Elastic and anelastic properties, vibrational anharmonicity, and fractal bond connectivity of superionic glasses

To quantify the thermally activated relaxations of the mobile silver ions in superionic silver phosphosulphate ${\left({\mathrm{Ag}}_2\mathrm{S}{\mathrm{O}}_4\right)}_x{\left(\mathrm{AgP}{\mathrm{O}}_3\right)}_{\mathrm{}(1-x)\mathrm{}}$ and phosphosulphide ${\left({\mathrm{Ag}}_2\mathrm{S}\right)}_x{\left(\mathrm{AgP}{\mathrm{O}}_3\right)}_{\mathrm{}(1-x)\mathrm{}}$ glasses, the broad attenuation peaks reported previously have been analyzed in terms of a Gaussian-type energy distribution. The parameters obtained are used to determine the influence of thermally activated relaxation processes on the temperature dependence of the ultrasonic wave velocity measured between 1.5 and 300 K. After subtraction of the relaxation effects together with those due to anharmonic interactions, another contribution to the temperature dependence of the ultrasonic velocity remains below 100 K, which follows a linear temperature dependence—as predicted by the soft-potential model (SPM) for relaxation of soft harmonic oscillators. The soft HO relaxation contribution to the ultrasonic velocity temperature dependences of silver phosphate-based glasses has a similar magnitude to those determined previously for lanthanide metaphosphate glasses. While the silver phosphate-based glasses have skeletons that are comprised of long chains of phosphate ions, the lanthanide metaphosphate glasses are close to having a three-dimensional structure. The agreement of the excess contribution to the temperature dependence of the ultrasonic velocity with the predictions of the SPM for both types of glass, in spite of their complete differences in structure, is further evidence for the universal applicability of the soft-potential model. To determine the vibrational anharmonicity of the long wavelength acoustic modes in superionic glasses, the hydrostatic pressure derivatives of the second-order elastic stiffness tensor components have been measured for these ${\left({\mathrm{Ag}}_2\mathrm{S}{\mathrm{O}}_4\right)}_x{\left(\mathrm{AgP}{\mathrm{O}}_3\right)}_{\mathrm{}(1-x)\mathrm{}}$, ${\left({\mathrm{Ag}}_2\mathrm{S}\right)}_x{\left(\mathrm{AgP}{\mathrm{O}}_3\right)}_{\mathrm{}(1-x)\mathrm{}}$, vitreous AgP${\mathrm{O}}_3$ and also for silver iodide molybdate ${\mathrm{}\left(\mathrm{AgI}\right)\mathrm{}}_{0.75}$ ${\left({\mathrm{Ag}}_2\mathrm{Mo}{\mathrm{O}}_4\right)}_{0.25}$. To examine further the effects of vibrational anharmonicity, the thermal expansions of the vitreous phosphates have also been measured. The linear thermal expansion coefficient becomes anomalously negative at lower temperatures for the ${\left({\mathrm{Ag}}_2\mathrm{S}{\mathrm{O}}_4\right)}_x{\left(\mathrm{AgP}{\mathrm{O}}_3\right)}_{\mathrm{}(1-x)\mathrm{}}$ and ${\left({\mathrm{Ag}}_2\mathrm{S}\right)}_x{\left(\mathrm{AgP}{\mathrm{O}}_3\right)}_{\mathrm{}(1-x)\mathrm{}}$ glasses. The wide variations found between the elastic and nonlinear acoustic properties of superionic silver phosphate, molybdate, and borate glasses stem from differences in the bonding and connectivities of the glass skeletons.