We analyze results for the Boson Peak from the neutron time of flight spectroscopy data on Ge-As-Se, and Raman spectra data on m-TCP and OTP, using a recent mode coupling model that takes into account the coupling of density fluctuations with vibrational modes in presence of defects in the supercooled state. From the experimental results for different materials we observe that for more fragile systems characterized by increasing fragility parameter m, a slower relaxation of the defect-density correlation is needed to give rise to the observed peak in the spectra. In Ref.[5] we have described an extension of the simple mode coupling formalism to include the distinct vibrational modes that develop at low temperatures in the amor- The present analysis demonstrates that the criteria for the appearance of the peak is crucially related to the dynamics of defect densities in the disordered system.In studying the feedback effects on dynamics due to slowly decaying density fluctua-1 tions at supercooled states, the memory function H[φ(t)] is obtained as a functional of the hydrodynamic correlation functions, in the following q independent form,where c 1 and c 2 are dimensionless constants determined in terms of the wave vector integrals due to the mode coupling vertex functions. φ L and φ T are the correlation functions for the longitudinal and transverse sound modes. The function F (t) is expressed give rise to the observed peak in the spectra.We have approximated here through δ relaxation of the defect density by single exponential mode. The full wave vector dependence has to be considered to account the coupling of the structural relaxation to the vibrational modes. The explicit temperature dependence of the peak is not captured in the present model. This can be computed through proper input for the static or thermodynamic properties that appear in the mode coupling integrals. Figure 3, demonstrates the key result of this paper that for more fragile systems δ, inverse of which relates to the defect density correlation, shows a sharper fall with temperature. Also we like to point out here that the temperature range 3 covered for the materials in this paper actually correspond to the part where the fragile glasses starts showing a sharp increase of viscosity on the Angell plot[8] -more fragile the liquid is, more dramatic is the increase giving a higher value for the fragility index m [9,15].
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