Anomalous isotope-mass effect in lithium borate glasses: Comparison with a unified relaxation model

Measurements of the frequency, temperature, and isotope-mass dependence of the electrical conductivity in a series of ${({}_{}{}^6{}_{}{}^{}\mathrm{Li},{}_{}{}^7{}_{}{}^{}\mathrm{Li})}_2$ O:2.${88\mathrm{B}}_2$ ${\mathrm{O}}_3$ glasses are quantitatively described by a unified model of relaxation. The data simultaneously show non-Debye behavior in the frequency dependence of the electric modulus and a nonclassical temperature-dependent isotope-mass effect. The relaxation model incorporates extra degrees of freedom intrinsic to glasses and predicts a correlation between the shape of the electric modulus dispersion curves and the magnitude of the isotope-mass effect. The predicted correlation is found to hold quantitatively at all temperatures with use of a value of the vibrational frequency which has been obtained by infrared-spectra measurements. The same model also quantitatively describes a wide range of other relaxation data.