Number Of Floppy Modes Research Articles

Comparative study of physical properties of As2Se3 and (As2Se3)90Ge10 glassy alloys doped with metallic impurities

To examine the compositional and chemical effects on the glassy system, one must first understand its network structure. Alloying glassy systems cause significant conformal and configurational changes. The optical and physical parameters of As2Se3 and (As2Se3)90Ge10 glassy alloys doped with metallic impurities (X = Bi, Cd, Pb, Sb) have been evaluated. A comparison of the physical properties of glassy alloys has been made as the doping elements increase, i.e., from binary to ternary to quaternary system, and an effort has been made to correlate the optical and physical parameters. The optical density (Dop) and penetration depth (δ) have been calculated from the reported absorption coefficient (α) data. The mean coordination number (<r>) and the number of floppy modes (Mf) calculations show that the floppy regions are decreasing, and hence, the rigidity is increasing when As–Se is doped with Ge and As–Se-Ge is doped with X. The density (ρ) and packing density (PD) have also been evaluated, which are interrelated to the parameters like refractive index (n) and δ. Cohesive energy (CE), mean bond energy (<E>), and glass transition temperature (Tg) values give an insight into the stability and average crosslinking of the system with alloying. The conduction and valence band potentials have supported the optical bandgap (Egopt) values variation.

Excess floppy modes and multibranched mechanisms in metamaterials with symmetries.

Floppy modes-deformations that cost zero energy-are central to the mechanics of a wide class of systems. For disordered systems, such as random networks and particle packings, it is well-understood how the number of floppy modes is controlled by the topology of the connections. Here we uncover that symmetric geometries, present in, e.g., mechanical metamaterials, can feature an unlimited number of excess floppy modes that are absent in generic geometries, and in addition can support floppy modes that are multibranched. We study the number Δ of excess floppy modes by comparing generic and symmetric geometries with identical topologies, and show that Δ is extensive, peaks at intermediate connection densities, and exhibits mean-field scaling. We then develop an approximate yet accurate cluster counting algorithm that captures these findings. Finally, we leverage our insights to design metamaterials with multiple folding mechanisms.

Viscoelasticity and dynamical gaps: Rigidity in crystallization and glass-forming liquids

Abstract Rigidity plays an important role on the relaxation properties of glass forming melts, yet it is usually determined from the average coordination number through the chemical composition. A discussion is presented on how viscoelasticity can be used as an alternative way to determine glass rigidity and to give clues about the relaxation processes. It is shown that the transverse current dynamical structure factor of dense glass and crystal forming fluids contain rich information about rigidity that can be related with the presence of a dynamical-gap for transversal vibrational-modes. Then, the number of floppy modes can be related with the dynamical gap size and with the liquid relaxation time. Furthermore, a dynamical average effective coordination number can be defined. Numerical simulations for hard-disks in a dense fluid phase are provided. A discussion is presented on the need to improve glass viscoelasticity models to describe consistently non-exponential stress and strain relaxation.

Reverse Monte Carlo Modeling of the Rigidity Percolation Threshold in Ge&amp;lt;SUB&amp;gt;x&amp;lt;/SUB&amp;gt;Se&amp;lt;SUB&amp;gt;1-x&amp;lt;/SUB&amp;gt; Glassy Networks

Based on Maxwell’s constraint counting theory, rigidity percolation in GexSe1-x glasses occurs when the mean coordination number reaches the value of 2.4. This corresponds to Ge0.20Se0.80 glass. At this composition, the number of constraints experienced by an atom equals the number of degrees of freedom in three dimensions. Hence, at this composition, the network changes from a floppy phase to a rigid phase, and rigidity starts to percolate. In this work, we use reverse Monte Carlo (RMC) modeling to model the structure of Ge0.20Se0.80 glass by simulating its experimental total atomic pair distribution function (PDF) obtained via high energy synchrotron radiation. A three-dimensional configuration of 2836 atoms was obtained, from which we extracted the partial atomic pair distribution functions associated with Ge-Ge, Ge-Se and Se-Se real space correlations that are hard to extract experimentally from total scattering methods. Bond angle distributions, coordination numbers, mean coordination numbers and the number of floppy modes were also extracted and discussed. More structural insights about network topology at this composition were illustrated. The results indicate that in Ge0.20Se0.80 glass, Ge atoms break up and cross-link the Se chain structure, and form structural units that are four-fold coordinated (the GeSe4 tetrahedra). These tetrahedra form the basic building block and are connected via shared Se atoms or short Se chains. The extent of the intermediate ranged oscillations in real space (as extracted from the width of the first sharp diffraction peak) was found to be around 19.6 ?. The bonding schemes in this glass are consistent with the so-called “8-N” rule and can be interpreted in terms of a chemically ordered network model.

Linear elastic trusses leading to continua with exotic mechanical interactions

We study the statics of some trusses, i.e. networks of nodes linked by linear springs. The trusses are designed in such a way that a few number of floppy modes are present and remain when considering the homogenized limit of the truss. We then obtain linear elastic materials with exotic mechanical interactions which cannot be described in the classical framework of Cauchy stress theory. For aim of simplicity, the structures described here are two-dimensional. The extension to the 3D case does not present any difficulty.

Glass transition phenomenology and flexibility: An approach using the energy landscape formalism

The thermodynamic phenomenology of the glass transition in chalcogenide glasses is studied by using rigidity theory, which treats covalent bonding as mechanical constraints. Since flexible systems have a certain number of nearly zero frequency modes (called floppy modes), these modes provide channels in the energy landscape of the glass, and as a consequence, the entropy and fragility depend upon the number of constraints, even for the supercooled melt. Using this approach, the variation of the glass transition temperature with the chemical composition can be obtained from the number of floppy modes, since low frequencies enhance in a considerable way the average quadratic displacement of atomic vibrations. The result reproduces the observed experimental variation of the glass transition temperature with chemical composition.

Contribution of floppy modes to the heat capacity jump and fragility in chalcogenide glasses

The jump of the heat capacity in chalcogenide glasses during glass transition is estimated using the number of floppy modes as a free energy. A comparison with experimental data shows good agreement, without using any free parameter. This result allows a determination of the change of the glass fragility and excess thermal expansivity as a function of the average coordination number.

Vibrational densities of states and network rigidity in chalcogenide glasses.

Vibrational spectra have been measured by neutron scattering for a series of Se-Ge and Se-As-Ge glasses, spanning a wide range in composition and, consequently, in network connectivity. Low-frequency floppy'' modes arising from underconstrained atomic configurations have been observed, in qualitative agreement with recent theories of the dynamics of network glasses. The number of floppy modes was found to depend only on the average coordination number {l angle}{ital r}{r angle}. There is some indication of a rigidity percolation threshold at {l angle}{ital r}{r angle}{approx}2.4, but the effect in the vibrational densities of states is not dramatic. The wave-vector dependence of the scattering at low vibrational energies ({approx}2 meV) is acoustic-phonon-like. Specific heats {ital C} calculated from the measured densities of states show a strongly composition-dependent bump in {ital C}/{ital T}{sup 3} near 4 K, in accord with experiment.