Compositional Variation of Short- and Intermediate-Range Structure

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J. Phys. Chem. C 2008, 112, 7263-7269

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Compositional Variation of Short- and Intermediate-Range Structure and Chemical Order in Ge-As Sulfide Glasses: A Neutron Diffraction Study S. Soyer Uzun,† S. Sen,*,† C. J. Benmore,‡ and B. G. Aitken§ Department of Chemical Engineering & Materials Science, UniVersity of California at DaVis, DaVis, California 95616, Argonne National Laboratory, Argonne, Illinois 60439, and Glass Research DiVision, Corning Inc., Corning, New York 14831 ReceiVed: December 7, 2007; In Final Form: February 27, 2008

The structures of chalcogenide glasses in the Ge-As-S system with Ge:As ) 1:1 and with S concentration varying between 33.3 and 70.0 atom% have been studied using neutron diffraction. Ge and As atoms are primarily heteropolar bonded to S atoms in stoichiometric and S-excess glasses. Formation of homopolar As-As bonds at low and intermediate levels of S-deficiency results in violation of chemical order and in the formation of As-rich structural moieties. Ge takes part in metal-metal bonding, predominantly via the formation of Ge-As bonds, only in the highly S-deficient glasses once all the As atoms are used up in homopolar bonding. Incorporation of tetrahedrally coordinated Ge into the structure disrupts the topological continuity of the low-dimensional As-rich clusters and the GeS2 network. These intermediate-range order structural orderings are manifested in the compositional dependence of the intensity, position, and width of the first sharp diffraction peak in the structure factor.

1. Introduction Chalcogenide glasses are unusual semiconductors with a wide transmission window in the infrared that can be altered by exposure to band gap light. These glasses have therefore found a wide range of applications in various passive and active optical devices.1-3 Moreover, recently there has been renewed interest in their potential usage in optical fiber amplifier applications as low phonon energy host materials for rare earth dopants.4 Various spectroscopic and diffraction techniques have been employed to investigate the short and intermediate range atomic structure of simple binary chalcogenide glasses in As-X, P-X and Ge-X (X ) S, Se) systems.3-14 However, systematic studies regarding the atomic structure of technologically relevant, complex glasses in the ternary and quaternary Ge-AsS/ Se/Te glass-forming systems have begun only recently, focusing primarily on the short-range order.15-20 It has been shown by combined Ge and As K-edge EXAFS spectroscopy that the covalent network structure of complex ternary and quaternary Ge-As-S,Se glasses with stoichiometric and S(Se)excess compositions consist of corner-sharing GeS(Se)4 tetrahedra and AsS(Se)3 trigonal pyramids.15-17 On the other hand, in S(Se) deficient glasses the formation of metal-metal bonds takes place between Ge and As atoms, although the nearestneighbor coordination numbers of Ge and As atoms remain 4 and 3, respectively, independent of composition. In spite of a relatively detailed knowledge of short-range order, the characteristics of intermediate-range structural order in these glasses have remained only poorly known. For example, intermediaterange order in the form of metal-rich structural domains in chalcogen-deficient glasses has been claimed to be important in controlling their physical properties.15-17 However, direct * Author to whom correspondence should be addressed. E-mail: sbsen@ ucdavis.edu. † University of California at Davis. ‡ Argonne National Laboratory. § Corning Inc.

TABLE 1: Compositional Parameters of GexAsxS100-2x Glasses Used in This Study chemical composition

%S in excess of stoichiometry

Ge15As15S70 Ge18.2As18.2S63.6 Ge20As20S60 Ge22.5As22.5S55 Ge25As25S50 Ge27.5As27.5S45 Ge30As30S40 Ge32.5As32.5S35 Ge33.3As33.3S33.3

33.3 0.0 -14.3 -30.2 -42.9 -53.3 -61.9 -69.2 -71.4

experimental studies of the existence, topology, and length-scale of these structural domains in complex chalcogenide glasses are lacking to date. In this paper, we report the results of a detailed study of shortand intermediate-range structural characteristics of GexAsxS100-2x chalcogenide glasses with 15 e x e 33.3 using neutron diffraction. The nearest and next-nearest neighbor bonding environments of Ge and As atoms and their interrelationships with the nature and characteristic length scales of intermediaterange structural units are investigated. 2. Experimental Section 2.1. Sample Synthesis. Ge-As sulfide glasses reported in this study were synthesized by melting mixtures of the constituent elements Ge, As, and S with g99.995% purity (metals basis) in evacuated (10-6 Torr) and flame-sealed fused silica ampoules at ∼1200 K for at least 24 h in a rocking furnace. The ampoules were quenched in water and subsequently annealed for 1 h at the respective glass transition temperatures. A more detailed description of the preparation method can be found elsewhere.19 The nominal compositions of the GexAsxS100-2x glasses studied here are listed in Table 1. 2.2. Neutron Diffraction. 2.2.1. Data Collection. Neutron diffraction experiments were carried out using the glass, liquid,

10.1021/jp7115388 CCC: $40.75 © 2008 American Chemical Society Published on Web 04/11/2008

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and amorphous materials diffractometer (GLAD) at the Intense Pulsed Neutron Source (IPNS) at Argonne National Laboratory.21 Crushed glass samples were taken in 9.5 mm diameter cylindrical vanadium cans, and data were collected over a Q range of 0.3 to 40 Å-1. The beam size was 2 × 4 cm2, and the duration of the data collection for each sample was ∼18 h. 2.2.2. Data Processing. The diffraction data were corrected using standard procedures for container and background scattering, absorption, multiple scattering, and inelasticity effects and were normalized to an absolute scale with the isotropic incoherent scattering from vanadium. The resulting total scattering structure factor FN(Q) is related to the total neutron static structure factor SN(Q) via the following expression:

FN(Q)

SN(Q) ) (

∑iciβi)2

1

) (

∑iciβi)2

∑ i,j

cibicjbj(Sij(Q) - 1)

(1)

where ci is the atomic concentration and bi is the coherent neutron scattering length of species i ) As (6.580 fm), Ge (8.185 fm), and S (2.847 fm) and Sij(Q) are the Faber-Ziman partial structure factors.22 The total neutron structure factor SN(Q) is related to the total radial distribution function, N(r), via Fourier transformation where N(r) is given by:

N(r) ) 4πr2F0g(r)

(2)

where F0 is the total number density and g(r) is the total pair distribution function. N(r)dr has a direct physical interpretation as the number of atoms that are present within a range (r, r + dr) from any given atom.23 A weighted average coordination number for a peak in N(r) extending from r1 to r2 can be described as:

C)

∫rr

2

N(r)dr

(3)

1

C can be related to the partial coordination numbers Ci(j) expressing the average number of j atoms within this r range from an i atom at the center:

C)

1 〈b〉2

∑ij cibibjCi(j)

bGe2 〈b〉

2

CGe(Ge) + 2cGe

2cGe

bGebS 〈b〉2

bGebAs 〈b〉2

CGe(S) + cAs

3. Results

2cAs

bAsbS 〈b〉2

CGe(As) +

bAs2 〈b〉2

CAs(As) +

CAs(S) + cS

factors are calculated from nominal glass compositions and known scattering lengths of Ge, As, and S using eq 5.

(4)

where 〈b〉2 is (∑icibi)2. For the Ge-As-S ternary system eq 4 becomes:

C ) cGe

Figure 1. (a) Neutron total structure factors SN(Q) for GexAsxS100-2x glasses. The curves are vertically displaced for clarity. Corresponding glass compositions are shown alongside each curve. (b) Expanded view of the low-Q area of SN(Q) showing compositional variation of the FSDP in detail. Inset shows example of an experimental FSDP (bold line) isolated after background subtraction and a Gaussian fit (thin line) vertically displaced for clarity.

bS2 〈b〉2

CS(S) (5)

which can be written as:

C ) WGeGeCGe(Ge) + WGeAsCGe(As) + WGeSCGe(S) + WAsAsCAs(As) + WAsSCAs(S) + WSSCS(S) (6) where Wij are the weighting factors indicating the contribution of each of the partial Ci(j) to C.23 Equation 6 is used to obtain the nearest-neighbor coordination numbers. The weighting

The experimental neutron structure factors SN(Q) and corresponding radial distribution functions N(r) for all GexAsxS100-2x glasses are shown in Figures 1 and 2. 3.1. First Sharp Diffraction Peak. The low-Q part of the SN(Q), especially the position and intensity of the first sharp diffraction peak (FSDP), exhibits significant changes with glass composition (Figure 1). A linear function is used to approximate the local background underneath the FSDP, thus allowing the FSDP to be isolated and fitted with a Gaussian or Lorentzian function. Although the peak shape could not be exactly reproduced with either function, somewhat better fits were obtained with Gaussian functions for most cases. Therefore, Gaussian fits were used to extract the position, width, and intensity parameters for the FSDP in all cases (Figure 1b, Table 2). The compositional dependence of the position of FSDP is shown in Figures 1b and 3. For the S-excess Ge15As15S70 glass, the FSDP is located at 1.15 Å-1, and it monotonically shifts to lower Q values with decreasing S content until it is located at 0.97 Å-1 for the most S-deficient Ge33.3As33.3S33.3 glass (Figure 3). On the other hand, the intensity of the FSDP rises sharply with increasing S-deficiency, reaching a maximum at x ) 20

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Figure 3. Variation in the position (filled circle) and intensity (open square) of the FSDP in GexAsxS100-2x glasses as a function of Ge (or As) content. Error bars for the FSDP position data are within the size of the symbols.

Figure 2. (a) Radial distribution functions N(r) for GexAsxS100-2x glasses. These functions are obtained by the Fourier transformation of the SN(Q) data given in Figure 1. The curves are vertically displaced for clarity. Corresponding glass compositions are shown alongside each curve. (b) Example of fitting the nearest-neighbor peak in the low-r region of the N(r) of a S-deficient glass with two Gaussian components. The experimental peak (bold line) and the fit (thin line) are vertically displaced for clarity. The individual simulation components (dashed line) are also shown.

TABLE 2: FSDP Parameters of GexAsxS100-2x Glasses Used in This Study FSDP parameters chemical composition position Ge15As15S70 Ge18.2As18.2S63.6 Ge20As20S60 Ge22.5As22.5S55 Ge25As25S50 Ge27.5As27.5S45 Ge30As30S40 Ge32.5As32.5S35 Ge33.3As33.3S33.3

(Å-1

)

1.153 ( 0.001 1.127 ( 0.001 1.093 ( 0.002 1.068 ( 0.001 1.041 ( 0.001 1.018 ( 0.002 0.995 ( 0.002 0.978 ( 0.003 0.973 ( 0.001

intensity

width (Å-1)

0.82 ( 0.01 0.98 ( 0.01 1.17 ( 0.01 1.16 ( 0.01 1.16 ( 0.01 1.06 ( 0.01 0.92 ( 0.01 0.77 ( 0.02 0.74 ( 0.01

0.334 ( 0.004 0.326 ( 0.004 0.277 ( 0.004 0.272 ( 0.004 0.261 ( 0.004 0.259 ( 0.004 0.263 ( 0.005 0.260 ( 0.007 0.267 ( 0.004

followed by a plateau in the compositional region of 20e x e 25. The FSDP intensity then rapidly decreases with further increase in S-deficiency (Figure 3). The width of the FSDP is found to decrease monotonically from 0.334 to 0.261 Å-1 with increasing S-deficiency in the composition range 15e x e 25 beyond which it increases slightly with further decrease in the S content down to x ) 33.3 (Figure 4). It is also interesting to note that the lowest-Q (Q e 0.3 Å-1) part of the SN(Q) for S-deficient glasses (x > 0.182) displays small-angle scattering (Figure 1a). The intensity of small-angle scattering increases with decreasing S content up to x ) 30 and then decreases with further increase in x. 3.2. Radial Distribution Function. 3.2.1. First Shell and the Nearest-Neighbor Coordination EnVironments. The peak(s) in N(r), located between 2 and 3 Å, represents the nearest-neighbor coordination environments of the Ge and As atoms in structure of these glasses (Figure 2). For the S-excess and stoichiometric glasses, the peak centered at ∼2.2 Å corresponds to both As-S and Ge-S nearest neighbor distances.7-12,15,16 A second peak

Figure 4. Variation in the width (filled circle) and the coherence length (open square) of intermediate-range order (2π/∆QFSDP) of the FSDP in GexAsxS100-2x glasses as a function of Ge (or As) content.

appears at ∼2.5 Å and grows rapidly in intensity with increasing S-deficiencies (Figure 2). This peak can be readily assigned on the basis of its position to Ge/As-Ge/As nearest neighbors in S-deficient glasses.7-12,15,16 However, the corresponding coordination numbers for Ge and As atoms cannot be readily derived from these peak areas without using additional bonding constraints. This is primarily because of the strong overlap of As-S and Ge-S nearest-neighbor correlations and of Ge-Ge, GeAs and As-As nearest-neighbor correlations due to the strong similarity in the corresponding bond lengths. Fortunately such constraints are readily available in the literature, from previous diffraction and spectroscopic studies of the short-range structures of similar glasses.4,6-12,15-19 As mentioned earlier, one of the most important and general constraints is that Ge and As atoms in chalcogenide glasses are almost always 4 and 3 coordinated, respectively. In addition, the following bonding constraints have been used to fit the first two peaks in N(r) to obtain the nearest-neighbor coordination environments of Ge and As atoms in these glasses. In the case of S-excess and stoichiometric glasses (x e 18.2) the peak centered at 2.24 Å (Figure 2) corresponds to both As-S and Ge-S correlations since both As-S and Ge-S bond lengths are known to be ∼2.24 Å in Ge-As sulfide glasses.15,16 For these glasses, eq 6 can then be rewritten in the following form for the peak centered at ∼2.24 Å:

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C ) WAsSCAs(S) + WGeSCGe(S)

Uzun et al.

(7)

where C is the total area of the peak centered at 2.24 Å in N(r). Using the constraint of CGe(S) ) 4.0 in eq 7 yields CAs(S) ) 3.0 and vice versa (Table 3). This result indicates that the neutron diffraction data are consistent with the previous EXAFS results on these glasses.15,16 It has been shown in a previous study that the Raman spectra of S-excess glasses in the GeAs-S system show the appearance of a band near 490 cm-1 corresponding to the stretching vibration of S-S bonds.18 The corresponding bond length has been reported to be ∼2.0 Å. The N(r) of the S-excess glass in Figure 2 indeed displays a weak shoulder near ∼2.0 Å, possibly indicating the presence of a small concentration of the expected S-S bonds. However, the low intensity of the shoulder, being close to the level of noise in the data, precludes the possibility of any meaningful analysis of this peak in terms of extraction of an average S-S coordination number. Such low intensity is consistent with the chemical composition of the S-excess glass which implies a rather small average CS(S) of ∼0.5, provided CGe(S) ) 4.0 and CAs(S) ) 3.0. The first shell in the case of S-deficient glasses was fitted with two Gaussian functions centered at ∼2.2 and 2.5 Å (Figure 2b). The effects of termination of the Fourier integral at a finite Q of ∼20 Å-1 are taken into account by convolution of the Gaussian peaks with the appropriate sinc function.24 For the low and intermediate levels of S-deficiencies (20e x e 25), eq 7 is still valid for the peak centered at 2.2 Å. Previous EXAFS results indicated that in this composition range only the As atoms participate in metal-metal bonding while the Ge atoms remain coordinated to 4 S atoms.15-17 Therefore, the peak positioned at ∼2.5 Å is attributed to only As-As correlations, and the number of As atoms surrounding a central As atom, CAs(As), can readily be obtained with high precision by fitting the peak positioned at 2.5 Å by a Gaussian function (Table 3). The CAs(As) values thus obtained from neutron diffraction in this composition range are in excellent agreement with the corresponding values expected from stoichiometry for complete exclusion of Ge from metal-metal bonding (Table 3). As mentioned earlier, the nearest-neighbor coordination numbers of Ge and As atoms in these glasses are always 4 and 3, respectively, irrespective of composition, and thus it is possible to obtain CAs(S) by subtracting CAs(As) from 3. This CAs(S) value was substituted into eq 7 to obtain CGe(S) from the area under the peak centered at 2.2 Å. The coordination environments for Ge and As atoms thus obtained are listed in Table 3. The CGe(S) values obtained for these glasses with 20e x e 25 from the neutron data are indeed similar to those obtained using Ge K-edge EXAFS in previous studies, within the limits of experimental error.15,16 Previous Ge and As K-edge EXAFS studies have shown that at the highest levels of S deficiencies (27.5e x e 33.3), Ge atoms start to contribute to metal-metal bonding and As participates only in As-As/Ge bonding. Therefore, the peak in N(r) located at ∼2.2 Å in these glasses corresponds only to Ge-S correlations. The CGe(S) values obtained from the area of this peak at ∼2.2 Å are listed in Table 4 and agree very well (within (0.1) with the values obtained in previous Ge K-edge EXAFS studies of these glasses.15,16 However, for these glasses the relative degree of chemical order in metal-metal bonding involving Ge and As atoms, i.e., whether the Ge and As atoms bond randomly or there is any preference for Ge-As bonds over As-As and Ge-Ge bonds, is not known a priori. In order to address this structural aspect, two extreme scenarios have been considered in fitting the peak in N(r) located at ∼2.5 Å:

one assumes that the Ge atoms would form only Ge-Ge bonds, and the other considers the case where the Ge atoms taking part in metal-metal bonding would bond to As atoms only. For the first case, eq 6 can be written for the peak located at ∼2.5 Å as:

C ) CAs(As) WAsAs + CGe(Ge) WGeGe

(8)

where C is the total area under the peak located at 2.5 Å which is obtained by a Gaussian fit. As mentioned earlier, previous EXAFS results indicated that the first shell coordination number of Ge is 4 irrespective of composition.15 CGe(Ge) can then be calculated for this case by simply subtracting CGe(S) from 4, and hence CAs(As) can be obtained from eq 8. On the other hand, for the second case, eq 6 can be written as:

C ) CAs(As) WAsAs + CGe(As) WGeAs

(9)

CGe(As) can again be calculated as before by subtracting CGe(S) from 4 and CAs(As) can then be obtained from eq 9. The corresponding coordination environments for the Ge and As atoms are listed in Table 4. It is clear that for the first scenario, where metal-metal bonds are allowed only between like atoms, the coordination number of As atoms progressively decreases to unreasonably low values with increasing S-deficiency. In contrast, more consistent coordination numbers closer to 3 are obtained for the second scenario when all metal-metal bonds for Ge are of the type Ge-As (Table 4). 3.2.2. Second Shell and the Next-Nearest Neighbor Coordination EnVironments. For the stoichiometric and S-excess glasses, the second shell in N(r) is dominated by a peak centered at ∼3.4 Å that can be readily correlated to the metal-metal nextnearest neighbors that are connected through a S atom, namely Ge-S-Ge, Ge-S-As, and As-S-As linkages (Figure 2). This peak has also been observed in previous Ge and As K-edge EXAFS spectroscopic studies of these glasses as a metal-metal next-nearest neighbor shell in the partial radial distribution functions of Ge and As atoms.15 As a function of decreasing S concentration, the second shell in N(r) shows the appearance and systematic growth of a peak centered at ∼3.8 Å while the peak at ∼3.4 Å decreases in intensity (Figure 2). This peak at ∼3.8 Å corresponds primarily to As-As next-nearest neighbors linked through another As atom, i.e., As-As-As linkages, since Ge atoms do not participate in metal-metal bonding in this compositional range. This assignment is consistent with the corresponding As-As next-nearest neighbor distance of ∼3.76 Å in crystalline As metal. As mentioned above, at the highest levels of S deficiencies, a fraction of the Ge atoms starts participating in metal-metal Ge-Ge/As bonding. Therefore, Ge-Ge/As next-nearest neighbors connected through another Ge/As atom in the structure may also contribute to the peak at ∼3.8 Å in glasses with 27.5e x e 33.3. 3.2.3. Correlations at r > 4.0 Å. At distances longer than ∼ 4 Å the N(r) has a broad peak covering the region between ∼ 5.0 and 5.5 Å in S-excess and stoichiometric glasses which is gradually replaced by a peak in the region between 5.5 and 6.0 Å with increasing S-deficiency (Figure 2). Violation of chemical order and preferential homopolar bonding of As atoms in S-deficient glasses is expected to result in the formation of Asrich metal clusters. Therefore, the peak in the region between 5.5 and 6.0 Å in highly S-deficient glasses is likely to be associated with the long-range (third neighbor and beyond) metal-metal correlations within the As-rich metal clusters. Similar correlations at comparable distances, i.e., between 5 and 6 Å are indeed characteristic of crystalline Ge and As metals.

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TABLE 3: Interatomic Distances and Coordination Numbers for Ge and As Atoms in GexAsxS100-2x Glasses with 15 e x e 25 first coordination shell composition

CGe(S) ((0.1)

CAs(S) ((0.1)

average Ge/As-S distance (Å) ((0.01 Å)

Ge15As15S70 Ge18.2As18.2S63. 6 Ge20As20S60 Ge22.5As22.5S55 Ge25As25S50

4.0 4.0 3.8 3.7 3.9

3.0 3.0 1.8a 0.9a 0.2a

2.24 2.24 2.24 2.23 2.24

CAs(As) ((0.1)

CAs(As)b

CAs(As)c

average As-As distance (Å) ((0.01 Å)

1.2 2.1 2.8

1.0 2.1 3.0

0.5 1.2 1.9

2.53 2.49 2.49

a These coordination numbers are obtained by subtracting CAs(As) from 3. b As-As nearest-neighbor coordination numbers expected from stoichiometry for complete exclusion of Ge from metal-metal bonding c As-As nearest-neighbor coordination numbers obtained from As K-edge EXAFS spectroscopy.15,16

TABLE 4: Interatomic Distances and Coordination Numbers for Ge and As Atoms in Highly S-Deficient GexAsxS100-2x Glasses with 27.5e x e 33.3 first coordination shell case 1a

case 2b

composition

CGe(S) ((0.1)

CAs(S)

average Ge-S distance (Å) ((0.01 Å)

CAs(As) ((0.1)

CGe(Ge) ((0.1)

CAs(As+Ge) ((0.1)

CGe(As) ((0.1)c

average Ge/ As-Ge/As distance (Å) ((0.01 Å)

Ge27.5As27.5S4 5 Ge30As30S40 Ge32.5As32.5S3 5 Ge33.3As33.3S3 3.3

3.6 2.9 2.4 2.1

-

2.24 2.24 2.25 2.25

3.0 2.8 2.7 2.5

0.4 1.1 1.6 1.9

3.1 2.8 2.8 2.8

0.4 1.1 1.6 1.9

2.48 2.47 2.47 2.46

a

c

This situation assumes the Ge atoms would bond to only Ge atoms. b This situation assumes the Ge atoms would bond to only As atoms. These coordination numbers are obtained by subtracting CGe(S) from 4.

4. Discussion 4.1. Local Coordination Environments of Ge and As Atoms and Short-Range Order. The nearest-neighbor shell in the neutron radial distribution functions of these glasses is shown to be consistent with the results of previous Ge and As K-edge EXAFS spectroscopic studies of these GexAsxS100-2x glasses. Similar to these EXAFS studies, the present neutron diffraction data suggest the following “bonding rules” for these glasses: (1) the first shell coordination numbers of Ge and As are 4 and 3, respectively, in all glasses irrespective of composition; (2) Ge and As atoms are primarily bonded to S atoms in stoichiometric and S-excess glasses; (3) at low and intermediate levels of S-deficiency only As atoms take part in homopolar As-As bonding, thus violating chemical order and (4) Ge starts to participate in metal-metal bonding only in the highly S-deficient glasses where all the As atoms are used up in homopolar bonding. A comparison of the expected concentration of As-As bonds in glasses with low and intermediate levels of S-deficiency between those derived from the present neutron and previous EXAFS data indicate that the neutron results are more accurate than As K-edge EXAFS spectroscopy in predicting the As-As coordination numbers (Table 3). Moreover, the As-As nearestneighbor distances for these glasses as obtained in this study are slightly longer (2.49 to 2.53 Å) and are more consistent with As-As nearest-neighbor distance of ∼2.52 Å in As metal than those obtained in previous EXAFS studies (∼2.46 Å).15,16 Another interesting and unique result obtained from the analysis of the neutron RDFs of highly S-deficient glasses with 27.5e x e 33.3 is that consistent coordination numbers of As atoms are obtained only when metal-metal bonding between dissimilar Ge and As atoms is considered rather than bonding exclusively between like metal atoms. This result implies incorporation of Ge atoms into As clusters as Ge starts to participate in metalmetal bonding in highly S-deficient glasses. The evolution of the bonding geometry at the next-nearest neighbor level as a function of glass composition is fully consistent with the short-range ordering scenario discussed

above. For example, the peak at ∼3.4 Å characteristic of the distances between Ge/As-Ge/As next-nearest neighbors connected through S atoms is gradually replaced with increasing S-deficiency by a peak at ∼3.8 Å. This latter peak represents correlations corresponding to metal-metal next-nearest neighbors connected through another metal atom. For example, an interatomic distance of ∼3.8 Å is similar to As-As next-nearest neighbor distances of ∼3.76 Å in As-As-As linkages in crystalline As metal. Similar As-As distances (∼3.8 to 4.2 Å) are also characteristic of the As-Ge-As linkages in crystalline GeAs2.25 Such As-Ge-As linkages may exist in the highly S-deficient glasses (27.5e x e 33.3) where Ge participates in metal-metal bonding. 4.2. Metal-Metal Bonding, Metal Clusters, and Intermediate-Range Order. Previous studies based on isotopesubstituted neutron diffraction and anomalous X-ray scattering have shown that the FSDP in chalcogenide glasses arises primarily from metal-metal correlations.26-29 This interpretation is consistent with the progressive change in QFSDP in these glasses from 1.14 to 0.96 Å-1 corresponding to an increase in the periodicity of the intermediate range order 2π/ QFSDP from ∼5.5 Å for the S-excess glass to ∼6.5 Å for the most S-deficient glass. A broad peak corresponding to these metal-metal correlations indeed appears in the RDF and moves from the region of 5.0-5.5 Å in S-excess and stoichiometric glasses to 5.5-6.0 Å in the most S-deficient glasses (Figure 2). With increasing S-deficiency the RDF shows replacement of shortrange metal-S and metal-S-metal correlations at ∼2.2 and 3.4 Å and longer-range correlations at ∼5.0-5.5 Å with metalmetal correlations at ∼2.4, 3.8, and 5.5-6.0 Å in predominantly homopolar-bonded metal clusters. As discussed earlier, these clusters primarily consist of As in glasses with low and intermediate levels of S-deficiency (20e x e 25). Ge is incorporated into these As-rich metal clusters in glasses with the highest levels of S-deficiency (27.5e x e 33.3). Therefore, the periodicity in the intermediate range order as manifested in the position of the FSDP results directly from a propagation of the short-range chemical order in these glasses.

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Figure 5. Variation in the amplitude of the FSDP (open squares) and molar volume (filled circles) in GexAsxS100-2x glasses as a function of Ge (or As) content. Molar volume data are from ref 19, and the corresponding error bars are within the size of the symbols.

Violation of chemical order and exclusive participation of As in homopolar bonding in the compositional range of 20e x e 25 would eventually lead to the formation of corner-sharing AsAs3 trigonal pyramids, possibly forming low-dimensional structural units or clusters coexisting with a predominantly GeS2 network. This topological ordering corresponds strongly with the rising trend of the coherence length of intermediate range order 2π/∆QFSDP in this composition range from ∼18 Å at x ) 15 to ∼ 24 Å at x ) 25 where all As atoms take part in homopolar As-As bonding (Figure 4). With further increase in S-deficiency, the Ge atoms start to participate in metalmetal bonding and interrupt the topological continuity of the As-rich clusters and the GeS2 network. This structural model can explain the slight decreasing trend of the coherence length in this compositional region with increasing S-deficiency (Figure 4). The size and relative abundance of these As clusters in glasses with 20e x e 25 may exert an important control on physical properties that are strongly dependent on the topological aspects of atomic packing. For example, the presence of such low-dimensional intermediate range structural units would be expected to lead to inefficient atomic packing resulting in an increase in the molar volumes of these glasses with respect to that of the stoichiometric glass characterized by more of a threedimensional structure of corner-shared GeS4 and AsS3 polyhedra. On the other hand, molar volume is also expected to decrease for glasses with x > 25 where tetrahedrally coordinated Ge starts participating in metal-metal bonding and increases the connectivity and thus the dimensionality of the As-rich metal clusters. Previous studies have correlated the intensity of the FSDP with the atomic packing efficiency in glasses.30 Hence, the intermediate range structural and topological aspects discussed above are expected to be manifested in the compositional variation of both the FSDP intensity and molar volume of these glasses. It is evident from Figure 5 that FSDP intensity and molar volume of these glasses are in fact strongly correlated and indeed both go through a maximum in glasses with 20e x e 25 that are characterized by the presence of the lowdimensional homopolar bonded As clusters. Finally, it is important to note here that a recent study of the compositional dependence of FSDP intensity in binary Ge-Se and As-Se glasses has shown radically different behavior between the two glass-forming systems.26 In both cases the FSDP intensity is related to the intermediate-range metal-metal correlations in the GeSe2 and As2Se3 network in stoichiometric and metal-deficient glasses. However, in the case of Se-deficient

Uzun et al. As-Se glasses, a sharp rise in the FSDP intensity with increasing As content is believed to result from additional intermediate-range As-As correlations. On the other hand, a sharp drop in FSDP amplitude in the corresponding Ge-Se glasses has been ascribed to a disruption of the intermediaterange order in the GeSe2 network due to the formation of GeGe bonds. These results are consistent with the compositional dependence of the FSDP intensity in ternary Ge-As-S glasses as reported in this study (Figure 3). The increase in the FSDP intensity with increasing S-deficiency in the compositional range of 15e x e 18.2 primarily indicates establishment of intermediate-range metal-metal correlations, as the GeS2 and As2S3 networks are fully established in the glass structure (Figure 3). Lack of any detectable small-angle scattering for these glasses corroborates this scenario where the structure is dominated by a homogeneous network (Figure 1a). Further increase in S-deficiency results in increasing FSDP intensity that saturates in glasses with 20e x e 25 which attests to the signature of additional intermediate-range As-As correlations, as only As atoms participate in homopolar bonding (Figure 3). The coexistence of the GeS2 network and As-rich metal clusters in this composition range is expected to give rise to strong composition and density fluctuations. This structural scenario is consistent with the increasing intensity of small-angle scattering observed in this compositional range (Figure 1a). A subsequent rapid drop in FSDP intensity in the compositional range of 25e x e 33.3 is indicative of the breakdown of intermediate-range correlations in the GeS2 network as Ge starts participating in metal-metal bonding (Figure 3).26 The glass structure is expected to be dominated by large metal-rich clusters at the highest levels of S-deficiency, consistent with the lowering in small-angle scattering intensity for glasses with x > 30 (Figure 1a). 5. Conclusions The present neutron diffraction results confirm our earlier conclusions regarding the nearest-neighbor coordination environments of Ge and As atoms in GexAsxS100-2x glasses based on previous Ge and As K-edge EXAFS spectroscopic studies. The periodicity of the intermediate range order 2π/ QFSDP increases from ∼ 5.5 Å for the S-excess glass to ∼6.5 Å for the most S-deficient glass. This increase in the length scale with increasing metal concentration corresponds to progressive substitution of metal-metal correlations in a predominantly heteropolar-bonded structure with that in a predominantly homopolar-bonded one. Sole participation of As in metal-metal bonding at low and intermediate levels of S-deficiency leads to the formation of low-dimensional As-rich clusters. The topological continuity of these low-dimensional clusters of As atoms and the remaining GeS2 network are disrupted in glasses with the highest levels of S-deficiency via the formation of Ge-As metal-metal bonds. This evolution of intermediate-range ordering and its topological influence on atomic packing are manifested in the compositional variation of the coherence length of intermediate range order and of the amplitude of the FSDP. Taken together these results provide a detailed picture of the nature and length-scale of intermediate-range order in complex ternary chalcogenide glasses that has not been available before. Acknowledgment. This work was supported by the National Science Foundation grant DMR 0603933 to SS. The IPNS Division, Argonne National Laboratory is supported by the U.S. DOE under contract number DE-AC02-06CH11357.

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