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 structures (space group D6h2) consists of six-membered silicate rings (Si6O18) linked by Be2+ and Al3+ ions. A valence force potential is used, consisting of central interactions between nearest neighbors and bond-bending interactions centered at the Si4+, Be2+, and Al3+ ions. The force constants are determined by fitting the calculated frequencies to the results of a complete study of the Raman spectra of a large single crystal. The calculated frequencies are in reasonable agreement with experiment, permitting unambiguous assignment of normal modes to the observed spectral lines. In several cases, the resulting interpretation of spectral features differs significantly from those published previously. Considerable mixing of Al and Be motions with those of the ring is found for the Raman-active modes near 750 cm−1 and above 850 cm−1, respectively. The normal modes and frequencies of the hypothetical isolated ring with C6h symmetry are determined by neglecting all interactions between the rings and the surrounding Be and Al atoms. This identification of normal modes characteristic of six-membered silicate rings and the effect of the environment of these modes may prove useful in the interpretation of infrared and Raman spectra of amorphous silicates.