A unified quantifier of mechanical disorder in solids

Abstract

Mechanical disorder in solids, which is generated by a broad range of physical processes and controls various material properties, appears in a wide variety of forms. Defining unified and measurable dimensionless quantifiers, allowing quantitative comparison of mechanical disorder across widely different physical systems, is therefore an important goal. Two such coarse-grained dimensionless quantifiers (among others) appear in the literature, one is related to the spectral broadening of discrete phononic bands in finite-size systems (accessible through computer simulations) and the other is related the spatial fluctuations of the shear modulus in macroscopically large systems. The latter has been recently shown to determine the amplitude of wave attenuation rates in the low-frequency limit (accessible through laboratory experiments). Here, using two alternative and complementary theoretical approaches linked to the vibrational spectra of solids, we derive a basic scaling relation between the two dimensionless quantifiers. This scaling relation, which is supported by simulational data, shows that the two apparently distinct quantifiers are in fact intrinsically related, giving rise to a unified quantifier of mechanical disorder in solids. We further discuss the obtained results in the context of the unjamming transition taking place in soft sphere packings at low confining pressures, in addition to their implications for our understanding of the low-frequency vibrational spectra of disordered solids in general, and in particular those of glassy systems.

arXiv comment11 pages, 8 figures

References in corpus (34)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Supercooled Liquids for Pedestrians
• Jamming of Soft Particles: Geometry, Mechanics, Scaling and Isostaticity
• Irreversible reorganization in a supercooled liquid originates from localised soft modes
• Vibrations and diverging length scales near the unjamming transition
• Models and algorithms for the next generation of glass transition studies
• On the Rigidity of Amorphous Solids
• Continuum limit of the vibrational properties of amorphous solids
• Statistics and properties of low-frequency vibrational modes in structural glasses
• Predicting plasticity in disordered solids from structural indicators
• Low-frequency vibrational modes of stable glasses
• Local inversion-symmetry breaking controls the boson peak in glasses and crystals
• Universal non-phononic density of states in 2D, 3D and 4D glasses
• Scaling of phononic transport with connectivity in amorphous solids
• Non-affine response: jammed packings versus spring networks
• Jamming in finite systems: stability, anisotropy, fluctuations and scaling
• Pinching a glass reveals key properties of its soft spots
• Universality of the nonphononic vibrational spectrum across different classes of computer glasses
• Spatial structure of quasi-localized vibrations in nearly jammed amorphous solids
• Phonon transport and vibrational excitations in amorphous solids
• A characteristic energy scale in glasses
• Wave attenuation in glasses: Rayleigh and generalized-Rayleigh scattering scaling
• Sound attenuation in stable glasses
• Two diverging length scales in the structure of jammed packings
• Universal disorder-induced broadening of phonon bands: from disordered lattices to glasses
• Structural heterogeneity and its role in determining properties of disordered solids
• Elastic moduli fluctuations predict wave attenuation rates in glasses
• Mechanical properties of simple computer glasses
• Finite-size effects in the nonphononic density of states in computer glasses
• Mechanical disorder of sticky-sphere glasses. I. Effect of attractive interactions
• Unifying description of the vibrational anomalies of amorphous materials
• Nonlocal elasticity near jamming
• An energy-landscape-based crossover temperature in glass-forming liquids
• Heterogeneous Elasticity: The tale of the boson peak

Cited by in corpus (9)

• Low-energy quasilocalized excitations in structural glasses
• Low-frequency excess vibrational modes in two-dimensional glasses
• The boson peak in the vibrational spectra of glasses
• Disordered crystals reveal soft quasilocalized glassy excitations
• Variability of mesoscopic mechanical disorder in disordered solids
• Scaling regimes and fluctuations of observables in computer glasses approaching the unjamming transition
• Experimental evidence for the ${\omega }^4$ tail of the nonphononic spectra of glasses
• Elementary processes in dilatational plasticity of glasses
• Critical fluctuations of elastic moduli in jammed solids