Self-organized criticality in the intermediate phase of rigidity percolation

Experimental results for covalent glasses have highlighted the existence of a new 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 non-percolating 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.Comment: 20 pages, 18 figure

The Thermally Reversing Window in Ternary GexPxS1-2x glasses

GexPxS1-2x glasses in the compositional range 0.05 < x < 0.19 have been synthesized and examined in temperature modulated differential scanning calorimetry (MDSC) and Raman scattering experiments. Trends in the non-reversing enthalpy DHnr(x) near Tg show the term to almost vanish in the 0.090(5) < x < 0.135(5) range, and to increase by an order of magnitude at x < 0.09, and at x > 0.135. In analogy to previous results on chalcogenide glasses, we identify compositions at x < 0.09 to be elastically floppy, those in the 0.090 0.135 to be stressed rigid. MDSC results also show the DHnr term ages in the stressed-rigid and floppy phases but not in the intermediate phase. The intermediate phase is viewed to be a self-organized phase of a disordered network. It consists of at least four isostatically rigid local structures; corner-sharing GeS4, edge-sharing GeS2, pyramidal P(S1/2)3 and quasi-tetrahedral S=P(S1/2)3 units for which evidence comes from Raman scattering. The latter method also shows existence of P4S7 and P4S10 molecules in the glasses segregated from the backbone. These aspects of structure contribute to an intermediate phase that is significantly narrower in width than in corresponding selenide glasses.Comment: 1 PDF file has text, 9 figures and 3 table

Long term aging of Selenide glasses: Evidence of sub-Tg endotherms and pre-Tg exotherms

Long term aging is studied on several families of chalcogenide glasses including the Ge-Se, As-Se, Ge-P-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 below Tg in glassy networks possessing a mean coordination number r in the 2.25 < r < 2.45 range. Two sets of AsxSe1-x samples aged for 8 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-Tg 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 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., which finds the onset of the reversibility window moved up to the stoichiometric composition (x = 40%). Here we show that the upshifted 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 networks upon long term aging, while the pre-Tg exotherm to NSPS. Finally, 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.Comment: In press - J. of Physics: Condensed Matte

Intermediate phase, network demixing, boson and floppy modes, and compositional trends in glass transition temperatures of binary AsxS1-x system

The structure of binary As_xS_{1-x} glasses is elucidated using modulated-DSC, Raman scattering, IR reflectance and molar volume experiments over a wide range (8%<x<41%) of compositions. We observe a reversibility window in the calorimetric experiments, which permits fixing the three elastic phases; flexible at x<22.5%, intermediate phase (IP) in the 22.5%<x<29.5% range, and stressed-rigid at x>29.5%. Raman scattering supported by first principles cluster calculations reveal existence of both pyramidal (PYR, As(S1/2)3) and quasi-tetrahedral(QT, S=As(S1/2)3) local structures. The QT unit concentrations show a global maximum in the IP, while the concentration of PYR units becomes comparable to those of QT units in the phase, suggesting that both these local structures contribute to the width of the IP. The IP centroid in the sulfides is significantly shifted to lower As content x than in corresponding selenides, a feature identified with excess chalcogen partially segregating from the backbone in the sulfides, but forming part of the backbone in selenides. These ideas are corroborated by the proportionately larger free volumes of sulfides than selenides, and the absence of chemical bond strength scaling of Tgs between As-sulfides and As-selenides. Low-frequency Raman modes increase in scattering strength linearly as As content x of glasses decreases from x = 20% to 8%, with a slope that is close to the floppy mode fraction in flexible glasses predicted by rigidity theory. These results show that floppy modes contribute to the excess vibrations observed at low frequency. In the intermediate and stressed rigid elastic phases low-frequency Raman modes persist and are identified as boson modes. Some consequences of the present findings on the optoelectronic properties of these glasses is commented upon.Comment: Accepted for PR

Origin of giant photocontraction in obliquely deposited amorphous Ge_xSe_{1-x} thin- films and the intermediate phase

Obliquely deposited amorphous Ge_xSe{1-x} thin-films at several compositions in the 0.15 < x < 0.333 range, and at several obliqueness angles in the 0 < alpha < 80 range at each x were evaporated on Si and glass substrates. Here alpha 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 SEM confirm the columnar structure of obliquely (alpha = 80) deposited films. Films, mounted in a cold stage flushed with N2 gas, were irradiated to UV radiation from a Hg-Xe arc lamp, an

Abrupt boundaries of intermediate phases and space filling in oxide glasses

Modulated DSC measurements on bulk (Na2O)x(GeO2)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 TO and LO mode frequencies exhibit anomalies between xc(1) = 14% (stress transition) and xc(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

Evidence of an intermediate phase in ternary Ge 7Se 93-x Sb x glasses

61.43.Fs Glasses, 65.60.+a Thermal properties of amorphous solids and glasses: heat capacity, thermal expansion, etc.,