Transition In Amorphous Solids Research Articles

Elastic to plastic transition in amorphous solids.

The response of amorphous solids to mechanical loads is accompanied by plasticity that is generically associated with "non-affine" quadrupolar events seen in the resulting displacement field. To develop a continuum theory, one needs to assess when these quadrupolar events have a finite density, allowing the development of a field theory. Is there a transition, as a function of the material parameters and the nature of the loads, from isolated plastic events whose density is zero to a regime governed by a finite density? And if so, what is the nature of this transition? The aim of the paper is to explore this issue. The motivation for the present study stems from recent research in which it was shown that gradients of the quadrupolar fields act as dipole charges that can screen elasticity. Analytically soluble examples of mechanical loading that lead to screening and emergent length scales (that are absent in classical elasticity) have been analyzed and tested. However, "gradients of quadrupolar fields" make sense only when the density of quadrupoles is finite, and hence, the issue is central to this article. The article introduces a notion of polarizability under the strain of Eshelby quadrupoles and concludes that the onset of a density of such quadrupoles with random orientations can only appear when the polarizability is finite.

A continuous constraint satisfaction problem for the rigidity transition in confluent tissues

Models of confluent tissues are built out of tessellations of the space (both in two and three dimensions) in which the cost function is constructed in such a way that individual cells try to optimize their volume and surface in order to reach a target shape. At zero temperature, many of these models exhibit a rigidity transition that separates two phases: a liquid phase and a solid (glassy) phase. This phenomenology is now well established but the theoretical understanding is still not complete. In this work we consider an exactly soluble mean field model for the rigidity transition which is based on an abstract mapping. We replace volume and surface functions by random non-linear functions of a large number of degrees of freedom forced to be on a compact phase space. We then seek for a configuration of the degrees of freedom such that these random non-linear functions all attain the same value. This target value is a control parameter and plays the role of the target cell shape in biological tissue models. Therefore we map the microscopic models of cells to a random continuous constraint satisfaction problem with equality constraints. We argue that at zero temperature, the rigidity transition corresponds to the satisfiability transition of the problem. We also characterize both the satisfiable (SAT) and unsatisfiable (UNSAT) phase. In the SAT phase, before reaching the rigidity transition, the zero temperature SAT landscape undergoes an replica symmetry breaking (RSB)/ergodicity breaking transition of the same type as the Gardner transition in amorphous solids. By solving the RSB equations we compute the SAT/UNSAT threshold and the critical behavior around it. In the UNSAT phase we also compute the average shape index as a function of the target one and we compare the thermodynamical solution of the model with the results of the numerical greedy minimization of the corresponding cost function.

Density-driven higher-order topological phase transitions in amorphous solids

Amorphous topological states, which are independent of the specific spatial distribution of microscopic constructions, have gained much attention. Recently, higher-order topological insulators, which are a new class of topological phases of matter, have been proposed in amorphous systems. Here, we propose a density-driven higher-order topological phase transition in a two-dimensional amorphous system. We demonstrate that the amorphous system hosts a topological trivial phase at low density. With an increase in the density of lattice sites, the topological trivial phase converts to a higher-order topological phase characterized by a quantized quadrupole moment and the existence of topological corner states. Furthermore, we confirm that the density-driven higher-order topological phase transition is size dependent. In addition, our results should be general and equally applicable to three-dimensional amorphous systems. Our findings may greatly enrich the study of higher-order topological states in amorphous systems.

Signatures of the spatial extent of plastic events in the yielding transition in amorphous solids.

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 that in turn determines the stress drop statistics. As reported earlier, the most unstable sites are located in a flat "plateau" region that decreases with system size. While the entrance into the plateau is set by the lower cutoff of the mechanical noise produced by individual STs, the departure from the usually assumed power-law (pseudogap) form of the residual stress distribution comes from far field effects related to spatially extended rearrangements. Interestingly, we observe that the average residual stress of the weakest sites is located in an intermediate power-law regime between the pseudogap and the plateau regimes, whose exponent decreases with system size. Our findings imply a new scaling relation linking the exponents characterizing the avalanche size and residual stress distributions.

Noise spectra in the reversible–irreversible transition in amorphous solids under oscillatory driving

We study the stress fluctuations in simulations of a two-dimensional amorphous solid under a cyclic drive. It is known that this system organizes into a reversible state for small driving amplitudes and remains in an irreversible state for high driving amplitudes, and that a critical driving amplitude separates the two regimes. Here we study the time series of the stress fluctuations below and above the reversible–irreversible transition. In the irreversible regime above the transition, the power spectrum of the stress fluctuations is broad and has a 1/fα shape with 1 < α < 2. We find that the low frequency noise power peaks near the stress at which dc yielding occurs, which is consistent with the behavior expected in systems undergoing a non-equilibrium phase transition.

The yielding transition in amorphous solids under oscillatory shear deformation

Amorphous solids are ubiquitous among natural and man-made materials. Often used as structural materials for their attractive mechanical properties, their utility depends critically on their response to applied stresses. Processes underlying such mechanical response, and in particular the yielding behaviour of amorphous solids, are not satisfactorily understood. Although studied extensively, observed yielding behaviour can be gradual and depend significantly on conditions of study, making it difficult to convincingly validate existing theoretical descriptions of a sharp yielding transition. Here we employ oscillatory deformation as a reliable probe of the yielding transition. Through extensive computer simulations for a wide range of system sizes, we demonstrate that cyclically deformed model glasses exhibit a sharply defined yielding transition with characteristics that are independent of preparation history. In contrast to prevailing expectations, the statistics of avalanches reveals no signature of the impending transition, but exhibit dramatic, qualitative, changes in character across the transition.

Disorder-Assisted Melting and the Glass Transition in Amorphous Solids

The mechanical response of solids depends on temperature, because the way atoms and molecules respond collectively to deformation is affected at various levels by thermal motion. This is a fundamental problem of solid state science and plays a crucial role in materials science. In glasses, the vanishing of shear rigidity upon increasing temperature is the reverse process of the glass transition. It remains poorly understood due to the disorder leading to nontrivial (nonaffine) components in the atomic displacements. Our theory explains the basic mechanism of the melting transition of amorphous (disordered) solids in terms of the lattice energy lost to this nonaffine motion, compared to which thermal vibrations turn out to play only a negligible role. The theory is in good agreement with classic data on melting of amorphous polymers (for which no alternative theory can be found in the literature) and offers new opportunities in materials science.

Athermal brittle-to-ductile transition in amorphous solids

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 that 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 cutoff length of the interparticle potential. On the basis of extensive numerical simulations of the response to pulling the material boundaries at a constant speed we offer an explanation of the onset of ductility via the increase in the density of plastic modes as a function of the potential cutoff length. Finally we can resolve an old riddle: In experiments brittle materials can be strained under grip boundary conditions and exhibit a dynamic crack when cut with a sufficiently long initial slot. Mysteriously, in molecular dynamics simulations it appeared that cracks refused to propagate dynamically under grip boundary conditions, and continuous pulling was necessary to achieve fracture. We argue that this mystery is removed when one understands the distinction between brittle and ductile athermal amorphous materials.

Equation of state and topological transitions in amorphous solids under hydrostatic compression

Equation of state (EoS) relating volume and pressure or other thermodynamics state variables is well-established in crystalline systems, but remains rather incomplete in structurally disordered materials such as metallic glasses. Recent experiments and calculation show that the EoS in some amorphous metals exhibits constitutive behavior deviating significantly from that predicted from many well-established EoS, suggesting fundamentally different mechanisms in operation. But due to the lack of long-range order, it is difficult to uncover the underlying atomic process directly from experiment. Here we report a systematic investigation of the constitutive response of a model ZrNi metallic glass under hydrostatic compression by using extensive molecular dynamics simulation. We show that at low-pressure, the EoS is dominated by large decrease in the excess volumes, presumably those of the valence electrons; and at high-pressure, hardcore repulsion takes over. The two is bridged by a polymorphic topological transition occurring in close association with Ni, one of the alloy elements with much lower compressibility and rigid neighbor bonds that exhibit the topological transition in both short and medium-range. The complex and detailed topological rearrangement reported here may form the general underlying mechanism for the EoS of many metallic glasses composed predominately of metals with different compressibility, such as early and late transition metals and some rare-earth metals. The necessity of the electronic structural change thought to be responsible for some reported EoS is discussed also in light of this work.

Statistical physics of the yielding transition in amorphous solids

The art of making structural, polymeric, and metallic glasses is rapidly developing with many applications. A limitation is that under increasing external strain all amorphous solids (like their crystalline counterparts) have a finite yield stress which cannot be exceeded without effecting a plastic response which typically leads to mechanical failure. Understanding this is crucial for assessing the risk of failure of glassy materials under mechanical loads. Here we show that the statistics of the energy barriers ΔE that need to be surmounted changes from a probability distribution function that goes smoothly to zero as ΔE=0 to a pdf which is finite at ΔE=0 . This fundamental change implies a dramatic transition in the mechanical stability properties with respect to external strain. We derive exact results for the scaling exponents that characterize the magnitudes of average energy and stress drops in plastic events as a function of system size.

Irreversible photobleaching, photorefraction and photoexpansion in GeS 2 amorphous film

The photoinduced irreversible effects in thermally evaporated amorphous GeS 2 films were investigated. The magnitude of the photobleaching induced by gap photons was found at around ≈13%. The photoinduced increase in the optical band gap and the increase in the slope of the short wavelength absorption edge are discussed within the Davis–Mott model and within Tauc's model for optical transitions in amorphous solids. Based on the optical measurements and the Atomic Force Microscopy we also observed photoexpansion at around ≈4.8% accompanied by a decrease in the refractive index from n = 2.02 for the virgin film to n = 1.94 for a film illuminated until a nearly steady state.

High-pressure phase transformations in liquids and amorphous solids

We outline the current state of experimental study and basic ideas fordescribing phase transitions in topologically disordered condensed matter, suchas liquids and amorphous solids. Reviewing briefly the study of moltenelementary substances under pressure, we pay primary attention to the resultsfor liquid Se, S, and P and also to those substances that have not beenrepresented in previous publications, mainly the liquid oxides B2O3 andGeO2.The experimental data reveal the possibility of rather sharp transformations inrelatively simple liquids that are smoothed at high temperatures. Comparing thetransitions in amorphous solids and in liquids, one should emphasize the metastableand non-ergodic nature of amorphous substances and the existence of static localatomic stresses fluctuating in thermally frozen amorphous networks. In particular,the kinetic study of amorphous–amorphous transformations (AATs) in SiO2 and GeO2 glasses andamorphous H2Oice under pressure highlights a number of anomalous features that distinguish theAATs from ordinary first-order transitions and from transformations in liquids.The recent in situ study of the volume changes in glassy silica a-SiO2upon compression at high temperatures provides a new conclusion asregards the existence of two pressure-induced AATs in a-SiO2with different microscopic mechanisms of structural rearrangements. We alsoperform the analysis of two possible kinetic scenarios for AATs, including sharpand diffuse transitions. The key relation determining the transformation scenariois the relationship between the radius of structural correlations in amorphous solidand the size of the critical nucleus of the growing disordered modification.The comparative analysis emphasizes the main difference between thetransformations in liquids and amorphous solids that consists in the factthat the transitions in liquids are mainly determined by thermodynamicrelationships, whereas the transitions in amorphous solids take place faraway from equilibrium and are governed by the corresponding kinetics.

Physical Mechanisms of the Non-Equilibrium Phase Transitions in Amorphous Solids

A theoretical approach to the non-equilibrium phenomena in disordered solids including explosive crystallization and solid state amorphization is proposed. We consider the special excited metastable states at the phase boundary as a driving force of the non-equilibrium phase transition. The decay of these metastable states leads to the appearance of the fundamental scales hierarchy in the sample structure that can by verified experimentally. A possible schemes of the formalisation of the proposed physical mechanisms in a different models are discussed.

Photoinduced optical changes in amorphous Se and Ge–Se films

Films of amorphous Se, Ge 15Se 85, and Ge 25Se 75 were prepared by thermal evaporation. Measurements of photodarkening at 78 K showed that the optical gap ( E g) and the slope of optical absorption edge ( B) are intercorrelated. The correlation between the photoinduced changes of E g and B is discussed within both the model of Davis and Mott and Tauc's model for optical transitions in amorphous solids.

Dynamical Theory for Temporal and Temperature-Induced Broadening of Single Molecule Lines

Abstract Temporal and temperature-induced broadening of zero-phonon hole associated with electronic impurity transitions in amorphous solids are described using an expression based on a dynamical theory for homogeneous spectral diffusion. Normal thermal broadening and broadening produced in thermal cycling are discussed. It is suggested that the proposed theoretical model is subject to testing by single molecule experiments.

Erratum: Model for the glass transition in amorphous solids based on fragmentation

A model for the glass transition in a heating process has been proposed. In the model, noncrystalline solids are assumed to be assemblies of pseudomolecules or structural units. When the noncrystalline solid is heated, a bond breaking process becomes dominant compared with a rebinding process of broken bonds. At high temperature, successive bond breaking causes the fragmentation of the solid and the fragment size becomes smaller as the temperature further increases. Consequently, the solid begins to show some viscous behavior when the fragment size reaches a critical value. To construct mathematical expressions for the fragmentation model, we employed a simple rate equation for the bond breaking process first and then obtained the temperature dependence of dangling bond density in a noncrystalline solid. Second, the expressions for the fragment density and size as a function of temperature were obtained based on the following assumptions: ~1! bond breaking takes place mainly at the boundaries between pseudomolecules, ~2! once buds of microcracks are generated, successive bond breaking occurs mostly at the tip of the microcracks, and ~3! the fragments are Voronoy polyhedra. Finally, the diffusion coefficient in the system was obtained by assuming the vacancy mechanism in solids and then the temperature dependence of viscosity was derived through Stokes-Einstein relation. To examine the present model, applications of the model to the phase changes of a-Si in heating processes are carried out and the results were discussed.

Model for the glass transition in amorphous solids based on fragmentation

A model for the glass transition in a heating process has been proposed. In the model, noncrystalline solids are assumed to be assemblies of pseudomolecules or structural units. When the noncrystalline solid is heated, a bond breaking process becomes dominant compared with a rebinding process of broken bonds. At high temperature, successive bond breaking causes the fragmentation of the solid and the fragment size becomes smaller as the temperature further increases. Consequently, the solid begins to show some viscous behavior when the fragment size reaches a critical value. To construct mathematical expressions for the fragmentation model, we employed a simple rate equation for the bond breaking process first and then obtained the temperature dependence of dangling bond density in a noncrystalline solid. Second, the expressions for the fragment density and size as a function of temperature were obtained based on the following assumptions: (1) bond breaking takes place mainly at the boundaries between pseudomolecules, (2) once buds of microcracks are generated, successive bond breaking occurs mostly at the tip of the microcracks, and (3) the fragments are Voronoy polyhedra. Finally, the diffusion coefficient in the system was obtained by assuming the vacancy mechanism in solids and then the temperature dependence of viscosity was derived through Stokes-Einstein relation. To examine the present model, applications of the model to the phase changes of a-Si in heating processes are carried out and the results were discussed. \textcopyright{} 1996 The American Physical Society.

Spectral diffusion of molecular electronic transitions in amorphous solids: Weak and strong two-level-system phonon coupling.

The two-level-system (TLS) model of glasses is used with nonphenomenological TLS distribution functions [R. Jankowiak et al., J. Phys. Chem. 90, 3896 (1986)] to account for the time-dependent spectral-diffusion data for cresyl violet and zinc porphin in ethanol glasses at low temperatures [K. A. Littau and M. D. Fayer, Chem. Phys. Lett. 176, 551 (1991); H. C. Meijers and D. A. Wiersma, Phys. Rev. Lett. 68, 381 (1992)]. The two distributions of faster and slower TLS relaxation rates required to fit the data are characterized for both weak and strong TLS-phonon coupling. Comparison of the values obtained for the TLS parameters with those determined earlier for specific heat, thermal conductivity, pure dephasing, and spontaneous filling of nonphotochemical holes establishes that the faster and slower distributions are associated with intrinsic and extrinsic TLS. The pronounced effects of strong coupling on the TLS relaxation-rate distributions are discussed.

Origin of the T1.3 power law of pure dephasing for impurity electronic transitions in amorphous solids

The standard tunnel model together with the diagonal modulation theory of dephasing has previously been used to explain the above power law for impurity electronic transitions for T ≲ 10 K. Crude approximations made in averaging over the two-level system (TLS) parameters led to the widely held view that the exponent is 1 + μ where μ is the exponent of the TLS density of states, ρ( E) = ρ 0 E μ. We show that this is incorrect and that the temperature dependence is determined by the average value of the TLS asymmetry parameter 〈Δ〉 E , where E is the tunnel splitting.

On the mechanism of nonphotochemical hole burning of optical transitions in amorphous solids

New temperature-dependent nonphotochemical hole burning results are reported for cresyl violet perchlorate in polyvinyl alcohol which indicate that the simple model for spectral hole production based on a static distribution of two-level systems (TLS) provides an inadequate description. One of the key observations reported is noted to have been made for a variety of other systems. A new mechanism, based on an “outside-in” hierarchy of constrained configurational tunneling events, is proposed in which the time evolution of free volumes plays an important role. The model is consistent with the available data and lends itself to testing by further experiments.