Ageing, fragility and the reversibility window in bulk alloy glasses

Extended aging of Ge-Se glasses below the glass transition temperature

Germanium selenide glasses of compositions spanning the whole glass-formation range are aged at room temperature for up to 20 years. A prominent enthalpy relaxation process is observed in all glasses, and its structural origin is analyzed by Raman spectroscopy. The structural relaxation is manifested in the Raman spectra as a decrease in the ratio of edge- to corner-sharing GeSe_4/2 tetrahedral units. This structural evolution can be explained in terms of configurational entropy and density changes. Changes in Raman features and enthalpy follow an identical stretched exponential relaxation function characteristic of aging in glasses. The compositional dependence of enthalpy relaxation after 20 years is in agreement with kinetic considerations based on the glass transition temperature of each glass. The relaxation behavior and heat capacity curves are consistent with standard glass relaxation models for all compositions. These results indicate that the non-reversing enthalpy obtained by modulated differential scanning calorimetry (MDSC), which suggests the existence of non-aging glasses, is not a reliable measure of the ability of a glass to relax. Instead, it is suggested that an interpretation of MDSC data in terms of complex heat capacity provides a more complete and reliable assessment of the relaxation properties of glasses.

Fragility and aging behavior of SixSe1-x glasses and liquids

The composition dependence of the fragility of Si_xSe_1-x liquids with 0.05 ≤ x ≤ 0.33 is determined using the calorimetric method and is found to be rather similar to that characteristic of their Ge analogues. In addition, the nature and the time scale of the structural relaxation of the Si₂₅Se₇₅ glass during aging at 40 K below T_g are measured using Raman spectroscopy. The structural relaxation in this glass, which belongs to the so-called intermediate phase, involves progressive conversion of the doubly edge-shared SiSe_4/2 tetrahedra E² into singly edge-shared E¹ and corner-shared E⁰ tetrahedra upon lowering of temperature. This tetrahedral speciation can be expressed in the form of the reaction 2 E² → E⁰ + E¹. The time scale of this tetrahedral conversion reaction corresponds well with that of shear relaxation. This result is inconsistent with the claim made previously in the literature that intermediate phase compositions do not undergo aging. Moreover, when taken together, the fragility and the structural relaxation results suggest that the constraint counting scheme typically adopted in the literature for edge- vs. corner-shared tetrahedra in chalcogenide networks may need to be revised. A rigid-polytope based constraint counting approach is shown to be more consistent with the experimental results.

From elemental tellurium to Ge2Sb2Te5 melts: High temperature dynamic and relaxation properties in relationship with the possible fragile to strong transition

We investigate the dynamic properties of Ge-Sb-Te phase change melts using first principles molecular dynamics with a special emphasis on the effect of tellurium composition on melt dynamics. From structural models and trajectories established previously [H. Flores-Ruiz et al., Phys. Rev. B 92, 134205 (2015)], we calculate the diffusion coefficients for the different species, the activation energies for diffusion, the Van Hove correlation, and the intermediate scattering functions able to substantiate the dynamics and relaxation behavior of the liquids as a function of temperature and composition that is also compared to experiment whenever possible. We find that the diffusion is mostly Arrhenius-like and that the addition of Ge/Sb atoms leads to a global decrease of the jump probability and to an increase in activated dynamics for diffusion. Relaxation behavior is analyzed and used in order to evaluate the possibility of a fragile to strong transition that is evidenced from the calculated high fragility (M = 129) of Ge₂Sb₂Te₅ at high temperatures.

Topological Control on the Structural Relaxation of Atomic Networks under Stress

Upon loading, atomic networks can feature delayed irreversible relaxation. However, the effect of composition and structure on relaxation remains poorly understood. Herein, relying on accelerated molecular dynamics simulations and topological constraint theory, we investigate the relationship between atomic topology and stress-induced structural relaxation, by taking the example of creep deformations in calcium silicate hydrates (C─S─H), the binding phase of concrete. Under constant shear stress, C─S─H is found to feature delayed logarithmic shear deformations. We demonstrate that the propensity for relaxation is minimum for isostatic atomic networks, which are characterized by the simultaneous absence of floppy internal modes of relaxation and eigenstress. This suggests that topological nanoengineering could lead to the discovery of nonaging materials.

Relaxation and physical aging in network glasses: a review

Recent progress in the description of glassy relaxation and aging are reviewed for the wide class of network-forming materials such as GeO2, Ge x Se1-x , silicates (SiO2-Na2O) or borates (B2O3-Li2O), all of which have an important usefulness in domestic, geological or optoelectronic applications. A brief introduction of the glass transition phenomenology is given, together with the salient features that are revealed both from theory and experiments. Standard experimental methods used for the characterization of the slowing down of the dynamics are reviewed. We then discuss the important role played by aspects of network topology and rigidity for the understanding of the relaxation of the glass transition, while also permitting analytical predictions of glass properties from simple and insightful models based on the network structure. We also emphasize the great utility of computer simulations which probe the dynamics at the molecular level, and permit the calculation of various structure-related functions in connection with glassy relaxation and the physics of aging which reveal the non-equilibrium nature of glasses. We discuss the notion of spatial variations of structure which leads to the concept of 'dynamic heterogeneities', and recent results in relation to this important topic for network glasses are also reviewed.

Stretched Exponential Relaxation of Glasses at Low Temperature

The question of whether glass continues to relax at low temperature is of fundamental and practical interest. Here, we report a novel atomistic simulation method allowing us to directly access the long-term dynamics of glass relaxation at room temperature. We find that the potential energy relaxation follows a stretched exponential decay, with a stretching exponent β=3/5, as predicted by Phillips's diffusion-trap model. Interestingly, volume relaxation is also found. However, it is not correlated to the energy relaxation, but it is rather a manifestation of the mixed alkali effect.

Rigidity transition in materials: hardness is driven by weak atomic constraints

Understanding the composition dependence of the hardness in materials is of primary importance for infrastructures and handled devices. Stimulated by the need for stronger protective screens, topological constraint theory has recently been used to predict the hardness in glasses. Herein, we report that the concept of rigidity transition can be extended to a broader range of materials than just glass. We show that hardness depends linearly on the number of angular constraints, which, compared to radial interactions, constitute the weaker ones acting between the atoms. This leads to a predictive model for hardness, generally applicable to any crystalline or glassy material.

Evolution of covalent networks under cooling: contrasting the rigidity window and jamming scenarios

We study the evolution of structural disorder under cooling in supercooled liquids, focusing on covalent networks. We introduce a model for the energy of networks that incorporates weak noncovalent interactions. We show that at low temperature these interactions considerably affect the network topology near the rigidity transition that occurs as the coordination increases. As a result, this transition becomes mean field and does not present a line of critical points previously argued for, the "rigidity window." Vibrational modes are then not fractons but instead are similar to the anomalous modes observed in packings of particles near jamming. These results suggest an alternative interpretation for the intermediate phase observed in chalcogenides.

Long term aging of selenide glasses: evidence of sub-Tg endotherms and pre-Tg exotherms

Long term aging, extending from months to several years, is studied on several families of chalcogenide glasses including the Ge-Se, As-Se, and Ge-As-Se systems. Special attention is given to the As-Se binary, a system that displays a rich variety of aging behavior intimately tied to sample synthesis conditions and the ambient environment in which samples are aged. Calorimetric (modulated DSC) and Raman scattering experiments are undertaken. Our results show all samples display a sub-Tg endotherm typically 10-70 °C below Tg in glassy networks possessing a mean coordination number r in the 2.25 < r < 2.45 range. Two sets of As(x)Se(100-x) samples aged for eight years were compared, set A consisted of slow cooled samples aged in the dark, and set B consisted of melt-quenched samples aged at laboratory environment. Samples of set B in the As concentration range, 35% < x < 60%, display a pre-T(g) exotherm, but the feature is not observed in samples of set A. The aging behavior of set A presumably represents intrinsic aging in these glasses, while that of set B is extrinsic due to the presence of light. The reversibility window persists in both sets of samples, but is less well defined in set B. These findings contrast with a recent study by Golovchak et al (2008 Phys. Rev. B 78 014202), which finds the onset of the reversibility window moved up to the stoichiometric composition (x = 40%). Here we show that the up-shifted window is better understood as resulting due to demixing of As4Se4 and As4Se3 molecules from the backbone, i.e., nanoscale phase separation (NSPS). We attribute sub-Tg endotherms to compaction of the flexible part of the networks upon long term aging, while the pre-Tg exotherm is to NSPS. The narrowing and sharpening of the reversibility window upon aging is interpreted as the slow 'self-organizing' stress relaxation of the phases just outside the intermediate phase, which itself is stress free and displays little aging.

Scaling and self-organized criticality in proteins: Lysozyme c

Proteins appear to be the most dramatic natural example of self-organized criticality (SOC), a concept that explains many otherwise apparently unlikely phenomena. Protein functionality is often dominated by long-range hydro(phobic/philic) interactions, which both drive protein compaction and mediate protein-protein interactions. In contrast to previous reductionist short-range hydrophobicity scales, the holistic Moret-Zebende hydrophobicity scale [Phys. Rev. E 75, 011920 (2007)] represents a hydroanalytic tool that bioinformatically quantifies SOC in a way fully compatible with evolution. Hydroprofiling identifies chemical trends in the activities and substrate binding abilities of model enzymes and antibiotic animal lysozymes c , as well as defensins, which have been the subject of tens of thousands of experimental studies. The analysis is simple and easily performed and immediately yields insights not obtainable by traditional methods based on short-range real-space interactions, as described either by classical force fields used in molecular-dynamics simulations, or hydrophobicity scales based on transference energies from water to organic solvents or solvent-accessible areas.

Scaling and self-organized criticality in proteins I

The complexity of proteins is substantially simplified by regarding them as archetypical examples of self-organized criticality (SOC). To test this idea and elaborate on it, this article applies the Moret-Zebende SOC hydrophobicity scale to the large-scale scaffold repeat protein of the HEAT superfamily, PR65/A. Hydrophobic plasticity is defined and used to identify docking platforms and hinges from repeat sequences alone. The difference between the MZ scale and conventional hydrophobicity scales reflects long-range conformational forces that are central to protein functionality.

A stringent test for hydrophobicity scales: two proteins with 88% sequence identity but different structure and function

Protein-protein interactions (protein functionalities) are mediated by water, which compacts individual proteins and promotes close and temporarily stable large-area protein-protein interfaces. In their classic article, Kyte and Doolittle (KD) concluded that the "simplicity and graphic nature of hydrophobicity scales make them very useful tools for the evaluation of protein structures." In practice, however, attempts to develop hydrophobicity scales (for example, compatible with classical force fields (CFF) in calculating the energetics of protein folding) have encountered many difficulties. Here, we suggest an entirely different approach based on the idea that proteins are self-organized networks, subject to evolving finite-scale criticality (like some network glasses). We test this proposal against two small proteins that are delicately balanced between alpha and alpha/beta structures, with different functions encoded with only 12% of their amino acids. This example explains why protein structure prediction is so challenging, and it provides a severe test for the accuracy and content of hydrophobicity scales. This method confirms KD's evaluation and at the same time suggests that protein structure, dynamics, and function can be best discussed without using CFF.

Abrupt boundaries of intermediate phases and space filling in oxide glasses

Modulated differential scanning calorimetry measurements on bulk (Na(2)O)(x)(GeO(2))(1-x) glasses show a sharp reversibility window in the 14%<x<19% soda range, which correlates well with a broad global minimum in molar volumes. Raman and IR reflectance transverse- and longitudinal-optic mode frequencies exhibit anomalies between x(c)(1) = 14% (stress transition) and x(c)(2) = 19% (rigidity transition), with optical elasticity power laws confirming the nature of the transitions. Birefringence measurements dramatize the macroscopically stress-free nature of the intermediate phase in the reversibility window.

Fast-ion conduction and flexibility of glassy networks

We observe two thresholds in the variations of electrical conductivity of dry (AgI)_{x}(AgPO3)_{1-x} solid electrolyte glasses, when the AgI additive concentration x increases to 9.5% and to 37.8%. Raman scattering complemented by calorimetric measurements confirms that these thresholds are signatures of the rigidity phase transitions at x=9.5% from a stressed rigid to an isostatically (stress-free) rigid phase, and at x=37.8% from isostatically rigid to a flexible phase. In the flexible phase, the electrical conductivity seems to increase as a power of x. This is in good agreement with the theoretical prediction based on 3D percolation.

Self-organized criticality in the intermediate phase of rigidity percolation

Experimental results for covalent glasses have highlighted the existence of a self-organized phase due to the tendency of glass networks to minimize internal stress. Recently, we have shown that an equilibrated self-organized two-dimensional lattice-based model also possesses an intermediate phase in which a percolating rigid cluster exists with a probability between zero and one, depending on the average coordination of the network. In this paper, we study the properties of this intermediate phase in more detail. We find that microscopic perturbations, such as the addition or removal of a single bond, can affect the rigidity of macroscopic regions of the network, in particular, creating or destroying percolation. This, together with a power-law distribution of rigid cluster sizes, suggests that the system is maintained in a critical state on the rigid-floppy boundary throughout the intermediate phase, a behavior similar to self-organized criticality, but, remarkably, in a thermodynamically equilibrated state. The distinction between percolating and nonpercolating networks appears physically meaningless, even though the percolating cluster, when it exists, takes up a finite fraction of the network. We point out both similarities and differences between the intermediate phase and the critical point of ordinary percolation models without self-organization. Our results are consistent with an interpretation of recent experiments on the pressure dependence of Raman frequencies in chalcogenide glasses in terms of network homogeneity.

Self-organization with equilibration: a model for the intermediate phase in rigidity percolation

Recent experimental results for covalent glasses suggest the existence of an intermediate phase attributed to the self-organization of the glass network resulting from the tendency to minimize its internal stress. However, the exact nature of this experimentally measured phase remains unclear. We modified a previously proposed model of self-organization by generating a uniform sampling of stress-free networks. In our model, studied on a diluted triangular lattice, an unusual intermediate phase appears, in which both rigid and floppy networks have a chance to occur, a result also observed in a related model on a Bethe lattice by Barré et al[Phys. Rev. Lett. 94, 208701 (2005)]. Our results for the bond-configurational entropy of self-organized networks, which turns out to be only about 2% lower than that of random networks, suggest that a self-organized intermediate phase could be common in systems near the rigidity percolation threshold.

Dynamics in the Presence of Attractive Patchy Interactions

We report extensive Monte Carlo and event-driven molecular dynamics simulations of a liquid composed of particles interacting via hard-sphere interactions complemented by four tetrahedrally coordinated short-range attractive ("sticky") spots, a model introduced several years ago by Kolafa and Nezbeda (Kolafa, J.; Nezbeda, I. Mol. Phys. 1987, 87, 161). To access the dynamic properties of the model, we introduce and implement a new event-driven molecular dynamics algorithm suited to study the evolution of hard bodies interacting, beside the repulsive hard-core, with a short-ranged interpatch square well potential. We evaluate the thermodynamic properties of the model in deep supercooled states, where the bond network is fully developed, providing evidence of density anomalies. Different from models of spherically symmetric interacting particles, the liquid can be supercooled without encountering the gas-liquid spinodal in a wide region of packing fractions phi. Around an optimal phi, a stable fully connected tetrahedral network of bonds develops. By analyzing the dynamics of the model we find evidence of anomalous behavior: around the optimal packing, dynamics accelerate on both increasing and decreasing phi. We locate the shape of the isodiffusivity lines in the (phi - T) plane and establish the shape of the dynamic arrest line in the phase diagram of the model. Results are discussed in connection with colloidal dispersions of sticky particles and gel-forming proteins and their ability to form dynamically arrested states.