Relaxation dynamics in the strong chalcogenide glass-former of Ge22Se78

The enthalpy relaxation is performed in the glassy Ge22Se78 to understand the dynamic behaviors. The structure of the glass is examined by X-ray diffraction and Raman spectra. The dynamic parameters such as the fragility, stretching exponent and non-linear factor are determined. A low fragility of m = 27 is exhibited for the chalcogenide, however, the stretching exponent is found not to have a larger value. The enthalpy relaxation spectra are constructed for various glass formers, and a relationship between the fragility and the symmetry of the spectra is demonstrated. The dynamic results are used to evaluate the structure of the Ge22Se78 glass.

Ge x Se 1−x chalcogenide glasses exhibit superior optical properties in the infrared region, and have been considerably applied in the industries such as solar cells and infrared optical fibers 1,2 . Due to the non-equilibrium nature of glassy materials and the tendency moving towards equilibrium states or stable states to release excess energy, the structure and properties might be subjected to variation at a specific temperature, which is initiated by the structural relaxation 3 . Therefore, the stability of glassy materials is directly related to the structural relaxation dynamics, which is critical to understand the property changes in such materials. The relaxation dynamics of the Se-rich Ge x Se 1−x glasses have been explored for decades [4][5][6] , however, a complete interpretation is still needed. In addition, the structure in Ge x Se 1−x glasses has been a subject of discussion concerning the connection patterns of the basic structural motifs of GeSe 4 tetrahedra and (Se) n units [7][8][9] . Besides the direct structure analyses method such as the diffraction methods 10 and NMR spectroscopy 11 , dynamic studies have proven to be capable of offering insights into the structure of glasses 12,13 .
Generally, the structural relaxation in glassy materials is largely governed by three dynamic aspects covering non-Arrhenius, non-exponential and non-linear behaviors 12 . The fragility m-index reflects how rapidly liquid viscosity or structural relaxation time changes at the glass transition temperature T g , and is quantified by dlog 10 (x)/d(T g /T) at T = T g in Angell plot, where x denotes the viscosity or the relaxation time 14 . The stretching exponent (or non-exponential factor) β KWW quantifies the degree of the non-exponential dynamics and is usually involved in the isothermal Kohlrausch-William-Watts (KWW) function in the time domain, KWW15 , where τ KWW is the structural relaxation time, and β KWW is the stretching exponent with 0 < β KWW ≤ 1 [16][17][18] . The non-linear factor defines how much the structural relaxation dynamics in glassy states depends on the thermal history.
Considerable efforts have been made to explore the dynamics in the Ge x Se 1−x melts and glasses, however, the reported results are not consistent. Based on the viscosity data of the Ge x Se 100−x melts, the fragility in the compositions of 10 < x < 25 is calculated to range from 22.5 to 32 4,5,19 . The enthalpy relaxation studies of Ge 8 Se 92 and Ge 12 Se 88 reported m = 58-59 20 . For the Ge x Se 100−x alloys with 10 < x < 33, the fragility m index was reported to be 14.8-29 using the modulated differential scanning calorimetry (mDSC) 6 . Recent studies of the enthalpy relaxation in Ge x Se 1−x (x ≤ 15) presented a continuous decrease in fragility from 68 to 28 measured with a constant ratio between the cooling and subsequent heating rates 21 . Similarly, the β KWW values (or the non-linear factor x) determined in the enthalpy relaxation measurements are not consistent. It is also found that the values of β KWW and x determined by the enthalpy relaxation are notably higher than those determined by the volume relaxation 22 .
Given accurate dynamic parameters are crucial to understand the relaxation behaviors and the structure in glassy materials 12,15 , here, the structural relaxation dynamics of the Ge 22 Se 78 chalcogenide glass is studied, referring to earlier studies in Ge x Se 1−x where a minimum fragility is identified to fall in the compositions of 19 < x < 26, preferentially in the range of 21.5 < x < 23 [4][5][6] . The dynamic parameters m, β KWW and x are determined using the enthalpy relaxation, because the method has proven to be capable of producing quite comparable results with the viscosity or dielectric-relaxation measurements 23,24 . The fragility of the Ge 22 Se 78 glass is determined to be low with m = 27. Surprisingly, a low stretching exponent is also revealed. The dynamic results are used to understand the structure of the Ge 22 Se 78 glass. Figure 1(a) and (b) present the XRD patterns and Raman spectra of the glassy Ge 22 Se 78 samples synthesized for 24 + 10 hours (details are presented in the Sample preparation section) and 24 + 168 hours. The nature of completely amorphous states is identified for the two samples by the XRD patterns using the wave vector gauged by q = 4π sinθ/λ. The intermediate-range order is unambiguously observed by the featured first-sharp-diffraction-peak (FSDP) at q = 1.09 Å −1 , given that the FSDPs in many non-metallic network glassy materials are typically located at q ~ 1-2 Å −1 25 . The Raman spectra displayed in Fig. 1(b) show two main regions: (a) a relatively sharp band with high intensity at ~195 cm −1 along with a shoulder located at ~210 cm −1 and (b) a broad band centered at 259 cm −1 with high-intensity, spanning from 225 to 280 cm −1 . The 195 cm −1 band in region (a) is assigned specifically to the breathing mode of corner-shared (CS) GeSe 4 tetrahedral units, and the 210 cm −1 band is assigned to the vibration of Se atoms involved in edge shared (ES) GeSe 4 tetrahedra 26,27 . The band in region (b) around 259 cm −1 is characteristic of pure Se and can be assigned to Se-Se stretching modes (SM) in (Se) n units 28,29 . Considering the similarity of Raman spectra between the glasses synthesized for 24 + 10 hours and 24 + 168 hours in the rocking furnace, the homogeneous glasses are expected to be achieved. Figure 2(a) and (b) show the heating heatflow curves around the glass transition for the two glassy Ge 22 Se 78 samples synthesized for 24 + 10 hours and 24 + 168 hours before quenching. Comparing the curves in the two panels, it is seen that the onset glass transition temperature of the sample synthesized for 24 + 168 hours is a bit lower. The heatflow curves are recorded at a fixed heating rate of 20 K/min after the glasses are quenched at different cooling rates of 20, 10, 5, 2.5 and 1 K/min, from which the fictive temperatures are determined. The fictive temperature, T f , firstly proposed by Tool 30 , and used to serve as an indicator of the states of glasses 23,31 , are subsequently determined. The T f of glasses can be calculated from the enthalpy-matching method for the heating curves using Moynihan's construction, following the relation,

Results
where T* is an arbitrary temperature above T g , C p-liquid and C p-glass denote the heat capacity of liquid and glassy states, respectively. Principally, T f of each glass quenched at a specific cooling rate can be independently calculated from the heating curve. In order to improve the accuracy, we chose the enthalpy-compensation method, = where T f s is the fictive temperature of a reference glass quenched at specific cooling/heating rates (i.e., − /+ 20 K/min), ΔH is the energy difference between the glass denoted by T f and the reference glass by T f s , and can be determined from the integral of the C p difference between the two glasses, ΔC p is the C p difference between the liquid and the glass at T g , which is shown in the inset of Fig. 3(a) 23 . Figure 3(a) shows the dependence of the fictive temperature T f on the cooling rate Q for the two glassy samples subjected to distinct synthesis time in melts. Using the expression of ln Q = A − E g /RT f , where R is the gas constant, A a constant, and E g the apparent glass transition activation energy 23 , the fragility m-index is determined to be 23 ± 2 for the glass synthesized for 24 + 10 hours and 27 ± 2 for the 24 + 168 hours in terms of m = E g /2.303RT g 32,33 .
The viscosity of Ge x Se 1−x systems are also reproduced in Fig. 3  work are largely comparable with the reported results based on different methods such as viscosity 4,5,19 and DSC measurements 6 .
The cooling/heating capacity C p curves of the Ge 22 Se 78 glass with synthesis time of 24 + 168 hours are shown in Fig. 4(a) using the rates of − /+ 20 K/min, and the corresponding enthalpies calculated by the integral of the C p curves, are presented in Fig. 4(b), showing a clear enthalpy hysteresis in the cycle. The hysteresis behaviors involved around glass transition during the cooling and heating cycles have been reported in the enthalpy and optical absorptivity measurements 34,35 , and ascribed to the relaxation in glass upon heating (energy release) in  glass and subsequent recovery towards equilibrium supercooled liquid at temperature well higher than T g 36 . The enthalpy relaxation spectrum of the Ge 22 Se 78 glass is shown in Fig. 4(c), giving the maximum relaxation enthalpy, ΔH R to be 0.708 J/g.   Figure 5 shows the heating and cooling C p curves for a group of glass forming liquids of diverse fragility with temperature normalized to their T f s values. Five more glass forming systems are used covering inorganic oxide, molecular 37 and metallic 38 glasses. Accordingly, the enthalpy relaxation spectra are plotted in Fig. 6 using the temperature reduced by the fictive temperature and, consequently, the peak values in the spectra read ∆H T / R f s . To understand the enthalpy relaxation spectra in temperature domain defined by the enthalpy difference curves, we define a parameter of S = F 2 /F 1 to reflect the symmetry of the spectra as shown in the inset of Fig. 7, where F 1 and F 2 denote the half width at half maximum of the peak in the left and right flanks, respectively, and therefore, F 1 + F 2 defines the full width at half maximum. Figure 7 presents the relation between the symmetry parameter S and fragility. The majority of the data are seen to fall into a master curve, and increased symmetry of the relaxation spectra is evident for strong liquids. Based on the correlation shown in Fig. 7, a complete symmetry might be expected for the strongest liquid of m min = 16.
The heating (upscan) C p curves of the glasses quenched at a cooling rate of 20 K/min are analyzed using the Tool-Narayanaswamy-Moynihan-Hodge (TNMH) equations, which emphasize the effects of fragility, nonlinear parameter x and stretching exponent β KWW 24,39 . The application of the TNMH equations requires the equality between the normalized C p curves and the temperature derivative of the fictive temperature, dT f /dT (detailed description is available in early studies 39 ). The fit of the TNMH equations to the normalized C p data therefore proceeds with the parameters of pre-exponential (A), apparent activation energy (E a = ln10RT g m), x and β KWW . With m = 27 available for the Ge 22 Se 78 glass, the fit gives the two parameters, β KWW and x, to be 0.43 ± 0.05 and 0.64 ± 0.05 respectively as shown in Fig. 8. It is noted that the mediate glass transition temperature T g and the marked glass-transition heat capacity increment for the Ge 22 Se 78 glass are advantageous for the enhanced

Discussion
The determination of the fragility for the Ge 22 Se 78 glass indicates that the glass former belongs to the category of strong dynamics according to the Angell's strong-fragile classification scheme 12 . The fragility of various glass formers has been explored for decades and, experimentally, the accessible m-index spans from the hitherto strongest SiO 2 of m = 20 to the most fragile cis/trans-decalin of m = 145 40 . The low fragility (m = 27) for the Ge 22 Se 78 alloy is somehow unexpected since, for inorganic substances, the extremely low fragility is generally associated with the network glass-forming materials with the MX 2 stoichiometry such as SiO 2 and GeO 2 , where the structures are built predominantly by tetrahedral MX 4 motifs 12,24,38,[40][41][42][43] . Numerically, the Ge 22 Se 78 fragility is quite comparable with those of BeF 2 (m = 24) and ZnCl 2 (m = 30) glasses 40 , which have strong directional bonds for the network structure 41,44 .
Studies found that strong glass formers with low m indexes generally have relatively high β KWW values (typically higher than 0.6 for the liquids with m < 40) 14,45 . Therefore, at a glance, the low enthalpy-relaxation-based β KWW of 0.43 is unusual when compared with the strong Ge 22 Se 78 glass of m = 27. In the earlier studies of the β KWW data produced by enthalpy relaxation and dynamic measurements such as dielectric and mechanical relaxations for various glass formers, excellent consistency is often exhibited 24,38,46 , suggesting the TNMH-based enthalpy relaxation can produce reliable stretching exponents. It appears that the low β KWW value of 0.43 makes the Ge 22 Se 78 glass to be an exception in the strong glass formers with simple compositions 14,45 .
Dynamic behaviors in glass formers have been recognized to be associated with the structural features of glasses and melts. Our recent studies of binary glass forming mixtures 47,48 showed that mixing always generates a negative shift of the actual fragility relative to the linear averaging of the fragility values of the two pure components, independent of the sign of the enthalpy of mixing. And in some cases 48 , the minimum fragility can be achieved at an intermediate composition in mixtures. Similarly, the studies of binary glass formers with weak intermolecular interactions detected the lower β KWW values than those of pure components, suggesting effective broadening of the relaxation dispersion 47,49 . In contrast, in the mixtures with strong intermolecular interactions manifested by large and negative enthalpies of mixing, enhanced β KWW values are evident 47 . For the Ge 22 Se 78 glass, it is, consequently, speculated that the low fragility m-index and the small β KWW value might be partly associated with the mixing effect. This is quantitatively consistent with the random connectivity of the basic structure motifs of GeSe 4 tetrahedra and (Se) n units in the Ge 22 Se 78 glass, as involved in the reported models 6,29,50 . Due to the unique structure of GeSe 2 (much different from those of GeO 2 or SiO 2 ) 51,52 , complexes have been argued to develop based on the basic structural motifs in the Ge 22 Se 78 glass [7][8][9]29,53 .
The present studies also detect a relation of x > β KWW for the Ge 22 Se 78 glass. This relation is quite rarely reported for most of glass formers, where x is generally smaller than β KWW 24,54 . As a few more glass formers are recently studied such as Zr 46  Methods Sample preparation. The sample glass Ge 22 Se 78 was prepared with the melt-quenching method 27 . Pure elements of Ge and Se (5N purity, Alfa) mixed according to specific fractions with weight of ~1.5 g are sealed into quartz tubes of 8 mm in diameter under a vacuum of 10 −3 Pa. The mixtures were heated up to 1230 K, higher than T m s of two pure components, and kept isothermally for 24 hours in a rocking furnace to promote the degree of mixing. Subsequently, the temperature was set to 1020 K, which is about 100 K above the liquidus temperature for additional 10 hours (24 + 10 hours) and 168 hours (24 + 168 hours), respectively. Glasses were finally obtained by quenching the melt into ice water. The composition of the sample with the synthesized time for 24 + 168 hours was analyzed taken randomly from the bulk using the energy dispersive spectrometer (EDS) analyses (supplemental material).
Sample analyses. The structure of the melt-quenched samples were checked via the x-ray power diffraction in a Rigaku D/MAX/2500/PC (Cu K α , λ = 1.54 Å) and Raman measurements on a Renishaw inVia micro Raman spectroscopy with a laser radiation of 514 nm. Heating and cooling heat capacity curves were obtained by using a differential scanning calorimeter (DSC, Perkin Elmer 8000) calibrated by using indium and zinc as references. The sample mass varied from 6 to 10 mg. The calorimetric glass transition temperature T g was defined as the onset temperature of the heat capacity jump from the glassy to the liquid state. Enthalpy relaxation was performed in two manners. One used a cooling/heating cycle at the same rates of 20 K/min, and the enthalpy difference between the cooling and subsequent heating defines the relaxation enthalpy. The other is based on the identification of the enthalpy difference in the glasses quenched by various cooling rates, of which the enthalpy difference is calculated from the integral of the heating C p difference among the glasses quenched at various cooling rates but fixed heating rate, typically 20 K/min. Usually, the heat capacity curve generated from cooling/heating rates of 20 K/min is set as the reference. This method has been described elsewhere 23 . The C p measurement temperature spans from T g − 100 K to T g + 50 K, which can guarantee that no relaxation occurs at low temperature regimes, and equilibrium (supercooled liquids) is reached at high temperature regimes.