A Surrogate for Debye-Waller Factors from Stokes Shifts

We show that short-time relaxation behavior characteristic of the intermediate scattering function at $q$ near the peak in the static structure factor can be obtained from time-resolved Stokes shifts (TRSS) in glassforming materials. We extract Debye- Waller factor ($\langle u^{2}\rangle$) analogs from the TRSS data from four glassforming liquids and apply these to a proposed relationship between $\alpha$ relaxation and the Debye-Waller factor; $\tau_{\alpha}=\tau _{\infty }\; \mbox{E}xp\left[ \frac{a^{2}}{2\langle u^{2}\rangle}+\frac{\sigma _{a^{2}}^{2}}{8\langle u^{2}\rangle^{2}} \right]$. This putative relationship has previously been evaluated using experimental Debye-Waller factors obtained in the time range (40 to 2000) ps. We show that the relation yields physically meaningful fit values only when relaxation on a 1 ps timescale is considered. We also observe an unexpected dependence of short-time Debye-Waller factors on fragility.