Direct evidence for a characteristic dynamic lengthscale in the intermediate phase of glasses

AC conductivity spectra of xAgI-(1-x)AgPO$_3$ fast ion conducting glasses spanning the flexible, intermediate (isostatically rigid) and stressed rigid phases are analyzed. The rescaled frequency dependent spectra are mapped into time-dependent mean square displacements out of which a typical lengthscale characterizing the spatial extent $\sqrt{\langle R^2(\infty)\rangle}$ of non-random diffusion paths is computed. The latter quantity is studied as a function of AgI composition, it is found to display a maximum in the intermediate phase, providing the first clear evidence of a typical lengthscale of a dynamical nature when a system becomes isostatically rigid and enters the intermediate phase.