic and the structural unit is a cubane-like tetramer of the same general type as [Me3Pt(/Z3-Cl)]4 (p. 1168). This is illustrated schematically for TeCU in Fig. 16.13d each Te is displaced outwards along a threefold axis and thus has a distorted octahedral environment. This can be visualized as resulting from repulsions due to the Te lone-pairs directed towards the cube centre and, in the limit, would result in the separation into... 

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