Stressed Rigid Phase Research Articles

The interplay between the topology of nanoclusters and the characteristic of boson peak in As-S glasses

The combination of mean coordination and concentration dependencies of elastic modules and low-frequency Raman scattering of As-S glasses brings new information about the spectroscopic boson peak (SBP) behavior. The analysis of the characteristic temperature positions of the thermometric boson peak (TBP) and the magnitude of heat capacity of As-S glasses was performed. This study was focused on the As-S compounds from the first glass-forming region with particular attention to the compositions of flexible, intermediate, and stressed-rigid phases. The origin of SBP and TBP is expected to have a structural nature. The spectral features found in the super low-frequency region of Raman spectra were assigned to quasi-localized "soft" modes.The sulfur-rich glass, g-As2S5, represents the intermediate phase with AsnSm clusters containing closed ends and several "soft" nanoclusters. These soft clusters can be responsible for intrinsic quasi-localized "soft" modes, the overall rigidity of the system, and quasi-elastic light scattering.

Progress, Challenges, and Rewards in Probing Melt Dynamics, Configurational Entropy Change, and Topological Phases of Group V‐ and Group IV‐Based Multicomponent Sulfide Glasses

The observation of reversibility windows (RWs) in binary GexS100−x, AsxS100−x and ternary GexAsxS100−2x glass systems permits constructing a global topological phase diagram in the GeAsS composition triangle. The RW denotes glass compositions for which the enthalpy of relaxation at Tg vanishes, leading to thermally reversing glass transitions. The phase diagram permits delineating glass compositions that are in the flexible phase (FP), intermediate phase (IP), and the stressed rigid phase (SRP) for all ternary GexAsxS100−2x glass compositions. For the IP compositions examined, a general lowering of the molar volumes, Vm, is observed in relation to those for non‐IP compositions, giving rise to a volumetric window. Melt dynamics of IP compositions reveal a fragility index, m < 20, lower than that for non‐IP melts for which m > 20 displays a fragility window, underscoring in part the reason for the delayed homogenization of melts in these sulfide glasses. The observations of the three types of window characteristics of IP compositions are feasible only when the homogeneous bulk glasses are synthesized, in which the variance ⟨Δx⟩ in As and Ge concentrations, x, across batch compositions is less than 0.01%. This is established by Fourier transform–Raman profiling of each batch of composition that is synthesized.

Physical properties and conductivity relaxation processes in sodium sulfo-borophosphate glasses

Many physical properties of a sodium-borophosphate glass system (BPSx) having the starting composition (30H3BO3 + xNa2SO4 + (60 − 2x) NaH2PO4 + 10ZnO) were detremined. It was found that the glass density ρ, the transition temperature Tg, and the optical gap energy decrease whereas the molar volume and Urbach ▵E energy increases with the substitution of Na2O by Na2SO4.The analysis of the evolution of the complex dielectric permittivity ε* and the complex electric modulus M* with temperature and composition of the glass indicates that the dielectric loss is dominated by ionic conduction, and the relaxation processes are non-Debye type. The evolution of the Kohlrausch–Williams–Watts (KWW) exponent β, estimated from the imaginary part of the electric modulus indicates that the investigated glass behaves as an intermediate elastic system as compared to flexible and stressed rigid phase. The obtained values of the decoupling index are of the same order of magnitude as observed for fast-ion conducting glasses.From the analysis of the experimental data, we may suggest that the glass sample BPS4 is the more thermally stable and has the highest ionic conductivity since it has the highest dielectric constant favorable for the dissociation of sodium salt.

Superstrong nature of covalently bonded glass-forming liquids at select compositions

Variation of fragility (m) of specially homogenized Ge(x)Se(100-x) melts is established from complex specific heat measurements and shows that m(x) has a global minimum at an extremely low value (m = 14.8(0.5)) in the 21.5% < x < 23% range of Ge. Outside of that compositional range, m(x) then increases first rapidly and then slowly to about m = 25-30. By directly mapping melt stoichiometry as a function of reaction time at a fixed temperature T > Tg, we observe a slowdown of melt-homogenization by the super-strong melt compositions, 21.5% < x < 23%. This range furthermore appears to be correlated to the one observed between the flexible and stressed rigid phase in network glasses. These spectacular features underscore the crucial role played by topology and rigidity in the properties of network-forming liquids and glasses which are highlighted when fragility is represented as a function of variables tracking the effect of rigidity. Finally, we investigate the fragility-glass transition temperature relationship, and find that reported scaling laws do not apply in the flexible phase, while being valid for intermediate and stressed rigid compositions.

Evidence of an intermediate phase in a quaternary Ag bearing telluride glass system using alternating DSC

Alternating Differential Scanning Calorimetric (ADSC) studies on quaternary Ge15Te80−xIn5Agx glasses show the non-reversing enthalpy (ΔHNR) at Tg to exhibit a broad global minimum in the 8%≤x≤16% range of Ag, an observation that is taken evidence for existence of an Intermediate Phase (IP) in that range. Glasses at x<8% are in the flexible phase while those at x>16% in the stressed-rigid phase. The nature of crystalline phases formed upon crystallization of bulk glasses are elucidated by XRD studies, and reveal presence of Te, GeTe, Ag8GeTe6, AgTe, In2Te3 and In4Te3 phases. These experiments also reveal that the fraction of Ag- bearing phases increases while those of Te- bearing ones decreases with increasing x, suggesting progressive replacement of Te–Te bonds by Ag–Te bonds.

Structure, topology, rings, and vibrational and electronic properties of GexSe1−xglasses across the rigidity transition: A numerical study

The structural, electronic, and vibrational properties of glassy Ge${}_{x}$Se${}_{1\ensuremath{-}x}$ are studied using density-functional-based molecular dynamics. The focus is on four compositions ($x=10%,20%,25%,33%$) spanning the rigidity transitions and representing typical compositions of flexible, intermediate, and stressed rigid systems. We investigate structural properties including structure factors, pair distribution functions, angular distributions, coordination numbers, and neighbor distributions and compare our results with experimental findings, when available. Most noticeable is the excellent agreement found in the reproduction of the structure in real and reciprocal space which allows tracking the effect of Ge composition on the structure. Ring statistics and ring correlations are examined and followed across the rigidity transition, and the details of typical small rings show a much more complex picture than established previously. A comparison is made with simple bond models and their validity is discussed. Topological constraint analysis is performed and shows that the onset of rigidity changes substantially the angular motion inside the Ge tetrahedra, which displays increased soft bending motions in the stressed rigid phase. We then investigate the vibrational properties via the vibrational density of states and the dielectric function (infrared absorption), and discuss them with respect to experimental findings. Finally, the electronic properties are computed and show an excellent agreement with respect to previous first-principles simulations and to experiments.

Angular rigidity in tetrahedral network glasses with changing composition

A set of oxide and chalcogenide tetrahedral glasses is investigated using molecular dynamics simulations. We show that the changes in the Ge composition affect mostly bending around germanium in binary Ge-Se systems, leaving Se-centered bending almost unchanged. In contrast, the corresponding Se twisting (quantified by the dihedral angle) depends on the Ge composition and is reduced when the system becomes rigid. It is also shown that angles involving the fourth neighbor around Ge is found to change when the system enters the stressed rigid phase. The same analysis reveals that unlike stoichiometric selenides such as GeSe${}_{2}$ and SiSe${}_{2}$, germania and silica display large standard deviations in the bond angle distributions. Within bond-bending constraints theory, this pattern can be interpreted as a manifestation of broken (i.e., ineffective) oxygen bond-bending constraints, whereas the silicon and germanium bending in oxides is found to be similar to the one found in flexible and intermediate Ge-Se systems. Our results establish the atomic-scale foundations of the phenomenological rigidity theory, thereby profoundly extending its significance and impact on the structural description of network glasses.

Direct Evidence of a Characteristic Length Scale of a Dynamical Nature in the Boolchand Phase of Glasses

The ac conductivity spectra of xAgI-(1 - x)AgPO(3) fast-ion conducting glasses spanning the flexible, intermediate (isostatically rigid), and stressed rigid phases are analyzed. The rescaled frequency-dependent spectra are mapped into time-dependent mean-square displacements out of which a typical length scale characterizing the spatial extent sqrt[(R(2)(∞))] of nonrandom subdiffusive regions of ionic motions is computed. The latter quantity is studied as a function of AgI compositions, and is found to display a maximum isostatic compositions, providing the first clear evidence of a typical length scale of a dynamical nature when a system becomes isostatically rigid and enters that phase.

Understanding amorphous phase-change materials from the viewpoint of Maxwell rigidity

Phase-change materials (PCMs) are the subject of considerable interest because they have been recognized as potential active layers for nonvolatile memory devices, known as phase-change random access memories. By analyzing first-principles molecular-dynamics simulations we develop a method for the enumeration of mechanical constraints in the amorphous phase and show that the phase diagram of the most popular system (Ge-Sb-Te) can be split into two compositional regions having a well-defined mechanical character: a tellurium rich flexible phase and a stressed rigid phase that encompasses the known PCMs. This sound atomic scale insight should open new avenues for the understanding of PCMs and other complex amorphous materials from the viewpoint of rigidity.

Molar volume minimum and adaptative rigid networks in relationship with the intermediate phase in glasses

We propose that the molar volume minimum observed in barium silicate glasses $(1\ensuremath{-}x){\text{SiO}}_{2}\ensuremath{-}x\text{BaO}$ is related to the onset of an adaptative rigid glassy network. We obtain in the compositional window $29%&lt;x&lt;33%$ a dramatic decrease in stressed rigid local units from the Raman analysis and at $x=31%$ the onset of barium ionic conduction. A random bond model [J. Barr\'e et al., Phys. Rev. Lett. 94, 208701 (2005)] and constraint counting algorithms permit defining of the free energy of the system, and analyzing of the elastic nature of three compositional ranges of interest: a stressed rigid phase at low $x$, a flexible phase at high $x$, and a stress-free intermediate phase where space filling is optimized.

Origin of giant photocontraction in obliquely deposited amorphousGexSe1−xthin films and the intermediate phase

Obliquely deposited amorphous Ge x Se 100-x thin films at several compositions in the 15%<x<33.3% range and at several obliqueness angles in the 0<α<80° range at each x were evaporated on Si and glass substrates. Here α designates the angle between film normal and direction of vapor transport. Raman scattering, IR reflectance, and optical absorption measurements were undertaken to characterize the vibrational density of states and optical band gaps. Edge views of films in scanning electron microscopy (SEM) confirm the columnar structure of obliquely (α=80°) deposited films. Films, mounted in a cold stage flushed with N 2 gas, were irradiated to UV radiation from a Hg-Xe arc lamp, and photocontraction (PC) of oblique films were examined. Compositional trend of PC exhibit a bell-shaped curve with a rather large effect (0.25 μm) centered in the 20% 25%, the stressed rigid phase, and at x 25 Se 75 ) that demix from a Ge-rich (∼Ge 40 Se 60 ) phase that fills the intercolumnar space. Loss of PC in such films is traced to the growth of the Ge-rich phase, which is intrinsically stressed and photoinactive. In contrast, Se-rich films are homogeneous, and loss of PC as x decreases below 20% is traced to the accumulation of network stress in the Se-rich nanofilaments. The microscopic origin of the giant PC effect in amorphous semiconducting thin films can be traced, in general, to three conditions being met: (i) growth of a columnar structure leading to porous films, (ii) formation of columns that are rigid but intrinsically stress free, and (iii) an appropriate flux of pair-producing radiation leading to photomelting of columns. These findings lead us to predict that PC will, in general, be maximized in obliquely deposited films of semiconducting networks glasses residing in their IP when irradiated with supra-band-gap radiation.

Amorphous materials: Properties, structure, and durability: Constrained interactions, rigidity, adaptative networks, and their role for the description of silicates

Silicate glasses can be seen as connectivity networks where specific tools are used for the understanding of the behavior with composition of their chemical and physical properties. These tools make use of the effective interatomic interactions and mechanical constraints such as those used for analyzing the stability of macroscopic trusses. We first describe how complex interactions and coordination numbers can be efficiently handled within a general framework. The ingredients of the general framework, also known as mean-field bond constraint theory, are then presented. The theory predicts flexible to stressed-rigid elastic phase transitions at threshold compositions (or mean-coordination numbers). Applications to alkali- and alkaline-earth-silicates are considered and experimental signatures of the phase transition identified. Finally, we focus on the latest development in the field, namely the appearance of a new self-organized intermediate phase between flexible and stressed-rigid phases. Experimental signatures of these phases are reviewed, and the tools of adaptative silicate networks used to understand their features.

Chemical alloying and light-induced collapse of intermediate phases in chalcohalideglasses

The elastic behaviour of binaryGexSe1−x glasses, examined in Raman scattering experiments earlier, has shown glasses atx<0.20 to be in the flexiblephase, those at x>0.25 to be in the stressed–rigid phase and those in the0.20<x<0.25 range to be in the intermediate phase (IP). The IP width in mean-coordination-number space,Δr = 0.10. We have nowexamined ternary Ge1/4Se3/4−yIy glasses in Raman scattering and modulated DSC experiments, and findthat the IP width dramatically collapses by an order of magnitude toΔr = 0.009(2). Alloying iodine for Se serves to scission the network backbone progressively as mixedGe(Se)4−mIm tetrahedra(m-units) emerge with1<m<4. The concentrationsof various m-units are quantitatively tracked in Raman scattering, and this shows them = 1 units to be rather special because they are isostatic. The present results onGe1/4Se3/4−yIy glasses, whencompared to those on Ge1/4S3/4−yIy glasses, reveal crucial differences in the way the reversibility window collapse occurs.Raman scattering examined as a function of the exciting light (647 nm) power in Ge1/4Se3/4−yIy glasses shows the IP to systematically collapse and to vanish once increases to 1.5 × 106 W cm−2. Here, an intense beam of near-bandgap light serves to optically pump the delicateintermediate range order prevailing in the IP and reversibly destroy it.

Onset of rigidity in glasses: From random to self-organized networks

In this paper, we review the signatures of a new elastic phase that is found in glasses with selected compositions. It is shown that in contrast with random networks, where rigidity percolates at a single threshold, networks that are able to self-organize to avoid stress will remain in an almost stress-free state during a compositional interval, a Boolchand intermediate phase, that is bounded by a flexible phase and a stressed rigid phase. We report the experimental signatures and describe the theoretical efforts that have been accomplished to characterize the Boolchand intermediate phase. We illustrate one of the methods used in more detail with the example of Group III chalcogenides and finally suggest further possible experimental signatures of self-organization.

Rings and rigidity transitions in network glasses

Three elastic phases of covalent networks, (I) floppy, (II) isostatically rigid and (III) stressed-rigid have now been identified in glasses at specific degrees of cross-linking (or chemical composition) both in theory and experiments. Here we use size-increasing cluster combinatorics and constraint counting algorithms to study analytically possible consequences of self-organization. In the presence of small rings that can be locally I, II or III, we obtain two transitions instead of the previously reported single percolative transition at the mean coordination number $\bar r=2.4$, one from a floppy to an isostatic rigid phase, and a second one from an isostatic to a stressed rigid phase. The width of the intermediate phase $~ \bar r$ and the order of the phase transitions depend on the nature of medium range order (relative ring fractions). We compare the results to the Group IV chalcogenides, such as Ge-Se and Si-Se, for which evidence of an intermediate phase has been obtained, and for which estimates of ring fractions can be made from structures of high T crystalline phases.

The Intermediate Phase in Ternary GexAsxSe1–2x Glasses

ABSTRACTMelt-quenched AsxGexSe1–2x glasses over the composition range, 0 &lt; x &lt; 0.26, are examined in Raman scattering, T-modulated Differential Scanning Calorimetry (MDSC), and 119Sn Mossbauer spectroscopy measurements. The non-reversing enthalpy near Tg, ΔHnr(x), accessed from MDSC shows a global minimum (∼ 0) in the xc(1) = 0.09 &lt; x &lt; xc(2) = 0.16 range, and increases by an order of magnitude both at x &lt; xc(1) and at x &gt; xc(2). Raman mode frequency of corner-sharing Ge(Se1/2)4 tetrahedra studied as a function of x, also shows three distinct regimes (or power-laws, p) that coincide with ΔHnr(x) trends. These regimes are identified with mechanically floppy (x &lt; xc(1)), intermediate (xc(1) &lt; x &lt; xc(2)), and stressed-rigid (x &gt; xc(2)) phases. The Raman elasticity power-law in the intermediate phase, p1 = 1.04(3), and in the stressed rigid phase, p2= 1.52(5), suggest effective dimensionalities of d = 2 and 3 respectively.

Rigidity transitions in binary Ge–Se glasses and the intermediate phase

Raman scattering measurements, undertaken on bulk Ge x Se 1− x glasses at 0< x<1/3, show evidence of two rigidity transitions as monitored by compositional trends in corner-sharing ( ν CS) and edge-sharing (ν ES ) Ge( Se 1/2) 4 mode frequencies. A second-order transition from a floppy to an unstressed rigid phase occurs near x c(1)=0.20(1) where both ν CS( x) and ν ES( x) show a kink. A first-order transition from an unstressed rigid to a stressed rigid phase occurs near x c(2)=0.26(1), where ν CS 2( x) displays a step-like discontinuity between x=0.25 and 0.26 and a power-law behavior at x> x c (2). In sharp contrast, earlier micro-Raman measurements that use at least three orders of magnitude larger photon flux to excite the scattering, showed only one rigidity transition near x c=0.23, the mid-point of the intermediate phase ( x c(1)< x< x c(2)). Taken together, these results suggest that the intermediate phase, observed in the low-intensity Raman measurements, undergoes a light-induced melting to a random network in the micro-Raman measurements.

Rigidity transitions and molecular structure ofAsxSe1−xglasses

T-modulated differential scanning calorimetry measurements on bulk ${\mathrm{As}}_{x}{\mathrm{Se}}_{1\ensuremath{-}x}$ glasses show that the glass transition temperature ${T}_{g}(x)$ variation at $x&lt;0.12$ is linear with a slope ${\mathrm{dT}}_{g}/dx=4.1\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}/\mathrm{at}.%\mathrm{As},$ and the nonreversing heat flow, $\ensuremath{\Delta}{H}_{\mathrm{nr}}(x)$ almost vanishes in the 0.291(1)x0.37(1) composition range. These thermal results analyzed by agglomeration theory and constraint theory suggest that in addition to $\mathrm{As}({\mathrm{Se}}_{1/2}{)}_{3}$ units, quasitetrahedral ${\mathrm{S}\mathrm{e}=\mathrm{A}\mathrm{s}(\mathrm{S}\mathrm{e}}_{1/2}{)}_{3}$ units also serve to crosslink ${\mathrm{Se}}_{q}$ chains at $x\frac{2}{5}.$ The results also suggest that rigidity onsets at ${r}_{c}(1)=2.29(1)$ and the transition to the stressed rigid phase occurs at ${r}_{c}(2)=2.37(1),$ below the chemical threshold at ${r}_{\mathrm{ct}}=2.40$ (or $x=\frac{2}{5}).$