Topological Ordering and Viscosity in the Glass-Forming Ge–Se System: The Search for a Structural or Dynamical Signature of the Intermediate Phase

. The topological ordering of the network structure in vitreous Ge x Se 1 (cid:1) x 10 was investigated across most of the glass-forming region (0 ⁄ x ⁄ 0.4) by using high- 11 resolution neutron diﬀraction to measure the Bhatia-Thornton number-number partial 12 structure factor. This approach gives access to the composition dependence of the mean coordination number ¯ n and correlation lengths associated with the network ordering. The thermal properties of the samples were also measured by using temperature- modulated diﬀerential scanning calorimetry. The results do not point to a structural 16 origin of the so-called intermediate phase, which in our work is indicated for the composition range 0 . 175 p 8 q ⁄ x ⁄ 0 . 235 p 8 q by a vanishingly-small non-reversing 18 enthalpy near the glass transition. The midpoint of this range coincides with the 19 mean-ﬁeld expectation of a ﬂoppy-to-rigid transition at x = 0.20. The composition 20 dependence of the liquid viscosity, as taken from the literature, was also investigated 21 to look for a dynamical origin of the intermediate phase, using the Mauro-Yue-Ellison- 22 Gupta-Allan (MYEGA) model to estimate the viscosity at the liquidus temperature. 23 The evidence points to a maximum in the viscosity at the liquidus temperature, and 24 a minimum in the fragility index, for the range 0 . 20 ⁄ x ⁄ 0 . 22. The utility of the 25 intermediate phase as a predictor of the material properties in network glass-forming 26 systems is discussed.


32
The structural disorder associated with covalently-bonded network-forming glassy 33 materials gives rise to a diversity of material properties, which leads to the importance 34 of glass in multiple technologies (Cusack 1987;Elliott 1990;Feltz 1993). It is 35 possible to predict many of the structure-related properties of these materials by using 36 constraint-counting theory, where the constraints originate from the bond-stretching 37 and bond-bending interatomic forces associated with the covalent bonds of network-38 forming motifs (Phillips 1979; Thorpe 1983). As the type and proportion of network-39 forming motifs is altered, the network topology will respond accordingly. Hence, 40 the connectivity and properties of covalently-bonded network-forming glasses can be 41 manipulated systematically by altering their composition. 42 On the basis of mean-field constraint-counting theory, a network is predicted to there are no dangling bonds, the transition at N c 3 corresponds to a mean coordination 49 numbern = 2.40 where the network is isostatically rigid and stress free (Phillips 1979; 50 Thorpe 1983). If the network can self-organise and thereby lower the free energy at 51 the temperature of its formation by the incorporation of structural configurations that 52 minimise the occurrence of over-constrained regions, then it is postulated that two 53 transitions can appear (Thorpe et al., 2000). In this case, the floppy and stressed-54 rigid phases are separated by a composition range known as the intermediate phase 55 where the network is isostatically rigid and stress free. The compositional width of this 56 phase is thought to be related to structural variability, i.e., the ability of a network to 57 incorporate a range of structural motifs (Massobrio et al., 2009;Sartbaeva et al., 2007). 58 In temperature-modulated differential scanning calorimetry (TMDSC) experiments, the 59 existence of a stress-free intermediate-phase is inferred from the non-reversing part of 60 the measured enthalpy ∆H nr , which takes a value close to zero near the glass transition 2. THEORY 113 The total structure factor measured in a neutron diffraction experiment on glassy 114 Ge x Se 1¡x is given by (Fischer et al., 2006) 115 Spqq 1 b 2 (1) 116 where S αβ pqq is the partial structure factor for chemical species α and β, and b 117 xb Ge p1 ¡ xqb Se is the mean coherent neutron scattering length. The close similarity where ρ is the atomic number density. The measurement window of a diffractometer 124 is limited to a maximum scattering vector q max such that M pq ¤ q max q 1, M pq ¡ 125 q max q 0.

126
If q max is sufficiently large that the effect of M pqq can be neglected, the overall mean 127 coordination number for the spatial range r 1 ¤ r ¤ r 2 follows from the expression  The coordination numbersn β α can be calculated on the basis of a chemically ordered 136 network (CON) or random covalent network (RCN) model, both of which satisfy the '8-

137
N' rule (Salmon 2007a with the desired mass ratio, were loaded into a silica ampoule of 5 mm inner diameter 151 and 1 mm wall thickness that had been etched using a 48 wt% solution of hydrofluoric 152 acid, rinsed using water then acetone, and baked dry under vacuum at 800 ¥ C for 153 3 h. The ampoule was loaded in a high-purity argon-filled glove box, isolated using a of 10 ¡5 Torr. The sealed ampoule was placed in a rocking furnace, which was heated at 156 a rate of 2 ¥ C min ¡1 from ambient to a temperature of 975 ¥ C, dwelling for 1 h each at 157 temperatures of 221 ¥ C, 685 ¥ C and 938 ¥ C, i.e., near to the melting and boiling points of 158 Se, and the melting point of Ge, respectively. The highest temperature was maintained 159 for 47 h before the rocking motion was stopped, and the furnace was placed vertically 160 for 1 h to let the melt collect at the bottom of the ampoule. The furnace was then 161 cooled at a rate of 2 ¥ C min ¡1 to a temperature 100 ¥ C above the liquidus temperature 162 T L (Figure 1), where the sample was left to equilibrate for 4 h, and the ampoule was 163 dropped into an ice/water mixture. The sample (of mass 3.6 g) was broken out of the 164 ampoule inside an argon-filled glove box and transferred into a vanadium container of 165 outer diameter 7 mm and wall thickness 0.1 mm ready for the diffraction experiment.    The present results show a shallow minimum around x = 0.19(4) corresponding to V m 184 = 17.95(5) cm 3 mol ¡1 .

185
The glass transition temperature T g was measured by using a TA Instruments Q200   The non-reversing enthalpy ∆H nr was obtained from the same TMDSC scans used 204 to obtain T g,rev by following the procedure described by Chen et al. (2010b), which 205 includes a frequency correction. Independent measurements were made on several 206 samples from each composition that had been aged at room temperature for a minimum 207 of 37 days, and the mean and standard deviation were taken to find ∆H nr and its error.

208
The results give ∆H nr 0, which is the defining characteristic of the intermediate phase,       (Salmon 1994). Indeed, the real-space periodicity 245 associated with these features is directly observable for several network-forming glasses, including Ge 0.333 Se 0.667 (Salmon 1994(Salmon , 2006Salmon et al., 2005Salmon et al., , 2006. The composition 247 dependence of the periodicity and correlation length associated with each of the first 248 three peaks in the measured Spqq functions is shown in Figures 7 and 8, respectively.

249
The full-width at half-maximum of a peak ∆q i was measured relative to a linear baseline

Real-space properties 259
The measured total pair-distribution functions gprq g NN prq are shown in Figure 9.   log 10 ηpT q log 10 η V p12 ¡ log 10 η Here, log 10 η V is the logarithm of the high-temperature viscosity, T g is the glass  (Table 1).

296
The measured data sets shown in Figure 12     The dependence of log 10 η pT L q for the Ge x Se 1¡x system, as calculated using the MYEGA model with log 10 rη V pPa sqs = ¡2.93, on the composition x and mean coordination numbern 2 p1 xq. The solid (black) squares correspond to the fitted data sets shown in Figure 11 where the associated m visc values are listed in Table 1. The solid (black) and solid (red) curves show the results obtained by taking m visc from the solid (black) curve in Figure 12 and T g {T L from either the solid (black) or broken (red) curve in Figure 13, respectively. The broken (black) and broken (red) curves show the results obtained by taking m visc from the broken (red) curve in Figure 12 and T g {T L from either the solid (black) or broken (red) curve in   The fragility index m visc and glass transition temperature T g,visc corresponding to a viscosity ηpT g,visc q = 10 12 Pa s. The results obtained by fitting viscosity data to the MYEGA model with log 10 rη V pPa sqs = ¡2.93 (Figure 11) are compared to values of m visc and T g,visc taken from the literature. Also listed are the values of the glass transition temperature T g,DSC taken from the onset of the glass transition in the total heat flow measured in the TMDSC experiments of the present work (Figure 4). At compositions for which both glass transition temperatures are available (Table 1), 330 a discrepancy À10 ¥ C is indicated, corresponding to a fractional uncertainty of À5 % 331 on the absolute values of T g . In order to examine the effect on T g {T L of an uncertainty 332 on T g , this ratio was also calculated after making a least-squares fit to the T g,rev values 333 shown in the inset to Figure 4.

334
The composition dependence of log 10 ηpT L q as predicted by the MYEGA model 335 with log 10 rη V pPa sqs = ¡2.93 is shown in Figure 14, where the ratio T g {T L was taken  Table 1, but disappears if 348 the composition dependence of m visc is taken from Senapati and Varshneya (1996).   the Ge x Se 1¡x and other chalcogenide network glass-forming systems.

498
The authors declare that the research was conducted in the absence of any commercial 499 or financial relationships that could be construed as a potential conflict of interest.