arXiv subjects

Valery Ilyin

Publications and source records attributed to Valery Ilyin.

At least 19 recordsLinked to original sources

arXiv2019

Instabilities of Time-averaged Configurations in Thermal Glasses

In amorphous solids at finite temperatures the particles follow chaotic trajectories which, at temperatures sufficiently lower than the glass transition, are trapped in "cages". Averaging their positions for times shorter than the diffusion time, one can define a time-averaged configuration. Under strain or stress, these {\em average} configurations undergo sharp plastic instabilities. In athermal glasses the understanding of plastic instabilities is furnished by the Hessian matrix, its eigenvalues and eigenfunctions. Here we propose an uplifting of Hessian methods to thermal glasses, with the aim of understanding the plastic responses in the time-averaged configuration. We discuss a number of potential definitions of Hessians and identify which of these can provide eigenvalues and eigenfunctions which can explain and predict the instabilities of the time-averaged configurations. The conclusion is that the non-affine changes in the average configurations during an instability is accurately predicted by the eigenfunctions of the low-lying eigenvalues of the chosen Hessian.

cond-mat.stat-mech↗

arXiv2018

Magneto-mechanical Coupling in Thermal Amorphous Solids

Standard approaches to magneto-mechanical interactions in thermal magnetic crystalline solids involve Landau functionals in which the lattice anisotropy and the resulting magnetization easy axes are taken explicitly into account. In glassy systems one needs to develop a theory in which the amorphous structure precludes the existence of an easy axis, and in which the constituent particles are free to respond to their local amorphous surroundings and the resulting forces. We present a theory of all the mixed responses of an amorphous solids to mechanical strains and magnetic fields. Atomistic models are proposed in which we test the predictions of magnetostriction for both bulk and nano-film amorphous samples. The application to nano-films with emergent self-affine free interfaces requires a careful definition of the film 'width' and its change due to the magnetostriction effect.

cond-mat.soft↗

arXiv2017

Breakdown of Nonlinear Elasticity in Stress-Controlled Thermal Amorphous Solids

In recent work it was clarified that amorphous solids under strain control do not possess nonlinear elastic theory in the sense that the shear modulus exists but nonlinear moduli exhibit sample to sample fluctuations that grow without bound with the system size. More relevant however for experiments are the conditions of stress control. In the present Communication we show that also under stress control the shear modulus exists but higher order moduli show unbounded sample to sample fluctuation. The unavoidable consequence is that the characterization of stress-strain curves in experiments should be done with a stress-dependent shear modulus rather than with nonlinear expansions.

cond-mat.soft↗

arXiv2015

Consequences of Disorder on the Stability of Amorphous Solids

Highly acurate numerical simulations are employed to highlight the subtle but important differences in the mechanical stability of perfect crystalline solids versus amorphous solids. We stress the difference between strain values at which the shear modulus vanishes and strain values at which a plastic instability insues. The temperature dependence of the yield strain is computed for the two types of solids, showing different scaling laws: $γ_{_{Y}}\simeq γ_{_{Y}}^{0}-C_1 T^{1/3}$ for crystals versus $γ_{_{Y}}\simeq γ_{_{Y}}^{0}- C_2 T^{2/3}$ for amorphous solids.

cond-mat.dis-nn↗

arXiv2015

The yield of Amorphous Solids Under Stress Control at Low Temperatures

The yield of amorphous solids like metallic glasses under external stress was discussed asserting that it is related to the glass transition by increasing temperature, or that it can be understood using statistical theories of various sorts. Here we study the approach to stress-controlled yield and argue that neither assertions can be supported, at least at low temperatures. The yield of amorphous solids at low temperatures is a highly structured phenomenon, characterized by a specific series of mechanical instabilities, and having no similarity at all to fluidization by increased temperature, real or fictive. The series of instabilities followed by stress controlled yield at low but finite temperature protocols can be predicted by analyzing athermal quasi-static strain controlled protocols, making the latter highly relevant for the deep understanding of the mechanical properties of amorphous solids.

cond-mat.soft↗

arXiv2014

Mechanical Properties and Plasticity of a Model Glass Loaded Under Stress Control

Much of the progress achieved in understanding plasticity and failure in amorphous solids had been achieved using experiments and simulations in which the materials were loaded using strain control. There is paucity of results under stress control. Here we present a new method that was carefully geared to allow loading under stress control either at $T=0$ or at any other temperature, using Monte-Carlo techniques. The method is applied to a model perfect crystalline solid, to a crystalline solid contaminated with topological defects, and to a generic glass. The highest yield stress belongs to the crystal, the lowest to the crystal with a few defects, with the glass in between. Although the glass is more disordered than the crystal with a few defects, it yields stress is much higher than that of the latter. We explain this fact by considering the actual microscopic interactions that are typical to glass forming materials, pointing out the reasons for the higher cohesive nature of the glass. The main conclusion of this paper is that the instabilities encountered in stress-control condition are the identical saddle-node bifurcation seen in strain-control. Accordingly one can use the latter condition to infer about the former. Finally we discuss temperature effects and comment on the time needed to see a stress controlled material failure.

cond-mat.stat-mech↗

arXiv2013

Percolating Plastic Failure as a Mechanism for Shear Softening in Amorphous Solids

``Shear softening" refers to the observed reduction in shear modulus when the stress on an amorphous solid is increased beyond the initial linear region. Careful numerical quasi-static simulations reveal an intimate relation between plastic failure and shear softening. The attaintment of the steady-state value of the shear modulus associated with plastic flow is identified with a percolation of the regions that underwent a plastic event. We present an elementary ``two-state" model that interpolates between failed and virgin regions and provides a simple and effective characterization of the shear softening.

cond-mat.soft↗

arXiv2013

Fokker-Planck equation with memory: the crossover from ballistic to diffusive processes in many-particle systems and incompressible media

The unified description of diffusion processes that cross over from a ballistic behavior at short times to normal or anomalous diffusion (sub- or superdiffusion) at longer times is constructed on the basis of a non-Markovian generalization of the Fokker-Planck equation. The necessary non-Markovian kinetic coefficients are determined by the observable quantities (mean- and mean square displacements). Solutions of the non-Markovian equation describing diffusive processes in the physical space are obtained. For long times, these solutions agree with the predictions of the continuous random walk theory; they are, however, much superior at shorter times when the effect of the ballistic behavior is crucial.

cond-mat.stat-mech↗

arXiv2012

The Plastic Response of Magnetoelastic Amorphous Solids

We address the cross effects between mechanical strains and magnetic fields on the plastic response of magnetoelastic amorphous solids. It is well known that plasticity in non-magnetic amorphous solids under external strain $γ$ is dominated by the co-dimension 1 saddle-node bifurcation in which an eigenvalue of the Hessian matrix vanishes at $γ_P$ like $\sqrt{γ_P-γ}$. This square-root singularity determines much of the statistical physics of elasto-plasticity, and in particular that of the stress-strain curves under athermal-quasistatic conditions. In this Letter we discuss the much richer physics that can be expected in magnetic amorphous solids. Firstly, magnetic amorphous solids exhibit co-dimension 2 plastic instabilities, when an external strain and an external magnetic field are applied simultaneously. Secondly, the phase diagrams promise a rich array of new effects that have been barely studied; this opens up a novel and extremely rich research program for magnetoplastic materials.

cond-mat.stat-mech↗

arXiv2011

Statistical Mechanics of Glass Formation in Molecular Liquids with OTP as an Example

We extend our statistical mechanical theory of the glass transition from examples consisting of point particles to molecular liquids with internal degrees of freedom. As before, the fundamental assertion is that super-cooled liquids are ergodic, although becoming very viscous at lower temperatures, and are therefore describable in principle by statistical mechanics. The theory is based on analyzing the local neighborhoods of each molecule, and a statistical mechanical weight is assigned to every possible local organization. This results in an approximate theory that is in very good agreement with simulations regarding both thermodynamical and dynamical properties.

cond-mat.stat-mech↗

arXiv2009

Stochastic Processes Crossing from Ballistic to Fractional Diffusion with Memory: Exact Results

We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation we demonstrate how to choose the memory kernel to exactly respect the two different asymptotics of the diffusion process. Having done so we solve for the probability distribution function (pdf) as a continuous function which evolves inside a ballistically expanding domain. This general solution agrees for long times with the pdf obtained within the continuous random walk approach but it is much superior to this solution at shorter times where the effect of the ballistic regime is crucial.

cond-mat.stat-mech↗

arXiv2009

Randomness-Induced Redistribution of Vibrational Frequencies in Amorphous Solids

Much of the discussion in the literature of the low frequency part of the density of states of amorphous solids was dominated for years by comparing measured or simulated density of states to the classical Debye model. Since this model is hardly appropriate for the materials at hand, this created some amount of confusion regarding the existence and universality of the so- called ``Boson Peak'' which results from such comparisons. We propose that one should pay attention to the different roles played by different aspects of disorder, the first being disorder in the interaction strengths, the second positional disorder, and the third coordination disorder. These have different effects on the low-frequency part of the density of states. We examine the density of states of a number of tractable models in one and two dimensions, and reach a clearer picture of the softening and redistribution of frequencies in such materials. We discuss the effects of disorder on the elastic moduli and the relation of the latter to frequency softening, reaching the final conclusion that the Boson peak is not universal at all.

cond-mat.mtrl-sci↗

arXiv2008

Theory of Specific Heat in Glass Forming Systems

Experimental measurements of the specific heat in glass-forming systems reveal anomalies in the temperature dependence of the specific heat, including the so called "specific heat peak" in the vicinity of the glass transition. The aim of this paper is to provide theoretical explanations of these anomalies in general and a quantitative theory in the case of a simple model of glass-formation. We first present new simulation results for the specific heat in a classical model of a binary mixture. We show that in addition to the formerly observed specific heat peak there is a second peak at lower temperatures which was not observable in earlier simulations. Second, we present a general relation between the specific heat and the bulk modulus and thus offer a smooth connection between the liquid and amorphous solid states. The central result of this paper is a connection between the micro-melting of clusters in the system and the appearance of specific heat peaks. We relate the two peaks to changes in the bulk and shear moduli. We propose that the phenomenon of glass-formation is accompanied by a fast change in the bulk and the shear moduli, but these fast changes occur in different ranges of the temperature. Lastly, we demonstrate how to construct a theory of the frequency dependent complex specific heat, expected from heterogeneous clustering in the liquid state of glass formers. A specific example is provided in the context of our model for the dynamics of glycerol. The theoretical frequency dependent specific heat agrees well with experimental measurements on glycerol. We conclude the paper by stating that there is nothing universal about the temperature dependence of the specific heat in glass formers - unfortunately one needs to understand each case by itself.

cond-mat.stat-mech↗

arXiv2008

Non-Universality of the Specific Heat in Glass Forming Systems

We present new simulation results for the specific heat in a classical model of a binary mixture glass-former in two dimensions. We show that in addition to the formerly observed specific heat peak there is a second peak at lower temperatures which was not observable in earlier simulations. This is a surprise, as most texts on the glass transition expect a single specific heat peak. We explain the physics of the two specific heat peaks by the micro-melting of two types of clusters. While this physics is easily accessible, the consequences are that one should not expect any universality in the temperature dependence of the specific heat in glass formers.

cond-mat.mtrl-sci↗

arXiv2008

Ageing and Relaxation in Glass Forming Systems

We propose that there exists a generic class of glass forming systems that have competing states (of crystalline order or not) which are locally close in energy to the ground state (which is typically unique). Upon cooling, such systems exhibit patches (or clusters) of these competing states which become locally stable in the sense of having a relatively high local shear modulus. It is in between these clusters where ageing, relaxation and plasticity under strain can take place. We demonstrate explicitly that relaxation events that lead to ageing occur where the local shear modulus is low (even negative), and result in an increase in the size of local patches of relative order. We examine the ageing events closely from two points of view. On the one hand we show that they are very localized in real space, taking place outside the patches of relative order, and from the other point of view we show that they represent transitions from one local minimum in the potential surface to another. This picture offers a direct relation between structure and dynamics, ascribing the slowing down in glass forming systems to the reduction in relative volume of the amorphous material which is liquid-like. While we agree with the well known Adam-Gibbs proposition that the slowing down is due to an entropic squeeze (a dramatic decrease in the number of available configurations), we do not agree with the Adam-Gibbs (or the Volger-Fulcher) formulae that predict an infinite relaxation time at a finite temperature. Rather, we propose that generically there should be no singular crisis at any finite temperature: the relaxation time and the associated correlation length (average cluster size) increase at most super-exponentially when the temperature is lowered.

cond-mat.stat-mech↗

arXiv2007

Statistical Mechanics of the Glass Transition in One-Component Liquids with Anisotropic Potential

We study a recently introduced model of one-component glass-forming liquids whose constituents interact with anisotropic potential. This system is interesting per-se and as a model of liquids like glycerol (interacting via hydrogen bonds) which are excellent glass formers. We work out the statistical mechanics of this system, encoding the liquid and glass disorder using appropriate quasi-particles (36 of them). The theory provides a full explanation of the glass transition phenomenology, including the identification of a diverging length scale and a relation between the structural changes and the diverging relaxation times.

cond-mat.mtrl-sci↗

arXiv2007

Mechanical Properties of Glass Forming Systems

We address the interesting temperature range of a glass forming system where the mechanical properties are intermediate between those of a liquid and a solid. We employ an efficient Monte-Carlo method to calculate the elastic moduli, and show that in this range of temperatures the moduli are finite for short times and vanish for long times, where `short' and `long' depend on the temperature. By invoking some exact results from statistical mechanics we offer an alternative method to compute shear moduli using Molecular Dynamics simulations, and compare those to the Monte-Carlo method. The final conclusion is that these systems are not "viscous fluids" in the usual sense, as their actual time-dependence concatenates solid-like materials with varying local shear moduli.

cond-mat.stat-mech↗

arXiv2006

Direct Identification of the Glass Transition: Growing Length Scale and the Onset of Plasticity

Understanding the mechanical properties of glasses remains elusive since the glass transition itself is not fully understood, even in well studied examples of glass formers in two dimensions. In this context we demonstrate here: (i) a direct evidence for a diverging length scale at the glass transition (ii) an identification of the glass transition with the disappearance of fluid-like regions and (iii) the appearance in the glass state of fluid-like regions when mechanical strain is applied. These fluid-like regions are associated with the onset of plasticity in the amorphous solid. The relaxation times which diverge upon the approach to the glass transition are related quantitatively.

cond-mat.stat-mech↗