Structure, Connectivity, and Configurational Entropy of GexSe100−x

Apr 9, 2010 - Structural study by Raman spectroscopy and 77 Se NMR of GeSe 4 and 80GeSe 2 –20Ga 2 Se 3 glasses synthesized by mechanical milling. El...
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J. Phys. Chem. C 2010, 114, 8601–8608

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Structure, Connectivity, and Configurational Entropy of GexSe100-x Glasses: Results from 77 Se MAS NMR Spectroscopy E. L. Gjersing and S. Sen* Department of Chemical Engineering and Materials Science, UniVersity of CaliforniasDaVis, DaVis, California 95616

B. G. Aitken Glass Research DiVision, Corning Incorporated, Corning, New York 14831 ReceiVed: February 15, 2010; ReVised Manuscript ReceiVed: March 22, 2010

High-resolution 77Se MAS NMR spectroscopy has been conducted at 11.7 T to investigate the short-and intermediate- range structure and chemical order in binary GexSe100-x glasses with 5 e x e 33.33. Four distinct Se environments are observed for the first time, corresponding to Se-Se-Se and Ge-Se-Se linkages as well as Ge-Se-Ge sites where the Se atom is shared by two GeSe4 tetrahedra in either corner-sharing or edge-sharing configuration. Assignments of corner and edge-shared tetrahedra were made based on the 77Se MAS NMR spectrum of crystalline β-GeSe2. Analysis of the compositional variation of the relative concentrations of these Se sites indicates that the structure of GexSe100-x glasses in this composition range can be described as a randomly interconnected network of GeSe4 tetrahedra and chains of Se atoms. The implications of this structural model are discussed in relation to the composition dependence of the glassforming ability and kinetic fragility of the corresponding parent liquids. I. Introduction Chalcogenide glasses are of wide-ranging importance in a variety of technological applications in the areas of photonics and telecommunication.1,2 The unique compositional flexibility of these glasses in the form of continuous alloying enables tuning of optical, electronic, thermo-mechanical and other properties via compositional “engineering”. A thorough understanding of the short and intermediate -range structure is therefore necessary to build predictive models of structure-property relationships in these glasses. Simple binary GexSe1-x chalcogenide glasses have been used as model systems for this purpose. This covalent glass-forming system has a wide glass formation region, which extends from pure selenium to up to x ) 0.43, that results in a wide range of connectivity and dimensionality governed by the average coordination number 〈r〉 ) 4x + 2(1 - x) with 2.0 e 〈r〉 e 2.8.3 This topological diversity within a single glass forming system has made these glasses model systems for studying the influence of topological constraints on the compositional variation of various physical properties in covalently bonded amorphous materials.4,5 It has been argued on the basis of the theory of constraintcounting that a wide range of physical properties of these glasses would be predominantly controlled by the average coordination number 〈r〉, irrespective of their actual chemical compositions.4,5 A simple counting of the bond length and angle constraints on the total number of degrees of freedom available to a mole of three-dimensionally connected atoms shows that the system of atoms would undergo a rigidity percolation type of transition at 〈r〉 ) 2.4.4,5 Detailed studies of the compositional dependence of elastic, thermodynamic, transport and electronic properties in chalcogenide glasses indicate that some properties indeed show such a transition at 〈r〉 ≈ 2.4.6-10 However, these topological arguments do not take into account the effects of the degree of chemical order in the intermediate-range length

scale and its compositional dependence in chalcogenide glass structure. Such chemical order in terms of the connectivity and mixing between GeSe4 tetrahedra and -Se-Se-Se- chains in the structure of GexSe1-x glasses can have important influences on the dimensionality and topology of the intermediaterange structural units. A systematic study of the intermediaterange chemical order in GexSe1-x glasses over a wide composition range and 〈r〉 values is clearly needed in order to test these hypotheses. The structure of GexSe1-x glasses has been studied extensively using a wide range of diffraction and spectroscopic techniques.11-18 These structural studies have primarily addressed the average short-range structure of these glasses, while the structural characteristics in the intermediate range beyond the nearest and next-nearest neighbor coordination shells still remain controversial. For example, it is well established that Ge and Se atoms are 4- and 2-coordinated, respectively, in GexSe1-x glasses. However, the relative extent of connectivity between the GeSe4 tetrahedra via corner- and edge- sharing and formation of Ge-Se-Ge linkages in Se-excess glasses with g66.67 at. % Se remains unclear. In this regard the proposed structural models range all the way from the chain-crossing model to the fully clustered or phase-separated model.16,17 The chain-crossing model is based on the avoidance of corner and edge sharing of GeSe4 tetrahedra, while the fully clustered or phase separated model predicts complete connectivity between the GeSe4 tetrahedra via corner- and edge-sharing. The cluster model therefore results in nanoscale structural heterogeneities in Seexcess glasses with separation into GeSe2-like and Se-like regions. On the other hand, the chain-crossing model is completely chemically ordered in the sense that any direct corner and edge sharing between the GeSe4 tetrahedra are precluded to the maximum allowed by the glass composition. However, previous Raman spectroscopy19,20 and neutron diffraction14

10.1021/jp1014143  2010 American Chemical Society Published on Web 04/09/2010

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studies have identified the presence of “wrong bonds” like Ge-Ge and Se-Se in GeSe2 glass, thus, making the chaincrossing model untenable for the stoichiometric composition. Moreover, the observation, in the Raman spectra of all Se-excess GexSe1-x glasses, of vibrational bands corresponding to the stretching modes of corner- and edge-shared GeSe4 tetrahedra implies clear departure from the chain-crossing model.21-23 Unfortunately, the absolute concentrations of these corner and edge-shared tetrahedra cannot be determined from the Raman spectra since the absolute scattering cross sections of these Raman bands are not known a priori. In a recent study Bureau and co-workers reported the 77Se static nuclear magnetic resonance (NMR) spectra, collected at a magnetic field of 7 T, of GexSe1-x glasses with 11.10 e x e 33.33.16,17 The spectral line shapes were interpreted to represent the existence of only two types of Se coordination environments in these glasses. These Se environments correspond to Se-Se-Se and Ge-Se-Ge linkages i.e. Se atoms either bonded to 2 Se or to 2 Ge atoms. The absence of Se-Se-Ge type environments in Bureau et al.’s analyses implied a fully clustered structural model of tetrahedral connectivity in Se-excess GexSe1-x glasses.16,17 Such structural heterogeneity is expected to manifest itself into nanoscale phase separation of these glasses into GeSe2-like and Se-like regions. However, previous studies based on other analytical methods have not shown any evidence of such phase separation. For instance, only one Tg is observed in Ge-Se glasses,24 in contrast to binary Ge-S glasses with excess sulfur which show evidence of two Tgs and nanoscale phase separation.25 Here we report the results of a high-resolution 77Se magicangle-spinning (MAS) NMR spectroscopic study at a magnetic field of 11.7 T of GexSe100-x glasses, with compositions ranging from x ) 5 to up to 33.33. Crystalline β-GeSe2 is used as a model compound, and its 77Se MAS NMR spectrum has been analyzed in order to compare and contrast the NMR parameters associated with Se atoms that are corner-shared and edge-shared between GeSe4 tetrahedra. This analysis also provides important insight into the influence of chemical environment, Ge-Se-Ge bond angle and Ge-Se bond length on 77Se NMR spectra. A model of the composition dependence of short- and intermediaterange structure, topology and chemical order in the GexSe100-x glasses is developed on the basis of these NMR results. II. Experimental Section Sample Synthesis. GexSe100-x glasses with 5 e x e 33.33 were synthesized in 10-20 g batches by melting mixtures of the constituent elements Ge and Se with g99.995% purity (metals basis) in evacuated (10-6 Torr) and flame-sealed fused silica ampules (8 mm I.D., 11 mm O.D.) at temperatures ranging between 1000 and 1200 K for at least 24 h in a rocking furnace. The ampules were quenched in water and subsequently annealed for 1 h at the respective glass transition temperatures.24 β-GeSe2 was obtained by slowly cooling the GeSe2 liquid from 1200 K to room temperature. Powder X-ray diffraction measurement confirmed this material to be phase pure. Raman Spectroscopy. The unpolarized Raman spectra of the GexSe100-x glasses were collected in a backscattering geometry using a Bruker RFS 100/S Fourier-transform (FT) Raman spectrometer equipped with a frequency-doubled Nd: YAG laser operating at a wavelength of 1064 nm. Laser power levels were varied between 20 and 50 mW. 77 Se MAS NMR. 77Se MAS NMR measurements were performed using a Bruker Avance 500 spectrometer at a magnetic field of 11.7 T (77Se resonance frequency of 95.4

Gjersing et al.

Figure 1. Unpolarized Raman spectra of the GexSe100-x glasses with compositions given alongside the spectra.

MHz). Powdered samples were packed into ZrO2 rotors with KelF caps and placed in a Bruker 4 mm triple-resonance MAS probe and were spun at 15 kHz. 77Se MAS NMR spectra of GexSe100-x glasses were collected using a Hahn echo pulse sequence (π/2-τ-π acquisition) with π/2 pulse length of 2.6 µs, τ ) 63 µs and a recycle delay of 60 s. Approximately 1300-1500 free induction decays (FID) were averaged to obtain each 77Se MAS NMR spectrum for glasses with Ge contents between 5 and 23%, whereas ∼3000 FIDs were averaged in the case of the Ge33.3Se66.7 glass. The 77Se single-pulse MAS NMR spectrum of the β-GeSe2 sample was collected at spinning speeds of 13 and 15 kHz, using a 4 mm Bruker triple-resonance MAS probe, a π/4 pulse (1.4 µs), and a recycle delay of 300 s. Approximately 200 FIDs were averaged to obtain the 77Se MAS NMR spectrum at each spinning speed. Another 77Se singlepulse MAS spectrum of β-GeSe2 was collected at a spinning speed of 23 kHz using a Bruker 2.5 mm double resonance probe with a π/4 pulse (0.75 µs) and a recycle delay of 120 s. Approximately 2000 FIDs were averaged to obtain this 77Se MAS NMR spectrum. An external reference of saturated H2SeO3 liquid was used for chemical shift calibration for all samples. III. Results The unpolarized FT-Raman spectra of the GexSe100-x glasses with 5.00 e x e 33.33 are shown in Figure 1. Two main regions in these spectra are distinguishable: (a) a relatively sharp highintensity band around 195 cm-1 along with a shoulder around 210 cm-1 and (b) a broad, high-intensity band centered at 259 cm-1 and spanning from 225 to 280 cm-1. In region (a) the 195 cm-1 band is assigned specifically to the breathing mode of corner-shared GeSe4 tetrahedral units, and the 210 cm-1 band is assigned to the vibration of Se atoms participating in edgesharing between neighboring GeSe4 tetrahedra.20,21,23 The highest

Properties of GexSe100-x Glasses

Figure 2. 77Se Hahn-echo MAS NMR spectra of GexSe100-x glasses with compositions listed alongside the spectra.

frequency band in region (b) is characteristic of that in the Raman spectrum of pure Se and can be assigned to Se-Se stretching in Se chains and rings.26 In addition, the Raman spectrum of the Ge33.3Se66.7 glass shows a sharp but low-intensity band centered at ∼180 cm-1 that has been assigned in previous studies to stretching of Ge-Ge homopolar bonds.27 The compositional evolution of these spectra agree well with those published in the literature by others22,23 and, with increasing Ge content, a progressive decrease in the intensity of the band in region (b) is observed in comparison to that of the bands in region (a). Moreover, the 210 cm-1 band shows a sudden increase in intensity relative to the 195 cm-1 band in Ge33.3Se66.7 glass (Figure 1). The 77Se MAS NMR spectra of the GexSe100-x glasses are shown in Figure 2. These spectra are characterized by two broad peaks centered at ∼400 and 800 ppm. The width of the peak at 400 ppm (∼35 to 40 kHz) is significantly larger than that of the peak at 800 ppm (∼20 kHz). Moreover, the relative intensity of the peak at 800 (400) ppm decreases (increases) progressively with increasing Ge content. Previous studies have conclusively shown that the line widths of these 77Se MAS NMR spectra are primarily controlled by the chemical shift distribution resulting from structural disorder in glasses.16,17 The 77Se MAS NMR spectrum of Ge5Se95 glass displays a principal peak at ∼835 ppm with a pronounced upfield tail of this peak that suggests the presence of a weak resonance centered around ∼570 ppm (Figure 2). The structural assignment of the resonance at ∼570 ppm will become clear in the following discussion. However, it may be noted that the position of the principal peak at ∼835 ppm agrees well with the isotropic chemical shift of for crystalline and glassy Se at 792 and at 840-860 ppm, respectively, as determined in previous studies by Bureau and co-workers.16,17 Since in crystalline and glassy Se all Se atoms are bonded to 2 nearest neighbor Se atoms, the peak at ∼835 ppm in the 77Se MAS NMR spectra of GexSe100-x glasses was assigned by Bureau et al.16,17 to Se environments with two Se nearest neighbors i.e. Se-Se-Se sites. On the other hand, the 77Se MAS NMR spectrum of Ge33.3Se66.7 glass displays

J. Phys. Chem. C, Vol. 114, No. 18, 2010 8603 a principal peak at ∼370 ppm (Figure 2). Previous neutron and X-ray diffraction and Ge K-edge extended X-ray absorption fine structure (EXAFS) spectroscopic studies have shown that the structure of this stoichiometric glass consists primarily of a network of corner- and edge-shared GeSe4 tetrahedra where Se atoms are bonded to 2 nearest neighbor Ge atoms.13-15 Therefore, the peak at ∼370 ppm in the 77Se MAS NMR spectrum of Ge33.3Se66.7 glass can be safely assigned to Se atoms in Ge-Se-Ge sites. In a previous 77Se NMR study Bureau and co-workers made the same structural assignment of this peak, although in their study the position of this peak in the 77Se static NMR spectrum of Ge33.3Se66.7 glass was reported to be at ∼410 ppm.16,17 However, it may be noted that the peak maximum in the 77Se static NMR spectrum reported in their study is not identical to that in the corresponding MAS spectrum reported here, possibly due to the effect of chemical shift anisotropy. The isotropic chemical shift of ∼570 ppm of the upfield resonance in the 77Se MAS NMR spectrum of the Ge5Se95 glass is located almost in the middle of 835 and 370 ppm, corresponding to the chemical shifts of Se-Se-Se and Ge-Se-Ge sites, respectively. Hence, we assign this shift to a Se environment that is intermediate between Se-Se-Se and Ge-Se-Ge, i.e., to Ge-Se-Se sites. This assignment is consistent with the 77 Se chemical shift of 550 ppm reported in previous studies for As-Se-Se sites in AsxSe1-x glasses.28,29 Due to the low Ge content of the Ge5Se95 glass, most of the GeSe4 tetrahedra are expected to be not linked to one another but to chains of Se atoms, resulting in the formation of Ge-Se-Se sites in addition to the predominant Se-Se-Se sites. Therefore, the small Ge concentration makes the Ge5Se95 glass an ideal candidate for observation of Ge-Se-Se sites in the 77Se MAS NMR spectrum. Further addition of Ge is expected to form Ge-Se-Ge sites in addition to Ge-Se-Se sites and overlapping signal from these two sites may make them difficult to resolve. This lack of resolution can be observed in the 77Se MAS NMR spectra of GexSe100-x glasses with x g 10 (Figure 2) and is expected to be even worse in the corresponding static spectra. The latter situation likely prompted Bureau and co-workers to fit a single, broad peak under the 77Se static NMR line shape at ∼400 ppm and assign it solely to Ge-Se-Ge sites.16,17 The 77 Se MAS NMR spectrum of the stoichometric Ge33.3Se66.7 glass shows the presence of a small but clear shoulder centered at ∼600 ppm indicating the presence of a small concentration of Ge-Se-Se sites (Figure 2). Although not as well resolved, an additional shoulder near 150 ppm is observed on the upfield side of this 77Se MAS NMR spectrum (Figure 2). The highest shielding of this 77Se NMR signal at ∼150 ppm is strongly suggestive of its association with Se atoms in edge-shared sites, as NMR chemical shifts for such sites are expected to be invariably shifted toward higher field compared to corner-shared sites.30 In order to test the tentative structural assignment of the resonance at 150 ppm to edge-shared Se sites, β-GeSe2 is used as a model compound and an analysis of its 77Se MAS NMR was carried out. Figure 3 displays the 77Se MAS NMR spectra of β-GeSe2 collected at spinning rates of 23, 15, and 13 kHz. Previous X-ray refinement studies of the crystal structure of β-GeSe2 had shown the presence of 8 distinct Se sites, among which 6 sites belong to corner-shared GeSe4 tetrahedra and the rest to edge-shared GeSe4 tetrahedra.31 As seen in the 23 kHz 77Se MAS NMR spectrum of β-GeSe2 (Figure 3), there are eight isotropic peaks present at 208, 224, 389, 396, 515, 542, 600, and 644 ppm, consistent with the 8 distinct Se sites in the crystal structure. These isotropic peak positions span a large range of chemical

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Figure 3. Single-pulse 77Se MAS NMR spectra of crystalline β-GeSe2 collected at different spinning rates indicated alongside each spectrum. Arrows indicate isotropic peaks and asterisks indicate spinning sidebands in the 23 kHz MAS spectra. The spinning sidebands and isotropic peaks in the 13 kHz and 15 kHz spectra are not shown due to the overlap of peaks.

TABLE 1:

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Se NMR Chemical Shift Parameters for the Se Sites in Crystalline β-GeSe2

isotropic chemical shift, δiso (ppm)

chemical shift anisotropy, ∆cs (ppm)

chemical shift asymmetry, ηcs

span, Ω (ppm)

skew, κ

relative fraction (%)

208 224 391 515 542 600 644

-350 -470 500 -450 -400 -350 -550

0.8 0.8 0.3 0.9 0.6 0.7 0.5

665 893 825 877 720 647 962

0.16 0.16 -0.64 0.08 0.33 0.24 0.43

12 12 27 13 12 12 12

shifts of nearly 440 ppm, indicating the sensitivity of the 77Se NMR chemical shift to the Ge-Se-Ge bond angle and Ge-Se bond length, since all the Se atoms are bonded to 2 Ge atoms in the crystal structure. In order to determine the chemical shift anisotropy (CSA) parameters for each site, the isotropic shifts from the 23 kHz spectra were used to fit the CSA patterns in the 13 kHz spectrum. These values were then checked for consistency with the 15 kHz spectrum and the results are shown in Table 1. CSAs were determined for seven sites with the two sites at 389 and 396 ppm being fit as one, centered at 391 ppm, as their CSAs are similar. The integrated percentage of each peak is in good agreement with the expected 12.5% (1/8) within the experimental error of (1%. This agreement is remarkable considering the low signal-to-noise and the wide range of chemical shifts that makes phasing of these spectra quite difficult. Although an exact assignment of the NMR peaks is difficult without ab initio calculations of chemical shifts, a brief discussion of the most likely assignments is presented. The structural parameters of the 2 edge-sharing Se sites in the βGeSe2 crystal structure are uniquely characterized by the smallest Ge-Se-Ge bond angles of ∼80° and longest average Ge-Se distances of ∼2.36 and 2.37 Å, whereas for the corner-shared Se sites the Ge-Se-Ge intertetrahedral angles range between 96° and 100° and average Ge-Se distances range between 2.35 and 2.36 Å.31 Small bond angles and large bond lengths are also uniquely characteristic of edge-shared fluorine sites in fluorozirconate crystals. Previous 19F MAS NMR studies of fluorozirconate crystals30 have shown that the edge-shared fluorine sites always resonate at a higher field (i.e., have a smaller chemical shift value) compared to the corner-shared sites

in the same crystal structure. Therefore, we have assigned the two sharp peaks with isotropic shifts of 222 and 204 ppm in the 77Se MAS NMR spectra of β-GeSe2 to the 2 edge-sharing Se sites (Figure 3). On the other hand, there are 2 peaks in these spectra with isotropic shifts of 389 and 396 ppm that are similar to the isotropic shift of the principal peak at ∼370 ppm in the 77 Se MAS NMR spectrum of Ge33.3Se66.7 glass. Therefore, the peaks at 389 and 396 ppm must correspond to corner-shared Ge-Se-Ge sites in β-GeSe2, with local environments around Se atoms that are similar to that found in the Ge33.3Se67.7 glass. Previous neutron and X-ray diffraction studies have shown that the average Ge-Se nearest-neighbor bond length is ∼2.35 to 2.36 Å in GeSe2 glass.14,15 Analyses of neutron diffraction results have indicated that the Ge-Se-Ge bond angle distribution in GeSe2 glass is centered around 98(1)° for corner-shared GeSe4 tetrahedra and around ∼80(1)° for the edge-shared configuration.32 As mentioned above, the average Ge-Se bond lengths of all corner-shared Se sites in β-GeSe2 vary within a very small range of 2.35 to 2.36 Å.31 However, the corresponding Ge-Se-Ge angles show a sizable variation between 96° and 100° that is possibly the most important structural parameter that controls 77Se NMR chemical shift. Therefore, our assignment of edge-shared Se sites with the smallest Ge-Se-Ge angles to the most upfield chemical shifts predicts that the two corner-shared Se sites with Ge-Se-Ge angles of 96.2° and 96.3° in the crystal structure should be associated with the next most upfield resonances at 389 and 396 ppm. The four other peaks in the 77Se MAS NMR spectra of the β-GeSe2 sample are located at 515, 542, 600, and 644 ppm, in the order of decreasing field of resonance. These peaks should then correspond to the remaining 4 corner-shared Se sites in the crystal

Properties of GexSe100-x Glasses

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TABLE 2: 77Se MAS NMR Spectral Simulation Parameters for the Four Se Sites: Se-Se-Se, Ge-Se-Se, Ge-Se-Ge CS (Corner-Shared Tetrahedra), and Ge-Se-Ge ES (Edge-Shared Tetrahedra) in Different GexSe1-x Glasses Se-Se-Se shift (ppm) ((15) width percentage ((3) Se-Se-Ge shift (ppm) ((20) width percentage ((5) Ge-Se-Ge CS shift (ppm) ((20) width percentage ((5) Ge-Se-Ge ES shift (ppm) ((15) width percentage ((3)

Ge5Se95

Ge10Se90

Ge13Se87

Ge17Se83

Ge20Se80

Ge23Se87

855 200 87

834 210 62

834 220 49

842 220 46

830 220 33

841 220 30

574 250 9

571 250 17

567 250 20

589 250 21

591 250 24

586 250 23

587 250 16

370 250 4

380 250 16

397 250 23

386 250 25

380 250 34

378 250 36

362 250 61

179

160 250 8

160 250 7

123 250 8

122 250 10

138 250 23

5

structure with progressively larger Ge-Se-Ge bond angles of 97.6°, 98.2°, 99.4°, and 100.1°, respectively.31 This assignment results in a nearly linear relationship between Ge-Se-Ge bond angles θ and corresponding isotropic shifts δiso for the cornershared Se sites following the relation: δiso ) -5930((100) + 65((5)* θ. Such a relationship predicts an average θ of ∼97° for the 370 ppm Ge-Se-Ge peak in the Ge33.3Se66.7 glass, consistent with the experimentally determined value of 98(1)° using neutron diffraction.32 Moreover, the high sensitivity of δiso on θ also predicts large peak widths for Se sites in glasses that are indeed observed in the 77Se MAS NMR spectra of the GexSe100-x glasses in Figure 2. The observation of four different Se coordination environments, corresponding to Se-Se-Se, Ge-Se-Se, and corner and edge-shared Ge-Se-Ge sites with δiso at approximately 800, 600, 400, and 150 ppm, respectively, in the 77Se MAS NMR spectra of the GexSe100-x glasses has prompted us to simulate these spectral line shapes with four Gaussian peaks. The choice of a Gaussian profile in these simulations is consistent with MAS NMR line shapes for I ) 1/2 nuclides such as 77Se that are heterogeneously broadened due to glassy structural disorder that is isotropic in nature in the absence of any motional narrowing. The peak widths ∆ (full width at halfmaximum) are kept constrained to 200-220 ppm for the Se-Se-Se site and to 250 ppm for all the other sites for all glasses. The corresponding simulation parameters for all 77Se MAS NMR glass spectra are listed in Table 2 and the simulations are shown in Figure 4. It is apparent from Figure 4 that a 4-site model accurately simulates the NMR data and shows a systematic evolution of the relative concentrations of the corresponding Se sites with glass composition (see Table 2). It is also remarkable that the δiso values of all sites vary within a relatively narrow range indicating the highly constrained and self-consistent nature of these simulations.

Ge33Se67

then rapidly reaches the highest value in the Ge33.3Se66.7 glass. This trend is also in agreement with that observed in the corresponding Raman spectra of these glasses. The fractional concentration of Ge-Se-Se sites starts at ∼9% in the Ge5Se95 glass, increases slightly to a maximum of 23 to 24% in the Ge20Se80 and Ge23Se77 glasses and then falls to 16% in the

IV. Discussion The compositional dependence of Se speciation in the GexSe100-x glasses, as obtained from the simulation of the corresponding 77Se MAS NMR spectra can be obtained from Table 2. The fractional concentration of Se-Se-Se sites monotonically decreases until it completely disappears in the Ge33.3Se66.7 glass, while that of the corner-shared Ge-Se-Ge sites steadily increases up to x ) 33.3, consistent with Raman spectroscopic results. The fractional concentration of edgeshared Ge-Se-Ge sites increases slowly to up to x ) 23 and

Figure 4. Experimental (thick black line) and simulated (thick gray line) 77Se Hahn-echo MAS NMR spectra for GexSe100-x glasses. Individual simulation components corresponding to the different Se sites are also shown (thin black lines).

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Figure 5. Comparison of the ratio of edge-sharing (ES) to cornersharing (CS) GeSe4 tetrahedral sites obtained from 77Se MAS NMR (gray box) and Raman (() spectra.

Ge33.3Se66.7 composition (Figure 4, Table 2). The relative ratio of edge- and corner-shared Ge-Se-Ge sites in a GexSe100-x glass can be obtained from the areas under the corresponding bands at 210 and 195 cm-1, respectively, in its Raman spectrum. The composition dependence of these relative ratios of edge and corner-shared Ge-Se-Ge sites are compared in Figure 5 with those obtained from the simulation of the 77Se MAS NMR spectra (see also Table 2). Interestingly, the ratios derived from Raman spectra are consistently lower than those obtained from 77 Se MAS NMR spectra by a factor of 1.5 ( 0.15. This discrepancy must result from the difference in Raman scattering cross sections of the Ge-Se stretching modes for corner- and edge-sharing GeSe4 tetrahedra and implies a scattering crosssection ratio of ∼1.5:1 for these vibrational modes. This scattering cross-section ratio is consistent with but somewhat higher than that (1.2:1) derived in a previous study using ab initio calculations based on density functional theory within the local density approximation.20 In addition to being consistent with Raman spectroscopy, the 77 Se MAS NMR results of Se speciation in the Ge33.3Se66.7 (GeSe2) glass as obtained here are also in good agreement with those obtained from recent neutron diffraction studies on this glass. For example, the latter have indicated that 20 ( 5% of Se atoms are forming Se-Se homopolar bonds in the structure of GeSe2 glass.14,15 As shown in Table 2, the line shape simulation of the 77Se MAS NMR spectrum of this glass indicates the presence of ∼16 ( 5%% of Se atoms in Ge-Se-Se linkages, completely consistent, within the limits of experimental error, with the estimate of Se-Se homopolar bond concentration from neutron diffraction results,. Additionally 77Se MAS NMR results presented here indicate that ∼23 ( 5% of Se atoms in the GeSe2 glass sample are involved in edge-sharing GeSe4 tetrahedra (Table 2). Neutron diffraction results of Salmon and co-workers14,15 have shown that the fraction of Ge atoms in edge-sharing configuration in GeSe2 glass is ∼34 ( 5%, which implies that ∼15 to 20% of the Se atoms are associated with these structural configurations, again consistent with the NMR derived value, within the limits of experimental error. The relative fraction of Se-Se-Se sites, as derived from 77Se MAS NMR, is compared in Figure 6 with those predicted by the chain-crossing and fully clustered models in order to elucidate the most appropriate structural model for these GexSe100-x glasses. It may be noted that for GexSe100-x glasses the relative fractions of Se-Se-Se sites as predicted by the fully clustered and chain-crossing models are [(100 - 3x)/(100 - x)]

Gjersing et al.

Figure 6. Compositional variation of the relative fraction of Se-Se-Se sites as obtained from simulation of the 77Se MAS NMR spectra (2) compared to predictions of the chain-crossing model (black line) and the clustered model (gray line).

Figure 7. Compositional variation of the relative fractions of Se-Se-Se (blue), Ge-Se-Se (green), and Ge-Se-Ge (red) sites as obtained from simulation of the77Se MAS NMR spectra (symbols) and corresponding predictions of random bonding model (dashed lines).

and [(100 - 5x)/(100 - x)], respectively [16,17]. It is clear from Figure 6 that for all compositions with 5 e x e 13 the NMR results are in agreement with the chain-crossing model, while for x g 17 the NMR data indicate a structure that is partially clustered, in between the extremes of chain-crossing and a fully clustered model. The NMR-derived compositional variations of the relative fractions of Se-Se-Se, Ge-Se-Se, and Ge-Se-Ge sites are also compared in Figure 7 with that expected from a statistically random model of connectivity between GeSe4 tetrahedra and Se-Se chain fragments.33 It is clear from Figure 7 that the experimental results show a reasonably good agreement with this statistically random connectivity model, implying that the structure of these glasses is better described by a random network of interconnected GeSe4 tetrahedra and Se-Se chains. However, it may be noted that, in the composition range of 10 to 20% Ge, the experimentally determined concentration of Ge-Se-Ge and Ge-Se-Se sites are somewhat systematically higher and lower, respectively, compared to the prediction of the random bonding model. Such deviation indicates an energetic preference for clustering of GeSe4 tetrahedra in the structure of these glasses. It is interesting to contrast these Se speciation results with that proposed in a recent high-temperature 77Se NMR study of glasses and supercooled liquids in the Ge-Se system by Lucas et al.34 These authors obtained the relative fraction of Se-Se-Se sites in Ge-Se glasses with a relatively high precision by collecting 77 Se NMR spectra in the supercooled liquid state at T > Tg that resulted in motional line narrowing of the Se-Se-Se resonance

Properties of GexSe100-x Glasses

J. Phys. Chem. C, Vol. 114, No. 18, 2010 8607 relation one would expect a correlated variation between m and entropy of mixing. This hypothesis is corroborated by the compositional variation of m of Ge-Se glass-forming liquids (Figure 8) that goes through a broad minimum in the same composition range (15 to 25% Ge) where the configurational entropy of mixing goes through a maximum.38 V. Summary

Figure 8. Compositional variation of (a) the entropy of ideal mixing of various Se sites in GexSe100-x glasses (filled squares) and of (b) the kinetic fragility parameter m (open triangles) of GexSe100-x liquids. Data for kinetic fragility are taken from ref 37.

centered at ∼830 ppm.34 However, the absence of motional narrowing of the Se sites bonded to Ge atoms resulted in a broad peak centered at ∼400 ppm under the 77Se static NMR line shape that was assigned exclusively to Ge-Se-Ge sites. Therefore, such NMR peak assignment led these authors to propose a fully clustered or phase-separated structural model for these glasses similar to that reported in previous studies by Bureau and co-workers.16,17 The Se speciation results obtained in this study may have important implications in our current understanding of the glassforming ability and the kinetic fragility of GexSe100-x liquids. The entropy of ideal mixing of Se-Se-Se, Ge-Se-Se, and corner and edge-sharing Ge-Se-Ge sites will be equal to -RΣixi ln(xi) where xi is the relative fraction of each type of Se species and R is the universal gas constant. The compositional dependence of this quantity is calculated using the Se speciation data given in Table 2 and is shown in Figure 8. Clearly the highest entropy of mixing is observed for glasses with 13 to 23% Ge (Figure 8). This entropy of mixing component is expected to result in the highest glass-forming tendency or stability against crystallization in this composition range. Indeed this composition range strongly overlaps with that reported in previous studies (10-20% Ge) as corresponding to the highest glass-forming ability in the binary Ge-Se system.3 The kinetic fragility m of a glass-forming liquid is defined as the slope of the variation of the logarithm of viscosity η with scaled temperature Tg/T where Tg is the calorimetric glasstransition temperature where the viscosity is typically universally 1012 Pa s, i.e., m ) (d log η)/(d(Tg/T)).35 According to the configurational entropy model of viscous flow proposed by Adam and Gibbs,36 the viscosity of a glass-forming liquid is a function of temperature and its configurational entropy Sc(T) such that log η(T) ) A + B/(TSc(T)) where A and B are material constants. The temperature dependence of Sc of the liquid is considered to be responsible for the non-Arrhenius temperature dependence of viscosity characteristic of fragile liquids and it typically increases with increasing temperature as the structure of the liquid is allowed to explore a greater variety of configurations. It can be shown that for the simple approximation of a linear rise in the configurational heat capacity Cpconf(Tg) of a liquid near glass transition the fragility scales as m ∼ Cconf p (Tg)/ Sc(Tg) where Sc(Tg) is the configurational entropy of the liquid at Tg, i.e., the configurational entropy frozen in the glass structure.37 If the entropy of mixing of the various Se environments in the binary Ge-Se glasses as mentioned above is the primary source of Sc(Tg) then on the basis of the inverse scaling

In summary, high-resolution 77Se MAS NMR spectra of GexSe1-x glasses with 0.05 e x e 0.33.3 have been analyzed to obtain information on the short and intermediate-range structure and chemical order. The NMR results indicate the presence of Se-Se-Se, Ge-Se-Se, and corner- and edgesharing Ge-Se-Ge species in these GexSe100-x glasses. The 77 Se isotropic chemical shifts for these Se sites are observed at approximately 800, 600, 400, and 150 ppm respectively. The compositional variation of the relative fractions of these Se sites is shown to be in good agreement with a statistically random model of connectivity between GeSe4 tetrahedra and Se-Se chain fragments. Therefore the 77Se MAS NMR results reported here provide information on chemical order at the next-nearest neighbor length scale. However, no direct connections can be made between these results and the intermediate-range order in these glasses at the length scale of ∼6 Å probed by the first sharp diffraction peak at ∼1 Å-1 in the Bhatia-Thornton concentration-concentration partial structure factor.12,14,15 Reverse Monte Carlo simulations based on structural constraints derived from both NMR and diffraction results will be important in addressing such issues in the future. The ratios of corner-shared to edge-shared Ge-Se-Ge sites in these glasses are found to be completely consistent with Raman spectroscopic results. Moreover, the observation of violation of chemical order and formation of Se-Se homopolar bonds, as well as the high ratio of edge-shared: corner-shared GeSe4 tetrahedra in the stoichiometric GeSe2 glass, are in good agreement with previous neutron diffraction results. Finally, the compositional variation of the configurational entropy of mixing of various Se environments in these glasses is shown to be consistent with the variations of the glass-forming tendency and fragility of the corresponding liquids. Acknowledgment. This work was supported by NSF Grant DMR-0906070 to S.S. References and Notes (1) Zakery, A.; Elliott, S. R. J. Non-Cryst. Solids 2003, 330, 1. (2) Shimakawa, K.; Kolobov, A. V.; Elliott, S. R. AdV. Phys. 1995, 44, 475. (3) Azoulay, R.; Thibierge, H.; Brenac, A. J. Non-Cryst. Solids 1975, 18, 33. (4) Phillips, J. C. J. Non-Cryst. Solids 1979, 34, 153. (5) Thorpe, M. F. J. Non-Cryst. Solids 1983, 57, 355. (6) Micoulaut, M.; Phillips, J. C. J. Non-Cryst. Solids 2007, 353, 1732. (7) Varshneya, A. K. J. Non-Cryst. Solids 2000, 273, 1. (8) Kamitakahara, W. A.; Cappelletti, R. L.; Boolchand, P.; Halfpap, B. L.; Gompf, F.; Neumann, D. A.; Mutka, H. Phys. ReV. B 1991, 44, 94. (9) Tatsumisago, M.; Halfpap, B. L.; Green, J. L.; Lindsay, S. M.; Angell, C. A. Phys. ReV. Lett. 1990, 64, 1549. (10) Stølen, S.; Grande, T.; Johnsen, H. Phys. Chem. Chem. Phys. 2002, 4, 3396. (11) Bychkov, E.; Benmore, C. J.; Price, D. L. Phys. ReV. B 2005, 72, 172107. (12) Petri, I.; Salmon, P. S.; Fischer, H. E. Phys. ReV. Lett. 2000, 84, 2413. (13) Zhou, W.; Paesler, M.; Sayers, D. E. Phys. ReV. B 1991, 43, 2315. (14) Salmon, P. S.; Petri, I. J. Phys.: Condens. Matter 2003, 15, S1509. (15) Salmon, P. S. J. Non-Cryst. Solids 2007, 353, 2959. (16) Bureau, B.; Troles, J.; Le Floch, M.; Gue´not, P.; Smektala, F.; Lucas, J. J. Non-Cryst. Solids 2003, 319, 145.

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