C-Axis

If the space group contains screw axes or glide planes, the Patterson fiinction can be particularly revealing. Suppose, for example, that parallel to the c axis of the crystal there is a 2 screw axis, one that combines a 180° rotation with... 

If one or two of the indices are zeros, there may be additional restrictions. We have seen that a 2jscrew axis parallel to the c axis of the unit cell produces pairs of atoms at x, y, z) and -x, -y, z + k). From equation... 

We now consider planar molecules. The electronic wave function is expressed with respect to molecule-fixed axes, which we can take to be the abc principal axes of ineitia, namely, by taking the coordinates (x,y,z) in Figure 1 coincided with the principal axes a,b,c). In order to detemiine the parity of the molecule through inversions in SF, we first rotate all the electrons and nuclei by 180° about the c axis (which is peipendicular to the molecular plane) and then reflect all the electrons in the molecular ab plane. The net effect is the inversion of all particles in SF. The first step has no effect on both the electronic and nuclear molecule-fixed coordinates, and has no effect on the electronic wave functions. The second step is a reflection of electronic spatial coordinates in the molecular plane. Note that such a plane is a symmetry plane and the eigenvalues of the corresponding operator then detemiine the parity of the electronic wave function. 

What is the moment of inertia of acetylene about its C—C axis ... 

In the symmetric top cases, Hrot can be expressed in terms of J2 and the angular momentum along the axis with the unique moment of inertia (denoted the a-axis for prolate tops and the c-axis of oblate tops) ... 

The c axis corresponds to both the short axis of the crystal and the axis along the molecular chain. The observed repeat distance in the c direction is what would be expected between successive substituents on a fully extended hydrocarbon chain with normal bond lengths and angles (see Sec. 1.2). 

A C poini group conlains a C axis of symmelry. By implication if does nol conlain a, i or elemenis. However, if musi conlain C, C, ... 

A C point group contains a C axis of symmetry and n a planes of symmetry, all of which contain the C axis. It also contains other elements which may be generated from these. 

When the operation is a rotation by an angle 4> about a C axis, in this case by an angle of 2n/3 radians about the C3 axis, the resulting coordinate transformation, a result which will not be derived here, is given by... 

A symmetric rotor must have either a C axis with n>2 (see Section 4.1.1) or an 54 axis (see Section 4.1.4). Methyl iodide has a C3 axis and benzene a Ce axis and, therefore, these are symmetric rotors whereas allene, shown in Figure 4.3(d), is also a symmetric rotor since it has an 54 axis which is the a axis allene is a prolate symmetric rotor. 

In a molecule such as the asymmetric rotor formaldehyde, shown in Figure 5.1(f), the a, b and c inertial axes, of lowest, medium and highest moments of inertia, respectively, are defined by symmetry, the a axis being the C2 axis, the b axis being in the yz plane and the c axis being perpendicular to the yz plane. Vibrational transition moments are confined to the a, b or c axis and the rotational selection mles are characteristic. We call them... 

The thermal conductivity, W/ (m-K), along the a axis teaches a maximum of 285 at — lOO C and falls rapidly with declining temperature. It is 251 at 20°C. Along the c axis it remains ca 837 to very low temperatures. The specific heat varies markedly with temperature (Fig. 5). The steep rise in above 3500 K probably results from reversible formation of vacancies or other thermal defects (4). 

The specific resistance of natural graphite crystals is ca Hem (room temperature) along the a axis parallel to the network basal plane. The resistance along the c axis (perpendicular to the basal plane) is ca 1 Q. The cja axis anisotropy ratio is, therefore, ca 10 . Screw dislocations within the crystal may short-circuit the current path parallel to the c axis and cause lower anisotropic ratios separation of planes may cause higher anisotropic ratios. 

Atochem, Centre de Recherche, France. C-Axis, Jonquiere, Quebec. 

P.D. Horn and Y.M. Gupta, Luminescence R-Line Spectrum of Ruby Crystals Shocked to 125 kbar along the Crystal c-Axis, Phys. Rev. B 39, 973-979 (1989). 

X-ray diffraction peaks were rather broad with coherence lengths as low as 20 nm and this was attributed to rapid quenching. It was proposed that the carbon atoms are arranged in polyyne chains (n = 4) along the c-axis. The density of Carbolite (1.46 g-cm ) is lower than values for other carbynes and for diamond and graphite - hence the name - and this was attributed to a rapid quenching process. 

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