Subject unit cells

These compounds have been the subject of several theoretical [7,11,13,20)] and experimental[21] studies. Ward and Elliott [20] measured the dynamic y hyperpolarizability of butadiene and hexatriene in the vapour phase by means of the dc-SHG technique. Waite and Papadopoulos[7,ll] computed static y values, using a Mac Weeny type Coupled Hartree-Fock Perturbation Theory (CHFPT) in the CNDO approximation, and an extended basis set. Kurtz [15] evaluated by means of a finite perturbation technique at the MNDO level [17] and using the AMI [22] and PM3[23] parametrizations, the mean y values of a series of polyenes containing from 2 to 11 unit cells. At the ab initio level, Hurst et al. [13] and Chopra et al. [20] studied basis sets effects on and y. It appeared that diffuse orbitals must be included in the basis set in order to describe correctly the external part of the molecules which is the most sensitive to the electrical perturbation and to ensure the obtention of accurate values of the calculated properties. 

The variation of the unit cell parameters versus temperature is reported in Figure 2. For the as-synthesized sample, at room temperature, the cell parameter are a=7.5675, b=l 8.1187, c=26.0605 A and the cell volume is 3573.2 A3. In the first step of heating (T <120 °C) only small variation of the cell parameters are shown. The volume variation is mostly due to the c parameter shortening, since it is the most subjected to temperature induced modifications. Between 120 and 360 °C a remains almost constant, c decreases of 0.1%, while b slightly increase-up to 215 °C- and subsequently regains its initial value. The combination of these variations leads an inflection in the volume contraction, slowing down its decrease. Above 390 °C the cell volume remains almost constant and only minor variations in the parameters are observed. The final values obtained after the refinement at 715 °C accounted a variation of -0.25, +0.07, -0.77 and -0.95% for a, b, c and V respectively. The minor variation of the cell parameters above 450 °C indicates that at this temperature the dehydration process is almost fulfilled. The TG curve in flowing air shows that the total mass variation of the as-synthesized phase is 15.8%. Dehydration process is almost fulfilled at about 500 °C above this temperature only... 

The interpretation of the HREELS spectrum and the structure belonging to the (2x2)-3CO LEED pattern has been the subject of some debate in the literature [57— 59], The CO stretch peak at the lower frequency had previously been assigned to a bridge-bonded CO [57], with obvious consequences for the way CO fills the (2x2) unit cell. A recent structural analysis from the same laboratory on the basis of tensor LEED has confirmed the structures of both the (V3xV3)R30° and the (2x2)-3CO as given in Fig. 8.14, i.e. with CO in linear and threefold positions in the (2x2)-3CO structure [58]. The assignments have also been supported by high-resolution XPS measurements [59],... 

The non-existence of a direct single rotation relationship within the MYKO series can be attributed to the influence on geometrical structures of CCl and CgHg molecules which are clathrated in the corresponding unit cells. In other words, MYKO-CeHfi and MYKO-CCI4 are subjected to highly symmetrical Dga and T, solvent fields respectively which induce in both cases a ternary symmetry which does not exist in genuine MYKO-XYL. 

The displacements of a particle j at r in unit cell /, subject to a phonon wave with wave vector q, obey the equation... 

The theoretical analysis for two-dimensional foams and emulsions has recently been expanded to three dimensions [38], with Kelvin s minimal tet-rakaidecahedron as the unit cell. The system is subjected to a uniaxial extensional strain. As the elastic limit, or yield point, is approached, the cell shape tends towards a rhombic dodecahedron however, at the yield point, the shrinking quadrilateral faces of the polyhedron have finite (albeit small) area. 

Sharp photographs with a low background intensity are produced by such cameras. Focusing cameras, however, are used less for identification than for special purposes such as the accurate determination o unit cell dimensions. Further information on this subject will be found on p. 193. 

This way of expressing the overall modes for the pair of molecular units is only approximate, and it assumes that intramolecular coupling exceeds in-termolecular coupling. The frequency difference between the two antisymmetric modes arising in the pair of molecules jointly will depend on both the intra- and intermolecular interaction force constants. Obviously the algebraic details are a bit complicated, but the idea of intermolecular coupling subject to the symmetry restrictions based on the symmetry of the entire unit cell is a simple and powerful one. It is this symmetry-restricted intermolecular correlation of the molecular vibrational modes which causes the correlation field splittings. 

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