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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.
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We compute the dielectric response of glasses starting from a microscopic system-bath Hamiltonian of the Zwanzig-Caldeira-Leggett type and using an ansatz from kinetic theory for the memory function in the resulting Generalized Langevin Equation. The resulting framework requires the knowledge of the vibrational density of states (DOS) as input, that we take from numerical evaluation of a marginally-stable harmonic disordered lattice, featuring a strong boson peak (excess of soft modes over Debye $simomega_{p}^{2}$ law). The dielectric function calculated based on this ansatz is compared with experimental data for the paradigmatic case of glycerol at $Tlesssim T_{g}$. Good agreement is found for both the reactive (real part) of the response and for the $alpha$-relaxation peak in the imaginary part, with a significant improvement over earlier theoretical approaches, especially in the reactive modulus. On the low-frequency side of the $alpha$-peak, the fitting supports the presence of $sim omega_{p}^{4}$ modes at vanishing eigenfrequency as recently shown in [Phys. Rev. Lett. 117, 035501 (2016)]. $alpha$-wing asymmetry and stretched-exponential behaviour are recovered by our framework, which shows that these features are, to a large extent, caused by the soft boson-peak modes in the DOS.
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 $omega^3$.
The search for other superconductors in the MgB2 class currently is focussed on Li{1-x}BC, which when hole-doped (concentration x) should be a metal with the potential to be a better superconductor than MgB2. Here we present the calculated phonon spectrum of the parent semiconductor LiBC. The calculated Raman-active modes are in excellent agreement with a recent observation, and comparison of calculated IR-active modes with a recent report provides a prediction of the LO--TO splitting for these four modes, which is small for the B-C bond stretching mode at ~1200 cm^{-1}, but large for clearly resolved modes at 540 cm^{-1} and 620 cm^{-1}.
We image local structural rearrangements in soft colloidal glasses under small periodic perturbations induced by thermal cycling. Local structural entropy $S_{2}$ positively correlates with observed rearrangements in colloidal glasses. The high $S_{2}$ values of the rearranging clusters in glasses indicate that fragile regions in glasses are structurally less correlated, similar to structural defects in crystalline solids. Slow-evolving high $S_{2}$ spots are capable of predicting local rearrangements long before the relaxations occur, while fluctuation-created high $S_{2}$ spots best correlate with local deformations right before the rearrangement events. Local free volumes are also found to correlate with particle rearrangements at extreme values, although the ability to identify relaxation sites is substantially lower than $S_{2}$. Our experiments provide an efficient structural identifier for the fragile regions in glasses, and highlight the important role of structural correlations in the physics of glasses.
When subjected to large amplitude oscillatory shear stress, aqueous Laponite suspensions show an abrupt solidification transition after a long delay time tc. We measure the dependence of tc on stress amplitude, frequency, and on the age-dependent initial loss modulus. At first sight our observations appear quantitatively consistent with a simple soft-glassy rheology (SGR)-type model, in which barrier crossings by mesoscopic elements are purely strain-induced. For a given strain amplitude {gamma}0 each element can be classified as fluid or solid according to whether its local yield strain exceeds {gamma}0. Each cycle, the barrier heights E of yielded elements are reassigned according to a fixed prior distribution {rho}(E): this fixes the per-cycle probability R({gamma}0) of a fluid elements becoming solid. As the fraction of solid elements builds up, {gamma}0 falls (at constant stress amplitude), so R({gamma}0) increases. This positive feedback accounts for the sudden solidification after a long delay. The model thus appears to directly link macroscopic rheology with mesoscopic barrier height statistics: within its precepts, our data point towards a power law for {rho}(E) rather than the exponential form usually assumed in SGR. However, despite this apparent success, closer investigation shows that the assumptions of the model cannot be reconciled with the extremely large strain amplitudes arising in our experiments. The quantitative explanation of delayed solidification in Laponite therefore remains an open theoretical challenge.
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