Geometric origin of excess low-frequency vibrational modes in weakly-connected amorphous solids
نویسندگان
چکیده
– Glasses have an excess number of low-frequency vibrational modes in comparison with most crystalline solids. We show that such a feature necessarily occurs in solids with low coordination. In particular, we analyze the density D(ω) of normal-mode frequencies ω and the nature of the low-frequency normal modes of a recently simulated system [1], comprised of weakly compressed spheres at zero temperature. We account for the observed a) convergence of D(ω) toward a non-zero constant as the frequency goes to zero, b) appearance of a lowfrequency cutoff ω, and c) power-law increase of ω with compression. We introduce a length scale l which characterizes the vibrational modes that appear at ω. There is something universal and mystifying about the low-energy behavior of amorphous solids[2, 3]. In comparison to most crystals, amorphous solids have a large excess number of low-frequency vibrational modes. In glasses these excitations are seen in the low-temperature specific heat as well as in the spectroscopy of the vibration modes in the terahertz range. These excitations affect the heat transport [3] and might well play an important role at the liquidglass transition [4] . Nevertheless, little is understood about the cause of such excitations. Whereas in a crystal the vibrations are simply plane waves, in a glass, even at low angular frequency ω, they are much more complicated. In this Letter, we show that an excess density of vibrational states is a necessary feature of weakly-connected amorphous solids such as systems with repulsive, short-range interactions. Our analysis elucidates the cause and the peculiar nature of these low-frequency excitations. This gives a new approach for studying some of the ubiquitous phenomena found in glasses. A dramatic illustration of excess low-frequency vibrations was found in recent computer simulations [5, 1] of soft-spheres with repulsive, finite range potentials at zero temperature and zero applied shear stress. These simulations were carried out as a function of the packing fraction, φ above the jamming threshold, φc, where the liquid acquires rigidity and becomes an amorphous solid [6]. O’Hern, Silbert et al. found that the average number of contacting neighbors per particle, z, the pressure, and the shear modulus vary as a power of (φ − φc). Moreover, these simulations reveal unexpected features in the density of vibrational mode
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تاریخ انتشار 2005