Fast Dynamics in Glass-Formers: Relation to Fragility and the Kohlrausch Exponent
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ABSTRACT From the Raman spectra and related inferences from low temperature specific heat data, Sokolov and coworkers have established that the ratio of the quasielastic and vibrational contributions at low temperatures (5-10K) up to Tg correlates well with the degree of fragility and P3 of the glass-former. As pointed out by Sokolov (see his contribution in this Volume) such a correlation between the fast dynamics and structural a-relaxation at Tg (i.e., m and 0) is intriguing, since at and below Tg, the a-relaxation time Ta is more than twelve orders of magnitude longer than the quasielastic contribution and the boson peak. We show in this paper how the Coupling Model (CM) may provide an explanation for this correlation.
INTRODUCTION In the past, studies of the relaxational properties of glass-forming materials were mainly confined to the macroscopic time regime (ca. >>1 nanosecond). Within the past several years, quasielastic neutron scattering (QENS), dynamic light scattering, and high frequency conductivity (dielectric) measurements have increased our knowledge concerning dynamics in the "mesoscopic" frequency range, v - 10 to 1000 GHz [1-8]. In this frequency range, all glassforming materials exhibit marked deviations from the acoustic vibrations, with Debye-like density of states (i.e., g(v)-v 2), found in crystalline solids. An excess harmonic vibrational contribution
appears at higher frequencies, along with a broad, anharmonic "relaxational" contribution at lower frequencies. The vibrational contribution dominates the spectrum at low temperatures, appearing as a peak, commonly referred to as the boson peak. After scaling the low frequency Raman spectra by the Bose factor, the vibrational contribution is found to vary only slightly with temperature, indicating nearly harmonic vibrations. Although the boson peak is generally ascribed to some quasilocal vibrations, its exact physical origin is unclear. The anharmonic, broad contribution, which we will refer to as the quasielastic contribution, appears in glasses even at temperatures well below the glass transition temperature Tg; it increases rapidly with temperature above Tg. The intensity of the quasielastic contribution relative to the boson peak differs for different glass-formers. It was found [1-3] that the relative contribution from quasielastic scattering is weak for "strong" glasses, like B20 3, even up to temperatures as high as 2.5 times Tg. On the other hand, the relative contribution from quasielastic scattering is strong for "fragile" glasses, such as 0.40KNO 3-0.60Ca(NO 3)2 , even at Tg. The relative intensity of the quasielastic contribution at Tg correlates well with the fragility, m, defined as [ 1-3,9,10] m=-=a log't,, /a (Tg / T) ,
(1)
where ct,,is the structural oa-relaxation time, and Tg is defined as the temperature at which ra, attains a value of 102 s. It has been shown [9] that m correlates strongly with the magnitude of the stretch exponent P3of the Kohlrausch function 81 Mat. Res. Soc. Symp. Proc. Vol. 455 0 1997 Materials Res
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