View factor symmetry rule

The determination of the view factors in a problem can be simplified furtlier if the geometry involved possesses some sort of symmetry. Therefore, it is good practice to check for the presence of any symmetry in a problem before attempting to detennine the view factors directly. The presence of symmetry can be determined by inspection, keeping the definition of the view factor in mind. Identical surfaces that are oriented in an identical manner with respect to another surface will intercept identical amounts of radiation leaving that surface. Therefore, the symmetry rule can be expressed as fwo (or more) surfaces that possess symmetry about a third surface will have identical view factors from that surface (Fig. 13-13). 

Metallo-phthalocyanines [M(Pc)] have attracted attention from view of their practical application to material science, but the vibrational spectra have been much less studied. This is partly due to low solubility in any solvent and difficulty in spectral analysis. The molecular vibrations of M(Pc) with D4h symmetry are factorized into 14 Aig + 13 A2g -I-14 Big -t- 14 B2g -I- 13 Eg -H 6 Ai + 8 A2 + 7 Bi -1- 28 E and their selection rules are the same as those described for M(OEP). 

It is instructive to note that the origin of these rules lies in the choice of coordinate system and that they may be derived without using structure factors. Any centered cell may be transformed into a primitive cell which, in general, does not convey the symmetry of the motif and which may thus be unsatisfactory from this point of view (Sections 1.4.1 and 2.6.1). Thus the transformation a = (a — b)/2, b = (a -h b)/2 transforms a C cell into a diamond-shaped primitive cell. The indices hkl transform in a covariant manner (Section 1.2.4), h = h — k)/2, k = h- - k)/2. As W and k must be integers according to the Laue equations, then h- -k must be an even number. The indices with h- -k odd do not correspond to a reciprocal lattice vector (Fig. 3.39). 

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