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Register a new userPoisson ratio and excess low-frequency vibrational states in glasses
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Eug`ene Duval
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In glass, starting from a dependence of the Angells fragility on the Poisson ratio [V. N. Novikov and A. P. Sokolov, Nature 431, 961 (2004)], and a dependence of the Poisson ratio on the atomic packing density [G. N. Greaves et al., Nat. Mater. 10, 823 (2011)], we propose that the heterogeneities are predominantly density fluctuations in strong glasses (lower Poisson ratio) and shear elasticity fluctuations in fragile glasses (higher Poisson ratio). Because the excess of low-frequency vibration modes in comparison with the Debye regime (boson peak) is strongly connected to these fluctuations, we propose that they are breathing-like (with change of volume) in strong glasses and shear-like (without change of volume) in fragile glasses. As a verification, it is confirmed that the excess modes in the strong silica glass are predominantly breathing-like. Moreover, it is shown that the excess breathing-like modes in a strong polymeric glass are replaced by shear-like modes under hydrostatic pressure as the glass becomes more compact.
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Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids. Recent simulational studies suggest that the density of the excess modes scales with their frequency $omega$ as $omega^4$ in two and higher dimensions. Here, we present extensive numerical studies of two-dimensional model glass formers over a large range of glass stabilities. We find that the density of the excess modes follows $D_text{exc}(omega)sim omega^2 $ up to around the boson peak, regardless of the glass stability. The stability dependence of the overall scale of $D_text{exc}(omega)$ correlates with the stability dependence of low-frequency sound attenuation. However, we also find that in small systems, where the first sound mode is pushed to higher frequencies, at frequencies below the first sound mode there are excess modes with a system size independent density of states that scales as $omega^3$.
We numerically study the evolution of the vibrational density of states $D(omega)$ of zero-temperature glasses when their kinetic stability is varied over an extremely broad range, ranging from poorly annealed glasses obtained by instantaneous quenches from above the onset temperature, to ultrastable glasses obtained by quenching systems thermalised below the experimental glass temperature. The low-frequency part of the density of states splits between extended and quasi-localized modes. Extended modes exhibit a boson peak crossing over to Debye behaviour ($D(omega) sim omega^2$) at low-frequency, with a strong correlation between the two regimes. Quasi-localized modes instead obey $D(omega) sim omega^4$, irrespective of the glass stability. However, the prefactor of this quartic law becomes smaller in more stable glasses, and the corresponding modes become more localized and sparser. Our work is the first numerical observation of quasi-localized modes in a regime relevant to experiments, and it establishes a direct connection between glass stability and soft vibrational motion in amorphous solids.
We conduct experiments on two-dimensional packings of colloidal thermosensitive hydrogel particles whose packing fraction can be tuned above the jamming transition by varying the temperature. By measuring displacement correlations between particles, we extract the vibrational properties of a corresponding shadow system with the same configuration and interactions, but for which the dynamics of the particles are undamped. The vibrational spectrum and the nature of the modes are very similar to those predicted for zero-temperature idealized sphere models and found in atomic and molecular glasses; there is a boson peak at low frequency that shifts to higher frequency as the system is compressed above the jamming transition.
We show that a {em vibrational instability} of the spectrum of weakly interacting quasi-local harmonic modes creates the maximum in the inelastic scattering intensity in glasses, the Boson peak. The instability, limited by anharmonicity, causes a complete reconstruction of the vibrational density of states (DOS) below some frequency $omega_c$, proportional to the strength of interaction. The DOS of the new {em harmonic modes} is independent of the actual value of the anharmonicity. It is a universal function of frequency depending on a single parameter -- the Boson peak frequency, $omega_b$ which is a function of interaction strength. The excess of the DOS over the Debye value is $proptoomega^4$ at low frequencies and linear in $omega$ in the interval $omega_b ll omega ll omega_c$. Our results are in an excellent agreement with recent experimental studies.
Numerical simulation is employed to study dynamical heterogeneities in model harmonic glasses whose atoms interact via three variants of the Lennard-Jones potential (monoatomic full Lennard-Jones, soft spheres, binary mixture). Heterogeneities are observed to exist in all three kinds of glasses, and in some cases they are observed to depend on temperature. The dimension of the heterogeneities is studied for the full Lennard-Jones case.
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