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Register a new userDisorder-induced vibrational anomalies from crystalline to amorphous solids
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The origin of boson peak -- an excess of density of states over Debyes model in glassy solids -- is still under intense debate, among which some theories and experiments suggest that boson peak is related to van-Hove singularity. Here we show that boson peak and van-Hove singularity are well separated identities, by measuring the vibrational density of states of a two-dimensional granular system, where packings are tuned gradually from a crystalline, to polycrystals, and to an amorphous material. We observe a coexistence of well separated boson peak and van-Hove singularities in polycrystals, in which the van-Hove singularities gradually shift to higher frequency values while broadening their shapes and eventually disappear completely when the structural disorder $eta$ becomes sufficiently high. By analyzing firstly the strongly disordered system ($eta=1$) and the disordered granular crystals ($eta=0$), and then systems of intermediate disorder with $eta$ in between, we find that boson peak is associated with spatially uncorrelated random flucutations of shear modulus $delta G/langle G rangle$ whereas the smearing of van-Hove singularities is associated with spatially correlated fluctuations of shear modulus $delta G/langle G rangle$.
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The boson peak (BP) is an excess of vibrational states over the Debye law appearing at terahertz frequencies. It is found in all glasses and marks the crossover between the long-wavelength behavior, where the solid can be considered as an isotropic continuum, and the region where the wavelength of the sound wave starts to experience the microscopic details of the structure. This chapter is devoted to a review of the main experimental observations regarding the vibrational dynamics of amorphous solids, as detected by neutron and X-ray scattering techniques. A first part of the chapter is devoted to the measurements of the BP and its evolution as a function of external parameters, such as temperature, pressure, or density. The second part of the chapter reviews the wavevector evolution of the dynamic structure factor, which provides evidence of a pseudo-acoustic propagating mode up to frequencies comparable to those of the BP. This longitudinal mode has a sound attenuation which follows the Rayleigh scattering law and a negative dispersion that can partially explain the deviation from the Debye law. At higher frequencies, the inelastic spectrum presents a complex pattern of vibrations, with evidences of two peaks in various systems. To conclude, we will highlight the information that can be gained on the nature of the glass vibrational modes from a comparison with the dynamics of the corresponding polycrystal.
Acoustic excitations in topologically disordered media at mesoscale present anomalous features with respect to the Debyes theory. In a three-dimensional medium an acoustic excitation is characterized by its phase velocity, intensity and polarization. The so-called Rayleigh anomalies, which manifest in attenuation and retardation of the acoustic excitations, affect the first two properties. The topological disorder is, however, expected to influence also the third one. Acoustic excitations with a well-defined polarization in the continuum limit present indeed a so-called mixing of polarizations at nanoscale, as attested by experimental observations and Molecular Dynamics simulations. We provide a comprehensive experimental characterization of acoustic dynamics properties of a selected glass, 1-octyl-3-methylimidazolium chloride glass, whose heterogeneous structure at nanoscale is well-assessed. Distinctive features, which can be related to the occurrence of the Rayleigh anomalies and of the mixing of polarizations are observed. We develop, in the framework of the Random Media Theory, an analytical model that allows a quantitative description of all the Rayleigh anomalies and the mixing of polarizations. Contrast between theoretical and experimental features for the selected glass reveals an excellent agreement. The quantitative theoretical approach permits thus to demonstrate how the mixing of polarizations generates distinctive feature in the dynamic structure factor of glasses and to unambiguously identify them. The robustness of the proposed theoretical approach is validated by its ability to describe as well transverse acoustic dynamics.
Surface stress and surface energy are fundamental quantities which characterize the interface between two materials. Although these quantities are identical for interfaces involving only fluids, the Shuttleworth effect demonstrates that this is not the case for most interfaces involving solids, since their surface energies change with strain. Crystalline materials are known to have strain dependent surface energies, but in amorphous materials, such as polymeric glasses and elastomers, the strain dependence is debated due to a dearth of direct measurements. Here, we utilize contact angle measurements on strained glassy and elastomeric solids to address this matter. We show conclusively that interfaces involving polymeric glasses exhibit strain dependent surface energies, and give strong evidence for the absence of such a dependence for incompressible elastomers. The results provide fundamental insight into our understanding of the interfaces of amorphous solids and their interaction with contacting liquids.
When an amorphous solid is deformed cyclically, it may reach a steady state in which the paths of constituent particles trace out closed loops that repeat in each driving cycle. A remarkable variant has been noticed in simulations where the period of particle motions is a multiple of the period of driving, but the reasons for this behavior have remained unclear. Motivated by mesoscopic features of displacement fields in experiments on jammed solids, we propose and analyze a simple model of interacting soft spots -- locations where particles rearrange under stress and that resemble two-level systems with hysteresis. We show that multiperiodic behavior can arise among just three or more soft spots that interact with each other, but in all cases it requires frustrated interactions, illuminating this otherwise elusive type of interaction. We suggest directions for seeking this signature of frustration in experiments and for achieving it in designed systems.
Understanding the mechanical response and failure of solids is of obvious importance in their use as structural materials. The nature of plastic deformation leading to yielding of amorphous solids has been vigorously pursued in recent years. Investigations employing both unidirectional and cyclic deformation protocols reveal a strong dependence of yielding behaviour on the degree of annealing. Below a threshold degree of annealing, the nature of yielding changes qualitatively, to progressively more discontinuous yielding. Theoretical investigations of yielding in amorphous solids have almost exclusively focused on yielding under unidirectional deformation, but cyclic deformation reveals several interesting features that remain largely un-investigated. Focusing on athermal cyclic deformation, I investigate a family of models based on an energy landscape description. These models reproduce key interesting features observed in simulations, and provide an interpretation for the intriguing presence of a threshold energy.
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