Selenium Chain Length Distribution in GexSe100–x Glasses: Insights

Article pubs.acs.org/JPCB

Selenium Chain Length Distribution in GexSe100−x Glasses: Insights from 77Se NMR Spectroscopy and Quantum Chemical Calculations Derrick C. Kaseman,† Karina Moreira Oliveira,† Teresa Palazzo,‡ and Sabyasachi Sen*,† †

Department of Materials Science & Engineering, University of California at Davis, Davis, California 95616, United States Department of Chemistry, University of California at Davis, Davis, California 95616, United States

‡

ABSTRACT: The statistics of selenium chain length distribution in GexSe100−x glasses with 5 ≤ x ≤ 20 are investigated using a combination of high-resolution, two-dimensional 77Se nuclear magnetic resonance (NMR) spectroscopy and quantum chemical calculations. This combined approach allows for the distinction of various selenium chain environments on the basis of subtle but systematic effects of next-nearest neighbors of Se atoms in −Se−Se−Se− linkages on the 77Se chemical shift tensor parameters. Simulation of the experimental 77Se NMR spectral line shapes indicates that Se chain speciation in these chalcogenide glasses follows the Flory−Schulz distribution, originally developed for organic chain polymers.

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INTRODUCTION Chalcogenide glasses constitute an important class of materials that have wide ranging applications as active and passive materials in the areas of optoelectronics, telecommunication, memory, and sensing that rely on their unique optical properties.1−3 GexSe100−x glasses have served as an archetypal model system in the literature for chalcogenide glasses. Glasses in this system can be made in the bulk form over a large composition range (0 ≤ x ≤ 42), and their physical properties have been studied in detail in the literature.4−8 Moreover, significant effort has been devoted in the recent past to the structural elucidation of GexSe100−x glasses using a wide range of diffraction and spectroscopic techniques in order to establish structure−property relationships at an atomistic level.9−24 When taken together, the results of these structural studies suggest that the atomic structure of GexSe100−x glasses can be described as a network comprised of Se−Se−Se chain segments cross-linked by GeSe4 tetrahedra, resulting in the formation of Ge−Se−Se and Ge−Se−Ge linkages, the latter being associated with corner- and edge-sharing tetrahedra. The compositional dependence of the relative fractions of these various selenium environments indicates that the structure of GexSe100−x glasses can be described as a stochastic random network comprised of randomly connected Se−Se−Se chain elements and GeSe4 tetrahedra.13−16,18,25 While these fundamental insights into the selenium speciation and connectivity have offered considerable insights into the structure−property relationships for GexSe100−x glasses, the nature of the intermediate-range order remains elusive. Information about the intermediaterange structure typically relies on modeling approaches, such as molecular dynamics and/or reverse Monte Carlo simulation, the latter being typically constrained by diffraction and other spectroscopic results.18,23,26−31 © 2016 American Chemical Society

Recent advances in nuclear magnetic resonance (NMR) spectroscopy may enable the investigation of intermediaterange structure by providing information regarding next-nearest neighbor (NNN) environments.16,32 NMR spectroscopy typically uses differences in the isotropic chemical shift to differentiate between nearest neighbor (NN) effects. In solids, the chemical shift tensor contains both isotropic and anisotropic contributions which broaden the line shapes resulting in overlapping peaks. Conventional solid-state magic angle spinning (MAS) NMR utilizes sample rotation to average this chemical shift anisotropy (CSA) induced line broadening but in the process loses the information on the CSA. Recent development of high-resolution two-dimensional (2D) NMR techniques allows for the separation of the isotropic and anisotropic components of the chemical shift into correlated dimensions, thus preserving complete information on the chemical shift tensor.16,32,33 The resultant isotropic spectrum has increased resolution and allows for the analysis of subtle changes in these spectra induced by NNN interactions. At the same time, the isotropic spectrum can be correlated to the anisotropic dimension which contains information on site symmetry that is a function of NN and NNN bonding environments. Analysis of both the isotropic and anisotropic components of the 77Se chemical shift tensor was recently used by Kaseman et al.16 to unambiguously identify the short-range structural units present in GexSe100−x glasses. This study also noted a systematic and monotonic shift of the mean isotropic peak position and increase in the CSA of the Se−Se−Se chain environments with increasing Ge concentration that were Received: March 16, 2016 Revised: April 27, 2016 Published: April 29, 2016 4513

DOI: 10.1021/acs.jpcb.6b02747 J. Phys. Chem. B 2016, 120, 4513−4521

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The Journal of Physical Chemistry B

The structures of these molecules, shown in Figure 1, were first optimized using density functional theory and a B3LYP 6-

qualitatively attributed to the effect of shortening of the average selenium chain length. Deschamps and co-workers34 have recently reported similar effects in AsxSe100−x glasses. These authors simultaneously and self-consistently simulated the 77Se MAS NMR line shapes of As−Se glasses with Se contents ranging between 60 and 86 atom % using six Gaussian peaks corresponding to six distinct Se environments to account for the effects of NN and NNN. Although these simulations were self-consistent, the peak positions and their structural assignments were arbitrary to a significant extent. Interestingly, it was shown that these 77Se MAS NMR line shapes could be simulated well if it is assumed that the composition dependence of the selenium chain length distribution in these glasses follows the Flory−Schulz statistics, originally proposed for organic chain polymer systems. In the present study, we utilize quantum chemical calculations of 77Se chemical shift tensor parameters to analyze previously reported16 high-resolution 2D 77Se magic angle turning phase adjusted spinning sidebands Car Purcell Meiboom Gill (MATPASS/CPMG) NMR spectra of GexSe100−x glasses in order to investigate the effects of selenium NNN on the 77Se NMR spectra. We demonstrate that subtle but significant changes in the isotropic and anisotropic components of the 77Se chemical shift can indeed be ascribed to NNN effects. The simulation of the pure isotropic 77Se NMR line shapes with constraints imposed from quantum chemical calculations show that the Flory−Schultz statistics is indeed obeyed by the selenium chain length distribution in GexSe100−x glasses.

Figure 1. Optimized structures of H3Se3GeSenGeSe3H3 molecules used for quantum chemical calculations of 77Se NMR parameters. The n value (between 1 and 7) associated with each structure corresponds to the number of Se atoms between the Ge atoms at either end. The colored halo around each Se atom denotes a unique Se environment in terms of the makeup of its nearest and next-nearest neighbors. These are Se−Ge−Se−Ge−Se (red halo), Se−Ge−Se−Se−Ge−Se (orange halo), Se−Ge−Se−Se−Se (blue halo), Ge−Se−Se−Se−Ge (yellow halo), Ge−Se−Se−Se−Se (green halo), and Se−Se−Se−Se−Se (purple halo).

311+G(d,p) basis set. These structures were shown to be minima on the potential energy surface via normal vibrational mode analysis (no imaginary frequencies present). After optimization, all bond angles and lengths were found to be consistent with those reported in previous studies on GexSe100−x glasses.19,27 Magnetic shielding tensors were calculated for each atom in the molecule using the gauge independent atomic orbitals (GIAO) method with a B3LYP 6311+G(d,p) basis set.37 The magnetic shielding values can be converted to chemical shifts following the convention, δiso = −(σiso − σref), where δiso is the isotropic chemical shift of the atomic site in the molecule and σiso and σref are the magnetic shielding values of the atomic site in the molecule and of the same atom in a reference material, respectively. The calculated σiso values corresponding to identical environments were averaged to yield the average magnetic shielding values, ⟨σiso⟩. In the present calculations, σref is taken to be zero and the calculated ⟨σiso⟩ values were converted to δiso using a scaling factor such that all chemical shifts are referenced to neat (CH3)2Se (δiso = 0 ppm). Such empirical scaling has been widely utilized in the literature for ab initio calculations of 1H and 13C NMR chemical shifts.38 This procedure scales the chemical shift by using experimental data to reduce systematic errors stemming from the effects of electronic coupling, which invariably change the calculated chemical shifts. The effects of the electronic coupling scale with the number of electrons surrounding the nucleus, as is evidenced by the uncorrected error in calculations involving 1H (±0.4 ppm) and 13C (> ±10 ppm).38 Therefore, such errors associated with calculated 77Se chemical shifts are expected to be even larger. The empirical scaling factor was determined by comparing calculated ⟨σiso⟩ values of −Se−Se−Se−Se−Se−, Ge−Se−Se, and Ge−Se−Ge type Se environments with the corresponding experimental δiso values of 864, 550, and 400 ppm, respectively, as reported for GexSe100−x glasses in previous studies.14,16 This comparison led to the scaling relation δisocalc = −0.6466⟨σiso⟩calc + 1130.4, where the superscript “calc” denotes calculated values. The R2 value of 0.995 associated with the linear regression for the empirical scaling indicated little random error, and such a scaling also remedies any effects induced from the termination of the GeSe4 tetrahedra with hydrogen. Furthermore, the robustness of the empirical scaling was checked by running these calculations on a cluster containing seven Se atoms with bond lengths, bond

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EXPERIMENTAL SECTION Glass Synthesis. The synthesis of the GexSe100−x glass samples (5 ≤ x ≤ 20) was reported in previous studies.15,16 These glasses were synthesized by melting mixtures of the constituent elements (99.995% metals basis purity) in an evacuated quartz ampule at temperatures ranging from 1000 to 1200 K for 24−48 h in a rocking furnace to ensure homogenization of the melt. Glasses were obtained by quenching the ampules in room temperature water. NMR Measurements. All 77Se NMR measurements were carried out at the National High Magnetic Field Lab (NHMFL) using a 19.6 T narrow bore magnet (77Se Larmor frequency = 158.8 MHz) equipped with a Bruker DRX console. Crushed glasses were taken in 4 mm ZrO2 rotors and spun at 10 kHz in a home-built probe with a Samoson MAS stator. Each 2D experiment consisted of 16 hypercomplex 1D experiments, and each 1D experiment was comprised of 96 averaged free induction decays (FID) and 64 echoes per FID. The π/2 and π pulse lengths were 2.0 and 4.0 μs, respectively. A 60 s recycle delay was utilized between successive FID, which, at this field, is sufficiently long to prevent significant differential relaxation between Se environments.35 All spectra were referenced externally to a saturated H2SeO3 solution (δiso = 1282 ppm). The details of the acquisition of high-resolution 2D 77Se MATPASS/CPMG NMR spectra of GexSe100−x glasses were reported in a previous study,16 and the same spectra are analyzed in the present study, utilizing the 77Se chemical shift tensor parameters obtained from quantum chemical calculations (vide inf ra). Quantum Chemical Calculations. Quantum chemical calculations of 77Se chemical shift tensor parameters were carried out on H3Se3GeSenGeSe3H3 molecules with 1 ≤ n ≤ 7 using the Gaussian 09 and Gaussview 5.0 software packages.36 4514

DOI: 10.1021/acs.jpcb.6b02747 J. Phys. Chem. B 2016, 120, 4513−4521

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The Journal of Physical Chemistry B

Table 1. Results of Quantum Chemical Calculations for 77Se NMR Parameters of Se Sites with Different NN and NNN Environments Se environment

NN

NNN

⟨σiso⟩ (ppm)

δisocalc (ppm)

δisocalc standard deviation (ppm)

Δ (ppm)

Δ standard deviation (ppm)

Se−Se−Se−Se−Se Ge−Se−Se−Se−Se Ge−Se−Se−Se−Ge Se−Ge−Se−Se−Se Se−Ge−Se−Se−Ge Se−Ge−Se−Ge−Se

Se, Se Se, Se Se, Se Ge, Se Ge, Se Ge, Ge

Se, Se Ge, Se Ge, Ge Se, Se Ge, Se Se, Se

406 517 665 956 1058 1108

868 796 700 512 446 413

40 17

170 400 402 305 251 245

23 25

50 90

73 27

chemical calculation results also show systematic shifts in δisocalc for Se environments which have the same NN but different NNN. In Se−Se−Se chain environments, the δisocalc shifts from 868 ppm for Se−Se−Se−Se−Se environments to 700 ppm for Ge−Se−Se−Se−Ge sites, with Ge−Se−Se−Se− Se sites lying between these resonances at 796 ppm. In Ge− Se−Se environments with different NNN, Se−Ge−Se−Se−Se and Se−Ge−Se−Se−Ge−Se, δisocalc = 512 and 446 ppm, respectively. A summary of the calculated chemical shift ranges is shown in Figure 2. The effects of NN on the 77Se chemical

angles, and dihedral angles constrained by the reported values for crystalline trigonal selenium.39 These calculations yield a 77 Se δisocalc = 810 ppm for the Se environment in the crystal, which compares favorably with the experimental value of 792 ppm.10 The remaining small discrepancies between experiment and calculation of NMR chemical shifts are unavoidable, but they are practically inconsequential in our subsequent analyses of the NMR spectra (vide inf ra). It may be noted here that 77Se NMR chemical shifts have been calculated previously by Kibalchenko et al.40,41 on periodic crystalline and glassy germanium selenide structures using the gauge including projector augmented wave (GIPAW) method to investigate the effect of nearest-neighbor environments. Although such a method is ideally free from possible artifacts that could be introduced by calculations on isolated molecular fragments used in the present study that are finite in length and are terminated by H atoms, systematic errors of comparable magnitude from various computational and physical approximations are equally likely.42 In the cases of Ge−Se−Ge and Ge−Se−Se−Se−Ge, the Se environment in bold can only be simulated with one cluster configuration. Each of the remaining types of Se environments could be simulated in multiple cluster configurations. Here we report the average value of the calculated chemical shift and its standard deviation for each of these Se environments, as obtained from calculations on multiple cluster configurations (Table 1). The details of the processing of experimental 2D 77 Se MATPASS/CPMG spectra can be found in a previous publication.32 The experimental and calculated chemical shift tensors are reported following the Haeberlen convention43

Figure 2. 77Se isotropic chemical shift ranges obtained from quantum chemical calculations, for the six unique Se environments shown in Figure 1. The color scheme used in Figure 1 to denote various Se environments is the same as that used in this figure to denote their corresponding shift ranges. These chemical shift ranges are compared with the range displayed by typical 77Se isotropic NMR spectral line shapes of GexSe100−x glasses, using the spectrum of Ge13Se87 glass (black line) as an example.

shift are well documented in the literature, and the computational results obtained in this study are in close agreement with the experimental results.10,11,14−16 On the other hand, the quantum chemical calculations provide unique insight into the effects of NNN on 77Se δiso which are practically impossible to estimate directly and quantitatively from experimental spectra alone. It is interesting to note that the effects of both NN and NNN on the 77Se δiso are nonlinear which clearly warrants the need for quantum chemical calculations to constrain δiso values for simulation of experimental spectra. Further analysis of the 77Se chemical shift tensor from the quantum chemical calculations provides insight into the CSA. The CSA magnitude obtained from these calculations Δcalc for the Se−Se−Se−Se−Se environment is relatively small, ∼170 ppm, which is in excellent agreement with the experimentally determined Se−Se−Se CSA magnitude Δexp, ∼150 ppm.16 Se− Se−Se chain environments with single or double replacement of NNN Se with Ge atoms, i.e., Ge−Se−Se−Se−Ge and Ge− Se−Se−Se−Se environments, exhibit a significantly larger value of Δcalc of ∼400 ppm compared to the corresponding experimental estimates of Δexp ∼ 180 ppm. It may be noted here that the Δexp for these sites, as estimated from the 77Se

|δzz − δiso| > |δxx − δiso| > |δyy − δiso|

δiso = 1/3(δxx + δyy + δzz)

Δ = δiso − δzz where δiso is the isotropic chemical shift, Δ is the magnitude of the CSA, and δzz, δyy, and δxx are the principal components of the chemical shift tensor.

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RESULTS The quantum chemical computational results of the effects of NN and NNN on the 77Se δiso for different selenium environments are summarized in Table 1. As Ge replaces Se as the NN, there is a progressive upfield shift (toward lower ppm values) of δisocalc with the δisocalc values for the Se−Se−Se, Ge−Se−Se, and Ge−Se−Ge sites ranging between 700−868 ppm, 446−512 ppm, and 413 ppm, respectively. These results are in close agreement with previously reported δisoexp ranges for GexSe100−x glasses as well as with the GIPAW calculations reported by Kibalchenko and co-workers on crystalline and glassy germanium selenides.10,11,14−16,40,41 The quantum 4515

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Table 2. Simulation Parameters for the 77Se MATPASS/ CPMG Isotropic NMR Line Shapes of GexSe100−x Glasses

MATPASS/CPMG spectra, is an average of those corresponding to the Se−Se−Se−Se−Se and Ge−Se−Se−Se−Se/Ge− Se−Se−Se−Ge environments, as the δiso ranges for these sites overlap significantly in the isotropic dimension. In addition, the limitations of the Gaussian 09 code with regard to the exaggeration of the electronic effects in estimations of CSA in NMR simulations is well-known.36 However, in spite of this overestimation, the trends in Δcalc are in agreement with the corresponding experimental estimations in previous reports.16 The Δexp for the Se−Se−Se sites increased from 150 to 180 ppm with increasing Ge content in the glass, and the center of gravity of the 77Se δiso for these sites shifted upfield (toward lower ppm values). When Ge atoms are substituted in at the NN positions, Δcalc increases from 170 to 296 ppm with a single substitution, i.e., for Ge−Se−Se sites, and Δcalc = 245 ppm for double Ge substitution, i.e., for Ge−Se−Ge sites. These Δcalc values are in remarkable agreement with the corresponding experimental estimations of Δexp ∼ 300 and 250−280 ppm, respectively, for the Ge−Se−Se and Ge−Se− Ge sites.16 It should be noted that the Δcalc values are based on the magnetic shielding tensor, which has not been scaled, as each of the three principle components of the chemical shift tensor would need to be scaled differently and require single crystal studies. Overall, the computational results support changes in the 77Se local electronic environments resulting in changes in both the isotropic and anisotropic parts of the CSA tensor due to the presence of Ge in NN or NNN positions. Robust and systematic studies of the effects of the bond lengths and angles are needed in the future to analyze the full effects of Ge substitution on the 77Se CSA tensor. These computational results provide an opportunity to resimulate the previously reported16 isotropic 77Se MATPASS/ CPMG spectral line shapes of GexSe100−x glasses with 5 ≤ x ≤ 20 to include the effects of NNN to obtain important constraints on the selenium chain length distribution. These isotropic 77Se MATPASS/CPMG spectral line shapes are simultaneously simulated with five Gaussian peaks whose positions and widths are kept constant for all simulations. These five peaks correspond to three Se−Se−Se environments with 0, 1, and 2 Ge NNNs and to the Ge−Se−Se and Ge−Se− Ge sites. The simulation parameters are summarized in Table 2, and the simulations are shown in Figure 3. The δisoexp values for the three Se−Se−Se chain environments thus obtained are in excellent agreement with the corresponding δisocalc values obtained from quantum chemical calculations (well within one standard deviation, where such estimates are available, see Table 1) with the largest deviation being 15 ppm. The broadening of each Se peak arises exclusively from the structural disorder stemming from the distribution of bond lengths and angles in the glass. Additional sources of line broadening in these 77Se NMR spectra include 73Ge−77Se and 77 Se−77Se dipolar coupling, which are fairly weak, owing to the low natural abundances of these nuclides as well as the small gyromagnetic ratio of 73Ge, and are practically completely mitigated through fast MAS. Therefore, it is reasonable to assume that the three Se−Se−Se environments have approximately the same peak width, which was constrained to 145 ppm. Although quantum chemical calculations predict two distinct Ge−Se−Se environments, the large overlapping range of δisocalc for Se−Ge−Se−Se−Ge−Se and Se−Ge−Se−Se−Se environments was simulated with a single peak with a width of ∼230 ppm. Finally, the Se−Ge−Se−Ge−Se environment was simulated with a single peak at 410 ppm, with a width similar to

composition simulation parameters δiso (ppm) fwhm (ppm) relative fraction (±5%) δiso (ppm) fwhm (ppm) relative fraction (±5%) δiso (ppm) fwhm (ppm) relative fraction (±5%) δiso (ppm) fwhm (ppm) relative fraction (±5%) δiso (ppm) fwhm (ppm) relative fraction (±5%)

Ge5Se95 G10Se90

Ge13Se87

Se−Se−Se−Se−Se 875 875 875 145 145 145 53.82 36.91 28.86 Se−Se−Se−Se−Ge 785 785 785 145 145 145 19.18 22.24 23.57 Ge−Se−Se−Se−Ge 685 685 685 145 145 145 2.47 2.37 2.44 Ge−Se−Se 545 545 545 230 220 230 21.59 28.72 29.01 Se−Ge−Se−Ge−Se 410 410 410 230 230 230 2.94 9.76 16.12

Ge17Se83

Ge20Se80

875 145 17.62

875 145 11.28

785 145 17.93

785 145 13.10

685 145 3.46

685 145 4.00

543 215 34.05

545 230 34.06

410 230 26.94

410 220 37.55

that of the Ge−Se−Se environments. The larger peak widths for the Ge−Se−Ge and Ge−Se−Se environments compared to those for the Se−Se−Se environments are consistent with previous experimental results10,11,16 and likely originates from the different degrees of sensitivity of the 77Se chemical shift parameters on the distributions of bond angles and bond lengths associated with these environments. The Se speciation, as obtained from the simulations of the 77 Se isotropic spectral line shapes, is consistent with the wellestablished model of the compositional evolution of the structure of the GexSe100−x network, in which Se chains become increasingly and randomly cross-linked by GeSe4 tetrahedra with increasing Ge concentration. Consequently, the relative fraction of the Se−Se−Se chain units decreases, while those of the Ge−Se−Se and Ge−Se−Ge environments increase. However, these simulations, besides confirming the conventional wisdom, provide novel insights into the quantitation of Se−Se−Se chain length distributions in these glasses. First of all, the Se NN speciation suggests that the chain crossing model is not tenable for the GexSe100−x glasses and, consequently, the selenium chains are not all of equal length in any of these glasses. Rather, the random connectivity of chain and tetrahedral units in GexSe100−x glasses implies a distribution of selenium chain lengths. The selenium chains that consist of five or more Se atoms will have the Se−Se−Se−Se−Se NNN environment, while those with three Se atoms correspond to the Ge−Se−Se−Se−Ge environments. The Ge−Se−Se−Se− Se environments could be present in chains consisting of four or more Se atoms. The simulations of the 77Se isotropic spectral line shapes in Figure 3 indicate that, out of all Se−Se−Se type environments, the relative fraction of the Se−Se−Se−Se−Se environments decreases steadily with increasing Ge content along with a concomitant increase in the fraction of Ge−Se− Se−Se−Ge environments, consistent with progressive shortening of selenium chain lengths (Figure 4). 2D MATPASS/CPMG NMR spectra also afford the opportunity to analyze the anisotropy of the chemical shift to 4516

DOI: 10.1021/acs.jpcb.6b02747 J. Phys. Chem. B 2016, 120, 4513−4521

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The Journal of Physical Chemistry B

Figure 4. Compositional variation of the relative fractions of Se−Se− Se−Se−Se (black squares) and Ge−Se−Se−Se−Ge (red circles) type environments, normalized to the total −Se−Se−Se− in GexSe100−x glasses. Lines through the data points are guides to the eye.

predicted by the quantum chemical calculations for Se−Se−Se environments. As mentioned earlier, for a given δisoexp, the Δexp is a juxtaposition of the anisotropic line shapes from all overlapping isotropic peaks. In order to isolate the effects of NNN exclusively for selenium chain environments, only Se− Se−Se δisoexp with