An alternative explanation of the change in T-dependence of the effective Debye-Waller factor at T
c or T
B
Authors: Ngai K. L. , Habasaki J. 
Published: September 2014

The cusp-like temperature dependence of the Debye-Waller factor or non-ergodicity parameter fQ(T) at some temperature Tc above Tg found by experiments in several fragile glassformers has been considered as critical evidence for validity of the ideal Mode Coupling Theory (MCT). A comprehensive review of experimental data of fQ(T) and beyond brings out various problems of the MCT predictions. For example, the molten salt, 0.4Ca(NO3)2-0.6KNO3 (CKN), was the first glassformer measured by neutron scattering to verify the cusp-like behavior of fQ(T) at Tc predicted by ideal MCT. While the fits of the other scaling laws of MCT to viscosity, light scattering, and dielectric relaxation data all give Tc in the range from 368 to 375 K, there is no evidence of cusp-like behavior of fQ(T) at Tc from more accurate neutron scattering data obtained later on by Mezei and Russina [J. Phys.: Condens. Matter 11, A341 (1999)] at temperatures below 400 K. In several molecular glass-formers, experiments have found at temperatures below Tc that [1−fQ(T)] is manifested as nearly constant loss (NCL) in the frequency dependent susceptibility. The NCL persists down to below Tg and is not predicted by the ideal MCT. No clear evidence of the change of T-dependence of fQ(T) at any Tc was found in intermediate and strong glassformers, although ideal MCT does not distinguish fragile and strong glassformers in predicting the critical behavior of fQ(T) a priori. Experiments found fQ(T) changes T-dependence not only at Tc but also at the glass transition temperature Tg. The changes of T-dependence of fQ(T) at Tc and Tg are accompanied by corresponding changes of dynamic variables and thermodynamic quantities at TB ≈ Tc and at Tg. The dynamic variables include the relaxation time τα(T), the non-exponentiality parameter n(T), and the generalized fragility m(T) of the structural α-relaxation. The thermodynamic quantities are the free volume deduced from positron annihilation spectroscopy, and the configurational entropy obtained from adiabatic calorimetry measurements. These changes of dynamic variables and thermodynamic quantities in temperature dependence at TB ≈ Tc occur concurrently with the change of fQ(T) and suggest the effects are related, and have to be explained altogether. Since this task cannot be carried out by the ideal MCT, we have provided a different interpretation of fQ(T) and an alternative explanation of the change in its T-dependence of fQ(T) at TB ≈ Tc as well as the other dynamic variables. We show fQ(T) originates from the dissipation of the molecules while caged by the anharmonic intermolecular potential, and manifested as the NCL at lower temperatures. The cusp-like change of T-dependence of fQ(T) at Tc originates from the corresponding change of free volume and configurational entropy at TB ≈ Tc, which also explains the simultaneous changes of the T-dependencies of the other dynamic variables. The alternative explanation is able to resolve the conundrum in CKN because TB is ≥400 K, and hence the change of T-dependence of fQ(T) at Tc ≈ TB was not observed in data taken at temperatures lower than 400 K by Mezei and Russina. The alternative explanation also can rationalize the difference between fragile and non-fragile glassformers in the strength of the observed changes of fQ(T) at Tc and Tg as well as the other dynamic quantities at TB ≈ Tc and Tg.