VIBRATIONAL ANALYSIS OF BERYL (BE3AL2SI6O18) AND ITS CONSTITUENT RING(SI6O18)

The normal modes of vibration and their frequencies are calculated for beryl a mineral whose crystal structure (space group D-6h(2)) consist s Of six-membered silicate rings (Si6O18) linked by Be2+ and Al3+ ions . A valence force potential is used, consisting of central interaction s between nearest neighbors and bond-bending interactions centered at the Si4+, Be2+, and Al3+ ions. The force constants are determined by f itting the calculated frequencies to the results of a complete study o f the Raman spectra of a large single crystal. The calculated frequenc ies are in reasonable agreement with experiment, permitting unambiguou s assignment of normal modes to the observed spectral lines. In severa l cases, the resulting interpretation of spectral features differs sig nificantly from those published previously. Considerable mixing of Al and Be motions with those of the ring is found for the Raman-active mo des near 750 cm(-1) and above 850 cm(-1),respectively. The normal mode s and frequencies of the hypothetical isolated ring with C-6h symmetry are determined by neglecting all interactions between the rings and t he surrounding Be and Al atoms. This identification of normal modes ch aracteristic of six-membered silicate rings and the effect of the envi ronment on these modes may prove useful in the interpretation of infra red and Raman spectra of amorphous silicates.