Relation of structural and elastic crossover length investigated by low-frequency Raman scattering inGexSe1−xglass

Abstract

Low-frequency Raman spectra ͑10 cm Ϫ1 -80 cm Ϫ1 ) have been studied in the Ge x Se 1Ϫx (0.02рxр0.40) glasses. The Raman spectra reduced by the Bose factor I R (), which are proportional to the vibrational density of states, show a power-law dependence of the frequency, , g()ϰ dϪ1 in a low-frequency region. The value d is a noninteger, which suggests that these glassy systems have fractal structures. The spectra I R () of Se-rich samples are classified into three regions whose vibrational properties are due to acoustic phonons, bending fractons, and stretching fractons, whereas that of the Ge-rich samples' two regions are due to acoustic phonons and stretching fractons. The difference of two types of these low-frequency properties are explained by correlation of the structural crossover length and the elastic crossover length l c . The threshold of these phenomena occurs near ͗r͘ϳ2.4, which may be related to the prediction of the Phillips-Thorpe constraint theory.

Ab initio calculation of vibrational frequencies of GexSe1−x glass

“…It is suggested that 198 cm À1 is the breathing vibrational mode of methane like Ge(Se 1/2 ) 4 with A 1 symmetry whereas 216 cm À1 is due to Se tetrahedral units.The A 1 mode in corner sharing and in the edge sharing tetrahedrons have been discussed [21]. Nakamura et al [22] have considered the application of ideas of fractional dimensionality to the Ge x Se 1Àx glass whereas the fractal interpretation of Raman scattering in silica gel has been studied earlier [23]. The existence of several different phases in GeSe 2 glass is well recognized [24].…”

Low Frequency Raman Spectra of Silica Aerogels with Double Fractal Structure

“…where S is a constant depending on the cluster shape (for spherical clusters S % 0:8, and for stick clusters S % 0:5) and v is the sound velocity [9,14]. In this work we investigated low frequency Raman spectra of sintered silica aerogel series.…”

Variational cluster approximation to the thermodynamics of quantum spin systems

“…We will now use the functional relations (7) and (8) to derive the spin VCA equations. To keep the formulae simple, we use a compact notation without explicit reference to the components of the functions, where appropriate.…”