Structure of Arsenic Selenide Glasses Studied by NMR: Selenium

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Arsenic Selenide Glasses Structure studied by NMR: Selenium Chain Lengths Distributions and the Flory Model Michael Deschamps, Cecile Genevois, Shuo Cui, Claire Roiland, Laurent Le Polles, Eric Furet, Dominique Massiot, and Bruno Bureau J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b02423 • Publication Date (Web): 11 May 2015 Downloaded from http://pubs.acs.org on May 16, 2015

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The Journal of Physical Chemistry

Arsenic Selenide Glasses Structure studied by NMR: Selenium Chain Lengths Distributions and the Flory Model Michaël Deschamps,a,* Cécile Genevois,a Shuo Cuib, Claire Roilandb, Laurent LePollèsb, Eric Furetb, Dominique Massiota, Bruno Bureaub a) CNRS, CEMHTI UPR3079, Univ. Orléans, F-45071 Orléans, France b) Institut des Sciences Chimiques de Rennes, UMR-CNRS 6226, Université de Rennes 1, 35042 Rennes cedex, France * Corresponding author: Prof. M. Deschamps, CNRS, CEMHTI UPR3079, site HT, CS 90055, 1D avenue de la Recherche Scientifique, F-45071 Orléans, France Email: [email protected] Phone: +33 2 38 25 55 11

ACS Paragon Plus Environment

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ABSTRACT

Five homogeneous arsenic selenide glasses with target compositions As2Se3, AsSe2, AsSe3, AsSe4.5 and AsSe6 were studied quantitatively by 77Se CPMG-MAS-NMR and TEM-EDX. The whole set of NMR spectra is simultaneously fitted with six distinct environments taking into account the effect of first and second neighbors on the position of the

77

Se resonance. The

selenium chains are bound at each end to trivalent arsenic atoms, and the chain lengths distribution can be modeled with the Flory theory, which is well known in polymer science, and is used here for the first time to model the probability to find each selenium environments in a selenide glass. No arsenic homopolar bond is detected in our experiments.

KEYWORDS: chalcogenide, 77Se, MAS, solid-state NMR, CPMG


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Introduction Chalcogenide glasses exhibit a wide range of physical properties such as infrared transparency, high refractive indices, and reversible amorphous to crystal transitions and can be easily shaped into optical devices.1-6 Among them, the arsenic selenide glasses AsxSe1-x are considered as a promising family, as glassy As2Se3 is a good candidate for all-optical switching,7 or as a midinfrared laser source8 and arsenic selenide glasses can be used for optic fibers.9 Recent studies also investigated the possibility to prepare these glasses using microwave heating.10 Numerous attempts were made to draw a link between the changes in the physical properties of arsenic selenide and the evolution of its molecular structure as the arsenic content varies, both at room temperature,11,12 and when the temperature is increased,13 during ageing of the glass,14 or when irradiated with a laser.15 To gain some insights into the arsenic selenide glass structures, recent studies relied on molecular dynamics16-18 combined to anomalous X-ray scattering,19 or 77

Se solid-state Nuclear Magnetic Resonance20-23 to characterize the environments and

connectivity of selenium and arsenic atoms. Many of these studies hint toward the existence of a small amount of As-As homopolar bond 12,16 with tetravalent arsenic atoms linked to two arsenic and two selenium atoms.19 Moreover, 77Se NMR spectroscopy can quantify three distinct selenium environments (selenium atoms linked to two, one or zero arsenic atoms) and shows that there is some disorder in the distribution of the lengths of the selenium chains that link arsenic atoms together, as opposed to what is inferred in the chain-crossing model (i.e. when the selenium chains are of similar lengths).20,23 Interestingly, it was suggested that the Flory model24 which describes the distribution of chain lengths in organic polymers could be applied to inorganic polymers (mostly silicates), as the underlying chemical phenomena share striking similarities, especially for glasses with covalent bonds and no ionic species. 25-27 The Flory


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theory provides a very simple model for the probability P(n) to find a chain of length n, which is equal to npn-1(1-p)2 where p is the probability to form a linkage between two monomers and the average chain length is given by 1+p/1-p. Moreover, Flory distribution are characterized by a single parameter p and not two as is the case for Gaussian distributions (which may not correctly reproduce the chain lengths distributions for arsenic-rich glasses with short chain lengths) or three for skewed Gaussian distributions. Therefore, the Flory framework was applied here as a model for the distribution of chain lengths. 77

Se is a spin ½ nucleus with a 7.63% natural abundance, a gyromagnetic ratio equal to 19% of

γ(1H) and a fairly large chemical shift range over 3000 ppm.28,29 However, as many diluted spins1/2, it usually features long longitudinal relaxation times around hundreds of seconds, which may affect the measured proportions of each selenium environment.23 Usually, three selenium environments are distinguished depending upon the nature of the two atoms (arsenic or selenium) they are connected with.20 However, as the 77Se atoms are excessively sensitive to their environments, it is often observed that the chemical shifts of these broad lines vary with the composition of the sample,20 precluding any simultaneous fitting of series of NMR spectra. Such an effect results from a dependence of the chemical shift with the nature of the second neighbors as was observed in 29Si NMR studies of silicate glasses for example.30,31 In the present study, we recorded quantitative natural abundance 77Se NMR spectra of a series of five chalcogenide glasses with targeted compositions As2Se3, AsSe2, AsSe3, AsSe4.5 and AsSe6 and fitted them with a 6 components model (shown in Figure 1 and detailed in Table 1) to take into account, for the first time, the nature of the second neighbors, while limiting the number of assumptions in the fitting procedure. This allowed us to extract the positions and widths of the six environments and using Flory’s chain lengths distributions, to first, ascertain the validity of such a model and


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second, retrieve key parameters such as the average chain lengths and the shape of their distribution. Materials and methods Synthesis Raw materials with 99.999% elemental abundance were used for the preparation of the AsxSe1-x glasses. Arsenic and selenium were further purified of the remaining oxygen by the volatilization technique, using the difference in vapor pressures, which is greater for oxides than for metals, in order to remove the oxide species. Hence the selenium and arsenic were heated for several hours under vacuum, at 250 and 290°C, respectively. After this treatment, the required amounts of selenium and arsenic were sealed in a silica tube under vacuum. The mixtures were maintained at 650°C for a further 12 h in a rocking furnace to ensure a good mixing and homogenization of the liquid. To condense the largest possible amount of vapor, the temperature was reduced to 500°C for 1 h. The samples were then quenched in air and annealed near the glass transition temperatures (Tg) to reduce the mechanical stresses resulting from the rapid cooling. XRD and Differential Scanning Calorimetry (DSC) confirmed the glassy nature of our samples. The glass transition temperatures were measured at 90°C (AsSe6, x = 0.143), 100°C (AsSe4.5, x = 0.182), 120°C (AsSe3, x = 0.25), 145°C (AsSe2, x = 0.333) and 185°C (As2Se3, x = 0.4). These temperatures are never reached while spinning the sample in the MAS rotor. EDX and TEM analysis EDX coupled to a CM20 Transmission Electron Microscope, operating at 80kV, was used in order to measure the chemical composition of each sample. A holder cooled by liquid nitrogen


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has permitted to work with a temperature below -120°C and thus to never attempt the transition temperature (Tg) of the glasses. EDX spectra were acquired during 20 seconds and with an electron probe of 40 nm in diameter. The five glass samples were analyzed and the compositions are shown in Table 2. For each glass, the composition was measured 10 times in different regions, and the molar fraction of arsenic is the mean of these values, while the error bars for the arsenic mol% were determined from the standard deviation of the ensemble of measurements. Solid-state NMR experiments Most of our 77Se (I = 1/2) magic angle spinning (MAS) NMR experiments were performed on a Bruker Avance 300 spectrometer (7.1T) operating at a Larmor frequency of 57.3 MHz for 77Se, using a 3.2 mm double-resonance Bruker probehead. The 77Se chemical shift was referenced to H2SeO3 saturated in water at 1288 ppm. The spinning frequency was set to 20 kHz to reduce the intensities of the spinning sidebands. Only two sidebands are predicted with previous CSA measurements20 and observed experimentally at this magnetic field, as its estimated magnitude of around 150-300 ppm corresponds to 9 to 18 kHz at this field. The linewidths of the Gaussian peaks stemmed from the distribution of isotropic chemical shifts, which comes from the structural disorder observed in the vitreous state. Therefore, whole echoes can be acquired and Fourier transformed in order to increase the S/N ratio and to obtain a pure absorption lineshape.32,33 The sensitivity of the NMR experiment can be enhanced by using a Carr–Purcell– Meiboom–Gill (CPMG) train of rotor-synchronized 180° pulses, in a similar manner to what our group had done before.23 After the 90° pulse, the receiver recorded a series of nCPMG = 32 echoes every 600 µs. To ensure complete relaxation of the 77Se magnetization and quantitative measurements, a recycling delay of 300 seconds was used between each of the 256 scans, resulting in an overall experimental time of 22 hours per experiment. The RF field was set to 50


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kHz (corresponding to 900 ppm and ensuring that the whole spectrum was irradiated correctly). The processing and reconstruction of the 1D 77Se CPMG spikelet-spectra were performed with the Dmfit software.34 To suppress the spinning sidebands and confirm that only one type of selenium environment was detected in glassy As2Se3, its CPMG spectrum was recorded at a lower magnetic field (4.7 T -or 200 MHz for 1H- Bruker WB spectrometer) and a much faster spinning speed (50 kHz) in a 1.3 mm double resonance probe, using a 90 kHz RF field (90° pulse length of 2.75 µs) and the same experimental parameters than on the 300 MHz spectrometer, except that 4096 scans were recorded to improve the signal-to-noise ratio as the sample was much smaller, and the total experimental time was approximately equal to two weeks (Figure S1 from the supplementary materials). MATPASS-CPMG is also another alternative to obtain sideband-free spectra.35 The simultaneous fit of the five spectra with normalized intensities was performed with the mathematical software MapleTM, which is a trademark of Waterloo Maple Inc. The fit was made by the minimization of a χ2 function calculated for the five experimental spectra. The contribution of each environment was simulated with three Gaussian lines, corresponding to the n = 0, n = +1 and n = -1 spinning sidebands, their relative intensities were obtained from the 77Se NMR spectrum of glassy selenium for the environments a, b and c, fitted from the series of spectra for the f sites and calculated with Dmfit from the values measured in previous works for environments d and e.36 It must be noted that fitting the spinning sideband intensities from the series of 77Se spectra lead to similar results, provided their intensities are set equal, as expected for a small anisotropy-to-MAS-rate ratio.37 The probabilities P(n) to find a chain of length n was set to npn-1(1-p)2 where p is a fitting parameter, and the proportions of each environment (a to f)


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were calculated accordingly, for example, a chain of length n = 5 giving rise to two environments of type e, two of type b and one of type a. The maximum chain length was set to 20 and no chain longer than 20 was needed to reproduce the NMR spectra. The starting values for p were calculated from the average chain length nav = 1+p/1-p (which is calculated from the analytical expression of P(n)) i.e. 1, 1.3, 2, 3 and 4 for As2Se3, AsSe2, AsSe3, AsSe4.5 and AsSe6 respectively. The positions and widths of each environment were fitted from the five 77Se NMR spectra, using as parameters three distinct chemical shifts δAsSeAs, δAsSeSe and δSeSeSe and widths σAsSeAs, σAsSeSe and σSeSeSe, depending upon the nature of the first neighbors. The natures of the second neighbors was taken into account with a single fitting parameter ∆, fitted to 34 ppm, describing the shift observed when the second neighbor is changed from As to Se. Interestingly, no significant improvement of the fit was observed when distinct values of ∆ were used for each environment.


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Results and discussion The results of the simultaneous fitting of the five 77Se spectra are summarized in Table 1 and 2, the fitted spectra are shown in Figure 2 with the contributions of the six selenium environments, and the chain lengths distribution are shown in Figure 3. Using our Flory model for the chain lengths distribution and six environments for selenium allowed us to nicely fit the five spectra. First, this is not the case when the “chain-crossing model” is used, i.e. when all the chains are assumed to have the same length (the corresponding fit is shown in the supplementary materials figure S2). This is clearly seen in the 77Se spectrum of AsSe3: if the “chain-crossing model” was valid, all the selenium chains would be made of two selenium atoms, all selenium atoms would be of type (e) and the spectrum should contain only one peak. Second, introducing ∆, the effect of the substitution of an arsenic to a selenium as second neighbor on the chemical shift had a strong effect on the fit quality, and this effect did not depend upon the nature of the first neighbor, or the number of second neighbors substituted from arsenic to selenium. This confirms what was generally observed in selenide glasses: fitting with three lines lead to chemical shifts varying with the composition and therefore, simultaneous fits of series of spectra were impossible.36 No improvement of the fit was observed when the widths of the Gaussian line were let to depend upon the nature of the second neighbor, and we did not consider the influence of the second neighbor on the linewidths. If one compares to previously published results, the chemical shift for a selenium atom only surrounded by selenium atoms in the middle of a chain of length larger than five is found at 864 ppm, very close to previously measured values for glassy selenium at 865 ppm.21,38 Adding one arsenic atom as second neighbor will lower the chemical shift by 34 ppm, leading to chemical shifts of 830 and 796 ppm for selenium with one and two arsenic as second neighbors. The width at half-maximum of the a,


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b and c Gaussian peaks was found to be 179 ppm, lower than the previously measured values which were probably affected by the presence of spinning sidebands.21 This value is itself lower than the widths of the three other environments (296 for d and e and 292 ppm for f), indicating a smaller geometrical disorder (resulting from the distribution of bond lengths and angles) for the selenium atoms belonging to the middle of the chains than for those that are close to trivalent arsenic atoms. The arsenic atoms may therefore act as reticulation centers in this polymer-like network and create larger geometric constraints around them, resulting in the larger linewidths for the associated d, e and f environments. The positions of the d and e environments –or the end-of-chain selenium atoms- are located at 558 and 592 ppm, in accordance with our previous work,23 but with slightly lower chemical shifts than previously measured values20 and the position of the selenium atoms connected to two arsenic atoms is found at 396 ppm, again at a lower chemical shift than what was found in similar glasses, but at a much higher value than the chemical shifts observed in crystalline As2Se3, which may be the result of shorter As-Se distances in our glasses than in the crystalline compounds.39 The measured average chain lengths, indicated in Figure 3, were obtained from the fitted value of p (with no constraint whatsoever on p). They are in excellent agreement with what was expected from the glass compositions and a model assuming that first, all arsenic atoms are trivalent and bound to three selenium atoms, and second, all selenium atoms are divalent. Considering a simple model in which all As atoms are trivalent and bound to selenium atoms, we can easily calculate the expected average chain lengths using the compositions obtained with EDX analysis: For a glass of composition AsxSe1-x (or AsSe(1-x)/x) each arsenic is linked to three selenium chains of length (1-x)/3x, and therefore, the average chain length is 2(1-x)/3x. The average chain lengths were found at 1.3, 2.1, 2.8 and 4.7 for the glasses of target compositions


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AsSe2, AsSe3, AsSe4.5 and AsSe6, respectively. They were obtained at 1.4, 2.1, 3.1 and 4.2 from the Flory model applied to the NMR spectra. These results are shown Figure 4, where we compared the compositions and chain lengths calculated from EDX analysis and the compositions and chain lengths inferred from our fits of the 77Se NMR spectra. The agreement is excellent and within the error bars of the EDX measurements. These results show that the arsenic selenide glasses obtained with arsenic contents lower than 40% are well described with a random distribution of chain lengths, as described with Flory distributions. Therefore, even though the average chain length is 4 in glassy AsSe6, chains having at least 8 selenium atoms still accounts for around 12% of all chains, and chains with 12 selenium atoms have still a 0.8% probability to be found in the Flory model. Moreover, no As-As homopolar bonds are required for the interpretation of the 77Se NMR spectra and no homopolar bonds in our glassy As2Se3 sample were detected, either in the ultrafast MAS/low field spectrum or by fitting our series of spectra. The intensity of the AsSeSe contribution (of type e) we introduced in the corresponding fitting function was found to vanish whatever hypothesis we made (even when the spinning sidebands of AsSeAs were made equal, as expected for low anisotropy-to-MAS-rate ratios). Conclusions We have shown that the Flory theory framework can be applied to arsenic selenide glasses to retrieve valuable information on the distribution of selenium chain lengths, which will be compared to results obtained from molecular dynamics and ab initio calculations.40 Within the precision of the composition measurements with EDX coupled to a TEM, no arsenic atom needs to be involved in homopolar linkages. The Flory theory provides a very convenient way to


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calculate the probability to find each 77Se environment, allowing the NMR spectra of a set of selenide glasses to be fitted simultaneously, while taking into account the important effect of second neighbors in selenium chains. Therefore we expect that the Flory framework may offer interesting possibilities in glasses presenting chains of molecular motifs and help the interpretation of their NMR spectra.


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Figure 1. Six distinct environments can be distinguished for selenium atoms in arsenic selenide glasses by 77Se NMR, taking into account the nature of the first and second neighbors. Selenium atoms are shown in yellow and arsenic in black. Three environments a, b and c can be distinguished for selenium atoms (in blue) belonging to the middle of a chain, two environments d and e for end-of-chain selenium atoms (purple) and one environment for selenium atoms between two arsenic atoms (in red). Their respective NMR contributions are shown in g.


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Figure 2. 77Se CPMG-NMR spectra of five arsenic selenide glasses, with increasing amounts of arsenic, recorded at 7 T and a MAS rate of 20 kHz, fitted using six distinct environments (as shown in Figure 1). Only the f environment is detected in As2Se3, and the fit was not improved by introducing an additional contribution from environment e. Moreover, the NMR spectrum of


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glassy As2Se3 at a MAS rate of 50 kHz and a lower magnetic field (4.7 T instead of 7 T) shows only one Gaussian line.


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Figure 3. Distributions of chain lengths obtained from the fit of the series of five 77Se NMR spectra, using a Flory distribution function where the probability to find a chain of length n is equal to npn-1(1-p)2 and p is a fitting parameter related to the average chain length by nav = 1+p/1-p. The nav values obtained from the fit are shown on the graphs in green, and are very close to the expected values, i.e. 4.2 instead of 4.7 for the glass with targeted composition AsSe6, 3.1 instead of 2.8 for AsSe4.5, 2.1 as expected for AsSe3 and 1.4 instead of 1.3 for AsSe2. Even if the average chain length is rather small, longer chain lengths can be observed, and chain lengths with probabilities lower than 0.1% were not shown in the graphs.


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Figure 4. Plots of the molar fraction of arsenic (left) and the chain lengths (right) calculated from the EDX composition vs the molar fraction and the average chain lengths inferred from the fits of the NMR spectra using the Flory model. The average chain length is deduced from EDX measurements assuming that all arsenic atoms are trivalent and bound to selenium atoms, and all selenium atoms are divalent, and therefore in the AsxSe1-x glass, the average chain length is 2(1x)/3x.


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TABLES. Table 1. The simultaneous fit of the five 77Se NMR spectra of glassy As2Se3, AsSe2, AsSe3, AsSe4.5 and AsSe6 provided NMR parameters for each of the 6 environments described in Figure 1.

Environment type

Chemical shift (ppm)

Se2-Se-Se2 (a)

δSeSeSe + 2∆ = 864

Gaussian peak width at half maximum (ppm)

+1/-1 spinning sidebands intensities (in % of the n = 0 spinning sideband)

6.6% As-Se-Se-Se2 (b)

δSeSeSe + ∆ = 830

As-Se-Se-Se-As (c)

δSeSeSe = 796

As-Se-Se2 (d)

δAsSeSe + ∆ = 592

As-Se-Se-As (e)

σSeSeSe = 179 Obtained from glassy Se 4.7%

Calculated from ref. [20]

δAsSeSe = 558

δAsSeAs = 396

4.7%

σAsSeSe = 296

9.4% As-Se-As (f)

6.2%

σAsSeAs = 292

8.0%

Fitted from the series of spectra


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Table 2. Molar fraction of arsenic obtained from EDX, theoretical (calculated from EDX assuming a random distribution of selenium atoms and trivalent arsenic atoms bound to selenium atoms) and measured average chain lengths for each glass, obtained from the simultaneous fit of their 77Se NMR spectra. The arsenic mole fraction inferred from the NMR results (assuming no As-As homopolar bonds are formed) is shown with the fitting parameter p and the proportions of AsSeAs, AsSeSe and SeSeSe environments. Only one environment is detected for the As2Se3 glass, as shown in its spectrum at low field/high MAS rate, shown in the supplementary materials in Figure S1. The decomposition of the five 77Se NMR spectra and the contributions of AseAs, AsSeSe and SeSeSe environments are shown in Figure S2.

Average chain length theoretical – Flory model and NMR

Glass

As mol% (EDX)

As mol% (NMR)

p

AsSe6

12.5±1.5%

4.7

4.2

13.8%

0.61

4%

41%

55%

AsSe4.5

19±1%

2.8

3.1

17.7%

0.51

7%

49%

44%

AsSe3

24±2%

2.1

2.1

24.5%

0.35

20%

55%

25%

AsSe2

34±1%

1.3

1.4

32.7%

0.16

52%

42%

6%

As2Se3

40±2%

1

1

40%

AsSeAs AsSeSe SeSeSe

100%


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AUTHOR INFORMATION Corresponding Author * To whom correspondence should be addressed: Prof. M. Deschamps, CNRS, CEMHTI UPR3079, site HT, CS 90055, 1D avenue de la Recherche Scientifique, F-45071 Orléans, France Email: [email protected] Phone: +33 2 38 25 55 11 Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Acknowledgments MD and CG acknowledge support from the CNRS and fruitful discussions with Dr. Franck Fayon (CNRS-CEMHTI, Orléans). Supporting information: Three figures are provided in the supporting information showing the

77

Se spectra of glassy

As2Se3 at ultra-fast MAS and low magnetic field, of the five glasses with the contributions of the AsSeAs, AsSeSe and SeSeSe environments and the best fits obtained with the “chain-crossing model”. This information is available free of charge via the Internet at http://pubs.acs.org


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ABBREVIATIONS NMR: Nuclear Magnetic Resonance MAS: Magic-Angle Spinning CPMG: Carr-Purcell-Meiboom-Gill or acquisition of a train of echo signals. TEM: Transmission Electron Microscope EDX: Energy Dispersive X-ray spectroscopy

REFERENCES (1) (2) (3) (4) (5) (6) (7)

(8) (9) (10)

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Structure of Arsenic Selenide Glasses Studied by NMR: Selenium

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