Structure and properties of Ge2.5PSx glasses

Structure and properties of Ge2.5PSx glasses

Journal of Non-Crystalline Solids 333 (2004) 28–36 Structure and properties of Ge2:5PSx glasses Brian R. Cherry a ...

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Journal of Non-Crystalline Solids 333 (2004) 28–36

Structure and properties of Ge2:5PSx glasses Brian R. Cherry a


, Josef W. Zwanziger


, Bruce G. Aitken


Department of Chemistry, Indiana University, Bloomington, IN 47405, USA b SP-FR-05, Corning Inc., Corning, NY 14831, USA Received 29 July 2003

Abstract Ge2:5 PSx glasses were studied with a combination of Raman spectroscopy, nuclear magnetic resonance, and neutron diffraction. From these experiments the distribution of bonding configurations was determined, and used to explain the compositional dependence of the index of refraction and the glass transition temperature. On reducing the sulfur content of these glasses below the stoichiometric amount, the sulfur deficit is accommodated by the progressive loss of the non-bridging sulfur of [email protected]=2 groups, followed by the conversion of the resultant PS3=2 groups into species such as P4 S3 characterized by P–P bonding. The presence of metal–metal bonds involving germanium, found in samples with the lowest sulfur content, was found to be the most important structural feature in determining the optical response.  2003 Elsevier B.V. All rights reserved. PACS: 61.43.Fs; 78.40.Pg

1. Introduction Due to their large refractive index and low maximum phonon energy, sulfide glasses, when doped with rare-earth ions, are characterized by large emission cross-sections and low non-radiative decay rates for the lanthanide f–f optical transitions. In cases where the fluorescence of interest is adversely affected by multiphonon decay, such as the technologically important 1 G4 fi 3 H5 transition of Pr3þ at 1300 nm, sulfides are ideal host glasses with high luminescent quantum efficiency [1]. Germanium sulfide glasses are especially appealing because they have a wide range of transparency covering a large portion of the infrared and visible spectrum, making them suitable for telecommunication applications. However, rare-earth solubility in glassy GeS2 is low; in the case of Pr, it is only 400 ppm [2]. Rare-earth * Corresponding author. Present address: Department of Chemistry, Dalhousie University, Halifax NS, Canada B3H 4J3. Tel.: +1-902 494 1960; fax: +1-902 494 1867. E-mail address: [email protected] (J.W. Zwanziger). 1 Present address: Sandia National Laboratories, New Mexico, P.O. Box 5800, Albuquerque, NM 87185-0888, USA.

0022-3093/$ - see front matter  2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2003.09.057

solubility in Ge-containing sulfide glasses has been shown to be enhanced by the incorporation of co-dopants such as gallium or phosphorus [3]. Moreover, addition of phosphorus to vitreous GeS2 results in sufficiently improved glass stability that optical fibers can be drawn from these glasses [4]. Furthermore, the germanium phosphorus sulfur system has a large glassforming region [5–7], so bulk samples can be made over a wide variety of compositions, providing a range of physical properties. Consequently, rare-earth-doped germanium phosphorus sulfide glasses are of interest for a variety of photonic applications, including fiber lasers, upconverters, and optical amplifiers [1,8]. Understanding how and why addition of phosphorus affects the structure and bulk properties of germanium sulfide glass is the object of this paper. To our knowledge there are only two previous structural studies of the Ge–P–S glass forming system: the work of Koudelka and Pisarcik [9], based solely on Raman data, and our own research on the (GeS2 )x (P2 S5 )1x or stoichiometric glasses [10], based on a combination of Raman spectroscopy, solid state NMR, and neutron diffraction. We found the (GeS2 )x (P2 S5 )1x glasses to consist of GeS4=2 tetrahedra and a mixture of [email protected]=2 and PS3=2 units, with the former thiophosphate

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2.2. NMR

Fig. 1. Glass forming region of the Ge–P–S system, bounded by the solid line; compositions studied here, indicated by filled circles; compositions studied previously ((GeS2 )1x (P2 S5 )x stoichiometry, Ref. [10]), filled squares.

units present in both network and cage or cluster configurations. These findings were consistent with the more limited previous study [9]. The samples discussed here have a constant germanium to phosphorus ratio of 2.5:1.0; the sulfur content is varied from 58.8% to 80% (see Fig. 1). This range spans compositions with extreme sulfur deficiencies to those with extreme sulfur excess, passing through the stoichiometric composition, at 68.2% sulfur. It was our hope that through large variations in the sulfur content, qualitatively different bonding configurations (such as metal–metal bonding) could be induced, thereby making significant changes in the optical properties.

The high-speed MAS experiments were performed at 161.977 MHz (9.4 T) on a Bruker Avance 400 spectrometer with a 2.5-mm Bruker MAS probe. Measurements were made at a spinning rate of 29 kHz. A 1 ls pulse length was used corresponding to a nutation angle of 25. This allowed recycle times to be shortened to 1–5 min, depending on the sample. T1 for these samples ranged from 2 to 12 min. A sweep width of 100 kHz was used. The dipole second moment experiments were performed at 81.211 MHz (4.7 T) on a Tecmag Libra spectrometer. A sweep width of 100 kHz was used. A non-spinning sample was used with a 4 ls, p=2 excitation pulse. The spin echo intensity was collected for 10 separate dephasing times covering a range from 50 to 450 ls. Recycle delays for these experiments were 30–60 min. Calibration was done on crystalline P4 S10 and Ag3 PO4 . All 31 P NMR experiments were referenced to 85% H3 PO4 . 2.3. Raman spectroscopy All Raman spectra were taken at the Purdue University Department of Chemistry laser facility. The micro-Raman instrument utilizes a 785 nm NIR diode laser as the source, a pair of holographic notch-filters to reject Rayleigh scattering, and a CCD detector. Samples were sealed in evacuated Pyrex ampoules and spectra were taken by focusing the microscope on the surface of the sample through the ampoule. A collection time of 15 s was used.

2. Experimental procedures

2.4. Neutron diffraction

2.1. Sample preparation and bulk characterization

The neutron diffraction experiments were performed at the pulsed neutron source ISIS, Rutherford Appleton Laboratory, Chilton, Didcot, UK, on the time-of-flight liquid and amorphous diffractometer (LAD). LAD is equipped with detector banks positioned at seven different scattering angles from 5 to 150. Time-of-flight spectra are recorded separately at each detector and individually corrected for background and container scattering, absorption, multiple scattering, inelastic scattering, and normalized to the scattering of a vanadium rod. The correction procedure yielded the total structure factor, SðQÞ, for each sample, which was transformed to the real-space total correlation function T ðrÞ. The total structure factor was truncated at Q ¼ 40 1 during transform. Because of the hygroscopic natA ure of some of the glass samples, they were removed from silica ampoules, crushed into chunks, and sealed in cylindrical vanadium cans in a glove box. Nevertheless, the sample with 80% S showed some evidence of hydrogen contamination, but this could be corrected for by assuming 0.1% H content in the data processing.

The glass samples were prepared and their bulk properties were measured at Corning Inc. Glasses were synthesized from 25 g mixtures of high purity elements that were loaded into 10 mm ID fused silica ampoules under dry N2 . Prior to batching, the ampoules were etched in 5%HF:5%HNO3 , rinsed in deionized water and then dried at about 1000 C. The filled ampoules were evacuated to 105 Torr, flame sealed, and then heated to 925 C in a rocking furnace. Following a 48 h hold at 925 C, the furnace temperature was reduced to 850 C for 10 min, after which cylindrical glass rods were formed by quenching the hot ampoules in water. Density was measured in water to ±0.001 g/cm3 using the Archimedes method. The glass transition temperature ðTg Þ was determined with a precision of ±5 C by differential scanning calorimetry (DSC) using a heating rate of 10 C/min. The refractive index was measured to ±0.01 by the apparent depth method at 589 nm with 5 mm thick samples.


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3. Results The bulk properties, including density, refractive index, optical absorption edge (wavelength where the transmittance of a 2 mm thick sample is 50% of that at 1000 nm), and glass transition temperature are tabulated as a function of glass composition in Table 1. This table also lists the measured second moment of the 31 P magnetic dipole homonuclear coupling distribution, M2 , for the samples for which it was determined. Fig. 2 shows the high-speed 31 P MAS-NMR spectra of the glasses in a field of 9.4 T (161.977 MHz resonant frequency) at a spinning rate of 29 kHz. The neutron diffraction results for the glasses containing 80%, 68.2%, 65%, and 58.8% sulfur are shown in Figs. 3 (total structure factors) and 4 (total correlation functions). Raman spectra of the glasses are shown in Fig. 5.

4. Discussion The objectives of this section are to interpret the data of the structural experiments performed above, to construct from this interpretation an atomistic model of the structure of Ge2:5 PSx glass, and finally to use this model to explain the observed bulk properties of these glasses.

Fig. 2. 31 P MAS-NMR spectra, at 29 kHz rotation frequency, for the Ge2:5 PSx glasses.

4.1. Interpretation of experiments 4.1.1. Solid-state NMR The high-speed MAS 31 P NMR spectra (Fig. 2) yield information on the types and prevalence of the different phosphorus bonding sites. The majority of the phosphorus sites are similar to those observed by us previously in (GeS2 )1x (P2 S5 )x glasses [10]; in fact the present sample with 68.2% sulfur is also a member of the (GeS2 )1x (P2 S5 )x series (with x ¼ 0:167) and is used here as a reference point. Column 2 of Table 1 gives the sample composition in terms of excess sulfur relative to this sample. As we discuss below, samples with significant sulfur excess or deficiency show additional phos-

phorus sites, as compared with the (GeS2 )1x (P2 S5 )x series. Typical chemical shifts for Ge–P–S glasses and their assignments are listed in Table 2, and the MAS spectra of the present glasses broken down into components in Table 3. As the sulfur content increases above the stoichiometric amount, the phosphorus in strained molecular cages or clusters, observed at shifts of 44 and 58 ppm, diminishes. Assignment of these resonances in the (GeS2 )1x (P2 S5 )x series was discussed in detail in [10]. Signals at roughly 103, 91, and 81 ppm are assigned to network [email protected]=2 sites with differing second neighbors. The 81and 91 ppm [email protected]=2 resonances gain intensity in

Table 1 Density, molar volume, glass transition temperature, refractive index, absorption edge, and second moment of samples


P dipole couplings of the various

Sulfur (% )

Excess sulfur (%)

Density (g/cm3 )

Molar volume (cm3 /mol)

Tg (C)

Refractive index (n)

Absorption edge (nm)

M2 (106 rad2 s1 )

80 75 69.6 68.2 66.7 65 63.2 61.1 58.8

86.7 40 6.7 0.0 )6.7 )13.3 )20.0 )26.7 )33.3

– – 2.544 2.558 2.577 2.610 – – 2.717

– – 16.030 160.94 16.146 16.127 – – 16.138

– – 281 300 342 337 336 334 336

– – 2.212 2.215 2.213 2.225 2.219 2.225 2.274

– – 509.4 506.3 508.9 508.6 508.8 510.5 540.1

1.6 – – 4.6 – – – 9.3 –

B.R. Cherry et al. / Journal of Non-Crystalline Solids 333 (2004) 28–36


Fig. 3. Total structure factor from neutron diffraction, SðQÞ, for the Ge2:5 PSx glasses.

the 6.7% sulfur excess glass. In the 40% S excess glass, the 91 ppm peak has the maximum intensity. Finally, when the excess sulfur reaches 86.7%, the 103 ppm resonance is the most intense. Second neighbor effects and strain account for the difference between these network phosphorus sites [10]. Each network [email protected]=2 unit has three bridging sulfur, and the electron withdrawing strength of the atoms these sulfurs bond to, and the strain the bonds create, produces the second neighbor effects that influence diso . It is likely that the 103 ppm site is due to [email protected]=2 units with all sulfur second neighbors, as are found in PS glasses at low P content [11]. The 91 ppm site most likely has one non-sulfur (Ge or P) second neighbor and the 81 ppm site has predominantly Ge or P second neighbors, though not in the form of molecular clusters. Different changes occur as sulfur content is decreased below the stoichiometric level. First, a large increase in the amount of network PS3=2 , at a shift of diso ¼ 123 ppm [10,11], is observed, which indicates that the nonbridging sulfur in [email protected]=2 is most easily lost. Furthermore, since PS clusters containing multiple PS3=2 sites are unstable [12], the cage/cluster signals at 58 ppm and 44 ppm diminish rapidly as well. As even more sulfur is removed (deficiencies of 20% or greater), however, a new cluster is observed, with signals at 73 and )111 ppm. We assign these signals to the apical and basal phosphorus, respectively, of P4 S3 [13,14]. The 31 P spin-lattice relaxation time, T1 was measured for this sample and found to be 4.3 and 0.8 s for the apical and basal phosphorus,

Fig. 4. Total correlation function from neutron diffraction, T ðrÞ, for the Ge2:5 PSx glasses, at 80%, 68.2%, 65%, and 58.8% sulfur.

respectively. As a point of comparison, the T1 values for all other phosphorus sites ranged from 120 to 720 s. The chemical shifts and measured T1 are identical to values for the plastic phase of P4 S3 , which is stable above 41 C [13,14]. In the glass samples, frictional heating due to the high speed of the MAS rotor elevates the sample temperature, so that the P4 S3 in the glass undergoes


B.R. Cherry et al. / Journal of Non-Crystalline Solids 333 (2004) 28–36 Table 2 Approximate glasses


P chemical shifts and their assignments in Ge–P–S

Shift (ppm)


123 103

Network PS3=2 Network [email protected]=2 , mainly S NNN Network [email protected]=2 , mainly P NNN Cage/cluster [email protected]=2 , PS3=2 Cage/cluster [email protected]=2

81 58 44 91

Network [email protected]=2 , P and S NNN Apical P in P4 S3 Basal P in P4 S3

73 )111

For the first five sites, see Ref. [10] for detailed discussion. The final two sites are observed only in highly sulfur-deficient compositions (see [13,14]). NNN stands for Ônext-nearest neighbor’.

Fig. 5. Raman spectra for the Ge2:5 PSx glasses.

dynamics similar to the plastic phase of pure P4 S3 , although in the glasses there is no phase separation. The second moment of 31 P–31 P magnetic dipole couplings, M2 , is also consistent with P4 S3 molecular units. The 61.1% S sample showed M2 of 9.3 · 106 rad2 s2 , the highest value of the measured GePS glass samples. The large M2 value is due to the three basal phosphorus, which in P4 S3 are each bonded to two phosphorus and one sulfur. P4 S3 is the most stable of the caged PS molecular compounds and has the highest phosphorus

Table 3 Shifts (ppm) and intensities for features observed in the 80% S

75% S



113 103 91 81 66 52 44

6.4 25.9 21 19.1 14.8 7 5.8

65% S 123 106 86 54 40 5

Shift 102.5 90.3 80.3 64 51

123 106 87 72 56 41 10 )109

4.1.2. Neutron diffraction The total structure factors SðQÞ of the Ge2:5 PSx samples are shown in Fig. 3. The first sharp diffraction 1 in each sample. The peak (FSDP) is seen near 1.05 A position of this peak is essentially the same as in the (GeS2 )1x (P2 S5 )x glasses and in GeS2 glass [10,15]. In (GeS2 )1x (P2 S5 )x glasses the FSDP decreased in inten-

P MAS-NMR spectra (Fig. 2), as a function of composition 69.6% S

Intensity 22.6 10.1 22.6 22.1 2.8

63.2% S 46.6 7 16.8 10.8 15.3 3.5


to sulfur ratio, making it particularly effective for compensating the sulfur deficiency. Finally, at 58.8% sulfur content the sulfur deficiency is so large that P4 S3 units alone cannot compensate the sulfur deficit. The very broad peak in the MAS spectra of this sample indicates the presence of distorted phosphorus environments that involve Ge–P and P–P bonding, as distinct from the P–P interactions seen in P4 S3 .

Shift 124 91 60 44 8

68.2% S Intensity 8.4 22.7 24.9 36.3 7.7

61.1% S 28.1 8.8 17.4 7.7 8 7.1 2 20.9

126.6 102.1 80.1 56.9 40 )110.4 72.9

Shift 127 86 60 44 5

66.7% S Intensity



15.3 10 15.3 46.6 12.8

122 107 83 55 41 10

30.6 7 10.4 18.8 25.4 7.8

58.8% S 12 6 15.6 8.1 8.8 39.3 10.2

130 96 75 58 42 3 )113 71

7.8 4.5 8.5 5.7 5.8 54.9 9.7 3.1

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Table 4 Intensities of the features in the total correlation function T ðrÞ as measured by neutron diffraction S (%)

 1.89 A

 2.09 A

 2.22 A

 2.44 A

 2.92 A

 3.43 A

 3.82 A

80 68.2 65 58.8

1.23 1.60 1.38 0.00

5.05 3.61 4.24 1.55

11.24 17.43 18.25 21.78

1.00 1.71 2.07 5.23

1.38 3.50 3.63 3.01

18.79 23.66 24.38 28.75

10.26 11.92 11.89 15.24

Glass compositions are given in column 1, while the remaining columns are labeled by the centers of gravity of the Gaussians used to deconvolute , for each composition. T ðrÞ (see Fig. 4). The body of the table gives the intensity of each feature, in barns/A

sity and widened with increasing P2 S5 content, suggesting that the local environment about germanium appears to be the same as in vitreous GeS2 . Germaniumcentered correlations are thought to be the principal contributor to the FSDP intensity [16,17]. The 68.2% sulfur glass is also a stoichiometric (GeS2 )1x (P2 S5 )x glass, with x ¼ 0:167. The FSDP moves to slightly 1 in the sulfur deficient glasses. In the smaller Q, 1.0 A sulfur excess glass, the FSDP decreases in intensity due to the smaller amount of germanium in this sample. The FSDP also broadens substantially in the sulfur excess glass; this points to an increase in the disorder in the glass structure compared to the stoichiometric glasses. 1 , indicating Finally, the FSDP shifts to larger Q, 1.1 A a change in the Ge–Ge medium range order as a function of sulfur content. As with the GeS2 –P2 S5 glasses, oscillations in SðQÞ are seen out to very large Q, which is evidence for well-defined short range order, that is, bonds of uniform length. Fig. 4 shows the total correlation function T ðrÞ for the 80%, 68.2%, 65%, and 58.8% sulfur glasses. The first coordination shell changes dramatically, depending on the amount of sulfur present in the glass. At stoichiometry, the first coordination shell peak is asymmetric on the short distance side. The short distance shoulder increases significantly in the excess sulfur glass. On the other hand, when sulfur is removed from the system, the shoulder on the short distance side vanishes and a new , apfeature on the long distance side, around 2.45 A pears. Table 4 gives the intensities of the features in T ðrÞ as a function of composition. The first peak in T ðrÞ, at 1.89 , is assigned to [email protected], while the second feature, at 2.09 A , is assigned to P–S and S–S interactions. These A assignments are based on bond lengths in crystal struc, which indicates [email protected] bonds, tures. The peak at 1.89 A while strong in the sulfur-excess compositions, is hard to detect in the sulfur-deficient compositions. However, Raman spectroscopy (see below) clearly detects this feature in all the samples with P 63.2% S. In the 80% S  peak is large due to the abundance of S– glass, the 2.09 A S bonding in this sample. In the sulfur deficient samples, this peak is small, for two reasons. First, at these compositions, there is very little, if any, sulfur–sulfur bonding. Second, the P–S pair-correlation weighting factor is

small; consequently, the P–S bonds contribute only weakly to T ðrÞ. , is due to Ge–S bonds. This The third peak, at 2.22 A peak steadily decreases with increasing sulfur content, due to the decrease in Ge concentration. In contrast to (GeS2 )1x (P2 S5 )x glasses, in which the Ge–S coordination number is always 4 [10], here in the sulfur-deficient samples the coordination number is only 3.5, because some of the germanium forms bonds with phosphorus and other germanium. Finally, in the most sulfur deficient glass, 58.8% S, the first coordination peak in T ðrÞ is asymmetric on the long distance side, due to a new peak . This peak is direct evidence of Ge–Ge and at 2.44 A Ge–P bonding [18].  is the Ge–Ge distance of two The peak at 2.92 A edge-sharing GeS4=2 polyhedra. The area of this peak is a maximum for the 68.2%S glass, which is also a stoichiometric (GeS2 )1x (P2 S5 )x composition. The formation of these edge-sharing groups indicates that the GeS network is similar to a-GeS2 , so it is not too surprising that the edge-sharing groups are less abundant in the non-stoichiometric samples. The final two peaks in T ðrÞ that were fit, at 3.43 and , are second coordination shell interactions. The 3.82 A  has contributions from Ge–Ge and S–S peak at 3.43 A pairs. Furthermore, Ge–S and P–S have approximately the same bond length, so Ge–P interactions also contribute to the area of this peak. The S–S interaction referred to is the distance between the sulfur in the same tetrahedral unit, while the Ge–Ge and Ge–P interactions are the distance between germanium or phosphorus of connected polyhedra. The peak shifts to , in the sulfur rich, 80% S, glass. a shorter distance, 3.41 A The shift is a result of an increase in the fraction of S–S second neighbor interactions, which come from the S–S second neighbors in sulfur chains and S8 rings. The sixth , might correspond to and final peak fit to T ðrÞ, at 3.82 A the sulfur–sulfur distance present in the Ge3 S3 sixmembered rings found in crystalline GeS2 .

4.1.3. Raman spectroscopy The Raman spectra are shown in Fig. 5. The symmetric stretching mode of GeS4=2 tetrahedra dominates the spectra, indicating that the germanium atoms are in


B.R. Cherry et al. / Journal of Non-Crystalline Solids 333 (2004) 28–36

Table 5 Estimated atomic fraction of germanium, phosphorus, and sulfur participating in various possible bonds, from NMR, neutron diffraction, and Raman data S (%)







S–Ge, S–P


80 75 69.6 68.2 66.7 65 63.2 61.1 58.8

0.143 0.179 0.217 0.227 0.238 0.250 0.263 0.276 0.221

– – – – – – – – 0.044

– – – – – – – 0.002 0.030

0.057 0.071 0.087 0.091 0.095 0.100 0.098 0.095 0.084

– – – – – – 0.007 0.014 0.004

– – – – – – – 0.002 0.030

0.429 0.536 0.652 0.657 0.667 0.650 0.632 0.611 0.588

0.371 0.214 0.044 0.025 Trace Trace – – –

Asterisk denotes stoichiometric (GeS2 )1x (P2 S5 )x glass. Trace amount of S–S character present in Raman spectra of 66.7% and 65% sulfur glasses.

GeS4=2 units, except for the extreme sulfur-deficient samples. The band around 700 cm1 , due to [email protected] bonds [9,19], is present in all samples with P 63.2% S. This result indicates that when the sulfur deficit drops below 20%, no [email protected]=2 units remain in the glass. The shoulder at 375 cm1 , which develops into a broad peak in the extreme sulfur excess samples, is associated with the vibration involving the phosphorus and the three bridging sulfurs of [email protected]=2 units [9,19]. This band is broad when compared to PS glass and to stoichiometric the (GeS2 )1x (P2 S5 )x glass with high P content [9,19]. In the non-stoichiometric GePS glasses studied here, there is a large variability in the combination of second neighbors (sulfur, germanium, and phosphorus) to which the sulfur of [email protected]=2 unit bridge. This creates a broad distribution of frequencies for this vibrational mode. On the other hand, in PS glass, the second neighbors of the [email protected]=2 units are all sulfur, and in compositions of GePS glass where this mode is sharp, the [email protected]=2 units are part of cages or clusters. The bands around 490 cm1 that indicate S–S bonding grow into a clear peak as excess sulfur is added. The maximum shifts to 471 cm1 as sulfur content increases in the 80% S glass. A similar shift was seen in PS glass, 490 cm1 in the 24% P glass to 478 cm1 in the 10% P glass [19]. The shift to lower frequency as sulfur is added reflects the decrease in the number of cross-links contained in the network. As a result, the network becomes less rigid, which lowers the frequency of the vibrations associated with the sulfur chains. The formation of S8 rings is indicated by the appearance of the bands at 142 cm1 and 209 cm1 in the 80% S glass [20]. As sulfur is removed, the [email protected]=2 units disappear for sulfur deficits greater than 20%. The formation of P4 S3 in samples with at least 20% sulfur deficiencies is confirmed in the Raman spectra: the sharp bands at 280 and 440 cm1 are the E and A1 of modes of P4 S3 [21,22]. The growth of a band at 250 cm1 in glasses with a 26.7% or greater sulfur deficit indicates Ge–Ge and Ge–P bonding [19].

4.2. Atomic model of Ge2:5 PSx glass Based on the NMR, neutron diffraction, and Raman data outlined above, we generated qualitative models of the glass structure for the Ge2:5 PSx compositions (Table 5 and Fig. 6). From the assignment of the P sites, Table 3, fits to the 31 P MAS-NMR spectra were used to quantify the P bonds for each sample. The onset of P–P bonding was detected and quantified from the )111 ppm peak. From the neutron and Raman data, it is known that the bonding of germanium is satisfied by sulfur in all the samples except for extreme sulfur deficient samples. The onset of Ge–P and Ge–Ge bonded was detected by the appearance of the 250 cm1 band in the Raman data. Fits to T ðrÞ of the neutron data for the 58.8% S sample in particular were used to quantify the amount of Ge–Ge present in that sample. The presence of S–S bonding was monitored by the 490 cm1 bands of

Fig. 6. Schematic of the structure of the Ge2:5 PSx glasses for: (a) the sulfur excess case and (b) the sulfur deficient case. Black circles represent phosphorus, gray is used for germanium, and the hollow circles are sulfur atoms.

B.R. Cherry et al. / Journal of Non-Crystalline Solids 333 (2004) 28–36

Fig. 7. Glass transition temperature Tg of the non-stoichiometric glasses plotted against atomic fraction sulfur.

the Raman data, and was found in samples with S content at or above 68.2% S (the stoichiometric composition). Therefore, the bonding could be quantified by assigning Ge–S bonds for every germanium in samples above 63.2% S. Above 65% S, all phosphorus participate in P–S bonding only. From the known atomic fractions, the amount of S–S bonding can be determined from the remaining S fraction after Ge and P bonding is satisfied. The Ômetal–metal’ bonding Ge–Ge, and Ge–P, was quantified as described above, using the NMR and neutron diffraction data for quantification and the Raman spectra to aid in identifying samples with these bonding pairs. The results of these fits are summarized schematically in Fig. 6, the main points being that in sulfur-excess compositions, there are sulfur rings and chains, GeS4=2 , and primarily [email protected]=2 units, while in sulfur-deficient compositions there are PS3=2 and P4 S3 units, and Ge–P and Ge–Ge bonds. 4.3. Thermal properties Based on the above structural model, we propose the following correlation of the glass transition temperature Tg with composition (see Table 1 and Fig. 7). In the samples with extreme sulfur excess, Tg is low because the glass structure consists predominately of long sulfur chains that are cross-linked by a small fraction of GeS4=2 and [email protected]=2 units. As the sulfur concentration is decreased, more GeS4=2 and [email protected]=2 cross-links are incorporated, increasing the network connectivity and, hence, Tg . This increase continues through the (GeS2 )1x (P2 S5 )x stoichiometry. As sulfur is decreased below the stoichiometric amount, Tg continues to rise due to the loss of the cage or cluster-like units, causing the network to become a larger fraction of the glass. Tg then reaches a plateau as more sulfur is removed, and then remains unchanged, despite the formation of a


Fig. 8. Calculated and experimental refractive index of Ge2:5 PSx glasses: (n) experimental values and (n) calculated values, scaled by a 0.857 factor to overlap the data points.

substantial amount of molecular P4 S3 . We suggest that this plateau in Tg arises for two reasons. First, the relative amount of highly cross-linking germanium units grows as sulfur is removed. Unlike in the high P2 S5 content stoichiometric glasses, the total amount of network species remains high even as the molecular units form. The second reason is the fact that floppy S–S units are no longer associated with the formation of PS3=2 units, due to the sulfur deficiency. The rigidity of the network is not diminished by soft S–S bonds as in the (GeS2 )1x (P2 S5 )x case. 4.4. Optical properties As in Ref. [10], we explain the index of refraction using the empirical model of Harrison [23]. In this approach, the (non-resonant) index of refraction n is derived from the dielectric constant v1 by n2 ¼ 1 þ 4pv1 , and the dielectric constant itself is estimated from bond polarizabilities. This approach differs significantly from that found in standard solid state physics texts [24], which focus on the polarizabilities of the ion-bound electrons and hence are appropriate for ionic, as opposed to covalent, solids. Harrison expresses the dielectric constant in a simple molecular-orbital formalism, with matrix elements fit empirically to data. The fit over a broad range of covalent compounds is excellent, and we use his approach here without modification [10,23]. The refractive index of the non-stoichiometric glasses gradually rises as the sulfur content drops from 80% to 61.1%, and then rises dramatically for the 58.8% sulfur glass (Table 1). As the atomic volume is roughly constant, the electron density is roughly constant as well. The gradual rise in the refractive index for the 80–61.1% sulfur glasses is due to the increase in the amount of Ge– S bonds as sulfur content decreases. The large increase


B.R. Cherry et al. / Journal of Non-Crystalline Solids 333 (2004) 28–36

in the refractive index for the 58.8% sulfur glass corresponds to the onset of Ge–Ge bond formation. Compared to the other types of bonds present (Ge–S, P–S, S– S, and P–P), Ge–Ge bonds have the longest bond dis), the largest covalency possible, and tance (2.45 A smallest orbital overlap matrix element. The susceptibility for Ge–Ge bonds is therefore also the largest. Thus, the presence of Ge–Ge bonds has a large effect on increasing the refractive index. Fig. 8 shows the agreement between the refractive index calculated with the empirical approach described above and our atomistic model (Table 5) as input, and the experimental data. The theoretical results were scaled by 0.857, so that the calculated values could be overlaid with the experimental data. The agreement with the compositional trend is excellent.

5. Conclusions Structural evolution in Ge2:5 SPx glasses is strongly influenced by the overwhelming tendency for germanium to assume tetrahedral coordination with four sulfur nearest neighbors. As a result, decreasing the sulfur content of these glasses below that corresponding to stoichiometry initially results in changes only in the phosphorus environment. The sequence of changes is conversion of [email protected]=2 tetrahedra into trigonal PS3=2 units through the loss of non-bridging sulfur, followed by the formation of sulfur-poor species, such as P4 S3 , characterized by the presence of P–P bonds. Using a combination of Raman, solid-state NMR and neutron diffraction data, we were able to construct a table of the different bonding units present in these glasses as a function of composition, and to use this table to compute the index of refraction based on an empirical model of bond polarizabilities. The compositional trend of the index of refraction was well accounted for and clearly showed the importance of metal-metal bonds in the optical response. Our model also accounts for the compositional trend in the glass transition temperature in this system.

Acknowledgements We thank Alex Hannon (ISIS) for his assistance with the neutron experiments and Randy Youngman (Corning) for many helpful discussions. We acknowledge Mark Powley and David Crooker for their technical assistance in the synthesis of the glass samples used in this study. We thank Corning Incorporated and the NSF for financial support (DMR-9870246).

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