Vibrational analysis of dioptase Cu6Si6O18 � 6(H2O) and its puckered six-membered ring

Abstract

The normal modes of vibration and their frequencies are calculated for dioptase, a mineral whose crystal structure (space group R $$\bar 3$$ or C 3 ) consists of puckered six-membered silicate rings (Si6O18) linked by Cu2+ ions and H2O groups. The calculation employs a valence force potential consisting of central interactions between nearest neighbors and bond-bending interactions centered at the Si4+ and Cu2+ ions. The force constants are determined by fitting the calculated frequencies to values obtained by measuring the single-crystal Raman spectra. The calculated frequencies are in reasonable agreement with experiment, permitting assignment of normal modes to the observed spectral frequencies. Considerable mixing of Cu and H2O motions with those of the ring is found for the Raman-active modes below 430 cm-1. The normal modes and frequencies of the hypothetical isolated ring with C 3i symmetry are determined by neglecting all interactions between the rings and the surrounding Cu and H2O. The identification of normal modes characteristic of the puckered six-membered silicate rings and the effect of the environment on these modes may prove useful in the interpretation of the Raman spectra of amorphous silicates.