Elemental Ge (99.999%, Alpha Aesar) and Se powders (99.999+%, Sigma-Aldrich), with the desired mass ratio, were loaded into a silica ampoule of 5 mm inner diameter and 1 mm wall thickness that had been etched using a 48 wt% solution of hydrofluoric acid, rinsed using water then acetone, and baked dry under vacuum at 800°C for 3 h. The ampoule was loaded in a high-purity argon-filled glove box, isolated using a Young’s tap, and then transferred to a vacuum line where it was sealed under a pressure of 10⁻⁵ Torr. The sealed ampoule was placed in a rocking furnace, which was heated at a rate of 2°C min⁻¹ from ambient to a temperature of 975°C, dwelling for 1 h each at temperatures of 221, 685, and 938°C, i.e., near to the melting and boiling points of Se, and the melting point of Ge, respectively. The highest temperature was maintained for 47 h before the rocking motion was stopped, and the furnace was placed vertically for 1 h to let the melt collect at the bottom of the ampoule. The furnace was then cooled at a rate of 2°C min⁻¹ to a temperature 100°C above the liquidus temperature T_L (Figure 1), where the sample was left to equilibrate for 4 h, and the ampoule was dropped into an ice/water mixture. The sample (of mass ∼ 3.6 g) was broken out of the ampoule inside an argon-filled glove box and transferred into a vanadium container of outer diameter 7 mm and wall thickness 0.1 mm ready for the diffraction experiment. Glassy samples prepared in this way showed no indication of Ge-O or Se-O impurity bands in the measured infrared transmission spectra, e.g., in the region around 735–781 cm⁻¹ (Savage and Nielsen, 1965). A sample of glassy GeSe₄, as prepared by using an almost identical procedure but with only 10 h of rocking, was investigated by both energy dispersive X-ray spectroscopy (EDS) and Raman spectroscopy, and was found to be homogeneous on a submicron to centimeter length scale (Pierre Lucas, private communication).

The density of each sample was measured using a Quantachrome MICRO-ULTRAPYC 1200e pycnometer operated with helium gas. The results are compared to those obtained from other measurements in Figure 2. The comparison shows that systematically smaller densities were obtained in the work by Bhosle et al. (2012b). In the latter, agreement is claimed with the molar volume V _m values given by Mahadevan et al. (1995), but the latter were incorrectly copied from the work of Feltz et al. (1983). As shown in Figure 3, the molar volumes measured by Feltz et al. (1983) are not in quantitative agreement with the work of Bhosle et al. (2012b). Nevertheless, the data sets of Bhosle et al. (2012b), Feltz et al. (1983), Ota et al. (1978), and Yang et al. (2013) point to a minimum value of V _m in the interval 0.20 ≲ x ≲ 0.25 (Bhageria et al., 2014). The present results show a shallow minimum around x = 0.19(4) corresponding to V _m = 17.95(5) cm³ mol⁻¹.

The glass transition temperature T_g was measured by using a TA Instruments Q200 Differential Scanning Calorimeter operated in a TMDSC mode. Each scan comprised a temperature increasing and a temperature decreasing part, both performed at a rate of 3°C min⁻¹ and temperature modulation of 1°C per 100 s. The maximum temperature was set to give complete coverage of the glass-transition region whilst avoiding crystallization. The T_g values taken from the onset of the glass transition as manifested in the total heat flow measured during the temperature increasing part of a scan are plotted in Figure 4. The results are in the range of values previously reported for glasses in the Ge_xSe_1−x system. In addition, in order to make a like-for-like comparison with the glass transition temperatures reported by Boolchand and coworkers from TMDSC experiments (Feng et al., 1997; Boolchand, 2000; Boolchand and Bresser, 2000; Wang et al., 2005; Bhosle et al., 2012a,b), a value T_g1 was taken from the midpoint of the glass-transition region for the reversing heat-flow in the temperature increasing part of a scan, and a value T_g2 was also taken from the midpoint of the glass-transition region for the reversing heat-flow in the temperature decreasing part of a scan, and the mean value Tg,rev=(Tg1+Tg2)∕2 was taken. The results for T_g,rev from the present work are in agreement with those previously obtained by Boolchand and coworkers, as shown by the inset to Figure 4.

The non-reversing enthalpy ΔH_nr was obtained from the same TMDSC scans used to obtain T_g,rev by following the procedure described by Chen et al. (2010b), which includes a frequency correction. Independent measurements were made on several samples from each composition that had been aged at room temperature for a minimum of 37 days, and the mean and standard deviation were taken to find ΔH_nr and its error. The results give ΔHnr≃0, which is the defining characteristic of the intermediate phase, for the composition range 0.175(8) ≤ x ≤ 0.235(8) (Figure 5). This composition range compares to previously reported “reversibility windows” of 0.225 ≤ x ≤ 0.230 (Feng et al., 1997), 0.20(1) ≤ x ≤ 0.26(1) (Boolchand et al., 2001a), or 0.195(5) ≤ x ≤ 0.260(5) (Bhosle et al., 2012b) for the Ge_xSe_1−x system. The composition range found in the present work is therefore shifted to lower x, and its mid-range value of x = 0.205(8) is in agreement, within the experimental error, with the expectation from mean-field constraint-counting theory of a rigid to floppy transition in the Ge_xSe_1−x system at x = 0.20 where n¯ = 2. 40 (Thorpe, 1983). The activation energy for enthalpy relaxation E_A, as measured by differential scanning calorimetry (DSC) experiments that employed different cooling rates (Lucas et al., 2009), also shows a minimum around x = 0.20 (Figure 5).

The neutron diffraction experiments were performed at room temperature (≃25°C) using the GEM (Hannon, 2005) and SANDALS (Soper, 1991) diffractometers at the ISIS pulsed neutron source. Diffraction patterns were measured for each sample in a vanadium container, the empty container, the empty instrument, and a vanadium rod of diameter 8.37(1) mm for normalization purposes. Each diffraction pattern was built up from the intensities measured for different detector groups, where these intensities were saved at regular intervals in order to test the diffractometer stability. The data sets were analyzed detector-by-detector using the GUDRUN analysis software (Soper, 2011). Inelasticity corrections were performed using the procedure described by Howe et al. (1989). The compositions x = 0, 0.100, 0.150, 0.175, 0.200, 0.230, 0.251, 0.260, 0.279, 0.302, 0.333, and 0.400 were investigated using GEM; the compositions x = 0, 0.191, 0.210, 0.218, 0.230, 0.235, and 0.269 were investigated using SANDALS. The uncertainty on these sample compositions Δx = ± 0.001.

The measured total structure factors S(q)≃SNNq for the Ge_xSe_1−x glasses are shown in Figure 6. For the x = 0 and x = 0.230 compositions, that were investigated using both GEM and SANDALS, the measured functions are in agreement within the experimental error. For glassy Se, S(q) has a small shoulder on the low-q side of the principal peak at q_PP = 1.91(2) Å⁻¹, which develops into an FSDP with increasing Ge content. The height of the FSDP is largest at the stoichiometric composition x = 1/3 where its position q_FSDP = 0.985(10) Å⁻¹. According to Fourier transform theory, a sharp peak of width Δq_i at a position q_i in S(q)≃SNNq is associated with real-space ordering of periodicity 2π/q_i and correlation length 2π/Δq_i (Salmon, 1994). Indeed, the real-space periodicity associated with these features is directly observable for several network-forming glasses, including Ge_0.333Se_0.667 (Salmon, 1994, 2006; Salmon et al., 2005, 2006). The composition dependence of the periodicity and correlation length associated with each of the first three peaks in the measured S(q) functions is shown in Figures 7 and 8, respectively. The full-width at half-maximum of a peak Δq_i was measured relative to a linear baseline drawn between points (usually minima) deemed to mark the start and end of a peak (Salmon, 1994). The parameters obtained from the GEM and SANDALS diffractometers are in agreement within the experimental error. The results do not show any notable feature that can be associated specifically with an intermediate phase, although there is a change in the correlation length associated with the FSDP at x≃0.26. The composition dependence of the periodicity 2π/q_FSDP as obtained from other diffraction experiments is also shown in Figure 7. A shoulder at x≃0.23, as reported in the X-ray diffraction work of Sharma et al. (2005), is not found in any of the other data sets.

The measured total pair-distribution functions g(r)≃gNN(r) are shown in Figure 9. The large q_max values accessed by the neutron diffractometers ensure that M(q) has a minimal effect on S(q) (equation (2)), so the g(r) functions do not show associated Fourier transform artifacts. The mean coordination number n¯ for each glass composition was therefore obtained by direct integration of the first peak in g(r) (equation (3)), i.e., there was no need to apply a fitting procedure in order to account for the effect of a finite q_max value (Petri et al., 2000; Salmon and Petri, 2003). The composition dependence of the measured n¯ values is shown in Figure 10, where the results are compared to those obtained from the EXAFS experiments of Zhou et al. (1991) and the first-principles molecular dynamics simulations of Inam et al. (2007). The predictions of the “8-N” rule are also given, where the curves for the CON and RCN models take into account the small mismatch between the coherent neutron scattering lengths of Ge and Se of natural isotopic abundance (Section 2). The results show that n¯ increases monotonically with x and, within the experimental error, the values are in accordance with the “8-N” rule. They do not show any notable feature that can be associated specifically with the intermediate phase, such as a deviation from the “8-N” rule as reported by Inam et al. (2007).

As shown by the inset to Figure 4, the T_g,rev results of the present work are, within the experimental error, the same as those previously measured by Boolchand and coworkers. As shown in Figure 5, the composition range of the intermediate phase found in the present work, 0.175(8) ≤ x ≤ 0.235(8), is centered on the mean-field expectation of a floppy-to-rigid transition at x = 0.20 (Thorpe, 1983), and is therefore shifted to smaller x values as compared to the work of Boolchand and coworkers. As shown in Figure 2, the composition dependence of the density found in the present work is different to that reported by Bhosle et al. (2012b), and more closely matches that measured by other authors.

Bhosle et al. (2012a,b) report a water-induced increase of density that accompanies a decrease in T_g,rev for glasses in the Ge_xSe_1−x system. In this way, an attempt was made to rationalize the low density values found in their work as compared to previous investigations (Figure 2). At a given composition, the density measured in the present work is also greater than reported by Bhosle et al. (2012a,b), but the T_g,rev values are the same, e.g., 174(2)°C at x = 0.19 for our sample versus 172(2)°C at x = 0.19 for the (dry) sample of Bhosle et al. (2012a). Also, the infrared spectra for samples made using our procedure do not indicate any water contamination (Section 3.1). Hence, it is difficult to reconcile the large discrepancy in the composition dependence of the glass density between Bhosle et al. (2012b) and previous work (Figure 2) with the presence of water contamination.

In the present work, the absence of a jump in the composition dependence of ΔH_nr at the boundaries of the intermediate phase (Figure 5) might be attributed to inhomogeneous glass that originates from the allocation of insufficient time to fully react Ge and Se in the liquid state before quenching to form a glass (Bhosle et al., 2012b). However, Ge_xSe_1−x glasses made by using an almost identical rocking-furnace procedure show no evidence of sample heterogeneity (Section 3.1). In the work of Gunasekera et al. (2013), a small fragility index m_DSC = 14.8(5) for Ge_0.22Se_0.78 (Figure 12) might be attributed to the preparation of homogeneous glass after a long reaction time of 144–216 h for samples of mass 2 g. However, systematically larger values of m_DSC = 23(2) and m_DSC = 27(2) are reported for Ge_0.22Se_0.78 samples of similar mass (∼1.5 g) prepared using short versus long reaction times of 34 and 192 h, respectively (Li et al., 2017).

The neutron diffraction results of the present work do not show any obvious structural signature of the intermediate phase. For example, they do not support a deviation from the “8-N” rule as reported by Inam et al. (2007) from first-principles molecular dynamics simulations, or a shoulder in the composition dependence of the periodicity 2π/q_FSDP as reported by Sharma et al. (2005) from X-ray diffraction experiments. This absence of a structural signature is consistent with the high-energy X-ray diffraction and EXAFS spectroscopy work of Shatnawi et al. (2008), who investigated samples for which ΔHnr≃0 for the range 0.20≲ x ≲0.25.

It is conceivable that a structural signature of the intermediate phase does not manifest itself at the pair-correlation function level, as accessed by diffraction experiments (Fischer et al., 2006). Modeling methods can, however, access information on higher-body correlation functions, and Micoulaut et al. (2013) used first-principles molecular dynamics to investigate the structure of several Ge_xSe_1−x glasses with compositions spanning the intermediate phase. Although a compelling structural signature of the intermediate phase was not found, constraint-counting algorithms show that broken bond-bending constraints are associated with the stressed-rigid phases at x = 1/3 and x = 0.40. As shown by Chen et al. (2010a), the electronic structure of a glass may offer evidence of a structural origin for the intermediate phase. By combining first-principles molecular dynamics simulations with the results obtained from X-ray absorption near-edge structure (XANES) experiments made at the K-edge of both Ge and Se, it was suggested that the intermediate phase for Ge_xSe_1−x glasses corresponds to a composition range in which there is interplay between regions that are either Se-rich or populated by clustered Ge(Se₄)_1/2 tetrahedra.

The defining feature of the intermediate phase is a composition range where ΔHnr≃0. The physical interpretation of this parameter is debated (Schawe, 1995; Reading, 1997), with Boolchand and coworkers attributing it to the enthalpy of relaxation at T_g (Bhosle et al., 2012a). It is conjectured that glasses within the intermediate phase are stable in the sense that, for different aging times at room temperature, there is no alteration to the total enthalpy change ΔHtot=ΔHr+ΔHnr across the glass transition: the reversing part ΔH_r does not alter and, unlike the floppy and stressed-rigid phases, the non-reversing part ΔH_nr remains vanishingly small (Boolchand et al., 2002; Bhosle et al., 2012b).

By contrast, the change in specific heat capacity C_p across the glass transition, as determined from the total enthalpy change measured in DSC experiments, has been used to monitor the effect on Ge_0.10Se_0.90 and Ge_0.20Se_0.80 glass fibers of aging at room temperature for periods of up to 58 months (King, 2011). The results show that glasses within the intermediate phase do relax, although the magnitude of change is markedly smaller for x = 0.20 as compared to x = 0.10. Some of this difference in response may originate from a difference in fictive temperatures: The glass fibers were quenched quickly from the melt and correspond to a high fictive temperature, whereas the samples of, e.g., Bhosle et al. (2012b) were temperature cycled above T_g during a TMDSC experiment before aging at room temperature, and therefore correspond to a low fictive temperature. Some of this difference in response may also originate from the size of the interval between T_g and the annealing temperature T_a, where the former increases with x (Figure 4). Zhao et al. (2013) looked at this issue by employing DSC to monitor the change in total enthalpy for bulk samples of melt-quenched glassy Ge_xSe_1−x (0 ≤ x ≤ 0.23) annealed for 1 h at T_g. The samples were subsequently aged for different durations of time with T_a set at a fixed interval below T_g. All of the samples showed the same aging characteristics, including those associated with intermediate phase compositions, with an aging rate and kinetics that depend on the interval T_g − T_a. A Raman spectroscopy investigation of Ge_0.20Se_0.80, in which a glass equilibrated at T_g = 160°C was subsequently aged at 120°C for a time period ranging from 6 to 240 h, showed structural relaxation with a characteristic timescale of ∼40 h during which there is a conversion from edge-sharing to corner-sharing Ge(Se₄)_1/2 tetrahedral units (Edwards and Sen, 2011). A conversion from edge-sharing to corner-sharing tetrahedral units was also observed by King (2011) in her Raman spectroscopy work on the aging of Ge_0.10Se_0.90 and Ge_0.20Se_0.80 glass fibers at room temperature.

Recently, m_DSC values smaller than the fragility index of silica have been reported for glasses within the intermediate phase window, leading to the notion of “super-strong” liquids (Gunasekera et al., 2013). This feature has been attributed to a slow homogenization of the melt when Ge_xSe_1−x glasses are prepared via a heating procedure in which elemental Ge and Se pieces are melted in a stationary vertically-mounted silica-ampoule, i.e., when a rocking furnace is not employed (Gunasekera et al., 2013; Bhageria et al., 2014). However, as discussed in Section 5, the numerical values for m_DSC reported by Gunasekera et al. (2013) lead to a temperature dependence of the viscosity that is notably different to that expected from viscosity measurements (Figure 11), leading to log₁₀η(T_L) values that are significantly larger than expected (Figure 14).

Lastly, it would be helpful if advocates of the intermediate phase could develop a method for predicting its occurrence and composition range for different classes of network glass-forming systems, and the concomitant effect on the material properties. For example, Ge_xSe_1−x and As_xSe_1−x are prototypical chalcogenide glass-forming systems that feature different network topologies. In the case of Ge_xSe_1−x, the intermediate phase window incorporates the composition x = 0.20 for which a rigid to floppy transition is expected on the basis of mean-field constraint counting theory, a minimum in the molar volume is reported for the intermediate phase window (Bhosle et al., 2012b; Bhageria et al., 2014), and the fragility index takes a minimum within this window at around x = 0.22 (Section 5). In the case of As_xSe_1−x, however, the intermediate phase window of 0.291(1) ≤ x ≤ 0.37(1) (Georgiev et al., 2000) or 0.20 < x < 0.37 (Ravindren et al., 2014) does not incorporate the mean-field composition of x = 0.40 for a floppy to rigid transition, a minimum in the molar volume may (Ravindren et al., 2014) or may not occur within this composition range (e.g., Feltz et al., 1983 report a minimum at x = 0.40), and a minimum in the fragility index m_visc occurs at x≃0.27 (Musgraves et al., 2011).