77Se Nuclear Spin–Lattice Relaxation in Binary Ge–Se Glasses

Article pubs.acs.org/JPCB

77

Se Nuclear Spin−Lattice Relaxation in Binary Ge−Se Glasses: Insights into Floppy Versus Rigid Behavior of Structural Units

Sabyasachi Sen,*,† Derrick C. Kaseman,† Ivan Hung,‡ and Zhehong Gan‡ †

Division of Materials Science, University of California at Davis, One Shields Avenue, Davis, California 95616, United States Center of Interdisciplinary Magnetic Resonance, National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, Florida 32310, United States

‡

ABSTRACT: The mechanism of 77Se nuclear spin−lattice relaxation is investigated in binary Ge−Se glasses. The 77Se nuclides in Se−Se−Se chain sites relax faster via dipolar coupling fluctuation compared to those in Ge−Se−Ge sites shared by GeSe4 tetrahedra that relax slower via the fluctuation of the chemical shift anisotropy. The relaxation rate for the Se−Se−Se sites decreases markedly with increasing magnetic field, whereas that for the Ge−Se−Ge sites displays no appreciable dependence on the magnetic field such that the extent of differential relaxation between the two Se environments becomes small at high fields on the order of 19.6 T. The corresponding dynamical correlation time is three orders of magnitude shorter (∼10−9 s) for the Se−Se−Se sites, compared to that for the Ge−Se− Ge sites (∼10−6 s). The large decoupling in the time scale between these Se environments provides direct experimental support to the commonly made assumption that the selenium chains are mechanically floppy, and the interconnected GeSe4 tetrahedra form the rigid elements in the selenide glass structure.

1. INTRODUCTION The compositional variation of the structural characteristics of archetypal chalcogenide glasses in the binary Ge−Se system has been studied extensively in the past, using a wide variety of spectroscopic and diffraction techniques.1−14 The results of these studies indicate that Ge and Se atoms largely follow the 8N coordination rule, being 4- and 2- coordinated, respectively, in the structures of these glasses. Consequently, the structure of amorphous Se consists of chains of Se atoms and addition of Ge results in the formation of GeSe4 tetrahedra that increasingly cross-link the Se chains as the Ge concentration increases. Finally, as the Ge concentration reaches 33.33 atom % for the composition GeSe2, the structure consists practically entirely of a tetrahedral network of corner- and edge- sharing GeSe4 tetrahedra. Recent studies based on high-resolution 2D 77 Se nuclear magnetic resonance (NMR) spectroscopy have enabled precise quantitation of Se speciation into Se−Se−Se, Ge−Se−Se, and Ge−Se−Ge environments as a function of glass composition.14 Furthermore, the results of these 77Se NMR spectroscopic studies have led to a deeper understanding of the connectivity and intermediate-range order in these glasses and have indicated a nearly random interconnection between GeSe4 tetrahedra and Se−Se chain fragments in the structure. More recently, Sykina, Bureau, and co-workers have made intriguing observations of strong differential nuclear spin− lattice relaxation (SLR) in the 77Se magic-angle-spinning (MAS) NMR spectra of a Ge−Se glass of composition GeSe4, synthesized using elements with natural isotopic abundance.15 These authors estimated that in this glass the NMR SLR time scale T1 of 77Se nuclides in the Se−Se−Se © 2015 American Chemical Society

chain environments was on the order of 100−150 s, whereas that for the Ge−Se−Ge environments was significantly longer at around 200−250 s. As a result, for typical recycle delays of ∼60−120 s used in the 77Se NMR spectroscopy of Ge−Se glasses, the resulting spectra may not be fully quantitative and would yield erroneous results for Se speciation. A separate 77Se NMR study on an As−Se glass of composition AsSe6 indicated an opposite behavior in the differential SLR, i.e., the Se−Se−Se environments displayed a longer T1 compared to that of the As−Se−As sites.16 Here we report the results of a study of 77Se NMR SLR in binary Ge−Se glasses at two different magnetic fields to unravel the mechanism of spin−lattice relaxation of 77 Se nuclides in these materials. The implications of these results in understanding the dynamics of the constituent structural units in these glasses and the relation of the latter to glass transition and rigidity percolation are discussed.

2. EXPERIMENTAL SECTION 2.1. Sample Synthesis. GexSe100−x glasses with x = 10, 20, and 23 were synthesized in 10 g batches by melting mixtures of the constituent elements with ≥99.995% purity (metals basis) in evacuated (10−6 Torr) and flame-sealed fused-silica ampules (8 mm ID, 11 mm OD) at 1100 K for 24 h in a rocking furnace. The ampules were quenched in water and subsequently annealed for 1 h at the respective glass transition temperatures. 2.2. 77Se NMR. Low-magnetic-field 77Se MAS NMR measurements were carried out using a Bruker Avance 500 Received: February 26, 2015 Revised: April 6, 2015 Published: April 7, 2015 5747

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The Journal of Physical Chemistry B spectrometer operating at a magnetic field of 11.7 T (77Se resonance frequency of 95.4 MHz). Crushed samples were packed into Si3N4 rotors with torlon caps and placed in a Doty 5 mm XC MAS probe and were spun at 15 kHz. 77Se MAS NMR spectra of GexSe100−x glasses were collected using a Hahn echo pulse sequence ((π/2)−τ−π−acquisition) with π/2 pulse length of 2.2 μs and with a single rotor period separating the π/ 2 and π pulses. Spectra for each GexSe100−x sample were collected at recycle delays of 60, 200, and 600 s. Approximately 200−800 free induction decays (FID) were averaged to obtain each 77Se MAS NMR spectrum. The 77Se NMR SLR data were collected on the GeSe4 (x = 20) glass sample at two different magnetic fields of 11.7 and 19.6 T using a saturation recovery pulse sequence. The measurements at 19.6 T were carried out using a narrow bore magnet at the National High Magnetic Field Laboratory (NHMFL) equipped with a Bruker DRX console operating at a resonance frequency of 159.8 MHz for 77Se. A home-built 4 mm probe (π/2 pulse length of 2.0 μs for 77Se) with a Samoson MAS stator was used. Crushed glass samples were packed into ZrO2 rotors and spun at 10 kHz. For all NMR SLR experiments, a comb of 16 π/2 rf pulses were used to saturate the magnetization. 77Se MAS NMR spectra were collected as a function of magnetization recovery delays ranging between 10 and 1200 s following the saturation, using a π/2 observation pulse at the lower field, whereas the Carr-Purcell Meiboom-Gill (CPMG) echo train acquisition was employed at the higher field. It may be noted here that the spin−spin relaxation (T2) effect during the CPMG echo train acquisition employed for SLR measurements at 19.6 T can only affect the relative weights but not the T1 values of the different 77Se resonances in the spectra. Depending on the delay time, 40−4000 free induction decays were collected and averaged to obtain each 77 Se NMR spectrum. At the magnetic field of 19.6 T and for a spinning speed of 10 kHz, the chemical shift anisotropy (CSA) induced broadening of the 77Se NMR line shapes is expected to be significantly higher than that at the lower magnetic field of 11.7 T. If such CSA-induced broadening leads to peak overlap, then the extraction of T1 for different Se environments may become problematic at 19.6 T. However, previous high-resolution 2D 77 Se NMR studies at this magnetic field have indicated that even at effectively infinite spinning speed the 77Se NMR spectra of the Ge−Se glasses are only somewhat narrower than the static spectra.14 Therefore, the 77Se NMR spectral line widths of these glasses are primarily broadened from a distribution of chemical shifts associated with structural disorder. Consequently, the magnetization recovery for a specific Se environment, when estimated from the intensity of the corresponding peak maximum, will likely have an insignificant contribution from the CSA overlap of the neighboring peaks in the 77Se NMR spectra.

Figure 1. 77Se Hahn-echo MAS NMR spectra of three GexSe100−x glasses at 11.7 T. Glass compositions are given alongside the spectra. Black lines denote spectra collected with a recycle delay of 60 s, and the superimposed red line in each case corresponds to the spectrum of the same glass collected with a recycle delay of 600 s, except for the Ge20Se80 composition where the red line corresponds to a recycle delay of 200 s. Note in each case the faster relaxation of the peak to the left, corresponding to the Se−Se−Se chain sites.

3. RESULTS AND DISCUSSION 3.1. 77Se SLR Mechanism in Ge−Selenide Glasses. The one-pulse 77Se MAS NMR spectra of the Ge−Se glasses obtained at 11.7 T corresponding to different recycle delays are shown in Figure 1. These spectra show a relatively narrow resonance centered at ∼800−850 ppm corresponding to Se− Se−Se chain environments and a broader resonance centered at around ∼400−450 ppm that is predominantly associated with Ge−Se−Ge environments.14 Previous high-resolution 2D 77Se

NMR spectroscopic studies and ab initio 77Se NMR chemical shift calculations have indicated the presence of another resonance near ∼550 ppm that can be assigned to Ge−Se− Se environments and/or to Se atoms edge-shared between two 5748

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Figure 2. Time dependence of the recovery of 77Se magnetization following saturation at 11.7 T for (a) Se−Se−Se and (b) Ge−Se−Ge environments in GeSe4 glass. Red lines are fits of the exponential recovery equation (see text for details) to the data points.

Figure 3. Time dependence of the recovery of 77Se magnetization following saturation at 19.6 T for (a) Se−Se−Se and (b) Ge−Se−Ge environments in GeSe4 glass. Red lines are fits of the exponential recovery equation (see text for details) to the data points.

relaxation in the 77Se NMR spectra. Hence, 77Se NMR spectra collected at such high magnetic fields may yield nearly quantitative Se speciation for Ge−Se glasses even when relatively short recycle delays are used, as has indeed been evidenced in a recent study.14 It is interesting to compare the above-mentioned T1 values for the Se−Se−Se and the Ge−Se− Ge sites in GeSe4 glass measured in this study at 11.7 and 19.6 T with those indirectly estimated by Sykina et al. at a significantly lower field of 7 T in their natural-abundance glass sample of the same composition.15 The lower estimate of the T1 of Ge−Se−Ge site at 7 T is ∼200 s, consistent with the measured value of 195 ± 12 s at 11.7 T. The measured T1 of the Se−Se−Se site at 11.7 T and its dependence on magnetic field suggests that its value would be significantly lower than 75 s at 7 T. However, Sykina et al. estimated a rather high value of ∼100 s for this T1 at 7 T.15 The source of this discrepancy is not obvious, but the method of indirect estimation used by these authors clearly tends to overestimate the 77Se T1 of the Se−Se−Se sites in GeSe4 glass.

GeSe4 tetrahedra. Clearly, for all Ge−Se glasses the ratio of the relative intensities of the peaks at ∼800 and 400 ppm is higher in the spectrum collected with the shorter recycle delay (Figure 1). Hence, the 77Se SLR of the Se−Se−Se chain environments is significantly faster compared to that of the nonchain Se−Se− Ge and Ge−Se−Ge environments. The 77Se magnetization Mz(t) recovered at various delay times t after saturation for the Se−Se−Se and the Ge−Se−Ge environments in GeSe4 glass were estimated from the saturation recovery spectral line shapes using the intensities of the respective peaks at ∼800 and 400 ppm and are shown in Figures 2 and 3. The data can be fitted well to singleexponential recovery such that Mz(t) = M0[1 − exp(−t/T1)], where M0 represents the equilibrium magnetization and was treated as a fitting parameter (Figure 2). These fits yield the T1 values of 75 ± 4 s (140 ± 7 s) and 195 ± 12 s (170 ± 10 s) for the Se−Se−Se and the Ge−Se−Ge sites in GeSe4 glass at 11.7 T (19.6 T). One of the important consequences of these results is that the similar 77Se SLR rates 1/T1 of the Se−Se−Se and Ge−Se−Ge sites at 19.6 T eliminate significant differential 5749

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the glass structure, τc is the characteristic time scale of dipolar coupling fluctuation, and ω = γB0 is the Larmor frequency of 77 Se, with B0 being the external magnetic field. It is clear from eq 2 that the dipolar spin−lattice relaxation rate depends on the magnetic field only via the spectral density term within the square brackets. At ambient temperature, τc is expected to be long enough such that the condition ωτc ≪ 1 will not be met at the magnetic fields used in this study (ω ≈ 109 Hz). Under this condition, the spectral density, and hence 1/T1, will be a function of the magnetic field. For SLR controlled by the temporal fluctuation of the CSA interaction, the relaxation rate is given by23

There are four possible contributions to the SLR mechanism of a nuclide with a nuclear spin quantum number I = 1/2, such as 77Se, so that the spin−lattice relaxation rate 1/T1 can be expressed as follows:17 1 1 1 1 1 = DD + CSA + SR + Sc T1 T1 T1 T1 T1

(1a)

In this equation, T1DD, T1CSA, T1SR, and T1Sc are the relaxation times associated with SLR resulting from temporal fluctuations of magnetic dipole−dipole, CSA, spin-rotation, and scalar interactions, respectively. Among these, the spin-rotation and scalar interactions are viable pathways for 77Se SLR only in small molecules and are not likely to be dominant in the case of large molecules or in the solid state with a network structure such as that characteristic of selenide glasses.18 The 77Se−73Ge heteronuclear dipole−dipole couplings are also not likely to be important considering the low natural abundances of the 77Se and 73Ge nuclides (∼7.6 and 7.8%, respectively) and more importantly the small gyromagnetic ratio γ (= −0.94 × 107 rad T−1 s−1) of 73Ge compared to that of 77Se (γ = 5.12 × 107 rad T−1 s−1). The SLR of nuclear spins can be controlled by temporal fluctuation of direct dipolar coupling to free electronic spins in paramagnetic impurities (e.g., transition metal and/or rare earth ions) or defects in the form of dangling bonds in the structure. Such impurities or defects are typically present in a material at concentration levels of a few tens to hundreds of parts per million and are either originally present in the reactants used for synthesis or get introduced during processing. This mechanism of SLR has been shown to be operative for spin I = 1/2 nuclides such as 29Si in solids where any internuclear dipolar coupling and nuclear spin diffusion are negligible.19−21 However, for this mechanism, the experimental observation of differential relaxation between the various Se environments can only be explained by invoking spatial separation of these environments in large clusters. In this scenario, the paramagnetic centers would have to be preferentially enriched in the clusters of Se−Se−Se chains in order for these Se environments to relax faster than the Se− Se−Ge and Ge−Se−Ge environments. Such a strong clustering of structural units has recently been shown to be inconsistent with the Se speciation results obtained from spectroscopic studies of Ge−Se glasses.14 More importantly, the concentration of paramagnetic impurities would be negligible for glasses synthesized from high-purity elemental reagents such as those used in the present study. Therefore, for 77Se NMR SLR in Ge−selenide glasses, eq 1a can be rewritten as 1 1 1 = DD + CSA T1 T1 T1

1 T1CSA

1 T1CSA

77

2 1 2 ⎛ μ0 ⎞ 4 2 1 ⎜ ⎟ γ ℏ I (I + 1) = [J(ω) + 4J(2ω)] 5 ⎝ 4π ⎠ T1DD r6

(2)

τc 1 + (ωτc)2

=

2 1 (Δσ )2 15 τc

(4b)

Equation 4b suggests that for the CSA fluctuation mechanism the relaxation rate is independent of magnetic field at low temperatures where the condition ωτc ≫ 1 is fulfilled. Therefore, the strong field dependence of the 77Se T1 values obtained for the Se−Se−Se sites in GeSe4 glass (Figures 2 and 3) is consistent with a dipolar coupling mechanism of SLR for these chain environments. It is to be noted here that eqs 2−4b are strictly valid for isotropic tumbling in the liquid state, whereas in the solid state, the motion controlling the fluctuation of dipolar or CSA fluctuation is expected to be significantly restricted such that the spectral density terms need to be modified. Unfortunately, such modifications are practically impossible without a priori knowledge of the dipolar or CSA tensor orientations and atomistic details of the dynamical processes responsible for SLR. Therefore, we have used eqs 2−4b in the subsequent discussion below to calculate the internuclear distances and correlation times for the motion responsible for 77Se SLR, with the caveat in mind that the resulting values should be treated as approximate rather than exact although the corrections factors are expected to be small.24 Kanert et al. had shown in a previous study that the 77Se SLR in crystalline Se consisting solely of Se−Se−Se chain environments is controlled by the two-phonon Ramanprocess-mediated fluctuation of the CSA.25 In this case, 1/T1 ≈ B02; therefore, the relaxation rate increases (relaxation gets faster) with increasing magnetic field. The same magnetic field dependence is also expected for a nonphonon-mediated mechanism of fluctuation of CSA when τc is very short such that the condition ωτc ≪ 1 is satisfied. However, the SLR of the Se−Se−Se sites in the Ge−Se glasses studied here cannot be explained by either of these mechanisms because 1/T1 shows an opposite behavior, i.e., it decreases with increasing magnetic field. For SLR via fluctuation of homonuclear dipolar coupling (eq 2), T1 measured on the same material at the same temperature but at different magnetic fields will simply scale linearly with the

The relaxation rate for the homonuclear Se− Se dipolar coupling mechanism is given by the following expression:22

where J(ω) =

(4a)

For restricted motion in the solid state, Δσ in eq 4a is the amplitude of modulation of the CSA for the Se environment whose relaxation is under consideration. This amplitude of modulation of the CSA is likely to be smaller than but proportional to the magnitude of the CSA Δσ*, the latter being relevant for isotropic tumbling in liquids. Under the condition ωτc ≫ 1 and for a specific τc, eq 4a can then be rewritten as23

(1b) 77

∝ ω 2(Δσ )2 J(ω)

(3)

In eqs 2 and 3, μ0 is the permeability constant, γ is the gyromagnetic ratio of 77Se, ℏ is Planck’s constant, I is the nuclear spin quantum number (I = 1/2 for 77Se), ⟨1/r6⟩ is the average of the inverse sixth power of the 77Se−77Se distance in 5750

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The Journal of Physical Chemistry B ratio of the respective spectral densities. The ratio R of the spectral density term in eq 2 at the two different magnetic fields used in the present study is shown in Figure 4 as a function of

Ge sites may also result from a dipolar coupling mechanism if the condition ωτc ≪ 1 is satisfied. An inspection of Figure 4 suggests that this condition will be satisfied if τc ≤ 10−10 s. However, it is well-known from previous variable-temperature 77 Se NMR studies and from the composition dependence of glass transition temperature Tg that the Se chain elements in the selenide glass structure are significantly more mobile and “floppy” compared to Se atoms in Ge−Se−Ge environments shared by GeSe4 tetrahedra, which are considered to be “rigid” units.7,11,26 Therefore, it is highly unlikely that τc for dipolar coupling fluctuation for Ge−Se−Ge sites would be shorter than that for the Se−Se−Se sites. Furthermore, for τc ≤ 10−10 s, eq 2 yields unphysically small ⟨r⟩ values (≤1.8 Å) compared to the shortest intratetrahedral Se−Se distances of ∼3.8−3.9 Å for the Ge−Se−Ge sites.27 Finally, it is to be noted that in an abundant spin system a single T1 is expected for all nuclides because the spin temperature homogenizes via spin diffusion. Indeed, Sykina et al. observed a single T1 of ∼75 s at 7 T and absence of any differential relaxation between the Se−Se−Se and the Ge−Se−Ge sites in a GeSe4 glass sample isotopically enriched with 100% 77Se.15 However, for low-abundance spins such as natural-abundance 77Se, high-speed MAS is expected to effectively suppress spin diffusion, and the different Se sites can display significantly different T1 values as shown in the present study.19 3.2. 77Se Differential SLR in Selenide Glasses: Floppy Versus Rigid Behavior. It is clear from the results of this study that in Ge−Se glasses the Se−Se−Se chain sites relax significantly faster than the Se sites associated with the GeSe4 tetrahedra. The motional correlation time τc associated with the 77 Se SLR is ∼10−9 s for Se−Se−Se sites and ∼10−6 s for the Ge−Se−Ge sites. This result corroborates with the observations made in a previous study on the basis of variabletemperature 77Se NMR spectroscopy that the Se chain motion in Ge−Se glasses and supercooled liquids near glass transition is orders of magnitude faster compared to that of the GeSe4 tetrahedra.11 These observations are also consistent with the conventional wisdom that the selenium chains constitute floppy elements in the selenide glass structure, whereas the cornerand edge-shared GeSe4 tetrahedra form the rigid elements.28 In fact, the experimental observation of the increase in the heat capacity of pure Se and Ge−Se binary glasses with increasing temperature has been attributed in previous studies to skeletal and group vibrations of the chain elements in the glass structure.29 Clearly, the frequencies of these low-frequency vibrational or librational motion of selenium chain elements could be on the order of ∼109 Hz and therefore be effective for 77 Se NMR SLR at ambient temperature. The time scale of this floppy chain dynamics would thus be strongly decoupled from that of the glass transition, the latter being dominated by the dynamics of the GeSe4 tetrahedral backbone. Consequently, the floppy-to-rigid transition of the network via rigidity percolation in Ge−Se glasses is likely to be irrelevant to the thermal onset of glass transition. This hypothesis is indeed in agreement with the observation in Ge−Se binary glasses of a monotonic variation of the glass transition temperature Tg across the rigidity percolation threshold where the average coordination number ⟨r⟩ = 2.4.25 3.3. Comments on the 77Se SLR in As−Selenide Glasses. As mentioned above, a previous 77Se MAS CPMG NMR spectroscopic study at 7 T by Deschamps et al. indicated that 1/T1 of the Se chain environments in an As−Se glass of

Figure 4. Ratio of spectral densities [J(ω) + 4J(2ω)] at 11.7 and 19.6 T for homonuclear dipolar coupling fluctuation, as a function of correlation time τc. (See eq 2 and text for details.)

τc for 77Se. The value of R becomes constant in two regimes: R = (159.8/95.4)2 = 2.8 where ωτc ≫ 1 and R = 1 where ωτc ≪ 1. However, R becomes a function of τc and changes from 1 to 2.8 as ωτc approaches 1. For the Se−Se−Se sites, the 77Se T1 ratio of ∼1.87 for measurements at 19.6 and 11.7 T allows for a unique determination of τc from Figure 4 to be 10−8.9 s at ambient temperature for the dipolar coupling fluctuation. This value of τc can be used in eq 2 to solve for ⟨r⟩, which yields ⟨r⟩ ≈ 2.0 Å, consistent with the literature reports of average Se−Se distances in Se chains of ∼2.3 Å in Ge−Se glasses.2−4 In fact, the strong distance dependence of 1/T1 in eq 2 practically ensures that the dipolar coupling contribution from 77Se−77Se distances longer than the nearest-neighbor bond length would be relatively insignificant. The 77Se T1 for the Ge−Se−Ge sites is observed to be nearly independent of the magnetic field, implying a CSA fluctuation mechanism to be responsible for the SLR of these selenium environments. As noted in eq 4b, the 1/T1 for the CSA mechanism is proportional to the square of the amplitude of modulation of the CSA Δσ associated with any Se environment. Although Δσ for the various Se environments in Ge−Se glasses is not known a priori, it is expected to be proportional to the magnitude of the CSA Δσ*. The values of Δσ* for the Se−Se−Se and Ge−Se−Ge environments in Ge−Se glasses were determined in a previous study based on 2D MAS-CSA correlation NMR spectroscopy.14 According to this study, Δσ* for the Se−Se−Se chain sites is approximately −150 ppm, whereas for the Ge−Se−Ge sites, it is ∼250−280 ppm. Therefore, it is not surprising that the CSA mechanism of SLR dominates over the dipolar mechanism for the Ge−Se−Ge sites. An upper bound for τc for the Ge−Se−Ge sites can be readily obtained for the CSA mechanism from eq 4b by approximating Δσ ≈ Δσ* = 250 ppm, which yields τc ∼ 10−6 s. This result is therefore consistent with the assumption that the condition ωτc ≫ 1 is satisfied for the experimental conditions used in this study. A 77Se T1 independent of B0 for the Ge−Se− 5751

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of previously published experimental results that 77Se SLR in As−Se glasses is controlled by the fluctuation of strong heteronuclear dipolar coupling between the 77Se and 75As nuclides.

composition AsSe6 was slower compared to that of the nonchain environments.16 It also indicated that at 7 T the 77 Se T1 was significantly shorter in As−Se glasses compared to that in Ge−Se glasses. Considering the fact that the corresponding Se environments in both As−Se and Ge−Se glasses are characterized by very similar Δσ* values the relatively short 77Se T1 in the As−Se system indicates that unlike in Ge−Se glasses a 77Se SLR mechanism other than CSA or homonuclear dipolar coupling fluctuation is operative for the SLR of 77Se nuclides in As−Se glasses. Because the natural abundance of 77Se is only 7.6%, the observation of faster SLR in As−Se glasses compared to that in Ge−Se glasses strongly suggests the possibility of a 77Se SLR mechanism involving heteronuclear dipolar coupling between 77Se and 75As nuclides. 75 As is an I = 3/2 nuclide that is likely to have very short T1 because of strong spin−lattice coupling that is typical of quadrupolar nuclides, and 75As is 100% abundant in nature with a gyromagnetic ratio γ (= 4.59 × 107 rad T−1 s−1) that is approximately five times that of 73Ge. Therefore, the 75As nuclides can act as a large reservoir with low spin temperature that is a relaxation sink for the 77Se nuclides. As relaxation via heteronuclear 75As−77Se dipolar coupling is a strong function of 75As−77Se distance r (1/T1 ≈ 1/r6) and high-speed MAS is expected to effectively suppress spin diffusion, one would expect faster relaxation of the nonchain Se−Se−As and As−Se−As environments compared to the Se− Se−Se chain environments because the 77Se nuclide in the latter environment is farther away from As atoms in the structure than in the former.19 This expectation is indeed consistent with the findings of Deschamps et al. for their study at 7 T. The differential relaxation at this field would be more pronounced than at higher magnetic fields because the Larmor frequency of 77Se at 7 T is 57.3 MHz, which is very similar to the typical quadrupolar frequency of ∼56−60 MHz reported for 75As nuclides in As−Se glasses.30 Such a match between the Larmor frequency of the dipolar 77Se nuclide and the quadrupolar frequency of the 75As nuclide would lead to level crossing and efficient energy transfer via dipolar coupling between these nuclides that should substantially increase the 1/ T1 for 77Se: a phenomenon known as the quadrupolar dip.31 The 75As−77Se dipolar coupling mechanism for SLR may get less efficient because of the minimization of the level-crossing effect as the Larmor frequency of 77Se becomes significantly higher at a higher field compared to the field-independent quadrupolar frequency of 75As. Further 77Se SLR studies of As− Se glasses over a range of magnetic fields are required in future to experimentally verify these conjectures.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: (530) 754-8397. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Science Foundation grant DMR GOALI-1104869. The National High Magnetic Field Laboratory is supported through the National Science Foundation Cooperative Agreement (DMR-1157490) and by the State of Florida.

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REFERENCES

(1) Bychkov, E.; Benmore, C. J.; Price, D. L. Compositional Changes of the First Sharp Diffraction Peak in Binary Selenide Glasses. Phys. Rev. B 2005, 72, 172107. (2) Petri, I.; Salmon, P. S.; Fischer, H. E. Defects in a Disordered World: The Structure of Glassy GeSe2. Phys. Rev. Lett. 2000, 84, 2413−2416. (3) Salmon, P. S. Structure of Liquids and Glasses in the Ge−Se Binary System. J. Non-Cryst. Solids 2007, 353, 2959−2974. (4) Salmon, P. S.; Petri, I. Structure of Glassy and Liquid GeSe2. J. Phys.: Condens. Matter 2003, 15, S1509−S1528. (5) Bureau, B.; Troles, J.; Le Floch, M.; Guenot, P.; Smektala, F.; Lucas, J. Germanium Selenide Glass Structures Studied by 77Se Solid State NMR and Mass Spectroscopy. J. Non-Cryst. Solids 2003, 319, 145−153. (6) Bureau, B.; Troles, J.; Le Floch, M.; Smektala, F.; Lucas, J. Medium Range Order Studied in Selenide Glasses by 77Se NMR. J. Non-Cryst. Solids 2003, 326−327, 58−63. (7) Lucas, P.; King, E. A.; Gulbiten, O.; Yarger, J. L.; Soignard, E.; Bureau, B. Bimodal Phase Percolation Model for the Structure of GeSe Glasses and the Existence of the Intermediate Phase. Phys. Rev. B 2009, 80, 214114. (8) Sugai, S. Stochastic Random Network Model in Ge and Si Chalcogenide Glasses. Phys. Rev. B 1987, 35, 1345−1361. (9) Edwards, T. G.; Sen, S. Structure and Relaxation in Germanium Selenide Glasses and Supercooled Liquids: A Raman Spectroscopic Study. J. Phys. Chem. B 2011, 115, 4307−4314. (10) Edwards, T. G.; Sen, S.; Gjersing, E. L. A Combined 77Se NMR and Raman Spectroscopic Study of the Structure of GexSe1‑x Glasses: Towards a Self Consistent Structural Model. J. Non-Cryst. Solids 2012, 358, 609−614. (11) Gjersing, E. L.; Sen, S.; Youngman, R. E. Mechanistic Understanding of the Effect of Rigidity Percolation on Structural Relaxation in Supercooled Germanium Selenide Liquids. Phys. Rev. B 2010, 82, 014203. (12) Gjersing, E. L.; Sen, S.; Aitken, B. G. Structure, Connectivity, and Configurational Entropy of GexSe100‑x Glasses: Results from Se-77 MAS NMR Spectroscopy. J. Phys. Chem. C 2010, 114, 8601−8608. (13) Zhou, W.; Paesler, M. A.; Sayers, D. E. Structure of GermaniumSelenium Glasses: An X-ray-Absorption Fine-Structure Study. Phys. Rev. B 1991, 43, 2315−2321. (14) Kaseman, D. C.; Hung, I.; Gan, Z.; Sen, S. Observation of a Continuous Random Network Structure in GexSe100‑x Glasses: Results from High-Resolution Se-77 MATPASS/CPMG NMR Spectroscopy. J. Phys. Chem. B 2013, 117, 949−954. (15) Sykina, K.; Bureau, B.; Le Pollès, L.; Roiland, C.; Deschamps, M.; Pickard, C. J.; Furet, E. A Combined 77-Se NMR and Molecular Dynamics Contribution to the Structural Understanding of the

4. CONCLUSIONS The magnetic field dependence of 77Se SLR in Ge−Se glasses indicates that Se−Se−Se chain sites relax via a dipolar-coupling fluctuation mechanism with τc ≈ 10−9 s. A CSA fluctuation mechanism dominates the field-independent SLR of Ge−Se− Ge sites with τc ≈ 10−6 s. The large decoupling in τc between the two Se sites is consistent with and provides the direct experimental confirmation of the floppy versus rigid behavior of the chain and tetrahedral structural elements in Ge−Se glasses. The extent of differential relaxation between the two Se environments markedly decreases at high fields on the order of 19.6 T such that nearly quantitative 77Se NMR spectra of Ge− Se glasses at these fields can be collected with relatively short recycle delays of ∼60−120 s. Finally, it is proposed on the basis 5752

DOI: 10.1021/acs.jpcb.5b01934 J. Phys. Chem. B 2015, 119, 5747−5753

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DOI: 10.1021/acs.jpcb.5b01934 J. Phys. Chem. B 2015, 119, 5747−5753