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Kinetic fragility of Se-based binary chalcogenide glasses
Journal of Non-Crystalline Solids 419 (2015) 39–44
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Kinetic fragility of Se-based binary chalcogenide glasses Roman Svoboda ⁎, Jiří Málek University of Pardubice, Faculty of Chemical Technology, Department of Physical Chemistry, Studentská 573, 532 10 Pardubice, Czech Republic
a r t i c l e
i n f o
Article history: Received 17 November 2014 Received in revised form 21 March 2015 Accepted 30 March 2015 Available online xxxx Keywords: Kinetic fragility; Chalcogenides; Viscosity; Enthalpy relaxation; Decoupling
a b s t r a c t Kinetic fragility was determined for a number of compositions from the Ge–Se, As–Se and Te–Se chalcogenide glassy systems. Values of fragility indices were evaluated from both viscosity and enthalpy relaxation data. Comparison of the viscosity and enthalpy fragilities shows marked decoupling in cases of low-Ge/As-content compositions and the whole Te–Se glassy system. A possible explanation regarding the increased viscosity fragilities involves the influence of dynamic structural heterogeneity (density fluctuations and clustering of structural elements) on shear viscosity in the glass transition region. In particular, the observed decoupling seems to occur in case of the materials exhibiting moderate-to-high activation energy of relaxation processes and large structural cooperativity. The origin of the fragility decoupling may lie either in different molecular movements being involved in the two processes (viscous flow versus structural relaxation) or in their different manifestation in terms of volume and enthalpy behavior. © 2015 Elsevier B.V. All rights reserved.
1. Introduction It is well known that a large number of liquids of all types can be solidified without undergoing crystallization. At fast enough cooling rates the nucleation and crystal growth processes can be kinetically avoided and the undercooled liquid then at a certain state of structural compactness undergoes glass transition (the corresponding temperature is denoted as Tg). Extensive variability of materials' behavior during the solidification can be recognized from both, steepness of the viscosity change with temperature and rate at which excess entropy changes at Tg. Angell [1–3] has introduced his viscosity classification based on the differentiation of the material's behavior in-between the “strong” and “fragile” extremes, using Tg as a scaling parameter, with the corresponding quantity being denoted as “kinetic fragility”. The kinetic fragility, m, is defined as: d log η m¼ d T g =T
≅
Eη =R T g ln ð10Þ
ð1Þ
T¼T g
where η is viscosity and Eη is the activation energy of the viscous flow evaluated at Tg. In Eq. (1) the so-called “viscosity Tg” or T12 is usually used; this value corresponds to the temperature at which
⁎ Corresponding author. E-mail address: [email protected] (R. Svoboda).
http://dx.doi.org/10.1016/j.jnoncrysol.2015.03.041 0022-3093/© 2015 Elsevier B.V. All rights reserved.
log(η/Pa ∙ s) = 12. Fragility usually ranges between m = 17 (“strong” systems with Arrhenian behavior) and m = 150 (“fragile” systems with nonArrhenian behavior) [1–3]. The “strong” glass-formers can be often characterized by covalent directional bonds forming a spatial network (e.g., SiO2, m = 28). On the other hand, fragile liquids are typically represented by molecular units interacting through isotropic van der Waals bonds (o-terphenyl, m = 80) [1–3]. High quality viscosity data are, however, difficult to obtain and the measurements are long and tedious — especially in the critical range of log(η/Pa · s) = 11–13. In addition, usually only data for good glassformers can be found in the literature because viscous flow is significantly affected even by small amounts of crystalline content in the glassy matrix and, hence, most materials are difficult/impossible to prepare in the form suitable for viscosity measurements (rather large samples with dimensions of several millimeters are needed in most experimental setups → high cooling rate needs to be applied in order to prepare perfect bulk glass of such size → quench-cooling leads to large amounts of mechanical stress, which result in brittle and hard to cut/shape material). Various possibilities, therefore, have been investigated as to how to avoid these problems and determine fragility including worse-than-ideal glass-formers as well. One of the most often used solutions employs correlation between viscous flow and structural relaxation — it was shown that for a number of materials the activation energy of viscous flow in the glass transition region is similar to the apparent activation energy of structural relaxation [4–6]. The actual simplification then lies in further assumption that the volume/shear and enthalpy relaxation processes follow similar kinetics and their activation energies are comparable. Under such conditions, the
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apparent activation energy of enthalpy relaxation Δh⁎ and calorimetric glass transition temperature Tg (both easily determined by differential scanning calorimetry) can be used to calculate the “enthalpic fragility” [7]: ment
d log τ ¼ d T g =T
≅
Δh =R T g ln ð10Þ
ð2Þ
T¼T g
where τ is the relaxation time. In the present article, we will explore the above-suggested correlations for Se-rich glassy compositions from the Te–Se, As–Se and Ge–Se binary chalcogenide systems.
measured as a function of time t, the viscosity is then determined according to [13,14]: η¼
9 Ft pffiffiffiffiffiffi 32 2R h3=2
ð3Þ
which holds for R ≫ h. Steady viscous flow free from the structural relaxation movements and primary creep needs to be achieved for correct determination of η (measurement times up to ~60 h were applied within the framework of the current article). Viscosity–temperature dependences measured in our laboratory were those for the Se, Te10Se90, Te20Se80, Te30Se70 and Ge2Se98 compositions; viscosities for the As–Se and the rest of the Ge–Se binary chalcogenide systems were taken from the literature [7,15–19].
2. Experimental 3. Results Glassy materials researched within the framework of this study were prepared from pure elements (5N, Sigma Aldrich) by the classical melt-quenching technique. After degassing of the fused silica ampoule containing proper amounts of elements, the ampoule was sealed and put in the rocking furnace. The mixture of elements was homogenized at a high enough temperature for 24 h. Melt-quenching was used to prepare the glasses. Amorphous nature of the glasses was verified by X-ray diffraction. Compositional homogeneity was confirmed from the position of the relaxation overshoot measured under defined thermal history. Enthalpy relaxation of the prepared glasses was studied using a conventional DSC 822e (Mettler, Toledo) equipped with EK90 Haake cooling accessory. The DSC calibration was done using melting temperatures of In, Zn and Ga. Daily checks of the baseline were performed. Dry nitrogen was used as the purge gas at a rate of 20 cm3/min. Each prepared glass was ground to powder with a particle size in the 125–180 μm range, and a thin layer of the powder was spread on the bottom of an aluminum pan so that thermal contact was improved. Masses of the samples were approximately 8–10 mg. Two types of thermal histories were applied to determine the apparent activation energy Δh⁎. Both these thermal histories are based on cyclic experiments, i.e., the samples are alternately cooled and heated through the glass transition region at various cooling and heating rates. In the case of the constant heating rate (CHR) cycles, the cooling rates vary and the heating rates remain constant. The second type of cyclic experiment is the so-called constant ratio (CR) cycle. In these cycles it is the ratio between the cooling and following heating rates q+/q−, which remains the same. The ratio is usually set equal to unity, i.e., the heating scans are performed at the same rate as that of the previous cooling step. Evaluation of Δh⁎ was undertaken using state-of-the-art methodological tools [8–11], including both curvefitting and various non-fitting procedures. Enthalpy relaxation behavior was examined for the following Se-rich chalcogenide compositions: Se, Te10Se90, Te20Se80, Te30Se70, Ge2Se98, Ge4Se96, Ge6Se94, Ge8Se92, Ge10Se90, Ge15Se85, As2Se98, As4Se96, As6Se94, As8Se92, As10Se90 and As15Se85. In addition, accessible literature data [7,12] will be considered for the comparisons. The Tg values used in Eq. (2) were evaluated (as half-height midpoint) from the CHR DSC heating scans performed at 10 °C·min−1. The viscosity of the chosen glasses/supercooled liquids was measured by means of the penetration method using a thermomechanical analyzer, TMACX03R (R.M.I. Company Ltd., Czech Republic). The detector is controlled through an electronic system, ensuring linearity better than 0.1% (full scale), high sensitivity (0.01 μm resolution), low noise (typically 0.02 μm without signal filtering), very good resolution and baseline flatness over broad temperature and time scales (b0.002 μm·K−1 and 0.008 μm·h−1, respectively). The long term stability of the temperature in the isothermal regime was ±0.2 °C; the usual reproducibility of the viscosity data is then approximately 0.1 log unit. During the penetration method a hemisphere of radius R loaded by force F penetrates into the flat specimen. The penetration depth h is
The DSC enthalpy relaxation data was evaluated in accordance with the state-of-the-art methodological procedures [8–11]. Based on the mutual correlation of curve-fitting results and the results obtained from non-fitting methods, a high level of both accuracy and precision was achieved for the Δh⁎ determination. In Fig. 1 the examples of the evaluations are shown. Fig. 1A and B shows Te30Se70 DSC data (corresponding to the CHR and CR cycles, respectively) fitted by the TNM model [20–22], where one of the parameters sought during the optimization was the apparent activation energy Δh⁎. Due to the significant correlations between the particular TNM parameters determined during the curve-fitting, these results should always be confirmed by non-fitting methods. In this regard, two new non-fitting methods were developed recently in our laboratory: direct Δh⁎ evaluation from CR cycles [11] and the modified simulation-comparative method [10]. In Fig. 1C the evaluations according to the former methodology are shown — Δh⁎ is proportional to the slope of the displayed dependence of the temperature corresponding to the maximum of the relaxation overshoot on heating rate. It has to be noted that, in order to employ this type of dependences in Δh⁎ evaluation, a special type of temperature program (CR cycles) needs to be applied during the DSC measurements and the results need to be further corrected for systematic error [11]. In no case is it possible to achieve the correct results by applying simple Arrhenian dependences to the heating scans of as-prepared samples [23,24]. The results obtained from the CR cycles [11] were then confirmed by the modified simulation-comparative method [10], which is based on a direct visual comparison of the experimental and theoretical data simulated based on the pre-determined values of Δh⁎ (the considered aspects are: height and width of the relaxation overshoot, slope of the onset ΔCp edge, temperature shift of the midpoint). More details about the particular Δh⁎ evaluations can be found in [10,25–27]. Determined values of apparent activation energy of enthalpy relaxation, together with the corresponding Tg values obtained at 10 °C·min− 1, are summarized in Table 1. The viscosity–temperature dependences of Se-rich chalcogenide glasses and undercooled liquids, determined in our laboratory [28–30], are shown in Fig. 2. In Fig. 2A the viscosities of the chosen Te–Se compositions are shown; as can be seen the Te10Se90 data show a relatively pronounced curvature, while the other two compositions (Te20Se80 and Te30Se70) exhibit purely Arrhenian dependences on temperature in the given T-range. In Fig. 2B the viscosity data for Se and Ge2Se98 chalcogenide glasses/undercooled liquids are shown; it is apparent that the addition of germanium into the selenium matrix markedly increases the impact of temperature changes on viscosity. The activation energy of viscous flow Eη was then evaluated from the viscosity data for temperature corresponding to the viscosity Tg, the so-called T12, i.e., the temperature when log(η/Pa · s) = 12. The determined values of Eη and T12 are again summarized in Table 1. Regarding the error analysis, the Tg and T12 values from Table 1 were determined with the precision of ± 0.05 °C and ± 0.1 °C,
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Fig. 1. Examples of evaluation of the apparent activation energy of structural relaxation Δh⁎: A. curve-fitting of CHR cycles (Te30Se70). B. curve-fitting of CR cycles (Te30Se70). C. novel non-fitting methodology [10] evaluating Δh⁎ from CR cycles (all compositions — each graph corresponds to one chalcogenide system with y standing for the at.% content of a given element introduced into the Se matrix).
respectively. The errors of Δh⁎ determination were approx. 5–15 kJ·mol − 1 (see Table 1). The errors of E η were for the nonArrhenian viscosity dependences estimated based on the maximum acceptable variance of the tangent line slope (see Table 1 for the error values). In addition, also the m errors for the Nemilov's viscosity data [18,19] were determined in the similar way. In cases where the lowtemperature viscosities could be reasonably fitted by the Arrhenian dependence, these fits provided severely underestimated error values. The Table 1 Activation energies of structural relaxation and viscous flow, Tg, T12 and kinetic fragilities evaluated from enthalpy (ment) and viscosity (m) data. Only the data determined in our laboratory are listed in the Table.
Se Te10Se90 Te20Se80 Te30Se70 Ge2Se98 Ge4Se96 Ge6Se94 Ge8Se92 Ge10Se90 Ge15Se85 As2Se98 As4Se96 As6Se94 As8Se92 As10Se90 As15Se85
Δh⁎ kJ·mol−1
Tg °C
Eη kJ·mol−1
T12 °C
ment –
m –
356 ± 2 316 ± 8 299 ± 8 287 ± 8 416 ± 17 353 ± 17 274 ± 8 262 ± 8 241 ± 8 212 ± 33 432 ± 8 432 ± 8 441 ± 17 441 ± 17 358 ± 8 274 ± 4
38.8 45.8 53.1 58.6 44.8 50.6 72.4 85.8 98.2 127.1 43.4 50.5 57.4 64.3 72.4 86.8
353 ± 13 476 ± 31 406 ± 23 370 ± 10 432 ± 35 – – – – – – – – – – –
29.1 35.8 42.1 47.7 39.6 – – – – – – – – – – –
59.6 ± 0.4 51.7 ± 1.3 47.9 ± 1.3 45.2 ± 1.3 68.3 ± 2.8 57.0 ± 2.8 41.5 ± 1.2 38.1 ± 1.2 33.9 ± 1.1 27.7 ± 4.3 71.3 ± 1.3 69.8 ± 1.3 69.6 ± 2.7 68.2 ± 2.7 54.0 ± 1.2 39.8 ± 0.6
61.0 ± 2.3 80.5 ± 5.3 67.4 ± 3.8 60.3 ± 1.6 72.2 ± 5.9 – – – – – – – – – – –
error values were in these cases (Te20Se80, Te30Se70 and Nemilov's As10Se90, Ge3Se97, Ge5Se95 and Ge10Se90) determined as a maximum variance of m and Eη values calculated by fitting different temperature data-ranges. All these error values were then projected into the error bars of the fragility indices depicted in Figs. 3–5; the error bars are not displayed if their magnitude is lower than the magnitude of the points. Note that the m errors are shown only for the above-mentioned data, where the evaluations were performed by the present authors based on the original viscosity/relaxation data. Nevertheless, as will be discussed in the following section, these data cover all the important compositional ranges displayed in Figs. 3–5. 4. Discussion Kinetic fragility was calculated from the data listed in Table 1 according to Eqs. (1) and (2). The results are summarized in the last two columns of Table 1 — symbol m denotes the fragility index determined from the viscosity data while ment stands for the fragility calculated from the enthalpy relaxation data. Figs. 3–5 display the compositional dependences of the calculated fragility indices for the three studied chalcogenide systems. Full circles correspond to the enthalpy fragilities and full triangles correspond to the viscosity fragilities. In addition, accessible literature data, depicted in empty symbols, are also shown in the figures — the same identification as in case of the present data applies also for the literature data. In Fig. 3 the kinetic fragility data for the Ge–Se chalcogenide glasses are depicted. It is apparent that the present data are in a good agreement with the rest of the literature data. The evolution of fragility with composition in the Ge–Se system also confirms the well-known findings — be it
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Fig. 2. Temperature dependences of shear viscosity obtained in our laboratory: A. data for Te–Se compositions. B. data for Ge–Se compositions (line in case of Se data corresponds to VFT fit of selected literature data [4]).
the marked increase of fragility with the initial Ge addition into the Se matrix or the floppy/rigid compositional regions separated by the percolation threshold at approximately 22 at.% of Ge [16,31]. The rather sharp decrease of fragility occurring above circa 5 at.% of Ge may be attributed to the significant portion of the GeSe4 tetrahedra being edge-shared even in Se-rich compositions and thus increasing stiffness of the structure by forming a rigid “backbone” [32,33]. In addition, the GeSe4 tetrahedra were reported to tend to cluster in the Se-rich glasses [32,33], which further increases macroscopic manifestation of the floppy nature of the structure. Regarding the initial sharp increase of the fragility index shown with the first Ge addition, this can be associated with the markedly increased interconnection of the selenium chain structure by the randomly dispersed GeSe4 tetrahedra, which, in consequence, leads to an increase in relaxation and flow activation energies due to the increased need for higher segmental cooperativity. The further addition of Ge atoms then leads to the formation of separately relaxing clusters, increasing their number and lowering their size [10,27]. Correspondingly, the paths for shear deformation change from long Se chains (pure a-Se), to Se chains interconnecting the GeSe4 tetrahedra clusters (low Ge contents), chains of corner-shared tetrahedra (intermediate Ge contents) and series of edge-shared tetrahedral (higher Ge contents). It was even suggested in [17] that at higher Ge contents it is the corner-to-edge sharing transition that plays a major role in the flow and enthalpy relaxation processes.
Fig. 3. Compositional dependence of fragility indices for Ge–Se chalcogenide system. In graph B) the enthalpy fragilities were shifted along the Y axis to demonstrate good correspondence of the compositional trends. The literature data were taken from [12,15–18].
Regarding the correlation between the viscosity and enthalpy fragilities, it can be seen in Fig. 3 that the present ment (full circles) data correspond very well with both the literature and currently measured viscosity fragilities (empty and full triangles, respectively). In the case
Fig. 4. Compositional dependence of the fragility indices for the As–Se chalcogenide system. The literature data were taken from [7,19].
R. Svoboda, J. Málek / Journal of Non-Crystalline Solids 419 (2015) 39–44
Fig. 5. Compositional dependence of the fragility indices for the Te–Se chalcogenide system. Stars correspond to values on non-exponentiality parameter β evaluated from enthalpy relaxation measurements [26,27].
of the initial germanium additions (Ge contents between 0–2 at.%) this correlation still needs to be confirmed since the m value calculated from Nemilov's viscosity data [18] for 1 at.% of Ge is not matched by any ment counterpart while representing a fragility maximum in the Ge–Se system. It should be noted that only a few points are reported in the high viscosity region of Nemilov's data for 1 and 3 at.% of Ge, thus the corresponding fragility values are determined with relatively high error. If we further compare the literature data for viscosity and enthalpy fragilities in the 15–40 at.% of Ge region, the only available ment data are those reported by Gunasekera et al. [12], which seem to be somewhat lower than the corresponding viscosity fragilities (▽) — see Fig. 3A. These ment values were, however, determined from temperature-modulated DSC (TMDSC) measurements, where the temperature corresponding to the maximum of the non-reversing signal peak was used in a Kissinger type dependence (the dependent variable was enthalpy relaxation time calculated as τe = tmod/2π where tmod is the modulation time period). Using the modulation time periods from 40 to 120 s, Gunasekera et al. thus explored only a relatively narrow range of relaxation times τe (from 6 to 19 s), which sort of questions the applicability of this thermal spectroscopic method for determination of ment fragility. For spectroscopic methods that provide directly the temperature dependence of relaxation time, the fragility index is usually determined at τ = 100 s. In the case of curved τ–T−1 dependences, the determination of the fragility index/activation energy from the data obtained at such higher temperatures (lower τes) may lead to significantly lower values of these quantities (similarly as discussed above in the case of Nemilov's data). This effect is indeed present in the case of Se-rich compositions but diminishes with increased Ge content where the τ–T−1 dependences start to exhibit Arrhenian behavior. This is confirmed if we correct Gunasekera's ment values so that the fragility for pure a-Se falls within the generally accepted range (see Fig. 3B). In such a case the other ment values determined in the 15–40 at.% Ge region appear to be slightly higher than expected if compared to the literature viscosity fragilities. Nonetheless, even in the case of higher Ge contents the TMDSC technique may still explore only certain spectra of relaxation times, which would consequently lead to biased values of Δh⁎. The question of the correlation of the viscosity fragilities and ment fragilities obtained from TMDSC is further complicated by the fact that in [12] the temperature history of the samples is not specified in sufficient detail — in the case of the measurements taken from as-prepared samples the maximum of the non-reversing signal peak is shifted to higher temperatures asymmetrically with respect to the modulation frequency, which can further compromise determination of Δh⁎ and ment. Nevertheless, as can be seen in Fig. 3B, apart from the absolute ment values the basic compositional trends of the fragility index determined from the TMDSC measurements very nicely reproduce
43
those provided by the viscosity data (including the precisely determined percolation threshold). In Fig. 4, the kinetic fragility data for the As–Se chalcogenide glasses are depicted. It is apparent that the present data are in a good agreement with the rest of the literature data. The only exception is again in the case of the fragility determined from Nemilov's viscosity data [19] for As5Se95 composition, where the low number of data points coupled with the uncertainty of the viscosity measurements and the significant curvature of the η–T−1 dependence may, however, lead to biased or imprecise m determination. The evolution of fragility with composition in the As–Se system again confirms both the increase in fragility with the initial As addition into the Se matrix and the characteristic fragility increase at the rigidity percolation threshold. Contrary to the Ge–Se system, where the fragility behavior was explained on the basis of structural heterogeneity [17], in the case of the As–Se materials the compositional fragility development can be associated with the dimensionality of the glassy structure [7]. In [7] the following dimensionalities 1D, 1D/2D, 3D, 2D, 3D + 0D and 1D/2D + 0D were reported for the following average coordination numbers brN = 2, 2.1, 2.3, 2.4, 2.5 and 2.6, respectively. We can interpret the dimensionalities also in terms of the structural connectedness: the initial As additions lead to formation of interconnections in-between the existing Se chains via the trigonal AsSe3/2 elements. Further As additions then result in the formation of highly interconnected rigid 3D structure with the As2Se3 bipyramids acting as the bonding structural units. For the stoichiometric As2Se3 structure only bi-pyramids should in theory exist in the system and thus only a planar two-dimensional structure is formed (opposed to the 3D networks formed for the neighboring Se-richer and As-richer glasses), which corresponds to a decrease of the structure rigidity (local fragility maximum in Fig. 4). For the As content N 50% the connectedness of the structure starts to decrease again due to the formation of the As4Se3 cages that are to the surrounding structural elements bonded only by van der Waals forces. Regarding the correlation of viscosity and enthalpy fragilities, almost excellent agreement was reported in [7] for the 10–40 at.% As region. Moreover, the present data also exhibit a very good correlation between m and ment (except for the above-described Nemilov's viscosity data for As5Se95 composition). Lastly, in Fig. 5 the kinetic fragility data for the Te–Se chalcogenide glasses are depicted. Contrary to the Ge–Se and As–Se chalcogenide systems, the Te–Se viscosity and enthalpy fragilities show a marked decoupling. Strictly speaking, there is in fact no physical reason for the two quantities (enthalpy and viscosity fragilities) to be similar. The former is related to the activation energy of structural relaxation changes whereas the latter is associated with the activation energy of the viscous flow. One can see that (despite the structural relaxation and viscous flow are very akin processes) different molecular movements and mechanisms are involved in the two processes. In addition, manifestations of enthalpy and volume behavior (viscous flow) can be also caused by different structural movements. Therefore, in theory there is no rule for the two fragility types to exhibit similar values. Nonetheless, as shown above for most Ge–Se and As–Se glasses they do. Hence, it is likely that it is the different dynamics of the structural ordering/bonding in the Te–Se system, which is responsible for the dissimilarity of the fragility behavior. Note that the difference between the T12 and calorimetric Tg values (which are determined at different experimental conditions) account only for a very small portion (Δm b 3%) of the depicted differences between the m and ment values. Structurally speaking, Te–Se glasses consist of heteropolar two-fold coordinated helical chains and rings, where the selenium atoms are more or less randomly replaced by tellurium ones [34–36]. The Te–Se bonds, however, appear to be prioritized over the Te–Te and Se–Se bonds [37–39]. The larger tellurium atoms do not seem to distort the molecular structures or to change the molecular density [37–39]. In the authors' opinion, one of the possible explanations for the observed decoupling of fragilities could be related to the specific structural relaxation features — namely the combination of moderate-to-high activation
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energies and highly exponential behavior (this is exactly the case of the Te–Se glassy system; see Fig. 5 where the values of the TNM parameter of non-exponentiality β are displayed). Following this assumption, higher Eη (and hence viscosity fragility) in the Te–Se glassy system could be explained on the basis of increased cooperativity of structural segments leading to a rise in the apparent energy barriers for viscous flow.
References
5. Conclusions
[8] [9] [10] [11] [12]
Fragility indices determined from viscosity and enthalpy relaxation measurements were compared for Se-rich glasses from Ge–Se, As–Se and Te–Se chalcogenide systems. Based on the present data, a possible decoupling mechanism for the two fragility types can be suggested: the activation energy of viscous flow (and hence shear viscosity fragility) is increased by structural cooperativity associated with relaxation processes (cooperative movements of the involved structural segments during the structural relaxation). Within the framework of this conception a sufficiently narrow distribution of relaxation times could thus contribute to the overall m value as can be observed in the case of all Te–Se glasses and low-Ge/As-content Ge–Se and As–Se compositions (where again the segmental cooperativity is relatively high [27]). Higher Ge/As contents then result in increased interconnectivity of the glassy network, which leads to a wider distribution of the relaxation times and, hence, a “kinetically stronger” classification of the glass. On the other hand, the kinetic fragility calculated directly from the enthalpy relaxation data seems not to be influenced in a similar way. The possible reason may lie either in different molecular movements being involved in the two processes (viscous flow versus structural relaxation) or in their different manifestation in terms of volume and enthalpy behavior. Further investigation is therefore needed. Acknowledgments This work has been supported by the Czech Science Foundation under project no. P106/11/1152.
[1] [2] [3] [4] [5] [6] [7]
[13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39]
C.A. Angell, J. Non-Cryst. Solids 131–133 (1991) 13. C.A. Angell, Science 267 (1995) 1924. C.A. Angell, Res. NIST 102 (1997) 171. J. Málek, R. Svoboda, P. Pustková, P. Čičmanec, J. Non-Cryst. Solids 355 (2009) 264. I.M. Hodge, J. Non-Cryst. Solids 131–133 (1991) 435. M. Chromčiková, M. Liška, J. Therm. Anal. Calorim. 84 (2006) 703. G. Yang, O. Gulbiten, Y. Gueguen, B. Bureau, J.-C. Sangleboeuf, C. Roiland, E.A. King, P. Lucas, Phys. Rev. B 85 (2012) 144107. R. Svoboda, J. Málek, J. Non-Cryst. Solids 378 (2013) 186. R. Svoboda, J. Therm. Anal. Calorim. 118 (2014) 1721. R. Svoboda, J. Málek, J. Therm. Anal. Calorim. 113 (2013) 831. R. Svoboda, Eur. Polym. J. 59 (2014) 180. K. Gunasekera, S. Bhosle, P. Boolchand, M. Micoulaut, J. Chem. Phys. 139 (2013) 164511. R. Brückner, D. Demharter, Glastech. Ber. 48 (1975) 12. P. Exnar, M. Hrubá, J. Uhlíř, J. Voldán, Silikáty 24 (1980) 169. U. Senapati, A.K. Varshneya, J. Non-Cryst. Solids 197 (1996) 210. S. Stolen, T. Grande, H.-B. Johnsen, Phys. Chem. Chem. Phys. 4 (2002) 3396. Y. Gueguen, T. Rouxel, P. Gadaud, C. Bernard, V. Keryvin, J.C. Sangleboeuf, Phys. Rev. B 84 (2011) 064201. S.V. Nemilov, Zh. Prikl. Khim. 37 (1964) 1020. S.V. Nemilov, G.T. Petrovskii, Zh. Prikl. Khim. 36 (1963) 977. O.S. Narayanaswamy, J. Am. Ceram. Soc. 54 (1971) 491. C.T. Moynihan, A.J. Easteal, M.A. DeBolt, J. Tucker, J. Am. Ceram. Soc. 59 (1976) 12. A.Q. Tool, J. Am. Ceram. Soc. 29 (1946) 240. R. Svoboda, P. Čičmanec, J. Málek, J. Therm. Anal. Calorim. 114 (2013) 285. R. Svoboda, J. Málek, Polymer 54 (2013) 1504. R. Svoboda, J. Málek, J. Non-Cryst. Solids 363 (2013) 89. R. Svoboda, P. Honcová, J. Málek, J. Non-Cryst. Solids 357 (2011) 2163. R. Svoboda, Acta Mater. 61 (2013) 4534. J. Barták, J. Málek, P. Koštál, H. Segawa, Y. Yamabe-Mitarai, J. Appl. Phys. 115 (2014) 123506. L. Balatka, Bachelor Thesis, University of Pardubice (2010). J. Barták, Bachelor Thesis, University of Pardubice (2007). V.M. Glazov, O.V. Situlina, Dokl. Chem. 187 (1969) 24. T.G. Edwards, S. Sen, J. Phys. Chem. B 115 (2011) 4307. E. Gjersing, S. Sen, B. Aitken, J. Phys. Chem. 114 (2010) 8601. R.K. Venugopal, A.K. Bhatnagar, J. Phys. D. Appl. Phys. 25 (1992) 1810. A. El-Korashy, H. El-Zahed, M. Radwan, A.M. Abdalla, Thin Solid Films 261 (1995) 328. K. Shimakawa, S. Nitta, Phys. Rev. B 17 (1978) 3950. N. Afify, A. Gaber, I. Abdalla, H. Talaat, Physica B 229 (1997) 167. M. Majid, S. Benazeth, C. Souleau, J. Purans, Phys. Rev. B 58 (1998) 6104. T. Tsuzuki, M. Yao, H. Endo, J. Phys. Soc. Jpn. 64 (1995) 485.
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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/ locate/ jnoncrysol
Kinetic fragility of Se-based binary chalcogenide glasses Roman Svoboda ⁎, Jiří Málek University of Pardubice, Faculty of Chemical Technology, Department of Physical Chemistry, Studentská 573, 532 10 Pardubice, Czech Republic
a r t i c l e
i n f o
Article history: Received 17 November 2014 Received in revised form 21 March 2015 Accepted 30 March 2015 Available online xxxx Keywords: Kinetic fragility; Chalcogenides; Viscosity; Enthalpy relaxation; Decoupling
a b s t r a c t Kinetic fragility was determined for a number of compositions from the Ge–Se, As–Se and Te–Se chalcogenide glassy systems. Values of fragility indices were evaluated from both viscosity and enthalpy relaxation data. Comparison of the viscosity and enthalpy fragilities shows marked decoupling in cases of low-Ge/As-content compositions and the whole Te–Se glassy system. A possible explanation regarding the increased viscosity fragilities involves the influence of dynamic structural heterogeneity (density fluctuations and clustering of structural elements) on shear viscosity in the glass transition region. In particular, the observed decoupling seems to occur in case of the materials exhibiting moderate-to-high activation energy of relaxation processes and large structural cooperativity. The origin of the fragility decoupling may lie either in different molecular movements being involved in the two processes (viscous flow versus structural relaxation) or in their different manifestation in terms of volume and enthalpy behavior. © 2015 Elsevier B.V. All rights reserved.
1. Introduction It is well known that a large number of liquids of all types can be solidified without undergoing crystallization. At fast enough cooling rates the nucleation and crystal growth processes can be kinetically avoided and the undercooled liquid then at a certain state of structural compactness undergoes glass transition (the corresponding temperature is denoted as Tg). Extensive variability of materials' behavior during the solidification can be recognized from both, steepness of the viscosity change with temperature and rate at which excess entropy changes at Tg. Angell [1–3] has introduced his viscosity classification based on the differentiation of the material's behavior in-between the “strong” and “fragile” extremes, using Tg as a scaling parameter, with the corresponding quantity being denoted as “kinetic fragility”. The kinetic fragility, m, is defined as: d log η m¼ d T g =T
≅
Eη =R T g ln ð10Þ
ð1Þ
T¼T g
where η is viscosity and Eη is the activation energy of the viscous flow evaluated at Tg. In Eq. (1) the so-called “viscosity Tg” or T12 is usually used; this value corresponds to the temperature at which
⁎ Corresponding author. E-mail address: [email protected] (R. Svoboda).
http://dx.doi.org/10.1016/j.jnoncrysol.2015.03.041 0022-3093/© 2015 Elsevier B.V. All rights reserved.
log(η/Pa ∙ s) = 12. Fragility usually ranges between m = 17 (“strong” systems with Arrhenian behavior) and m = 150 (“fragile” systems with nonArrhenian behavior) [1–3]. The “strong” glass-formers can be often characterized by covalent directional bonds forming a spatial network (e.g., SiO2, m = 28). On the other hand, fragile liquids are typically represented by molecular units interacting through isotropic van der Waals bonds (o-terphenyl, m = 80) [1–3]. High quality viscosity data are, however, difficult to obtain and the measurements are long and tedious — especially in the critical range of log(η/Pa · s) = 11–13. In addition, usually only data for good glassformers can be found in the literature because viscous flow is significantly affected even by small amounts of crystalline content in the glassy matrix and, hence, most materials are difficult/impossible to prepare in the form suitable for viscosity measurements (rather large samples with dimensions of several millimeters are needed in most experimental setups → high cooling rate needs to be applied in order to prepare perfect bulk glass of such size → quench-cooling leads to large amounts of mechanical stress, which result in brittle and hard to cut/shape material). Various possibilities, therefore, have been investigated as to how to avoid these problems and determine fragility including worse-than-ideal glass-formers as well. One of the most often used solutions employs correlation between viscous flow and structural relaxation — it was shown that for a number of materials the activation energy of viscous flow in the glass transition region is similar to the apparent activation energy of structural relaxation [4–6]. The actual simplification then lies in further assumption that the volume/shear and enthalpy relaxation processes follow similar kinetics and their activation energies are comparable. Under such conditions, the
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apparent activation energy of enthalpy relaxation Δh⁎ and calorimetric glass transition temperature Tg (both easily determined by differential scanning calorimetry) can be used to calculate the “enthalpic fragility” [7]: ment
d log τ ¼ d T g =T
≅
Δh =R T g ln ð10Þ
ð2Þ
T¼T g
where τ is the relaxation time. In the present article, we will explore the above-suggested correlations for Se-rich glassy compositions from the Te–Se, As–Se and Ge–Se binary chalcogenide systems.
measured as a function of time t, the viscosity is then determined according to [13,14]: η¼
9 Ft pffiffiffiffiffiffi 32 2R h3=2
ð3Þ
which holds for R ≫ h. Steady viscous flow free from the structural relaxation movements and primary creep needs to be achieved for correct determination of η (measurement times up to ~60 h were applied within the framework of the current article). Viscosity–temperature dependences measured in our laboratory were those for the Se, Te10Se90, Te20Se80, Te30Se70 and Ge2Se98 compositions; viscosities for the As–Se and the rest of the Ge–Se binary chalcogenide systems were taken from the literature [7,15–19].
2. Experimental 3. Results Glassy materials researched within the framework of this study were prepared from pure elements (5N, Sigma Aldrich) by the classical melt-quenching technique. After degassing of the fused silica ampoule containing proper amounts of elements, the ampoule was sealed and put in the rocking furnace. The mixture of elements was homogenized at a high enough temperature for 24 h. Melt-quenching was used to prepare the glasses. Amorphous nature of the glasses was verified by X-ray diffraction. Compositional homogeneity was confirmed from the position of the relaxation overshoot measured under defined thermal history. Enthalpy relaxation of the prepared glasses was studied using a conventional DSC 822e (Mettler, Toledo) equipped with EK90 Haake cooling accessory. The DSC calibration was done using melting temperatures of In, Zn and Ga. Daily checks of the baseline were performed. Dry nitrogen was used as the purge gas at a rate of 20 cm3/min. Each prepared glass was ground to powder with a particle size in the 125–180 μm range, and a thin layer of the powder was spread on the bottom of an aluminum pan so that thermal contact was improved. Masses of the samples were approximately 8–10 mg. Two types of thermal histories were applied to determine the apparent activation energy Δh⁎. Both these thermal histories are based on cyclic experiments, i.e., the samples are alternately cooled and heated through the glass transition region at various cooling and heating rates. In the case of the constant heating rate (CHR) cycles, the cooling rates vary and the heating rates remain constant. The second type of cyclic experiment is the so-called constant ratio (CR) cycle. In these cycles it is the ratio between the cooling and following heating rates q+/q−, which remains the same. The ratio is usually set equal to unity, i.e., the heating scans are performed at the same rate as that of the previous cooling step. Evaluation of Δh⁎ was undertaken using state-of-the-art methodological tools [8–11], including both curvefitting and various non-fitting procedures. Enthalpy relaxation behavior was examined for the following Se-rich chalcogenide compositions: Se, Te10Se90, Te20Se80, Te30Se70, Ge2Se98, Ge4Se96, Ge6Se94, Ge8Se92, Ge10Se90, Ge15Se85, As2Se98, As4Se96, As6Se94, As8Se92, As10Se90 and As15Se85. In addition, accessible literature data [7,12] will be considered for the comparisons. The Tg values used in Eq. (2) were evaluated (as half-height midpoint) from the CHR DSC heating scans performed at 10 °C·min−1. The viscosity of the chosen glasses/supercooled liquids was measured by means of the penetration method using a thermomechanical analyzer, TMACX03R (R.M.I. Company Ltd., Czech Republic). The detector is controlled through an electronic system, ensuring linearity better than 0.1% (full scale), high sensitivity (0.01 μm resolution), low noise (typically 0.02 μm without signal filtering), very good resolution and baseline flatness over broad temperature and time scales (b0.002 μm·K−1 and 0.008 μm·h−1, respectively). The long term stability of the temperature in the isothermal regime was ±0.2 °C; the usual reproducibility of the viscosity data is then approximately 0.1 log unit. During the penetration method a hemisphere of radius R loaded by force F penetrates into the flat specimen. The penetration depth h is
The DSC enthalpy relaxation data was evaluated in accordance with the state-of-the-art methodological procedures [8–11]. Based on the mutual correlation of curve-fitting results and the results obtained from non-fitting methods, a high level of both accuracy and precision was achieved for the Δh⁎ determination. In Fig. 1 the examples of the evaluations are shown. Fig. 1A and B shows Te30Se70 DSC data (corresponding to the CHR and CR cycles, respectively) fitted by the TNM model [20–22], where one of the parameters sought during the optimization was the apparent activation energy Δh⁎. Due to the significant correlations between the particular TNM parameters determined during the curve-fitting, these results should always be confirmed by non-fitting methods. In this regard, two new non-fitting methods were developed recently in our laboratory: direct Δh⁎ evaluation from CR cycles [11] and the modified simulation-comparative method [10]. In Fig. 1C the evaluations according to the former methodology are shown — Δh⁎ is proportional to the slope of the displayed dependence of the temperature corresponding to the maximum of the relaxation overshoot on heating rate. It has to be noted that, in order to employ this type of dependences in Δh⁎ evaluation, a special type of temperature program (CR cycles) needs to be applied during the DSC measurements and the results need to be further corrected for systematic error [11]. In no case is it possible to achieve the correct results by applying simple Arrhenian dependences to the heating scans of as-prepared samples [23,24]. The results obtained from the CR cycles [11] were then confirmed by the modified simulation-comparative method [10], which is based on a direct visual comparison of the experimental and theoretical data simulated based on the pre-determined values of Δh⁎ (the considered aspects are: height and width of the relaxation overshoot, slope of the onset ΔCp edge, temperature shift of the midpoint). More details about the particular Δh⁎ evaluations can be found in [10,25–27]. Determined values of apparent activation energy of enthalpy relaxation, together with the corresponding Tg values obtained at 10 °C·min− 1, are summarized in Table 1. The viscosity–temperature dependences of Se-rich chalcogenide glasses and undercooled liquids, determined in our laboratory [28–30], are shown in Fig. 2. In Fig. 2A the viscosities of the chosen Te–Se compositions are shown; as can be seen the Te10Se90 data show a relatively pronounced curvature, while the other two compositions (Te20Se80 and Te30Se70) exhibit purely Arrhenian dependences on temperature in the given T-range. In Fig. 2B the viscosity data for Se and Ge2Se98 chalcogenide glasses/undercooled liquids are shown; it is apparent that the addition of germanium into the selenium matrix markedly increases the impact of temperature changes on viscosity. The activation energy of viscous flow Eη was then evaluated from the viscosity data for temperature corresponding to the viscosity Tg, the so-called T12, i.e., the temperature when log(η/Pa · s) = 12. The determined values of Eη and T12 are again summarized in Table 1. Regarding the error analysis, the Tg and T12 values from Table 1 were determined with the precision of ± 0.05 °C and ± 0.1 °C,
R. Svoboda, J. Málek / Journal of Non-Crystalline Solids 419 (2015) 39–44
41
Fig. 1. Examples of evaluation of the apparent activation energy of structural relaxation Δh⁎: A. curve-fitting of CHR cycles (Te30Se70). B. curve-fitting of CR cycles (Te30Se70). C. novel non-fitting methodology [10] evaluating Δh⁎ from CR cycles (all compositions — each graph corresponds to one chalcogenide system with y standing for the at.% content of a given element introduced into the Se matrix).
respectively. The errors of Δh⁎ determination were approx. 5–15 kJ·mol − 1 (see Table 1). The errors of E η were for the nonArrhenian viscosity dependences estimated based on the maximum acceptable variance of the tangent line slope (see Table 1 for the error values). In addition, also the m errors for the Nemilov's viscosity data [18,19] were determined in the similar way. In cases where the lowtemperature viscosities could be reasonably fitted by the Arrhenian dependence, these fits provided severely underestimated error values. The Table 1 Activation energies of structural relaxation and viscous flow, Tg, T12 and kinetic fragilities evaluated from enthalpy (ment) and viscosity (m) data. Only the data determined in our laboratory are listed in the Table.
Se Te10Se90 Te20Se80 Te30Se70 Ge2Se98 Ge4Se96 Ge6Se94 Ge8Se92 Ge10Se90 Ge15Se85 As2Se98 As4Se96 As6Se94 As8Se92 As10Se90 As15Se85
Δh⁎ kJ·mol−1
Tg °C
Eη kJ·mol−1
T12 °C
ment –
m –
356 ± 2 316 ± 8 299 ± 8 287 ± 8 416 ± 17 353 ± 17 274 ± 8 262 ± 8 241 ± 8 212 ± 33 432 ± 8 432 ± 8 441 ± 17 441 ± 17 358 ± 8 274 ± 4
38.8 45.8 53.1 58.6 44.8 50.6 72.4 85.8 98.2 127.1 43.4 50.5 57.4 64.3 72.4 86.8
353 ± 13 476 ± 31 406 ± 23 370 ± 10 432 ± 35 – – – – – – – – – – –
29.1 35.8 42.1 47.7 39.6 – – – – – – – – – – –
59.6 ± 0.4 51.7 ± 1.3 47.9 ± 1.3 45.2 ± 1.3 68.3 ± 2.8 57.0 ± 2.8 41.5 ± 1.2 38.1 ± 1.2 33.9 ± 1.1 27.7 ± 4.3 71.3 ± 1.3 69.8 ± 1.3 69.6 ± 2.7 68.2 ± 2.7 54.0 ± 1.2 39.8 ± 0.6
61.0 ± 2.3 80.5 ± 5.3 67.4 ± 3.8 60.3 ± 1.6 72.2 ± 5.9 – – – – – – – – – – –
error values were in these cases (Te20Se80, Te30Se70 and Nemilov's As10Se90, Ge3Se97, Ge5Se95 and Ge10Se90) determined as a maximum variance of m and Eη values calculated by fitting different temperature data-ranges. All these error values were then projected into the error bars of the fragility indices depicted in Figs. 3–5; the error bars are not displayed if their magnitude is lower than the magnitude of the points. Note that the m errors are shown only for the above-mentioned data, where the evaluations were performed by the present authors based on the original viscosity/relaxation data. Nevertheless, as will be discussed in the following section, these data cover all the important compositional ranges displayed in Figs. 3–5. 4. Discussion Kinetic fragility was calculated from the data listed in Table 1 according to Eqs. (1) and (2). The results are summarized in the last two columns of Table 1 — symbol m denotes the fragility index determined from the viscosity data while ment stands for the fragility calculated from the enthalpy relaxation data. Figs. 3–5 display the compositional dependences of the calculated fragility indices for the three studied chalcogenide systems. Full circles correspond to the enthalpy fragilities and full triangles correspond to the viscosity fragilities. In addition, accessible literature data, depicted in empty symbols, are also shown in the figures — the same identification as in case of the present data applies also for the literature data. In Fig. 3 the kinetic fragility data for the Ge–Se chalcogenide glasses are depicted. It is apparent that the present data are in a good agreement with the rest of the literature data. The evolution of fragility with composition in the Ge–Se system also confirms the well-known findings — be it
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Fig. 2. Temperature dependences of shear viscosity obtained in our laboratory: A. data for Te–Se compositions. B. data for Ge–Se compositions (line in case of Se data corresponds to VFT fit of selected literature data [4]).
the marked increase of fragility with the initial Ge addition into the Se matrix or the floppy/rigid compositional regions separated by the percolation threshold at approximately 22 at.% of Ge [16,31]. The rather sharp decrease of fragility occurring above circa 5 at.% of Ge may be attributed to the significant portion of the GeSe4 tetrahedra being edge-shared even in Se-rich compositions and thus increasing stiffness of the structure by forming a rigid “backbone” [32,33]. In addition, the GeSe4 tetrahedra were reported to tend to cluster in the Se-rich glasses [32,33], which further increases macroscopic manifestation of the floppy nature of the structure. Regarding the initial sharp increase of the fragility index shown with the first Ge addition, this can be associated with the markedly increased interconnection of the selenium chain structure by the randomly dispersed GeSe4 tetrahedra, which, in consequence, leads to an increase in relaxation and flow activation energies due to the increased need for higher segmental cooperativity. The further addition of Ge atoms then leads to the formation of separately relaxing clusters, increasing their number and lowering their size [10,27]. Correspondingly, the paths for shear deformation change from long Se chains (pure a-Se), to Se chains interconnecting the GeSe4 tetrahedra clusters (low Ge contents), chains of corner-shared tetrahedra (intermediate Ge contents) and series of edge-shared tetrahedral (higher Ge contents). It was even suggested in [17] that at higher Ge contents it is the corner-to-edge sharing transition that plays a major role in the flow and enthalpy relaxation processes.
Fig. 3. Compositional dependence of fragility indices for Ge–Se chalcogenide system. In graph B) the enthalpy fragilities were shifted along the Y axis to demonstrate good correspondence of the compositional trends. The literature data were taken from [12,15–18].
Regarding the correlation between the viscosity and enthalpy fragilities, it can be seen in Fig. 3 that the present ment (full circles) data correspond very well with both the literature and currently measured viscosity fragilities (empty and full triangles, respectively). In the case
Fig. 4. Compositional dependence of the fragility indices for the As–Se chalcogenide system. The literature data were taken from [7,19].
R. Svoboda, J. Málek / Journal of Non-Crystalline Solids 419 (2015) 39–44
Fig. 5. Compositional dependence of the fragility indices for the Te–Se chalcogenide system. Stars correspond to values on non-exponentiality parameter β evaluated from enthalpy relaxation measurements [26,27].
of the initial germanium additions (Ge contents between 0–2 at.%) this correlation still needs to be confirmed since the m value calculated from Nemilov's viscosity data [18] for 1 at.% of Ge is not matched by any ment counterpart while representing a fragility maximum in the Ge–Se system. It should be noted that only a few points are reported in the high viscosity region of Nemilov's data for 1 and 3 at.% of Ge, thus the corresponding fragility values are determined with relatively high error. If we further compare the literature data for viscosity and enthalpy fragilities in the 15–40 at.% of Ge region, the only available ment data are those reported by Gunasekera et al. [12], which seem to be somewhat lower than the corresponding viscosity fragilities (▽) — see Fig. 3A. These ment values were, however, determined from temperature-modulated DSC (TMDSC) measurements, where the temperature corresponding to the maximum of the non-reversing signal peak was used in a Kissinger type dependence (the dependent variable was enthalpy relaxation time calculated as τe = tmod/2π where tmod is the modulation time period). Using the modulation time periods from 40 to 120 s, Gunasekera et al. thus explored only a relatively narrow range of relaxation times τe (from 6 to 19 s), which sort of questions the applicability of this thermal spectroscopic method for determination of ment fragility. For spectroscopic methods that provide directly the temperature dependence of relaxation time, the fragility index is usually determined at τ = 100 s. In the case of curved τ–T−1 dependences, the determination of the fragility index/activation energy from the data obtained at such higher temperatures (lower τes) may lead to significantly lower values of these quantities (similarly as discussed above in the case of Nemilov's data). This effect is indeed present in the case of Se-rich compositions but diminishes with increased Ge content where the τ–T−1 dependences start to exhibit Arrhenian behavior. This is confirmed if we correct Gunasekera's ment values so that the fragility for pure a-Se falls within the generally accepted range (see Fig. 3B). In such a case the other ment values determined in the 15–40 at.% Ge region appear to be slightly higher than expected if compared to the literature viscosity fragilities. Nonetheless, even in the case of higher Ge contents the TMDSC technique may still explore only certain spectra of relaxation times, which would consequently lead to biased values of Δh⁎. The question of the correlation of the viscosity fragilities and ment fragilities obtained from TMDSC is further complicated by the fact that in [12] the temperature history of the samples is not specified in sufficient detail — in the case of the measurements taken from as-prepared samples the maximum of the non-reversing signal peak is shifted to higher temperatures asymmetrically with respect to the modulation frequency, which can further compromise determination of Δh⁎ and ment. Nevertheless, as can be seen in Fig. 3B, apart from the absolute ment values the basic compositional trends of the fragility index determined from the TMDSC measurements very nicely reproduce
43
those provided by the viscosity data (including the precisely determined percolation threshold). In Fig. 4, the kinetic fragility data for the As–Se chalcogenide glasses are depicted. It is apparent that the present data are in a good agreement with the rest of the literature data. The only exception is again in the case of the fragility determined from Nemilov's viscosity data [19] for As5Se95 composition, where the low number of data points coupled with the uncertainty of the viscosity measurements and the significant curvature of the η–T−1 dependence may, however, lead to biased or imprecise m determination. The evolution of fragility with composition in the As–Se system again confirms both the increase in fragility with the initial As addition into the Se matrix and the characteristic fragility increase at the rigidity percolation threshold. Contrary to the Ge–Se system, where the fragility behavior was explained on the basis of structural heterogeneity [17], in the case of the As–Se materials the compositional fragility development can be associated with the dimensionality of the glassy structure [7]. In [7] the following dimensionalities 1D, 1D/2D, 3D, 2D, 3D + 0D and 1D/2D + 0D were reported for the following average coordination numbers brN = 2, 2.1, 2.3, 2.4, 2.5 and 2.6, respectively. We can interpret the dimensionalities also in terms of the structural connectedness: the initial As additions lead to formation of interconnections in-between the existing Se chains via the trigonal AsSe3/2 elements. Further As additions then result in the formation of highly interconnected rigid 3D structure with the As2Se3 bipyramids acting as the bonding structural units. For the stoichiometric As2Se3 structure only bi-pyramids should in theory exist in the system and thus only a planar two-dimensional structure is formed (opposed to the 3D networks formed for the neighboring Se-richer and As-richer glasses), which corresponds to a decrease of the structure rigidity (local fragility maximum in Fig. 4). For the As content N 50% the connectedness of the structure starts to decrease again due to the formation of the As4Se3 cages that are to the surrounding structural elements bonded only by van der Waals forces. Regarding the correlation of viscosity and enthalpy fragilities, almost excellent agreement was reported in [7] for the 10–40 at.% As region. Moreover, the present data also exhibit a very good correlation between m and ment (except for the above-described Nemilov's viscosity data for As5Se95 composition). Lastly, in Fig. 5 the kinetic fragility data for the Te–Se chalcogenide glasses are depicted. Contrary to the Ge–Se and As–Se chalcogenide systems, the Te–Se viscosity and enthalpy fragilities show a marked decoupling. Strictly speaking, there is in fact no physical reason for the two quantities (enthalpy and viscosity fragilities) to be similar. The former is related to the activation energy of structural relaxation changes whereas the latter is associated with the activation energy of the viscous flow. One can see that (despite the structural relaxation and viscous flow are very akin processes) different molecular movements and mechanisms are involved in the two processes. In addition, manifestations of enthalpy and volume behavior (viscous flow) can be also caused by different structural movements. Therefore, in theory there is no rule for the two fragility types to exhibit similar values. Nonetheless, as shown above for most Ge–Se and As–Se glasses they do. Hence, it is likely that it is the different dynamics of the structural ordering/bonding in the Te–Se system, which is responsible for the dissimilarity of the fragility behavior. Note that the difference between the T12 and calorimetric Tg values (which are determined at different experimental conditions) account only for a very small portion (Δm b 3%) of the depicted differences between the m and ment values. Structurally speaking, Te–Se glasses consist of heteropolar two-fold coordinated helical chains and rings, where the selenium atoms are more or less randomly replaced by tellurium ones [34–36]. The Te–Se bonds, however, appear to be prioritized over the Te–Te and Se–Se bonds [37–39]. The larger tellurium atoms do not seem to distort the molecular structures or to change the molecular density [37–39]. In the authors' opinion, one of the possible explanations for the observed decoupling of fragilities could be related to the specific structural relaxation features — namely the combination of moderate-to-high activation
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energies and highly exponential behavior (this is exactly the case of the Te–Se glassy system; see Fig. 5 where the values of the TNM parameter of non-exponentiality β are displayed). Following this assumption, higher Eη (and hence viscosity fragility) in the Te–Se glassy system could be explained on the basis of increased cooperativity of structural segments leading to a rise in the apparent energy barriers for viscous flow.
References
5. Conclusions
[8] [9] [10] [11] [12]
Fragility indices determined from viscosity and enthalpy relaxation measurements were compared for Se-rich glasses from Ge–Se, As–Se and Te–Se chalcogenide systems. Based on the present data, a possible decoupling mechanism for the two fragility types can be suggested: the activation energy of viscous flow (and hence shear viscosity fragility) is increased by structural cooperativity associated with relaxation processes (cooperative movements of the involved structural segments during the structural relaxation). Within the framework of this conception a sufficiently narrow distribution of relaxation times could thus contribute to the overall m value as can be observed in the case of all Te–Se glasses and low-Ge/As-content Ge–Se and As–Se compositions (where again the segmental cooperativity is relatively high [27]). Higher Ge/As contents then result in increased interconnectivity of the glassy network, which leads to a wider distribution of the relaxation times and, hence, a “kinetically stronger” classification of the glass. On the other hand, the kinetic fragility calculated directly from the enthalpy relaxation data seems not to be influenced in a similar way. The possible reason may lie either in different molecular movements being involved in the two processes (viscous flow versus structural relaxation) or in their different manifestation in terms of volume and enthalpy behavior. Further investigation is therefore needed. Acknowledgments This work has been supported by the Czech Science Foundation under project no. P106/11/1152.
[1] [2] [3] [4] [5] [6] [7]
[13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39]
C.A. Angell, J. Non-Cryst. Solids 131–133 (1991) 13. C.A. Angell, Science 267 (1995) 1924. C.A. Angell, Res. NIST 102 (1997) 171. J. Málek, R. Svoboda, P. Pustková, P. Čičmanec, J. Non-Cryst. Solids 355 (2009) 264. I.M. Hodge, J. Non-Cryst. Solids 131–133 (1991) 435. M. Chromčiková, M. Liška, J. Therm. Anal. Calorim. 84 (2006) 703. G. Yang, O. Gulbiten, Y. Gueguen, B. Bureau, J.-C. Sangleboeuf, C. Roiland, E.A. King, P. Lucas, Phys. Rev. B 85 (2012) 144107. R. Svoboda, J. Málek, J. Non-Cryst. Solids 378 (2013) 186. R. Svoboda, J. Therm. Anal. Calorim. 118 (2014) 1721. R. Svoboda, J. Málek, J. Therm. Anal. Calorim. 113 (2013) 831. R. Svoboda, Eur. Polym. J. 59 (2014) 180. K. Gunasekera, S. Bhosle, P. Boolchand, M. Micoulaut, J. Chem. Phys. 139 (2013) 164511. R. Brückner, D. Demharter, Glastech. Ber. 48 (1975) 12. P. Exnar, M. Hrubá, J. Uhlíř, J. Voldán, Silikáty 24 (1980) 169. U. Senapati, A.K. Varshneya, J. Non-Cryst. Solids 197 (1996) 210. S. Stolen, T. Grande, H.-B. Johnsen, Phys. Chem. Chem. Phys. 4 (2002) 3396. Y. Gueguen, T. Rouxel, P. Gadaud, C. Bernard, V. Keryvin, J.C. Sangleboeuf, Phys. Rev. B 84 (2011) 064201. S.V. Nemilov, Zh. Prikl. Khim. 37 (1964) 1020. S.V. Nemilov, G.T. Petrovskii, Zh. Prikl. Khim. 36 (1963) 977. O.S. Narayanaswamy, J. Am. Ceram. Soc. 54 (1971) 491. C.T. Moynihan, A.J. Easteal, M.A. DeBolt, J. Tucker, J. Am. Ceram. Soc. 59 (1976) 12. A.Q. Tool, J. Am. Ceram. Soc. 29 (1946) 240. R. Svoboda, P. Čičmanec, J. Málek, J. Therm. Anal. Calorim. 114 (2013) 285. R. Svoboda, J. Málek, Polymer 54 (2013) 1504. R. Svoboda, J. Málek, J. Non-Cryst. Solids 363 (2013) 89. R. Svoboda, P. Honcová, J. Málek, J. Non-Cryst. Solids 357 (2011) 2163. R. Svoboda, Acta Mater. 61 (2013) 4534. J. Barták, J. Málek, P. Koštál, H. Segawa, Y. Yamabe-Mitarai, J. Appl. Phys. 115 (2014) 123506. L. Balatka, Bachelor Thesis, University of Pardubice (2010). J. Barták, Bachelor Thesis, University of Pardubice (2007). V.M. Glazov, O.V. Situlina, Dokl. Chem. 187 (1969) 24. T.G. Edwards, S. Sen, J. Phys. Chem. B 115 (2011) 4307. E. Gjersing, S. Sen, B. Aitken, J. Phys. Chem. 114 (2010) 8601. R.K. Venugopal, A.K. Bhatnagar, J. Phys. D. Appl. Phys. 25 (1992) 1810. A. El-Korashy, H. El-Zahed, M. Radwan, A.M. Abdalla, Thin Solid Films 261 (1995) 328. K. Shimakawa, S. Nitta, Phys. Rev. B 17 (1978) 3950. N. Afify, A. Gaber, I. Abdalla, H. Talaat, Physica B 229 (1997) 167. M. Majid, S. Benazeth, C. Souleau, J. Purans, Phys. Rev. B 58 (1998) 6104. T. Tsuzuki, M. Yao, H. Endo, J. Phys. Soc. Jpn. 64 (1995) 485.