The starting materials for the synthesis included small pieces (~ 3 mm in diameter) of 99.999% pure Se nodules from Alfa Aesar, 99.999% pure Ge lumps from Alfa Aesar and stoichiometric As₂Se₃ from Noah Technologies. We handled these materials in a model HE-493/MO-5 Glove box from Vacuum Atmospheres, which is designed to be flushed with dry N₂ gas continuously and with a relative humidity of <0.01%. We sealed small pieces of the starting materials of about 3 mm in size or less, in the desired weight ratio, in evacuated quartz tubes of 5 mm ID and 1 mm wall thickness. Prior to their use, we dried quartz tubes in a vacuum oven at 80°C for at least 24 h. Batch size were kept at 1.5 g, and the starting materials encapsulated in evacuated quartz tubes at a pressure of 2 × 10⁻⁷ Torr using a liquid Nitrogen trapped diffusion pump system. We heated quartz tubes to 950°C for typically 10 days, keeping them vertical in a box furnace. Water impurity doping of chalcogenide glasses, unwittingly assists homogenization of melts, increases the enthalpy of relaxation of glasses, decreases T_g, and increases the fragility index of melts (Bhosle et al., 2012a,b). These extrinsic features are not representative of the dry melts/glasses.

A Thermo-Nicolet Nexus 870 based FT-Raman system, using 1,064 nm radiation from a Nd-YAG laser, focused to a 50 μm spot size (micro-setting), was used to excite the scattering. The collection optics also has provision for a macro-setting with a laser spot size of 1 mm. Glass specimen wetting 5 mm ID evacuated quartz tubes were mounted on a digitally controlled x-y-z stage to focus the laser beam entering along the quartz tube diameter (x-axis adjustment) and onto the quartz tube glass specimen interface (z-axis adjustment) to optimize the signal. The y-axis adjustment of the sample stage permitted to access specific locations along the glass column for recording Raman scattering. Spectra were acquired at typically six locations about 2 mm apart along the glass specimen column of typically 20 mm in length (y-axis adjustment). The software permits comparing observed lineshapes normalized to the highest scattering strength mode, and that facilitated directly variations in glass specimen stoichiometry by comparing the scattering strength of the corner sharing (CS) of GeSe₄ tetrahedra (near 200 cm⁻¹) with the broad band of a triad of modes (Dash et al., 2017) associated with Se_n chains-uncorrelated, Se_n chain-correlated, and Se₈ rings (near 250 cm⁻¹). Periodically, quartz tubes were water quenched after lowering their T to 650°C and Raman spectra taken at 6 locations along the 20 mm long melt column. By using a laser beam spot size of 50 μm or less, one probes glass homogeneity to a finer scale, which is essential to get a true representation of glass/melt homogeneity. It is important to emphasize that in these homogeneity studies the full batch composition was profiled. This of course is necessary since the stoichiometry of a small part of the batch is tied to the stoichiometry of the rest of the batch (Gunasekera et al., 2013). Figure 1 shows a partial summary of the observed spectra; and one finds how the starting melt, which is rich in Ge(Se) atoms at the bottom(top) of the vertical melt column, steadily homogenizes as Ge atoms diffuse up while Se atoms diffuse down the melt column. After 2 days of alloying the variance in Ge stoichiometry, <Δ×>_Ge is found to be about 1.04%, but it systematically decreased by almost three orders of magnitude to nearly 0.01 % or lower after 10.5 days of alloying (Figure 2). In these profiling experiments, one could successfully decode the heterogeneity of the batch to a level of 0.01% range in the variance of Ge by merely sampling only a tiny volume fraction of 2% of the batch column. The existence of a gravitationally induced segregation that sets up in the melt column at the beginning of the alloying process as quartz tubes are held vertical, aids in tracking how Ge- and Se-atoms, respectively, diffuse the melt column (Gunasekera et al., 2013) to homogenize with no rocking. Had we rocked the melt column it would have been difficult to detect the isolated super-strong melt inclusions spread across the melt column unless one probed more like 10–30% or more of the batch volume, which surely would have been an enormous task in itself.

There are other aspects of the homogenization studies that we mention in passing. The scale on which a batch is examined in the Raman profiling experiments matters because TPs are determined by atomic scale network connectivity or mean coordination number <r>, fixed by the local Ge, As, and Se stoichiometry. Furthermore, the scale on which a batch is examined in the Raman profiling experiments matters. A sample may be homogeneous after 2 days of alloying on a spatial scale of 1 mm (laser spot size) but not on a finer scale of 50 μm (laser spot size) as we have noted (Bhosle et al., 2012a). Finally, melt homogenization kinetics are broadly determined by the slowest diffusing species or the species with the highest viscosity, which occurs in the IP. Most compositions in the Ge_xAs_xSe_100−2x ternary, at x > 5%, take typically 7–11 days to homogenize in our chosen geometry. The IP compositions such as x = 10 and 13.3% take a few days longer to homogenize than non-IP ones. The fragility index of IP melts apparently controls the kinetics of melt homogenization, as we will comment later in discussion of results. In very select cases where a stoichiometric glass is being synthesized at a composition where there exists a distinct well-defined underlying simple crystalline phase, delayed homogenization could be circumvented. In the present ternary, we are unaware of any crystalline phase or phases that occur and that may expedite the homogenization process.

Finally, in our present efforts we aimed to synthesize the most homogeneous melts to explore the physics of TPs in network glasses. Once these fundamental issues are understood, new strategies can be implemented to reduce the alloying time of glass synthesis by at least an order of magnitude to achieve homogeneous melts/glasses.

Modulated Differential Scanning Calorimetry (MDSC) has proven to be a reliable (Thomas, 2005; Bhosle et al., 2012b) and rather direct means to independently establish the glass transition temperature T_g, and the modulation frequency corrected enthalpy of relaxation of a glass at T_g (ΔH_nr) with minimal scanning-rate-related kinetic upshifts. The procedure for obtaining the frequency corrected enthalpy of relaxation was developed as early as in 1995 by Len Thomas (Thomas, 2005), and more recently confirmed in numerical simulations (Guo et al., 2012). The measured ΔH_nr term is a pivotal calorimetric observable of a glass, that characterizes not merely its non-ergodic state but is crucially linked to the flexibility and rigidity of networks (Micoulaut, 2010) provided these are dry and homogenous. Furthermore, MDSC also permits measuring the fragility index “m,” of a melt. We illustrate the principles of both these methods by showing results of ternary Ge_xAs_xSe_100−2x glasses at select compositions. We used a Q2000 TA Instruments MDSC with glass samples in hermetically sealed T_zero Al pans (Thomas, 2005) to achieve the best baselines in the calorimetric scans.

A Thermo-Nicolet FTIR Nexus 870 research bench with a Raman module was used to record Raman scattering from the bulk glasses encapsulated in evacuated quartz tubes. The bulk glass specimen was positioned on an xyz stage of the instrument and the scattering was excited using the 1,064 nm radiation from a Nd-YAG laser tightly focused to a 50 μm spot size. In a typical run 126 mW of laser power was used, the radiation focused at the quartz/ bulk glass interface and an acquisition of 100 cycles took 7 min of acquisition time. In section Quantitative Mapping of melt homogeneity by FT Raman Profiling below, we provide details of the quantitative mapping of glass/melt homogeneity from these Raman scattering data that profiled the bulk glass.

Densities of our glass samples were determined by using Archimedes principle with 200 proof alcohol being the immersion fluid. We established the density of alcohol by using a Si crystal wafer of a known density (ρ_si = 2.323 g/cm³). We mounted the Si crystal on a quartz fiber that was suspended from a Mettler-Toledo model B154 digital microbalance, with a resolution of 0.1 mg, and weighed it in air. The quartz fiber is then submerged into the fluid and the balance tared to negate the buoyant force on the fiber. The Si crystal was then placed on the quartz fiber hook and submerged into the fluid and the weight of the Si crystal in alcohol recorded. Having the weight of the Si crystal in air and in alcohol then enabled one to calculate the density of the alcohol.

To establish the accuracy and reproducibility of our method, the density of a Ge single crystal was independently measured, and a value of 5.324(6) g/cm³ was found, which is comparable to the published standard value of 5.323 g/cm³.

We emphasize that the glass samples used in density experiments are to be no <100 mg in weight. This allows the density to be measured to an accuracy of 0.25% or less. Each sample's density measurement was repeated 5 times.

We provide, as an example, the calculations used to establish the density of the alcohol, ρ_alc, and the density of a Ge_xAs_xSe_100−2x glass specimen at x = 14%, ρ_sample.

Weight of Silicon in air (w_air): 104.8 mg; Weight of Silicon in alcohol (w_alc): 69.3 mg; Density of Silicon (ρ_si) = 2.323 g/cm³

Weight of sample in air (w_air): 127.2 mg; Weight of sample in alcohol (w_alc): 104.7 mg; Density of alcohol (ρ_alcohol): 0.786 g/cm³

The molar volumes of the bulk glass were then deduced from the mass density.

Molar mass of sample: 77.52 g/mol, Density of sample: 4.45 g/cm³.

Trends in molar volumes of the ternary glasses are summarized in the next section.

We performed a series of First principles molecular dynamics simulations (Car and Parrinello, 1985), using the canonical (NVT) ensemble, for the computation of the mean square displacement and the diffusion constant, on the same Ge_xAs_xSe_100−2x systems containing N = 249 atoms at 11 different compositions (2, 4, 5, 8, 9, 10, 15, 17, 18, 19, 21%) with the number of As, Ge and Se atoms fulfilling the desired stoichiometry. A periodically repeated cubic cell was used, whose size changes according to the number density of the glasses (see section Molar Volumes). For the simulation of the present liquids, we used density functional theory (DFT) in combination with plane wave basis sets. The electronic scheme has been chosen after a series of methodological investigations on different liquid chalcogenide glasses and liquids (Micoulaut et al., 2009; Massobrio et al., 2010; Bouzid et al., 2015). These showed that a generalized gradient approximation (GGA) for the exchange correlation energy improves substantially the description of both short and intermediate-range order as compared to the local density approximation (LDA) (Massobrio et al., 1999). In addition, it was demonstrated that the exchange-correlation functional reducing the metallic character of the bonding (a Becke, Lee, Yang and Parr (BLYP) functional) led to systems with a reduced number of miscoordinated atoms and metallic character (Micoulaut et al., 2009), and improved the reproduction of structure functions obtained from neutron diffusion in the liquid and amorphous state (Bauchy et al., 2013; Micoulaut et al., 2013; Yildirim et al., 2016b).

Using these recipes, the electronic structure of the As-Ge-Se liquids was described within DFT and evolved self-consistently during the motion using a GGA for the exchange and correlation parts of the total energy, according to Becke (B) and LYP, respectively (Becke, 1988; Lee et al., 1988). Valence electrons were treated explicitly, in conjunction with norm-conserving pseudopotentials to account for core-valence interactions. The wave functions were expanded at the γ-point of the supercell and the energy cutoff was set at 20 Ry. Starting configurations were taken from binary Ge-Se liquids (Yildirim et al., 2016b) and As atoms were appropriately inserted in order to meet the desired stoichiometry. Loss of the memory of the initial configurations has been achieved through preliminary runs at 2,000 K over 50 ps. For all investigated compositions and temperatures (1,500 and 1,200 K), statistical averages in the liquid state were obtained over 20–25 ps of trajectory with a time step of Δt = 0.12 fs and a fictitious mass of 1,000 a.u.

The calorimetric results on homogeneous Ge_xAs_xSe_100−2x glasses show that T_g(x) increases monotonically with x over a wide range 0 < x < 25% of compositions (Figure 5A). These results show that Ge- and As- atoms serve to cross-link (Micoulaut and Naumis, 1999) polymeric Se_n chains as GeSe₂ tetrahedra both CS and Edge-Sharing (ES), and AsSe(_1/2)₃ pyramids form in the chemical composition range 8% <×< x_c = 18.2%. At x > x_c homopolar Ge-Ge and As-As bonds must form part of the same backbone as the one prevailing at x < x_c, for T_g(x) to continue to increase at x > x_c.

The variation of the non-reversing enthalpy of relaxation at T_g (ΔH_nr), in the glasses shows a sharply defined square-well like minimum (Figure 5B), and it is highlighted by the light blue panel, i.e., the thermally reversing window. The vanishing of the frequency corrected enthalpy of relaxation at T_g, ΔH_nr, in the 9.5% < x < 17.0. % range constitutes evidence that it represents the region of phase space (Micoulaut, 2010; Bauchy and Micoulaut, 2015; Mantisi et al., 2015) where glass transitions become thermally-reversing in character. The ΔH_nr is minuscule in the IP, which is a clear evidence that the samples are dry and do not contain water impurities (Vaills et al., 2005). The dynamic reversibility of glass transitions corresponds to the overshoot in the endotherm vanishing, and is identified with the formation of isostatically-rigid local structures (Bauchy and Micoulaut, 2015), with the count of bonding constraints per atom, n_c = 3, and satisfy the Maxwell-Phillips rigidity criteria (Maxwell, 1864; Phillips, 1979). Such networks are rigid but unstressed and possess a liquid-like entropy.

The variation of the melt fragility index, m(x), displaying a Gaussian like minimum (Figure 5C) with m < 20 for IP compositions, and serves to define a fragility window or, at least, a fragility minimum, in which melts are viewed to be super-strong, in the strong-fragile classification (Angell, 1995) of melts. Note that the dashed line drawn in Figure 5C marks the fragility index of SiO₂ glass taken as m = 20, and it divides the m(x) plot into three regions; (i) a low x region (x < 9.5%) and (ii) a high x region (x > 17%) and (iii) an intermediate x -region. Note that fragility window coincides with the reversibility window in x-space and the three regions mentioned above represent, respectively, the flexible phase (x < 9.5%), stressed-rigid phase (x > 17.0%), and the intermediate phase (9.5% < x < 17.0%).

Intermediate phase melts, with m< 20, are quite special; these are super-strong and their viscosity at 950°C where we alloyed the starting materials are significantly greater than those of their non-IP composition counterparts. Finally, the close correlation in composition between melt- and glass- properties leads to the central finding of this work, viz, that melt fragility index encode glass TPs. Parallel findings have recently been noted in binary Ge-Se (or S) (Bhosle et al., 2012a,b; Gunasekera et al., 2013; Chakraborty and Boolchand, 2014) glasses and are suggestive that the melt-glass correlation could well be a general feature of glass science.

The variation in molar volumes of the present ternary glasses as a function of composition is plotted in Figure 5D. The average behavior shows V_m to decrease from 18.5 to 17.5 cm³/mol, reflecting the increased cross-linking of the networks. The plot also shows an additional reduction of V_m in the reversibility window shown by the hashed mark region. These data show that glass compositions are compacted (Boolchand et al., 2013), a feature observed in the IP of other glasses as well (Bhosle et al., 2012a,b; Chakraborty and Boolchand, 2014). The network compaction is broadly viewed as the consequence of the stress-free nature of the glass backbone where the effect of longer range forces such as van der Waals and Coulombic come into play, largely because the strong short-range covalent forces are balanced by the 3D network dimensionality. The average reduction in V_m(x), with increasing x, is a consequence of the increased mean coordination number, <r> = 2 + 3x, that increases linearly with x leading to space filling, i.e., more atoms being packed per unit volume. Here the mean coordination number follows if one assumes that Ge, As, and Se atoms are, respectively, 4, 3-, and 2-fold coordinated conforming to the 8-N bonding rule.

Raman scattering has been particularly useful in elucidating the glass structure evolution of the present chalcogenides. The observed Raman line shapes as a function of increasing As and Ge alloying content “x” are displayed in Figure 7. We are greatly assisted in mode assignments because of the availability (Jackson and Pederson, 1990; Pederson and Jackson, 1990, 1991; Quong et al., 1993; Porezag and Pederson, 1996; Porezag, 1997; Briley and Pederson, 1998; Jackson et al., 1999) of the expected normal mode frequencies of the various As-centered and Ge-Centered local structures from NRLMOL cluster calculations (Table 1). Furthermore, Raman scattering in the Ge-Se binary glasses, intensely investigated in previous work (Bhosle et al., 2011, 2012a), have confirmed the Ge-centered local structure mode frequencies. The case of the As-Se binary glasses has also been investigated (Chen et al., 2010; Ravindren et al., 2014), although some ambiguities in mode assignments have persisted, issues that we will address here.

At low x (< 5%), the spectra are dominated by the broad band near 250 cm⁻¹ coming from polymeric Se_n chains and some contribution from Se₈ rings and compacted Se_n chains. These display a triad of modes (234, 259, and 260 cm⁻¹) as shown in Table 1 and have been confirmed in experiments on very dilute Ge doped Se glasses (Yannopoulos and Andrikopoulos, 2004; Dash et al., 2017). Detailed results in binary Ge_xSe_100−x glasses (Bhosle et al., 2012a) reveal that the vibrational modes near 197 cm⁻¹ comes from Corner-sharing and the one near 217 cm⁻¹ from edge sharing GeSe₂ tetrahedra. With increasing x, and particularly near x = 15% the square shaped band in the 225–275 cm⁻¹ range has contributions from modes of As-centered pyramidal (235 cm⁻¹, 265 cm⁻¹) and quasi-tetrahedral (198, 271 cm⁻¹) units.

Perhaps the most striking result to emerge from these spectra on homogeneous glasses in the present work is the mode near 350 cm⁻¹ (shown in the inset of Figure 8) that steadily increases with x. Although the increase is slight in QT₁, by comparing it to its bond bending vibrational mode, QT₂, there is undoubtedly an increase in the concentration of the quasi-tetrahedra with increasing x. In a previous study (Qu et al., 2002; Qu, 2004), this particular mode was not observed in glasses probably because these were not especially homogenized. This particular mode is predicted near 364 cm⁻¹ (Table 1) and involves stretch of the double bonded Se = As(Se_1/2)₃ in a quasi-tetrahedral local structure. With increasing x, the QT mode near 350 cm⁻¹ sits at the edge of the more strongly excited mode of Ge ES units near 320 cm⁻¹ and is thus eventually masked in the inset of Figure 8.

The strongest QT mode occurs at 198 cm⁻¹ and it overlaps with the mode of CS tetrahedral units, making a quantitative determination of the QT local structures at best difficult.

In the present contribution, we also focus on the dynamics of the obtained simulations. Structural properties will be considered and discussed elsewhere. The calculation of the mean-square displacement (msd) <r²(t)> of the three tagged atoms (As, Ge, Se) leads to a usual profile in a log-log plot representing <r²(t)> with time, i.e., a ballistic regime at short time where the behavior scales as t² and a diffusive regime that sets in for most compositions (1,500 K) at around 1–5 ps. Note that, because of the chosen high temperatures considered herein, no cage-like motion is obtained. The diffusion constant D_i (i = As, Ge, Se) can be obtained using the Einstein relation limit:

and both D_Se and D_As are plotted as a function of content for the isotherms 1,500 and 1,200 K (Figure 9). Experimental diffusivity values for such system are unavailable but one can check that the values of D_i are globally compatible with similar systems. For instance, it has been found (Yildirim et al., 2016a) that Ge diffusion is of about 5.10⁻⁵ cm².s⁻¹ in Ge₂₀Se₈₀ liquids at 1,373 K, i.e., rather close to the value obtained for a similar Se content in the present case (6.4.10⁻⁵ cm².s⁻¹ for Ge₁₀As₁₀Se₈₀ at 1,500 K). Such values have been found to be compatible with viscosity results (Stølen et al., 2002; Gueguen et al., 2011) at high temperature once a Stokes-Einstein equation is used to estimate the viscosity (Sipp and Richet, 2002).

An inspection of the behavior with composition clearly indicates that the diffusivity results contain features of the underlying TPs. D_i is very small for highly cross-linked melts (x > 17%, e.g., D_Se = 2.5 10⁻⁵ cm².s⁻¹ for x = 21% and 1,500 K), increases slightly in the IP, and then becomes very large (about 10 times larger at x = 4%), with the substantial increase of D manifesting in the flexible phase. In contrast to the Ge-Se, wherein IP melts were found to display a minimum in diffusivity (Yildirim et al., 2016b), in the present Ge-As-Se, melts in the IP (9–17%) remain nearly constant in diffusivity. However, it should be noted that, for such elevated temperatures, extrema can be barely visible, as noted earlier for high temperature Ge-Se liquids (Yildirim et al., 2016a).

The nature of the dynamics is also very strongly dependent on composition and the distance of motion for the atoms (e.g., Se atoms in the inset of Figure 9) increases substantially in liquids that are flexible. For stressed-rigid phase compositions, the msd is rather small, e.g., <r²(t)>=19Ų for x = 21% at 1,200 K, corresponding to a distance of several interatomic distances only (4.5 Å) and larger distances can hardly be explored due to the large cross-link density. As the Se content increases, IP compositions seem to lead to a slight increase <r²(t)>, barely visible from the figure. The most noticeable change is obtained at the intermediate to flexible boundary and at both investigated temperatures, <r²(t)> starts to dramatically increase at 8–9% to reach nearly 200 Ų for x = 2%.

Three decades ago, ternary Ge_xAs_xSe_100−2x melts were investigated in terms of viscosity (Tatsumisago et al., 1990) and flexure measurements (Böhmer and Angell, 1992). Both sets of experiments made use of the same stock of glasses. These were synthesized by alloying the pure elements in evacuated quartz tubes at a T range in the 600–1,150°C range for 24 h. The fragility index results as a function of glass composition from both sets of experiments (Böhmer and Angell, 1992) yielded remarkably similar results (Figure 11). And, for ease of comparison, we have included the present results (Figure 5C) in Figure 11 as well. It is comforting to see that in all three data sets, fragility index of melts within a narrow range of compositions near x = 13.3% or <r>= 2.40 display a strong character, while those at x < 9.5% and x > 17% become increasingly fragile.

On the other hand, the actual values of the fragility index, m, reported in the viscosity and flexure measurements are significantly greater from those measured in the present MDSC work. The difference is as large as 60 units in m near pure Se to about 30 units near <r> = 2.40 or x = 13.3 mole% and about eight units in m near the composition x = 20 in the stressed-rigid phase. We have also measured the fragility index of the present Ge-As-Se glasses using the Moynihan approach (Moynihan et al., 1974). If the Tg's in the DSC measurement are established from the inflection point of the heat flow, trends in m(x) (Figure 11) are quite similar to those found using MDSC (Figure 5C). In particular in the IP range m approach a value close to 20.

We can think of two possible factors contributing to this large disparity in melt fragility index on the same glass ternary system. The first factor could be the role of the experimental method. In viscosity and flexure, one probes the shear stress relaxation time, while in the calorimetric measurement the enthalpy relaxation time—and it has been suggested that different properties of glasses and melts may exhibit distinct relaxation times (Potuzak et al., 2011; Yu et al., 2015, 2017). On the other hand what is of relevance here is the variation in the T dependence of the relaxation time, and not the relaxation time magnitude itself. For example, fragility index of melts measured by Dielectric spectroscopy (Carpentier et al., 2003), Dynamic Light scattering (Fabian and Sidebottom, 2009), and MDSC (Mohanty et al., 2019), involve measuring different kinds of relaxation times, but when these are plotted against inverse Temperature close to T_g, yield nearly the same slope, i.e., fragility index. The second factor could be the sample make up. For small (1.5-g) batch sizes, as shown in Figures 1, 2, we noted at least 1.5 mole% spread in Ge stoichiometry near x = 9% for melts alloyed for 24 h at 950°C. In the viscosity (Tatsumisago et al., 1990) and flexure (Böhmer and Angell, 1992) measurements, which require much larger samples than the ones synthesized presently, the synthesis of homogeneous bulk glasses is unlikely to be achieved with the alloying treatment described (Tatsumisago et al., 1990; Böhmer and Angell, 1992). Melt heterogeneity would invariably lead to increased fragility index as noted in recent work as well (Ravindren et al., 2014). The large differences in the magnitude of m between the present work and these earlier reports at the same composition, x, probably result from glass sample make up. Heterogeneity of melts would invariably lead the fragile component to rapidly diffuse through a melt leaving the least mobile super-strong component to be largely localized in small pockets. The delayed homogenization of chalcogenide melts, such as those reported here in the present ternary, may well be a generic factor contributing to the large spread in fragility index at the same melt/glass composition.

The challenges in the synthesis of homogeneous chalcogenide glasses came to the fore when FT-Raman profiling measurements (Bhosle et al., 2012a,b) were first brought to bear on understanding how melt/glass batches actually homogenize in real time upon alloying of the starting materials. The delayed nature of the homogenization over 7–10 days of alloying rather than 1 or 2 days was subsequently found to be a fairly pervasive feature of all chalcogenides examined since. And it was traced to the super-strong nature of melts in the IP with fragility index m < 20 that slow down the diffusive mixing of the batch composition (Gunasekera et al., 2013). In 2003, we had synthesized Ge_xAs_xSe_100−2x glasses by alloying the starting materials at 960°C for 48 h, which we now recognize only lead to partially homogeneous glasses- i.e., the variance, <Δ×>, of Ge stoichiometry across the 1.5 g batches are estimated near 1.5 mole% from the results of Figure 2. The reversibility window in these glasses displayed edges that were smeared when examined after 1 month of aging (Qu, 2004) for that reason. But upon long term aging (6 months, 3 years) at room temperature the reversibility window evolved and showed that, for glasses at x < 10%, the ΔH_nr(x) term increased and the reversibility window edge near x = 10% sharpened up (Figure 10A).The aging induced increase of ΔH_nr(x) at x > 17% was much less pronounced, understandably so because the T_g values of these stressed-rigid glasses are measurably greater than those of the flexible ones at x < 10% (Figure 5A), leading to substantially reduced kinetics of aging as determined by the T/T_g ratio. In spite of that limitation, one finds that both the rigidity- and stress- transitions became better defined upon aging, to closely approach the transitions observed in the especially homogenized glasses.

The aging behavior of the homogeneous glasses examined in the present work stands in sharp contrast to the findings on the partially homogenized glasses studied earlier. We could clearly observe sharp rigid- and stress- elastic phase transitions in the fresh rejuvenated glasses (Figure 5B). It helps one understand how homogeneity of melts/glasses is intimately tied to the observation of the IP in these glasses. Melt/glass homogenization is precursive to observation of a sharp square-well like reversibility window permitting one to fix the three TPs (Boolchand et al., 2018).

MDSC experiments also show that the non-ergodic enthalpy of relaxation ΔH_nr(x), builds up significantly upon aging of non-IP glass compositions to about 2.0 cal/g after 3 years of room temperature aging (Qu, 2004) (Figure 10A). Thus, in fully relaxed glasses the underlying configurational entropy change associated with T_g, ΔS_conf exceeds 0.08 cal/g/°C. In the estimate, we take the width of T_g to be 25°C. Finally, the heat capacity change at T_g, ΔC_p(x) associated with the reversing heat flow of 0.015 cal/g/°C, suggests that the underlying change in vibrational entropy, ΔS_vib, is nearly half that of ΔC_p(x), a value of 0.008 cal/g/°C. Thus ΔS_conf (= 80 mcal/g/°C) is an order of magnitude greater than ΔS_vib (= 8 mcal/g/°C). A correlation of strong (fragile)- melts with a small (large) magnitude of ΔC_p across T_g has been suggested (Angell, 2000). That correlation is also observed in the present findings (Figure 10B). But the present results also show a far more striking correlation of melt fragility with the enthalpy of relaxation, ΔH_nr(x) of the glass.

We note that ΔH_nr(x) is vanishingly small in glasses resulting from superstrong melts, but it increases by several orders of magnitude in glasses that result from fragile melts. The ΔH_nr(x) term results from the non-reversing heat flow and it contributes an entropy change (ΔS_conf) that is configurational, which far exceeds ΔS_vib resulting from the jump in C_p across T_g, ΔC_p, which comes from the reversing heat flow. We view the presence of the rather high value of ΔS_conf term in the IP to suggest that the configurational entropy of IP melts decreases minimally (ΔH_nr(x) = 0) for IP glasses, underscoring that networks characterizing the IP have a rather high entropy, i.e., a liquid-like entropy. On the other hand, the much higher value of ΔH_nr(x) in the relaxed non-IP glass compositions constitutes a signature that their phases have undergone substantial reconstruction upon aging and possess a lower configurational entropy than their high-T melt counterparts (Figure 5C).

In the Flexible phase (x < 10%), the large increase in ΔH_nr upon aging (Figure 5B), and in the projected melt configurational entropy S_c (Figure 5C), we trace to the polymeric Se_n chains. As x decreases in the 0% < x < 10% range, the Se_n chains grow in length with n ~ 250 in pure Se. The uncorrelated Se_n chains characteristic of the fresh glass, particularly if they are long (n > 15) will reconstruct with each other and get correlated (Dash et al., 2017), while some of the long chains will transform to Se₈ rings, as documented (Dash et al., 2017) in the Se-rich (x < 8%) phase of binary Ge_xSe_100−x glasses from Raman scattering. Specifically, the broad band near 250 cm⁻¹ in Raman scattering of these Se-rich glasses is composed of a triad of modes identified respectively with (i) correlated Se_n chains, (ii) uncorrelated Se_n chains and (iii) Se₈ rings, and aging induced changes in the scattering strength of these modes have assisted in identifying the microscopic origin of aging (Dash et al., 2017) and would understandably apply to the flexible phase of the present ternary as well.

In the Stressed-rigid phase of the present ternary glasses (x > 17.0%), the glass backbone is composed of high mean coordination number <r> local structures. These include CS- (2.40) and ES- GeSe₂ (2.67) tetrahedra and Pyramidal As(Se_1/2)₃ (2.40). The backbone compacts as revealed by the steadily decreasing Molar volumes (Figure 5D). And aging will further lead to a compaction of the network resulting in the configurational entropy to decrease or ΔH_nr to increase (Figure 5B). On the other hand, in the IP, quite remarkably, the presence of an isostatically rigid and stress-free backbone, endows glasses with a new functionality to adapt and self-organize. And aging is qualitatively suppressed in this phase.

One of the more challenging issues in glass science is to predict the compositional windows across which networks can self-organize to display IPs and the underlying molecular structure manifestations. Some important clues on the microscopic origin of self-organization effects can be sought by examining the molecular structure of glasses. The IPs in the Ge-Se and As-Se binary systems, and the present Ge_xAs_xSe_100−2x ternary are established. It is useful to inquire if these windows display any correlations, and, if so, what one might learn on the molecular structure of the IP from such correlations. We comment on some of these issues next.

Adam-Gibbs (Adam and Gibbs, 1965) suggested that the viscosity of a melt increases as its excess configurational entropy (S_c) decreases as it is cooled to T_g described by the relation,

Since the viscosity of a melt is viewed to be a thermally-activated process,

and from the two relations above, one must then require that the inverse of the activation energy for shear relaxation time provides a measure of the excess entropy loss (S_c) upon cooling of a melt,

From Equation (9), one recognizes that the inverse of the activation energy for shear relaxation time provides a measure of the excess configurational entropy of the melt as it cools.

Since the fragility index deduced from calorimetric measurements are often correlated with those inferred from viscosity or shear relaxation times, one then expects the inverse activation energy, 1/E_a, from calorimetric measurements to provide a measure of configurational entropy loss as a melt is cooled.

The inverse activation energy for enthalpy relaxation (1/E_a) in the present Ge-As-Se chalcogenide melts as a function of composition, Figure 5C, displays a maximum near the center of the IP. The result unambiguously shows that as an IP melt cools from a high T to T = T_g, the configurational entropy S_c remains high, and indeed, that is also the reason the resulting glass has a near vanishing non-reversing enthalpy, ΔH_nr(x). Such glass compositions are viewed as possessing liquid-like structures with a high S_c and for that reason show minimal aging (Boolchand and Goodman, 2017). The low propensity for aging of isostatic glasses also echoes the fact that isostatic systems have been shown to exhibit minimum creep deformations under sustained load (Pignatelli et al., 2016; Bauchy et al., 2017). On the other hand, the non-IP glass compositions have their structure evolve with either polymeric Se_n chains (as in t-Se, entropy sinks) forming at x < 9.5% or CS and ES- GeSe₂ tetrahedra and pyramidal As(Se_1/2)₃ units forming at x > 17%, and leading the ΔH_nr(x) term to increase, and thus lower the configurational entropy of the melt/glass (Figures 5B,C). IP glass compositions display a high glass-forming tendency, show minimal aging, and are thus Ideal glasses. These ideas of IP glasses as ideal glasses are at variance with the notion that ideal network glasses possess low configurational entropy and form at T close to the Kauzmann temperature (Angell, 1995). On the other hand, the high configurational entropy of IP glass compositions and their functionality to adapt are much closer to the recent ideas of a competition between entropy and energy to stabilize the intermediate phase (Yan, 2018).

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.