Interionic vibrations and glass transitions in ionic oxide metaphosphate glasses

Abstract

The far infrared spectrum of each ionic metal‐metaphosphate glass, (MPO₃)_n (M = Li, Na, K, Rb, Cs) and [M(PO₃)₂]_n (M = Ca, Sr, Ba), contains a broad absorption band whose peak frequency, ω₀, and halfbandwidth, Δω_1/2, are strongly dependent on the mass and charge of the glass‐modifying cation. Each such band, which appears as the envelope of the optical phonon spectrum of the crystalline form of the material, is assigned to a density of coupled oscillator pseudo phonon states, which assignment is shown to be consistent with experimental linear vibrations of ω₀ with Δω_1/2 and of ω₀² with < A >, the integrated absorbance, within the complete set of glasses. The net effect of coupling the oscillators in the vitreous (disordered) system is equivalently treated as a single damped harmonic oscillator. The damping coefficient, b = μΔω_1/2, is constant in each series as is the complex part of the refractive index at ω₀, κ(ω₀), and the Lorentzian band is used to compute the force constant, F, b, and < n >_T, < q² >₀, and < q² >_T, the excitation quantum number and mean square amplitudes at temperatures 0 °K and T, for each glass. A relationship between T_g and the vibrations is derived: T_g = F(< q² >₀/k) + < n >_Tghcω₀/k by which the experimental linear relationship between T_g and F for each series is understood to relate variations in T_g to those in zero point vibrational energy. Reexpressed, this shows that the energy required to pull the anion site away from the cation permitting the glass transition to ensue, F(< q² >_Tg – < q² >₀), is a constant for each series of metaphosphate glasses.