Models Of Amorphous Solids Research Articles

Origins of complexity in the rheology of Soft Earth suspensions

When wet soil becomes fully saturated by intense rainfall, or is shaken by an earthquake, it may fluidize catastrophically. Sand-rich slurries are treated as granular suspensions, where the failure is related to an unjamming transition, and friction is controlled by particle concentration and pore pressure. Mud flows are modeled as gels, where yielding and shear-thinning behaviors arise from inter-particle attraction and clustering. Here we show that the full range of complex flow behaviors previously reported for natural debris flows can be reproduced with three ingredients: water, silica sand, and kaolin clay. Going from sand-rich to clay-rich suspensions, we observe continuous transition from brittle (Coulomb-like) to ductile (plastic) yielding. We propose a general constitutive relation for soil suspensions, with a particle rearrangement time that is controlled by yield stress and jamming distance. Our experimental results are supported by models for amorphous solids, suggesting that the paradigm of non-equilibrium phase transitions can help us understand and predict the complex behaviors of Soft Earth suspensions.

Anomalous elasticity and emergent dipole screening in three-dimensional amorphous solids.

In recent work, we developed a screening theory for describing the effect of plastic events in amorphous solids on its emergent mechanics. The suggested theory uncovered an anomalous mechanical response of amorphous solids where plastic events collectively induce distributed dipoles that are analogous to dislocations in crystalline solids. The theory was tested against various models of amorphous solids in two dimensions, including frictional and frictionless granular media and numerical models of amorphous glass. Here we extend our theory to screening in three-dimensional amorphous solids and predict the existence of anomalous mechanics similar to the one observed in two-dimensional systems. We conclude by interpreting the mechanical response as the formation of nontopological distributed dipoles that have no analog in the crystalline defects literature. Having in mind that the onset of dipole screening is reminiscent of Kosterlitz-Thouless and hexatic transitions, the finding of dipole screening in three dimensions is surprising.

Thermally activated flow in models of amorphous solids

Amorphous solids yield at a critical value Σ_{c} of the imposed stress Σ through a dynamical phase transition. While sharp in athermal systems, the presence of thermal fluctuations leads to the rounding of the transition and thermally activated flow even below Σ_{c}. Here we study the steady-state thermal flow of amorphous solids using a mesoscopic elastoplastic model. In the Hébraud-Lequex (HL) model we provide an analytical solution of the thermally activated flow at low temperature. We then propose a general scaling law that also describes the transition rounding. Finally, we find that the scaling law holds in numerical simulations of the HL model, a two-dimensional (2D) elastoplastic model, and previously published molecular dynamics simulations of 2D Lennard-Jones glass.

Avalanche-size distributions in mean-field plastic yielding models

We discuss the size distribution N(S) of avalanches occurring at the yielding transition of mean-field (i.e., Hebraud-Lequeux) models of amorphous solids. The size distribution follows a power law dependence of the form N(S)∼S(-τ). However (contrary to what is found in its depinning counterpart), the value of τ depends on details of the dynamic protocol used. For random triggering of avalanches we recover the τ=3/2 exponent typical of mean-field models, which, in particular, is valid for the depinning case. However, for the physically relevant case of external loading through a quasistatic increase of applied strain, a smaller exponent (close to 1) is obtained. This result is rationalized by mapping the problem to an effective random walk in the presence of a moving absorbing boundary.

Critical behavior of repulsively interacting particles adsorbed on disordered triangular lattices

A simple model for amorphous solids, consisting of a triangular lattice with a fraction of attenuated bonds randomly distributed (which simulate the presence of defects in the surface), is used here to find out, by using grand canonical Monte Carlo simulations, how the adsorption thermodynamics of repulsively interacting monomers is modified with respect to the same process in the regular lattice. The degree of disorder of the surface is tunable by selecting the values of (1) the fraction of attenuated bonds ρ (0 ≤ρ≤ 1) and (2) the attenuation factor r (0 ≤r≤ 1), where r is defined as the ratio between the value of the lateral interaction associated to an attenuated bond and that corresponding to a regular bond. Adsorption isotherm and differential heat of adsorption calculations have been carried out showing and interpreting the effects of the disorder. A rich variety of behavior has been observed for different values of ρ and r, varying between two limit cases: bond-diluted lattices (r = 0 and ρ≠ 0) and regular lattices (r = 1 and any value of ρ). In addition, the critical behavior of the system was studied, showing that the order-disorder phase transition observed for the regular lattice survives, though with modifications, above a critical curve (ρ-r-temperature).

Rate-dependent shear bands in a shear-transformation-zone model of amorphous solids

We use shear transformation zone (STZ) theory to develop a deformation map for amorphous solids as a function of the imposed shear rate and initial material preparation. The STZ formulation incorporates recent simulation results [T. K. Haxton and A. J. Liu, Phys. Rev. Lett. 99, 195701 (2007)] showing that the steady state effective temperature is rate dependent. The resulting model predicts a wide range of deformation behavior as a function of the initial conditions, including homogeneous deformation, broad shear bands, extremely thin shear bands, and the onset of material failure. In particular, the STZ model predicts homogeneous deformation for shorter quench times and lower strain rates, and inhomogeneous deformation for longer quench times and higher strain rates. The location of the transition between homogeneous and inhomogeneous flow on the deformation map is determined in part by the steady state effective temperature, which is likely material dependent. This model also suggests that material failure occurs due to a runaway feedback between shear heating and the local disorder, and provides an explanation for the thickness of shear bands near the onset of material failure. We find that this model, which resolves dynamics within a sheared material interface, predicts that the stress weakens with strain much more rapidly than a similar model which uses a single state variable to specify internal dynamics on the interface.

Amorphous Semiconductors Studied by First-principles Simulations: Structure and Electronic Properties

AbstractAtomistic models of amorphous solids enable us to study properties that are difficult to address with experimental methods. We present a study of two amorphous semiconductors with a great technological importance, namely a- Si:H and a-SiN:H. We use first-principles density functional theory (DFT), i.e. the interatomic forces are derived from basic quantum mechanics, as only that provides accurate interactions between the atoms for a wide range of chemical environments (e.g. brought about by composition changes). This type of precision is necessary for obtaining the correct short range order. Our amorphous samples are prepared by a cooling from liquid approach. As DFT calculations are very demanding, typically only short simulations can be carried out. Therefore most studies suffer from a substantial amount of defects, making them less useful for modeling purposes. We varied the cooling rate during the thermalization process and found it has a considerable impact on the quality of the resulting structure. A rate of 0.02 K/fs proves to be sufficient to prepare realistic samples with low defect concentrations. To our knowledge these are the first calculations that are entirely based on first-principles and at the same time are able to produce defect-free samples. Because of the high computational load also the size of the systems has to remain modest. The samples of a-Si:H and a-SiN:H contain 72 and 110 atoms, respectively. To examine the convergence with cells size, we utilize a large cell of a-Si:H with a total of 243 atoms. As we obtain essentially the same structure as with the smaller sample, we conclude that the use of smaller cells is justified. Although creating structures without any defects is important, on the other hand a small number of defects can give valuable information about the structure and electronic properties of defects in a-Si:H and a-SiN:H. In our samples we observe the presence of both the dangling bond (undercoordinated atom) and the floating bond (over-coordinated atom). We relate structural defects to electronic defect states within the band gap. In a-SiN:H the silicon-silicon bonds induce states at the valence and conduction band edges, thus decreasing the band gap energy. This finding is in agreement with measurements of the optical band gap, where increasing the nitrogen content increases the band gap.

Comparison of macroscopic mechanical properties and shear band characteristics established by acoustic emission measurements in Fe85-xCoxB15 amorphous alloys ribbons

A complex statistical and spectral analysis of acoustic emission during tensile deformation of the Fe 85-x Co x B 15 (x=19. 21, 30, 40, 50) metallic glasses is performed aiming at clarification of the effect of topological order on inhomogeneous plastic flow and shear resistance. A correlation is established between the critical shear stress for the catastrophic shear bands and quantitative characteristics of acoustic emission pulses, corresponding to local shear bands., This correlation is understandable within the framework of existing in the literature polycluster model of amorphous solids, which considers some suitable intercluster boundaries as main regions for nucleation and spreading of plastic shears.

On the behaviour of carrier velocities for high bias fields in a model of disordered molecular solids

Abstract The dependence of the carrier velocity on the width of energy (diagonal) disorder for a model of amorphous solids is analysed using a numerical simulation technique. In contrast with the behaviour in the low-driving-field region where the carrier velocity always decreases with increasing disorder, for high bias fields, the presence of small amounts of disorder induces non-monotonic behaviour, showing a maximum of the carrier velocity at non-zero disorder strength. A discussion of this phenomenon in terms of the distribution of jumps in the three spatial directions of the system is carried out. Some evidence suggesting that this behaviour might occur in real materials is presented.

Electron localization in amorphous solids: numerical studies for the distorted diamond lattice

The authors present a numerical study of localization properties on models for amorphous solids in three dimensions. Tight-binding Hamiltonians that are based on the diamond structure are used to describe the electronic structure of amorphous modifications of carbon, silicon and germanium. The localization behaviour of electronic states is calculated by studying the sensitivity of eigenvalues to a change in boundary conditions. A wide spectrum of localization effects can be observed, including electron localization both at the band edges and weak localization within the bands. The origin of electron localization is discussed using a population analysis of eigenfunctions.

A gauge model of amorphous solids containing defects II. Chern-Simons free energy

Abstract Continuum line defects are modelled by a theory of SO(3) connections in the orthonormal frame bundle over the body manifold of a solid. Variations of the Chern-Simons free-energy integral lead to spaces of constant curvature and constant torsion as equilibrium configurations.

A gauge model of amorphous solids containing defects

Abstract A gauge model of amorphous solids is formulated as a theory of connection in the orthonormal-frame bundle over the body manifold with the structure group SO(3). The construction of free-energy integrals and the properties of maximally symmetric configurations are discussed.

Ultrasonic velocity change in sintered SiC and ain at low temperatures

Ultrasonic attenuation and velocity changes of sintered SiC samples with 1, 2, and 3 wt% AIN as the sintering additives are investigated as a function of temperature at low temperatures. Below ∼1K, the velocity increases logarithmically with temperature (lnT dependence). This lnT dependence of the velocity is one of the characteristics of amorphous materials. The results are analysed in terms of Two Level Tunneling System (TLS) model for amorphous solids. For comparison, sintered AlN was also studied and it was found that no detectable lnT dependence of velocity exists in this material. Available results suggest the existence of a relation between the disorder characterized by TLS detected at low temperatures and a reduction in the thermal conductivity at and above room temperature.

Micro-structures of an amorphous alloy (Cu57Hf43) detected by tdpac measurements

TDPAC spectra of181Hf were measured for an amorphous alloy (Cu57Hf43) prepared by meltspinning for the first time. It is obtained that two Hf sites exist in the amorphous alloy. The short-range order in the amorphous alloy is discussed from a viewpoint of the polytope model of amorphous solids.

Sur les paramètres essentiels et l'énergie interne des solides amorphes covalents. Modèle en 3 dimensions

We propose a 3-dimensional generalization of the previously reported two-dimensional model for amorphous solids. A parametrization of the elementary cell is presented as well as the density and the potential energy by atom of amorphous solids, as functions of these parameters Generalisation dans trois dimensions du modele bidimensionnel precedemment propose

Inelastic neutron scattering from amorphous solids. I. Calculation of the scattering law for model structures

We present a method for calculating the one- and two-phonon law $S(Q,\ensuremath{\omega})$ for models of amorphous solids. The calculation is considerably simplified by explicitly performing the necessary orientation averages. We illustrate use of the method by calculating the one-phonon scattering from long-wavelength acoustic waves in an amorphous solid. In the small-$Q$ region a Brillouin scattering is predicted.

Transformations between random networks and dense random-packed models for amorphous solids

Random network models used in describing a covalently bonded material such as amorphous silicon or germanium can be transformed to a dense random-packed model used in describing metallic amorphous ...