Crystal selection rules

S.Z.D. Cheng, C.Y. Li and L. Zhu, Commentary on polymer crystallization Selection rules in different length scales of a nucleation process, Eur. Phys. J. 

J Birman. Theory of infrared and Raman processes in crystals selection rules in diamond and zinc blende. Phys Rev 127 1489, 1967. 

From a knowledge of the crystal structure it is possible to calculate selection rules for each orientation position and thus gain considerable insight into the vibrational motions of the crystal. The interpretation of such spectra, which show a lot of detail, goes well beyond characterization applications. ... 

Graphite exhibits strong second-order Raman-active features. These features are expected and observed in carbon tubules, as well. Momentum and energy conservation, and the phonon density of states determine, to a large extent, the second-order spectra. By conservation of energy hut = huty + hbi2, where bi and ill) (/ = 1,2) are, respectively, the frequencies of the incoming photon and those of the simultaneously excited normal modes. There is also a crystal momentum selection rule hV. = -I- q, where k and q/... 

Observed on the wing of the CS2 bending mode. Occurs in violation of the selection rules of the point group Dsd but is IR active under the Csi factor group of the crystal. Could also be a combination vibration or caused by the CS2 impurity which was present in the sample (see text)... 

Example 5.4. Crystal formation with a selected rule... 

Up to now, only Raman active modes at the r point of the Brillouin zone have been observed as coherent phonons in bulk crystals.2 The selection rule can be... 

Polymer films were produced by surface catalysis on clean Ni(100) and Ni(lll) single crystals in a standard UHV vacuum system H2.131. The surfaces were atomically clean as determined from low energy electron diffraction (LEED) and Auger electron spectroscopy (AES). Monomer was adsorbed on the nickel surfaces circa 150 K and reaction was induced by raising the temperature. Surface species were characterized by temperature programmed reaction (TPR), reflection infrared spectroscopy, and AES. Molecular orientations were inferred from the surface dipole selection rule of reflection infrared spectroscopy. The selection rule indicates that only molecular vibrations with a dynamic dipole normal to the surface will be infrared active [14.], thus for aromatic molecules the absence of a C=C stretch or a ring vibration mode indicates the ring must be parallel the surface. 

In general it is not necessary to measure all possible configurations in order to identify all the phonons. However, it should be pointed out that frequently violations of the selection rules appear or that in a particular orientation forbidden phonons appear. These are believed to be caused by disorders in the single crystal. 

Donovan, B., Angress, F. Lattice vibrations. London Chapman and Hall 1971. Turrell, G. lniia.red and Raman spectra of crystals. New York Academic Press 1972. Fateley, W. G., Dollish, F. R., McDevitt, N. T., Bentley, F. F. Infrared and raman selection rules for molecular and lattice vibrations The correlation method. New York J. Wiley 1972. 

Electron configuration of Bp" is (6s) (6p) yielding a Pip ground state and a crystal field split Pap excited state (Hamstra et al. 1994). Because the emission is a 6p inter-configurational transition Pap- Pip. which is confirmed by the yellow excitation band presence, it is formally parity forbidden. Since the uneven crystal-field terms mix with the (65) (75) Si/2 and the Pap and Pip states, the parity selection rule becomes partly lifted. The excitation transition -Pl/2- S 1/2 is the allowed one and it demands photons with higher energy. 

Annealed films deposited from a A,A-dimethylselenourea/citrate/ammonia bath were shown to exhibit a (0001) XRD reflection at 26 = 13°, a reflection normally forbidden in hexagonal CdSe [the (0002) reflection is the one normally seen] [13]. This was explained by a breaking of the selection rules due to the small crystal size. Interestingly, this peak was very weak in thin films and prominent in... 

It is easy to show by group-theoretical arguments that the mixing of the even and odd ionic states occurs only if the crystal field lacks a center of symmetry, that is, is not holohedral. The selection rules appropriate for ions in a static crystal field have been given by Hellwege (26). However,... 

In (a) the ion is so situated as to be in a noncentrosymmetric field, even when it is not vibrating. In this case electric-dipole emission is allowed. In (b) there is inversion symmetry when the ion is not vibrating, but vibration carried it to some other point Py at which the center of symmetry is lost. It should be self-evident that, even when the ion is in a noncentrosymmetric environment, vibrations may be important. That is, changes in the crystal-field symmetry induced by the vibronic motion will lead to violations of the crystal-field-selection rules. 

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