We present here potential dependent mechanical properties of amorphous silicon studied through molecular dynamics (MD) at low temperature. On average, the localization of elementary plastic events and the co-ordination defect-sites appears to be correlated. For Tersoff potential and SW potential the plastic events centered on defects-sites prefer 5-fold defect sites, while for modified Stillinger-Weber potential such plastic events choose 3-fold defect sites. We also analyze the non-affine displacement field in amorphous silicon obtained for different shear regime. The non-affine displacement field localizes when plastic events occur and shows elementary shear band formation at higher shear strains.
The distribution of local residual stresses (threshold to instability) that controls the statistical properties of plastic flow in athermal amorphous solids is examined with an atomistic simulation technique. For quiescent configurations, the distribution has a pseudogap (power-law) form with an exponent that agrees well with global yielding statistics. As soon as deformation sets in, the pseudogap region gives way to a system size dependent plateau at small residual stresses that can be understood from the statistics of local residual stress {\em differences} between plastic events. Results f…
Exponential band edges have been observed in a variety of materials, both crystalline and amorphous. In this paper, we infer the structural origins of these tails in amorphous and defective crystalline Si by direct calculation with current {\it ab initio} methods. We find that exponential tails appear in relaxed models of diamond with suitable point defects. In amorphous silicon (a-Si), we find that structural filaments of short bonds and long bonds exist in the network, and that the tail states near the extreme edges of both band tails are are also filamentary, with much localization on the s…
Amorphous solids are yield stress materials that flow when a sufficient load is applied. Their flow consists of periods of elastic loading interrupted by rapid stress drops, or avalanches, coming from microscopic rearrangements known as shear transformations (STs). Here we show that the spatial extent of avalanches in a steadily sheared amorphous solid has a profound effect on the distribution of local residual stresses $x$. We find that in this distribution, the most unstable sites are located in a system size dependent plateau. While the entrance into the plateau is set by the lower cutoff o…
Plastic instabilities in amorphous materials are often studied using idealized models of binary mixtures that do not capture accurately molecular interactions and bonding present in real glasses. Here we study atomic scale plastic instabilities in a three dimensional molecular dynamics model of silica glass under quasi-static shear. We identify two distinct types of elementary plastic events, one is a standard quasi-localized atomic rearrangement while the second is a bond breaking event that is absent in simplified models of fragile glass formers. Our results show that both plastic events can…
We perform extensive simulations of a 2D LJ glass subjected to quasi-static shear deformation at T=0. We analyze the distribution of non-affine displacements in terms of contributions of plastic, irreversible events, and elastic, reversible motions. From this, we extract information about correlations between plastic events and about the elastic non-affine noise. Moreover, we find that non-affine motion is essentially diffusive, with a clearly size-dependent diffusion constant. These results, supplemented by close inspection of the evolving patterns of the non-affine tangent displacement field…
A number of current theories of plasticity in amorphous solids assume at their basis that plastic deformations are spatially localized. We present in this paper a series of numerical experiments to test the degree of locality of plastic deformation. These experiments increase in terms of the stringency of the removal of elastic contributions to the observed elasto-plastic deformations. It is concluded that for all our simulational protocols the plastic deformations are not localized, and their scaling is sub-extensive. We offer a number of measures of the magnitude of the plastic deformation, …
We present the results of numerical simulations of an atomistic system undergoing plastic shear flow in the athermal, quasistatic limit. The system is shown to undergo cascades of local rearrangements, associated with quadrupolar energy fluctuations, which induce system-spanning events organized into lines of slip oriented along the Bravais axes of the simulation cell. A finite size scaling analysis reveals subextensive scaling of the energy drops and participation numbers, linear in the length of the simulation cell, in good agreement with the observed real-space structure of the plastic even…
We demonstrate that surface morphogenesis in compressed thin films may result from spatially correlated plastic activity. A soft glassy film strongly adhering to a smooth and rigid substrate and subjected to uniaxial compression, indeed, does not undergo any global elastic pattern-forming instability, but responds plastically via localized burst events that self-organize, leading to the emergence of a series of parallel ridges transverse to the compression axis. This phenomenon has been completely overlooked, but results from common features of the plastic response of glasses, hence should be …
We present an information-based total-energy optimization method to produce nearly defect-free structural models of amorphous silicon. Using geometrical, structural and topological information from disordered tetrahedral networks, we have shown that it is possible to generate structural configurations of amorphous silicon, which are superior than the models obtained from conventional reverse Monte Carlo and molecular-dynamics simulations. The new data-driven hybrid approach presented here is capable of producing atomistic models with structural and electronic properties which are on a par with…
While perfect crystals may exhibit a purely elastic response to shear all the way to yielding, the response of amorphous solids is punctuated by plastic events. The prevalence of this plasticity depends on the number of particles $N$ of the system, with the average strain interval before the first plastic event, $\overline{Δγ}$, scaling like $N^α$ with $α$ negative: larger samples are more susceptible to plasticity due to more numerous disorder-induced soft spots. In this paper we examine this scaling relation in ultra-stable glasses prepared with the Swap Monte Carlo algorithm, with regard to…
We build a minimal, mean-field, model of plasticity of amorphous solids, based upon a phenomenology of dissipative events derived, in a preceding paper [A. Lemaitre, C. Caroli, arXiv:0705.0823] from extensive molecular simulations. It reduces to the dynamics of an ensemble of identical shear transformation zones interacting via the dynamic noise due to the long ranged elastic fields induced by zone flips themselves. We find that these ingredients are sufficient to generate flip avalanches with a power-law scaling with system size, analogous to that observed in molecular simulations. We further…
We study the statistical properties of the yielding transition in model amorphous solids in the limit of slow, athermal deformation. Plastic flow occurs via alternating phases of elastic loading punctuated by rapid dissipative events in the form of collective avalanches. We investigate their characterization through energy vs. stress drops and at multiple stages of deformation, thus revealing a change of spatial extent of the avalanches and degree of stress correlations as deformation progresses. We show that the statistics of stress and energy drops only become comparable for large events in …
By means of molecular dynamics simulations based on the Billeter et al. [S. R. Billeter, A. Curioni, D. Fischer, and W. Andreoni, Phys. Rev. B {\bf 73}, 155329] environment-dependent classical force field we studied the structural features of SiN$_x$ samples at various stoichiometries. Our results are in good agreement with experimental data and are able to reproduce some features which so far were not reproduced by simulations. In particular, we identified units containing N--N bonds, which are thought to be responsible for an unassigned peak in the radial distribution function obtained from …
Strongly correlated amorphous solids are a class of glass-formers whose inter-particle potential admits an approximate inverse power-law form in a relevant range of inter-particle distances. We study the steady-state plastic flow of such systems, firstly in the athermal, quasi-static limit, and secondly at finite temperatures and strain rates. In all cases we demonstrate the usefulness of scaling concepts to reduce the data to universal scaling functions where the scaling exponents are determined a-priori from the inter-particle potential. In particular we show that the steady plastic flow at …
The impact of severe plastic deformation by high-pressure torsion on the relaxation of the glassy and supercooled liquid states of Pd$_{40}$Ni$_{40}$P$_{20}$ was investigated using a combination of differential scanning calorimetry, low-temperature heat capacity and fluctuation electron microscopy. The changes in the calorimetric signals due to deformation and subsequent heat treatments were analyzed and a correlation between deformation (rejuvenation) and annealing (relaxation) was found in relation to medium-range order (MRO). Moreover, a coupling between the occurrence of an exothermic peak…
Localized basis ab initio molecular dynamics simulation within the density functional framework has been used to generate realistic configurations of amorphous silicon carbide (a-SiC). Our approach consists of constructing a set of smart initial configurations that conform essential geometrical and structural aspects of the materials obtained from experimental data, which is subsequently driven via first-principles force-field to obtain the best solution in a reduced solution space. A combination of a priori information (primarily structural and topological) along with the ab-initio optimizati…
We apply principal component analysis, a method frequently used in image processing and unsupervised machine learning, to characterize particle displacements observed in the steady shear flow of amorphous solids. PCA produces a low-dimensional representation of the data and clearly reveals the dominant features of elastic (i.e. reversible) and plastic deformation. We show that the principal directions of PCA in the plastic regime correspond to the soft (i.e. zero energy) modes of the elastic propagator that governs the redistribution of shear stress due to localized plastic events. Projections…
We discuss an inverse approach for atomistic modeling of glassy materials. The focus is on structural modeling and electronic properties of hydrogenated amorphous silicon and glassy GeSe2 alloy. The work is based upon a new approach "experimentally constrained molecular relaxation (ECMR)". Unlike conventional approaches (such as molecular dynamics (MD) and Monte Carlo simulations(MC), where a potential function is specified and the system evolves either deterministically (MD) or stochastically (MC), we develop a novel scheme to model structural configurations using experimental data in associa…
Amorphous solids appear to react elastically to small external strains, but in contrast to ideal elastic media, plastic responses abound immediately, at any value of the strain. Such plastic responses are quasi-localized in nature, with the ``cheapest" one being a quadrupolar source. The existence of such plastic responses results in {\em screened elasticity} in which strains and stresses can either quantitatively or qualitatively differ from the un-screened theory, depending on the specific screening mechanism. Here we offer a theory of such screening effects by plastic quadrupoles, dipoles a…
We have studied the statistics of plastic rearrangement events in a simulated amorphous solid at T=0. Events are characterized by the energy release and the ``slip volume'', the product of plastic strain and system volume. Their distributions for a given system size $L$ appear to be exponential, but a characteristic event size cannot be inferred, because the mean values of these quantities increase as $L^α$ with $α\sim 3/2$. In contrast to results obtained in 2D models, we do not see simply connected avalanches. The exponent suggests a fractal shape of the avalanches, which is also evidenced b…
We develop a theory for plastic flux creep in a topologically disordered vortex solid phase in type-II superconductors. We propose a detailed description of the plastic vortex creep of the dislocated, amorphous vortex glass in terms of motion of dislocations driven by a transport current $j$. The {\em plastic barriers} $U_{pl}(j)\propto j^{-μ}$ show power-law divergence at small drives with exponents $μ=1$ for single dislocation creep and $μ= 2/5$ for creep of dislocation bundles. The suppression of the creep rate is a hallmark of the transition from the topologically ordered vortex lattice to…
We investigate the microscopic mechanisms giving rise to plastic depinning and irreversible flow in vortex matter. The topology of the vortex array crucially determines the flow response of this system. To illustrate this claim, two limiting cases are considered: weak and strong pinning interactions. In the first case disorder is strong enough to introduce plastic effects in the vortex lattice. Diffraction patterns unveil polycrystalline lattice topology with dislocations and grain boundaries determining the electromagnetic response of the system. Filamentary flow is found to arise as a conseq…
The deformation and flow of disordered solids, such as metallic glasses and concentrated emulsions, involves swift localized rearrangements of particles that induce a long-range deformation field. To describe these heterogeneous processes, elastoplastic models handle the material as a collection of 'mesoscopic' blocks alternating between an elastic behavior and plastic relaxation, when they are too loaded. Plastic relaxation events redistribute stresses in the system in a very anisotropic way. We review not only the physical insight provided by these models into practical issues such as strain…
We present a mathematical description of amorphous solid deformation and plasticity by extending the concept of instantaneous normal modes (INMs) to deformed systems, which allows us to retain the effect of strain on the vibrational density of states (VDOS). Starting from the nonaffine lattice dynamics (NALD) description of elasticity and viscoelasticity of glasses, we formulate the linear response theory up to large deformations by considering the strain-dependent tangent modulus at finite values of shear strain. The (nonaffine) tangent shear modulus is computed from the vibrational density o…
We study the linear response to strain in a mean field elastoplastic model for athermal amorphous solids, incorporating the power-law mechanical noise spectrum arising from plastic events. In the "jammed" regime of the model, where the plastic activity exhibits a non-trivial slow relaxation referred to as aging, we find that the stress relaxes incompletely to an age-dependent plateau, on a timescale which grows with material age. We determine the scaling behaviour of this aging linear response analytically, finding that key scaling exponents are universal and independent of the noise exponent …
Brittle materials exhibit sharp dynamical fractures when meeting Griffith's criterion, whereas ductile materials blunt a sharp crack by plastic responses. Upon continuous pulling ductile materials exhibit a necking instability which is dominated by a plastic flow. Usually one discusses the brittle to ductile transition as a function of increasing temperature. We introduce an athermal brittle to ductile transition as a function of the cut-off length of the inter-particle potential. On the basis of extensive numerical simulations of the response to pulling the material boundaries at a constant s…
Recent experiments and simulations of amorphous solids plastically deformed by oscillatory drive have foundsurprising behavior - for small strain amplitudes the dynamics can be reversible, which is contrary to the usual notion of plasticity as an irreversible form of deformation. This reversibility allows the system to reach limit-cycles in which plastic events repeat indefinitely under the oscillatory drive. Reaching reversible limit-cycles, can take a large number of driving cycles and it was surmised that the plastic events encountered during the transient period are not encountered again a…
We study energy minimized configurations of amorphous solids with a simple shear degree of freedom. We show that the low-frequency regime of the vibrational density of states of structural glass formers is crucially sensitive to the stress-ensemble from which the configurations are sampled. In both two and three dimensions, a shear-stabilized ensemble displays a $D(ω_{\min}) \sim ω^{5}_{\min}$ regime, as opposed to the $ω^{4}_{\min}$ regime observed under unstrained conditions. We also study an ensemble of two dimensional, strained amorphous solids near a plastic event. We show that the minimu…
Tribological properties of materials play an important role in engineering applications. Up to now, a number of experimental studies have identified correlations between tribological parameters and the mechanical response. Using molecular dynamics simulations, we study abrasive wear behavior via nanoscratching of a Cu$_{64.5}$Zr$_{35.5}$ metallic glass. The evolution of the normal and transverse forces and hardness values follows the behavior well known for crystalline substrates. In particular, the generation of the frontal pileup weakens the response of the material to the scratching tip and…
The deformation of disordered solids relies on swift and localised rearrangements of particles. The inspection of soft vibrational modes can help predict the locations of these rearrangements, while the strain that they actually redistribute mediates collective effects. Here, we study soft modes and strain redistribution in a two-dimensional continuous mesoscopic model based on a Ginzburg-Landau free energy for perfect solids, supplemented with a plastic disorder potential that accounts for shear softening and rearrangements. Regardless of the disorder strength, our numerical simulations show …
Mechanical deformation of amorphous solids can be described as consisting of an elastic part in which the stress increases linearly with strain, up to a yield point at which the solid either fractures or starts deforming plastically. It is well established, however, that the apparent linearity of stress with strain is actually a proxy for a much more complex behavior, with a microscopic plasticity that is reflected in diverging nonlinear elastic coefficients. Very generally, the complex structure of the energy landscape is expected to induce a singular response to small perturbations. In the a…
