Phase undistorted

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]... 

Summary The importance of structural studies for the identification of small molecules and for the interpretation of their reactivity is illustrated with examples of silicon-containing compounds. Such compounds are best studied in the gas phase, so that their structures are undistorted by intermolecular interactions, and may be compared with those calculated theoretically. Examples are given of silicon compounds which show major differences between their gas and solid phase structures, even when the intermolecular interactions are quite weak. 

If the material is divided in a crystalline and an amorphous phase, and the crystals are undistorted with atoms fixed at their ideal positions in space, the integral... 

Note 1 In the equation for g, the term go is usually equal to zero because the undistorted state of nematics is the state of uniform alignment. However, for chiral nematics, a nonzero value of go allows for the intrinsic twist in the structure. In order to describe g for smectic phases, an additional term must be added, due to the partially solid-like character of the smectic state and arising from positional molecular deformations. 

However, at this point we should note that the electron-doped superconductors are not strictly single phase. Electron diffraction studies on both single crystals and ceramic superconducting samples have shown that they almost invariably, contain two phases one phase has the undistorted T -Nd2Cu04 structure,... 

At present it is not known whether the superlattice or the undistorted T phase or both are responsible for superconductivity, although there are reports that single crystals of Nd185Ce015CuO4 with high Meissner fractions (>60%) do not contain any superlattice (28). 

The trisulphides (and triselenides) of Ti, Zr, Hf, Nb and Ta crystallize in onedimensional structures formed by MSg trigonal prisms that share opposite faces. Metal atoms in these sulphides are formally in the quadrivalent state, and part of the sulphur exists as molecular anions, M S2 S . TaSj shows a metal-insulator transition of the Peierls type at low temperatures (Section 4.9). NbSj adopts a Peierls distorted insulating structure suggesting the possibility of a transformation to a metallic phase at high temperatures, but does not transform completely to the undistorted structure. Electronic properties and structural transitions of these sulphides have been reviewed (Rouxel et al, 1982 Meerschaut, 1982 Rouxel, 1992). 

The plane containing a and c in Fig. 24.9 is the plane in the f.c.c. phase that initially contained the vectors a" and c". If the b.c.t. phase is now given a rigid-body rotation so that a" —> a and c" —> c, the undistorted plane in the b.c.t. phase will be returned to its original inclination in the f.c.c.-axis system and will therefore be an invariant plane of the overall deformation. In the present case, this can be achieved by a rotation around the axis indicated by u in Fig. 24.9 (see Exercise 24.3). The solution of the problem is now complete. The invariant plane is known, and the orientation relationship between the two phases and total shape change can be determined from the combined effects of the known lattice-invariant deformation, lattice deformation, and rigid-body rotation. 

Figure 11 2 2. undistorted high symmetry structure of B atoms in a-b plane and symmetry breaking by the in-plane, out-of phase displacements Af /atom. The motion of B1-B2 atoms in out-of phase positions along the perimeters of circles with radius Af centred at the undistorted B atoms positions generates an infinite number of distorted structures. The figure indicates beside the undistorted structure also one of the distorted structures that correspond to the E2g(b) phonon mode distortion (bold line)... 

It is likely that oligothiophenes, as many other organic materials, exhibit an intrinsic tendency to form several polymorphic phases, such that small grains of structural minority phases can be easily formed. The respective vibronic energies can be obtained which are in very close agreement (AE <15 cm [) to those reported for matrix isolated 4T. This result clearly indicates that the observed luminescence come from undistorted 4T molecules. 

Several important and recent aspects of the physical properties of these molecular superconductors have been left by the roadside. It is the case, for example, for the physics of quasi-one-dimensional conductors at very high magnetic field when the undistorted phase exhibiting a metal-like behavior at zero field should become localized [152]. Reentrance of a superconducting instability is also expected at very low temperature under... 

In order to obtain optimum resolution and undistorted multiplet patterns, pure-phase absorptive two-dimensional HOHAHA or HEHAHA... 

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