Knowledge Bank

The far IR spectra of metal metaphosphate and tetraborate glasses yield broad absorption bands whose resonant frequencies $(\omega Res)$ and half-band-widths $(\Delta \omega 1/2)$ are strongly dependent on the mass and charge of the glass-modifying cation. Metal cations in the glass undergo localized vibrations on near-octahedral oxygen sites; however, in the crystalline form of these materials, the broad cation motion band splits into the crystal lattice spectrum. That these low frequency cation modes in glass arise from translational pseudo-lattice vibrations is shown by the linear dependences of relative integrated intensities with $\omega Res2$, and $\omega Res$ with $\Delta \omega 1/2$. A classical underdamped $(\omega Res>\Delta \omega 1/2)$ forced harmonic oscillator model is suggested to explain the large half-bandwidths of the cation motion bands. At their respective glass transition temperatures, mean square amplitudes of vibration for metal metaphosphate glasses vary linearly with the square of the equilibrium cation-oxygen separations , which implies that at some critical ratio, , the glass transition phenomenon ensues.