Relative Contribution of Stoichiometry and Mean Coordination to the

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Relative Contribution of Stoichiometry and Mean Coordination to the Fragility of Ge−As−Se Glass Forming Liquids Ting Wang,† Ozgur Gulbiten,‡ Rongping Wang,† Zhiyong Yang,*,† Anita Smith,† Barry Luther-Davies,† and Pierre Lucas*,‡ †

Centre for Ultrahigh Bandwidth Devices for Optical Systems (CUDOS), Laser Physics Centre, Research School of Physics and Engineering, Australian National University, Canberra 0200, Australia ‡ Department of Materials Science and Engineering, University of Arizona, Tucson, Arizona 85712, United States ABSTRACT: The structural relaxation properties of 34 compositions of Ge− As−Se glass forming liquids are investigated by differential scanning calorimetry (DSC). The fragility index (m) and activation energies for enthalpy relaxation (Ea) exhibit universal trends with respect to stoichiometry and mean coordination (⟨r⟩), respectively. The liquid fragility which defines the full temperature dependence of the relaxation processes shows no well defined trend with respect to ⟨r⟩ but instead is found to be closely determined by the excess or deficiency in selenium with respect to stoichiometry. The mean coordination on the other hand appears to be an accurate predictor of the activation energy near the glass transition where most constraints are still intact. No intermediate phase is observed in either case. These results emphasize that chemical effects rather than topological effects appear to control the wide ranging structural mobility of these glass forming liquids. The consequences of these findings in terms of the thermal stability of the corresponding glasses are discussed. It is similarly found that sub-Tg relaxation is controlled by stoichiometry rather than topology. near ⟨r⟩ = 2.47−10 while optical cutoff and photostructural changes showed simple inflections,11,12 and thermal transport properties and elastic modulus showed no visible trend at ⟨r⟩ = 2.4.7,9 Recently, Boolchand and co-workers have reported the existence of the so-called “intermediate phase” (IP) between the floppy and rigid phases, representing a self-organized network characterized by zero nonreversing heat flow in temperature modulated differential scanning calorimetry (MDSC).13−15 The IP in GexSe1−x has been found over an ⟨r⟩ range of 2.40−2.5016 while in GexAsxSe1−2x glasses it appears over a range of ⟨r⟩ between 2.27 and 2.46.13 Glasses in the intermediate phase are reported to be nonaging which should be beneficial to the stability of photonic devices.17,18 However recent results on the Ge−Se system show that these glasses actually undergo significant aging when annealed at temperatures that allow measurements within the observation time scale.19 These findings are also consistent with previous annealing measurements on Ge−As−Se glasses.11 In terms of practical applications this study is motivated by recent findings that a small group of Ge−As−Se glass films around ⟨r⟩ ≈ 2.45 were found to be rather stable when annealed at temperatures approaching their Tg while those with higher and lower ⟨r⟩ relaxed toward the bulklike state.17 The goal of this work was to understand the interplay between

I. INTRODUCTION Chalcogenide network glasses are materials containing one of the chalcogen elements (S, Se, or Te) covalently bonded to elements of similar electronegativity such as As, Ge, Si, and Sb, etc. Depending on their chemical compositions and structures, chalcogenides can display metallic, semiconducting, or insulating properties and have important applications in electronics and photonics.1−4 Chalcogenide glasses have been used to study the influence of topological constraints on the compositional variation of various physical properties in covalently bonded amorphous solids. While it is understood that the structure and physical properties of chalcogenide glasses can be tuned by the chemical composition, it has been argued on the basis of the theory of constraint counting that the physical properties of these glasses are predominantly controlled by the mean coordination number (⟨r⟩, which is the sum of the products of the individual abundance times the coordination of the constituent atoms), irrespective of their actual chemical compositions.5,6 A simple counting of the bond length and angle constraints relative to the total number of degrees of freedom available to a mole of three-dimensionally connected atoms shows the existence of a percolation transition at ⟨r⟩ = 2.40 from an underconstrained “floppy” network to an overconstrained “rigid” phase.5,6 The compositional dependence of various physical properties of Ge−As−Se glasses has been previously investigated along several composition tie lines.7−12 Volume, viscosity, heat capacity, and mechanical relaxation showed a global minimum © 2014 American Chemical Society

Received: December 13, 2013 Revised: January 18, 2014 Published: January 22, 2014 1436

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Table I. Compositions and Respective Mean Coordination Number ⟨r⟩, Glass Transition Temperature (Tg), Activation Energies (Ea), and Fragility Index (m) for GexAsySe1−x−y Glasses compositions Ge−As−Se (at. %)

⟨r⟩

Se-rich/-poor (at. %)

Tg (°C)

Ea (kJ/mol)

m

5−10−85 17.5−11−71.5 11.5−24−64.5 18−23−59 20−20−60 15−34−51 22−24−54 25−20−55 30−20−50 35−15−50 33−20−47 5−20−75 7.5−15−77.5 10−10−80 12.5−5−82.5 5−30−65 10−20−70 15−10−75 7.5−35−57.5 10−30−60 12.5−25−62.5 15−20−65 20−10−70 22.5−5−72.5 18.75−17.5−63.75 15−25−60 10−35−55 27−18−55 24−24−52 21−30−49 18−36−46 6.25−32.5−61.25 25−10−65 31.25−2.5−66.25

2.20 2.46 2.47 2.59 2.60 2.64 2.68 2.70 2.80 2.85 2.86 2.30 2.30 2.30 2.30 2.40 2.40 2.40 2.50 2.50 2.50 2.50 2.50 2.50 2.55 2.55 2.55 2.72 2.72 2.72 2.72 2.45 2.60 2.65

+60 +20 +5.5 −11.5 −10 −30 −26 −25 −40 −42.5 −49 +35 +40 +45 +50 +10 +20 +30 −10 −5 0 +5 +15 +20 0 −7.5 −17.5 −26 −32 −38 −44 0 0 0

95.44 182.22 200.99 263.39 278.50 257.16 298.79 318.41 361.11 375.85 377.31 136.88 123.63 124.39 117.99 165.16 155.37 156.78 210.29 220.23 224.32 217.68 207.78 212.13 255.37 243.35 219.90 332.88 318.97 302.63 289.74 197.56 297.45 365.80

285.61 258.57 259.15 304.91 318.41 332.88 353.14 367.61 402.35 422.61 429.37 262.44 262.44 268.23 274.02 241.21 246.04 251.83 276.92 273.06 266.3 264.37 265.34 273.58 283.67 289.46 293.32 357.96 363.75 370.51 375.33 249.91 305.86 341.56

40.54 26.97 28.59 29.73 30.19 32.79 32.25 32.43 33.15 33.98 34.45 33.43 34.58 35.20 36.64 28.77 29.98 30.60 29.90 28.93 27.98 28.13 28.81 27.85 28.00 29.30 31.04 30.89 32.13 33.63 34.82 27.70 28.02 27.94

not less than 30 h, and then the ampule was removed from the rocking furnace at a predetermined temperature and airquenched. The resulting glass boule was subsequently annealed at a temperature 30 °C below Tg and then slowly cooled to room temperature. The bulk glasses were then sectioned and polished for further testing. The amorphous nature of each glass was verified by X-ray diffraction. DSC measurements were performed on a Mettler Toledo DSC1 equipped with an intercooler, and the data were analyzed with the STARe software. Indium and zinc standards were used to calibrate the temperature scale. About 20 mg of powder for each sample was sealed into an aluminum pan. In order to erase the thermal history of the glasses, all of the studied samples were heated far above Tg and then cooled far below Tg and reheated at the same rate. The temperature was scanned over a range from room temperature to 480 °C with different scanning rates under a uniform nitrogen gas flow of 50 mL/min. The chemical compositions of the glasses are reported in Table I and illustrated in Figure 1. The samples can be categorized as follows: (1) 20 compositions which can be divided into 5 groups with the same ⟨r⟩ = 2.30, 2.40, 2.50, 2.55, and 2.72, respectively (depicted by colored dots in Figure.1); (2) 14 other compositions distributed across the glass forming region (depicted by black dots in Figure 1).

topological and stoichiometric factors and their relative impact on the relaxation process in the liquid and the glassy states. For that purpose 34 samples of Ge−As−Se glasses with compositions distributed across the glass formation domain and covering a wide range of stoichiometry and average coordination were prepared and systematically investigated. The composition dependences of the glass transition temperature (Tg), the activation energy for structural enthalpy relaxation (Ea), and the fragility index (m) were measured, and the resulting trends are used to rationalize previous empirical observations on relaxation behavior of this family of glass.

II. EXPERIMENT Ge−As−Se glasses were synthesized from high purity (5 N) germanium, arsenic, and selenium elements by traditional meltquenching technique. The raw materials with a total mass of approximately 10 g were weighed inside a dry nitrogen glovebox and loaded into a precleaned quartz ampule. The loaded ampule was dried under vacuum (10−6 Torr) at 110 °C for 4 h to remove surface moisture from the raw materials. The ampule was then sealed under vacuum using an oxygen hydrogen torch, and introduced into a rocking furnace to melt the contents at 900 °C. The melt was homogenized for a period 1437

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Figure 3. Tg as a function of mean coordination number.

dependence is obtained, and the activation energy Ea is then calculated from the slope of these plots. The variation of Ea as a function of mean coordination number is displayed in Figure 4a and shows a sharp local minimum at ⟨r⟩ = 2.40. For comparison the variation of Ea is also plotted as a function of the departure from stoichiometry quantified as the degree to which the glasses were Se-rich or Sepoor according to (Se-rich/-poor)/% = (100 − x − y) − 2x − 1.5y = 100 − 3x − 2.5y for GexAsyS1−x−y. The data shown in Figure 4b show no clear dependence, although a very broad minimum is found for compositions containing a slight excess of selenium. m characterizes and quantifies the extent to which glass forming liquids depart from the Arrhenius viscosity behavior as they approach the glass transition region with strong glass formers having the smallest values of m.8 The fragility index can be calculated from Tg and Ea using the following relation:22,23

Figure 1. Glass formation domain of the Ge−As−Se ternary system showing the 34 compositions investigated in this study, color-coded according to their mean coordination number.

III. RESULTS Figure 2a shows DSC traces obtained at heating rates ranging from 5 to 30 K/min for a Ge6.25As32.5As61.25 (⟨r⟩ = 2.45) sample. The variation of Tg as a function of mean coordination number ⟨r⟩ is shown in Figure 3. The value of Tg is shown to increase linearly with increasing ⟨r⟩. It has been well established that the value of Tg closely correlates with the connectivity and rigidity of the vitreous network.20 Indeed, increasing the concentration of the network forming elements such as Ge or As should lead to increased Tg, as is shown in the data. No global maximum was observed, which is consistent with earlier reported results.8 The dependence of the glass transition temperature on the heating rate (Q) was found to obey the following equation:21 E d ln Q =− a ⎛1⎞ R d⎜ T ⎟ ⎝ g⎠ (1)

m=

Ea RTg * ln 10

(2)

where Ea is the activation energy and Tg* is the glass transition temperature at 10 K/min. The fragility index for the complete set of glasses is plotted as a function of departure from stoichiometry and ⟨r⟩ in Figure 5a,b respectively. The fragility index exhibits a sharp minimum for glasses of stoichiometric compositions where sufficient Se is present for all Ge and As atoms to be linked by exactly one Se. Compositions containing

where Ea and R are the activation energy for the glass transition and the ideal gas constant, respectively. The variations of ln Q as a function of 1000/Tg is depicted in Figure 2b for a series of representative glass samples with different ⟨r⟩ values. A linear

Figure 2. (a) DSC curves of a Ge6.25As32.5Se61.25 glass obtained at different heating rates after cooling at the same rate from far above Tg. (b) Plot of ln Q as a function of 1000/Tg, showing the linear regression used to obtain Ea for the following glass compositions: Ge10As10Se80 (⟨r⟩ = 2.3), Ge10As20Se70 (⟨r⟩ = 2.4), Ge17.5As11Se71.5 (⟨r⟩ = 2.46), and Ge22.5As5Se72.5 (⟨r⟩ = 2.5). 1438

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Figure 4. Ea (a) as a function of mean coordination number and (b) as a function of departure from stoichimetry in atomic percent of selenium.

Figure 5. Fragility index as a function of (a) departure from stoichimetry in atomic percent of selenium and (b) mean coordination number.

an excess or deficiency in Se both become distinctly more fragile with increasing departure from stoichiometry. The sharp minimum in fragility is exemplified by the fact that all five stoichiometric samples almost perfectly overlap on Figure 5a. On the other hand, no clear trend is visible between fragility and mean coordination number as depicted on Figure 5b.

The cooperative relaxation theory of Adam Gibbs has been widely used to explain the transport properties and fragility of glass forming liquids. It constitutes the basis for some of the most recent viscosity models,26 and it is commonly used to correlate energy landscape formalisms and viscosity.27,28 Its success derives from its explicit correlation between configurational entropy (Sc) and transport properties of supercooled liquid according to

IV. DISCUSSION A. Liquid Fragility and Stoichiometry. The mean coordination is often invoked to explain various features of chalcogenide glasses; however, the results of Figures 4a and 5a emphasize that simple chemical effects such as deviation from stoichiometry appear to be more relevant in predicting fundamental physical properties such as fragility. Indeed, the mean coordination is only properly defined at low temperature where all constraints are still intact. It can therefore be effectively correlated to low temperature properties such as molar volume24 but may be inappropriate for predicting behaviors above Tg. The activation energy at Tg may correlate with ⟨r⟩ because it reflects the energy required to gain mobility relative to a state where all constraints are intact. On the other hand, the fragility is defined by the rate at which these constraints are broken with increasing temperature above Tg, and this process appears to be rather independent of the mean coordination but instead is controlled by the departure from stoichiometry. Previous studies have also suggested that the short-range order rather than the topology controls the physical properties of Ge−As−Se glasses.25

η = η0 exp

C TSc

(3)

where η is the viscosity and C is a constant. Below we discuss how the structural features of Ge−As−Se glasses may affect the configurational entropy of the supercooled liquid and in turn the compositional dependence of the fragility in terms of energy landscape. From an energy landscape point of view the fragility of a glass forming liquid can be correlated to the topography of the corresponding landscape.28,29 A strong landscape has a uniform topology with basins of similar depth separated by saddles of similar height that progressively lead down to a general energy minimum corresponding to the ideal glass at the bottom of the landscape. The activation energy required to sample neighboring basins during relaxation is therefore similar at high temperature (near the top of the landscape) and at low temperature (near the bottom of the landscape) thereby indicating an Arrhenius behavior characteristic of strong liquids. On the other hand fragile landscapes have nonuniform topology with a high density of shallow basins at the top of 1439

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the landscape interspersed between widely separated deep minima. Sampling basins at high temperature therefore involve a small activation energy requiring the rearrangement of a few molecules. At low temperature, however, sampling widely separated basins involves the rearrangement of many molecules and overcoming large energy barriers. The activation energy therefore increases steeply near Tg in a non-Arrhenius way characteristic of fragile glasses. The energy landscape formalism is consistent with the dynamical features observed in Ge−As−Se glasses. Stoichiometric glasses contain mainly heteropolar bonds30 that require similar energy to be broken31 and should therefore result in a uniform type of energy barrier throughout the entire landscape in a way similar to SiO2.28 This feature leads to strong behavior as observed experimentally in Figure 5a. On the other hand, Serich compositions contain a disparity of structural domains exhibiting floppy and rigid behavior which can be associated with different well depths including shallow potential wells from floppy selenium chains and deeper wells from rigid heteropolar regions. A similarly heterogeneous topography is generated in Se-deficient glasses where homopolar bonds introduce shallow wells that can be easily sampled and result in greater degrees of freedom characteristic of fragile systems. Stoichiometric factors therefore appear to largely define the energy landscape topology of Ge−As−Se glasses and in turn their fragility. B. Fragility and Structural Relaxation in Glass. Correlation between Glass Relaxation and Fragility. The temperature dependence of melt viscosities is critical to most industrial glass fabrication processes such as molding, drawing, and floating, etc. An accurate knowledge of the fragility is therefore critical to optimize processes involving the liquid phase. However, the fragility is also a useful factor in predicting some properties of the glass below Tg. Indeed the fragility defines the rate at which the system departs from equilibrium upon losing ergodicity, and consequently it controls the glass tendency to undergo structural relaxation below Tg. This is particularly relevant for chalcogenide glasses because their low Tg enables significant relaxation processes even at room temperature.32,33 The correlation between sub-Tg relaxation and fragility can be qualitatively illustrated by extrapolating fragility plots below the glass transition, as shown in Figure 6a for three hypothetical glass forming liquids spanning the whole range of fragility with m = 16, 55, and 200. These curves are plots of a modified version of the Vogel−Tamman−Fulcher (VTF) equation34 that is normally used to fit viscosity data but has been converted to reduced entropy units following the analogy found by Martinez and Angell between excess entropy and viscosity for a wide range of glass forming liquids.35 The excess entropy is scaled to its value at Tg, and the temperature is scaled to Tg so that each glass forming system can be compared on the same master curve. This provides a qualitative illustration of the entropy variation in glass formers with various m values. Of particular interest is the low temperature part of the plot in the region below Tg. The horizontal dashed line represents the frozen excess entropy of the glass that has solidified at Tg, while the solid lines represent the equilibrium entropy of the corresponding liquids cooled infinitely slowly. This plot then illustrates the departure from equilibrium of various glass formers as they vitrify at Tg. To more clearly illustrate the correlation between fragility and tendency for relaxation, the low Tg data have been replotted in reversed units in Figure 6b in a form reminiscent of a Kauzmann plot for the

Figure 6. (a) Schematic reperesntation of three hypothetical glass formers based on a modified VTF equation with m ranging from 16 to 200; (b) variation of the equilibrium excess entropy below Tg in comparison to the value frozen at Tg showing the build up of the driving force for relaxation for glass formers of different m.

same three glass formers, although the expected curvature for Sexc is not reflected due to the simplistic equation used. Nevertheless, Figure 6b qualitatively illustrates how fragile glassy systems depart from equilibrium at a faster rate than strong systems and consequently build up a larger driving force and large propensity for relaxation as the temperature drops below Tg. This is of prime importance for sensitive applications such as integrated infrared optics where relaxation processes can lead to volume and refractive index changes that may impair the device functions.3,4,17 In this case, strong glasses with minimal tendency for relaxation are the optimal choice of material. In that respect, the results of Figure 5a effectively explain previous experimental results which showed that Ge− As−Se films of stoichiometric compositions exhibited negligible relaxation upon annealing near Tg while off-stoichiometry compositions exhibited significant relaxation, even those with a mean coordination of ⟨r⟩ = 2.4.17 Sub-Tg relaxation is therefore controlled by stoichiometric factors rather than topological factors. Absence of an Intermediate Phase in the Ge−As−Se System. An intermediate phase has been previously suggested in the Ge−As−Se system using MDSC measurements performed on a subset of Ge−As−Se samples.13 However, the present data indicate that no intermediate phase is generally present in these glasses. Instead Figures 4a and 5a show a sharp minimum in transport properties at ⟨r⟩ = 2.4. This difference most likely arises from the fact that intermediate phases in chalcogenide glasses are only observed using measurements of nonreversible enthalpy (ΔHnr). Yet it has been argued since the early days of MDSC that the nonreversible enthalpy does not have a well defined physical meaning36 and cannot be equated to the enthalpy relaxation.37 Instead the MDSC signal should 1440

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Notes

be interpreted in term of heat capacity spectroscopy using the real and imaginary components of the complex heat capacity.38−41 This suggests that the observation of an intermediate phase in Ge−As−Se glasses is likely the result of an instrumental artifact associated with the nonreversible quantity ΔHnr. Similarly, the nonaging window observed in these glasses16,42,43 is likely an artifact of experimental conditions. Indeed Figure 6 clearly shows that a glass falls out of thermodynamic equilibrium as it goes through Tg and significantly departs from its equilibrium entropy no matter how strong it is. A finite driving force for relaxation must therefore build up for any glass, but aging/relaxation can be kinetically prevented if the structural relaxation time is much longer than the observation time when low annealing temperatures are used. Nevertheless, raising the annealing temperature closer to Tg permits reduction of this relaxation time to the observation time scale. This was recently demonstrated by Zhao et al. in a series of Ge−Se glasses19 which showed large relaxation effects for all glasses including compositions from the so-called “nonaging window”.16 The magnitude of the relaxation enthalpy was shown to correlate well with the fragile behavior of the glasses, as expected from Figure 6b. An identical observation was made by Calvez et al. in the Ge−As−Se system,11 where strong compositions relaxed significantly less that fragile ones when annealed at a fixed temperature below Tg. The absence of relaxation previously observed in the nonaging window is therefore likely the result of the low annealing temperature used in these experiments (room temperature16,42,43) far below Tg, where relaxation times quickly reach geological time scales and no relaxation can be observed within the measurement time.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the Australian Research Council through its Centres of Excellence (Grant CE110001018), Discovery Project (Grant DP110102753), and Discovery Early Career Researcher Award (Grant DE120101036). This research was also supported by NSFECCS under Grant No. 1201865.

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V. CONCLUSION The thermodynamic properties of a large number of Ge−As− Se glasses were measured using differential scanning calorimetry. The activation energy for enthalpy relaxation shows a sharp minimum at the percolation threshold ⟨r⟩ = 2.4 but no clear trend with departure from stoichiometry. On the other hand the fragility index shows a net minimum for glasses of stoichiometric compositions while no clear tendency is obtained as a function of ⟨r⟩. These data reflect that simple chemical effects such as departure from stoichiometry appear to largely control the transport properties over a wide temperature range and in turn must control the topology of the energy landscape. Ge−As−Se glasses are of particular interest for integrated optic applications due to their high nonlinearity and wide optical transparency. However, their low Tg may result in significant relaxation during the lifetime of a device which could impair proper function. Selection of glass composition with minimal propensity for relaxation is therefore desirable. In that respect, a strong glass former with a high Tg would show a minimal driving force for relaxation and very slow relaxation kinetics which should be optimal for sensitive applications. The present results indicate that stoichiometry rather than mean coordination is the most relevant selection criteria for selecting such glasses. These findings rationalize previous experimental observation of thermal stability in Ge−As−Se thin films.

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REFERENCES

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dx.doi.org/10.1021/jp412226w | J. Phys. Chem. B 2014, 118, 1436−1442