ARTICLE pubs.acs.org/JPCC
Structural Composition of First-Neighbor Shells in GeSe2 and GeSe4 Glasses from a First-Principles Analysis of NMR Chemical Shifts Mikhail Kibalchenko,*,† Jonathan R. Yates,‡ Carlo Massobrio,§ and Alfredo Pasquarello† †
Chaire de Simulation a l'Echelle Atomique (CSEA), Ecole Polytechnique Federale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland Department of Materials, University of Oxford, Oxford, OX1 3PH, United Kingdom § Institut de Physique et de Chimie des Materiaux de Strasbourg, 23 rue du Loess, BP43, F-67034 Strasbourg Cedex 2, France ‡
ABSTRACT: Isotropic chemical shifts and quadrupole coupling parameters of 77Se and 73Ge nuclei in GeSe2 and GeSe4 glasses are determined through density-functional NMR calculations on amorphous model structures generated by ab initio molecular dynamics. The comparison with experimental NMR spectra enables structural assignments for 77Se chemical shifts, pointing to fractional compositions of nearest-neighbor coordinations which are consistent with both neutron diffraction and NMR experiments.
’ INTRODUCTION Amorphous chalcogenide glasses have been studied for their reversible and irreversible photoinduced phenomena for many decades.1 Their nonlinear and photosensitive properties are especially attractive for applications utilizing all-optical processes.2,3 To tune for particular properties it is necessary to have a thorough understanding of the structural properties of such glasses. Binary GexSe1 x glasses can be described by a random network of corner-sharing GeSe4 tetrahedral arrangements similar to the network of the SiO2 glass. However, unlike for SiO2, these glasses also show tetrahedra in edge-sharing (ES) configurations.4 6 The variety of structural motifs in these glasses is further enriched by the breakdown of the chemical order due to the similar electronegativities of Ge and Se atoms. This leads to the formation of homopolar bonds7 and most likely also to the appearance of undercoordinated and overcoordinated atoms.8 10 GeSe2 is the most studied representative of the class of binary GexSe1 x glasses, and its structure has been the focus of numerous experimental7,11 14 and theoretical investigations.9,15 17 However, it still remains unclear whether the characterizations achieved with different experimental techniques all point to a coherent description of the bonding network. Another glass receiving much attention10,13,14 is the GeSe4 glass. At this relative composition of Ge and Se, the glass is found in an intermediate phase at the rigidity threshold, where several physical properties are observed to undergo abrupt changes.18,19 The structural characterization of the intermediate phase is currently attracting considerable attention, particularly in view of achieving a description of the structural transition at the atomic scale.10,20,21 Most recently, solid-state nuclear magnetic resonance (NMR) experiments have been used to study structural motifs in GexSe1 x glasses.13,14,22 The measured 77Se NMR spectra are typically composed of two dominating peaks corresponding to r 2011 American Chemical Society
Se Se Se and Ge Se Ge linkages. However, the interpretation of these spectra as far as the contribution of Se Se Ge linkages are concerned has resulted in conflicting conclusions.13,14 For the intermediate phase of GeSe4, the occurrence of such contributions in sizable amounts would indicate that the two dominant structural motifs are connected in a fully bonded network.14 On the other hand, their absence would support a bimodal model consisting of two loosely connected phases.13 A recent density-functional investigation has favored the former interpretation through the assignment of calculated 77Se NMR chemical shifts to specific atomic configurations found in GeSe2, Ge4Se9, and GeSe crystals.17 However, it remains unclear to what extent the limited set of atomic configurations in these crystals is representative of the vitreous system. Here we calculate NMR parameters within densityfunctional theory for amorphous model structures of GeSe2 and GeSe4, generated previously via ab initio molecular dynamics.9,10 These models show a rich structural variety, which is expected to be well representative of the amorphous phase. Our analysis supports structural motifs for these glasses which are consistent with NMR and neutron diffraction experiments.
’ METHODS AND MODELS The electronic structure was described within the PBE (Perdew Burke Ernzerhof)25 approximation to density-functional theory (DFT). Magnetic shielding and electric field gradient (EFG) tensors were calculated for the GeSe2 and GeSe4 models through the gauge including projector augmented wave (GIPAW)26 approach implemented in the CASTEP code.27,28 The CASTEP code uses an implementation of DFT calculations Received: February 10, 2011 Revised: March 17, 2011 Published: March 29, 2011 7755
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Table 1. Average and Standard Deviation of the Calculated 77Se Isotropic Chemical Shifts δiso (ppm) for Various Bonding Configurations in the Glass Models of GeSe2 and GeSe4a GeSe2 config. Se Se Se
f
mean δiso
GeSe4 σδiso
f
glasses combined
mean δiso
σδiso
mean δiso
σδiso
crystals (ref 17) mean δiso
σδiso
6%
832
156
29%
828
254
828
240
824
-
Ge Se Ge (ES)
28%
631
215
7%
619
270
628
224
655
43
Se Se Ge Ge Se Ge (CS)
18% 36%
633 405
199 221
46% 16%
586 319
276 194
597 376
259 214
495 315
59 155
Se 3Ge
13%
337
208
1%
497
-
351
203
176
-
a
The atomic fraction f of each bonding configuration is given in percent. Combined data resulting from an average of the two models and assignments based on crystalline systems (from ref 17) are also given.
based on plane-wave basis sets and periodic boundary conditions. All calculations were carried out using ultrasoft pseudopotentials29,30 and a maximum plane-wave energy of 500 eV. The Brillouin zone was sampled through a Monkhorst Pack31 grid with a density of 4 4 4 k-points. These parameters were chosen to converge the results to within 2 ppm and 1 ppm for 77Se and 73Ge isotropic shieldings, respectively, and to within 0.1 MHz for 73Ge quadrupole coupling constants. Experiment provides the isotropic chemical shift δiso which is defined relative to a reference shielding σref such that δiso = (σiso σref), where σiso is the trace of the symmetric part of the magnetic shielding tensor. The reference shielding σref was taken at 1494 ppm for 77Se and at 1215 ppm for 73 Ge following refs 17 and 24, respectively. The quadrupole coupling constants CQ and the asymmetry parameters η were calculated from the EFG tensor.32,33 For the quadrupole moment of 73Ge, the value of 19.60 10 30 m2 was taken (ref 23). The model structures of vitreous GeSe2 and GeSe4 adopted in this work consist of 120 independent atoms in periodically repeated cubic cells with sides of 15.16 and 15.27 Å, respectively, corresponding to the experimental densities at ambient temperature.9,10 The total structure factors and the total paircorrelation functions of these models show quantitative agreement with neutron diffraction data.9,10 Both models show a rich variety of bonding configurations including corner-sharing and edge-sharing tetrahedra, homopolar bonds, and undercoordinated and overcoordinated atoms.9,10 NMR chemical shifts, quadrupole coupling constants, and asymmetry parameters were calculated for all atoms in these models.
’ NMR CHEMICAL SHIFTS OF SE We first focus on 77Se chemical shifts, for which experimental NMR spectra are available for both glasses.13,14 The Se atoms were grouped according to their local coordination, which we defined using cutoff radii of 2.7 and 3 Å for Se Se and Se Ge bonds, respectively. Five sites were distinguished corresponding to Se Se Se linkages, Se Se Ge linkages, and Ge Se Ge linkages in edge-sharing (ES) and corner-sharing (CS) configurations and Se atoms bonded to three Ge atoms (Se 3Ge). In Table 1, we give the average and the standard deviation of the calculated isotropic shifts for each bonding configuration in the two models. The isotropic shifts averaged over both models are overall in good agreement with assignments derived from a limited set of crystalline configurations.17 However, we now better appreciate the range of shifts associated with the various coordination sites. For instance, the contributions from Ge Se Ge linkages in ES arrangements and from Se Se Ge
Figure 1. Simulated 77Se spectra of (a) GeSe2 and (b) GeSe4 glasses, reconstructed on the basis of the calculated chemical shifts for the various bonding configurations of Se atoms, and compared to experimental 77Se NMR spectra.14 The contributions of the calculated shifts are represented by Gaussian distributions with parameters taken from Table 1. The thick dashed curve corresponds to the calculated values of the individual Se shifts, represented with a Gaussian broadening of 50 ppm.
linkages show considerably more overlap than anticipated on the basis of the calculated shifts in the crystalline configurations. The most noticeable difference between the vitreous and crystalline systems concerns the isotropic shifts of the Se 3Ge coordination sites. Our calculations for the glass models situate the mean of these shifts at 351 ppm indicating that they are practically indistinguishable from shifts of Se atoms in CS configurations. In contrast, the shift of such a 3-fold configuration in the GeSe 7756
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Table 2. Sets of Atomic Fractions for Se Bonding Configurations in GeSe2 and GeSe4 Glasses, Adopted in the Simulated Spectra in Figure 2a config.
δiso
σ
GeSe2
GeSe4 33%
Se Se Se
828
141
0%
Ge Se Ge (ES)
628
132
17%
3%
Se Se Ge
597
152
20%
21%
Ge Se Ge (CS)
376
126
63%
43%
a
The values used for the isotropic shifts (δiso) and the standard deviations (σ) are also given (in ppm).
crystal was found at a much lower value (176 ppm).17 Inspection of second nearest-neighbor effects in the amorphous models reveals that the chemical shifts of Se atoms with the same nearestneighbor shells are on average reduced by about 150 ppm when one of its Ge neighbors either forms a homopolar Ge Ge bond or shows a 3-fold or 5-fold coordination. This explains the low value for Se 3Ge sites in the GeSe crystal, where all the Ge atoms are 3-fold coordinated. In Figure 1, we show the distribution of the calculated isotropic chemical shifts of all Se atoms in the glass models of GeSe2 and GeSe4 glasses (thick dashed lines). Despite the adopted broadening of 50 ppm, the curves still show some structure which cannot be related to any underlying bonding configuration. To suppress such statistical fluctuations, we reconstructed the NMR spectra by considering for each kind of Se bonding configuration a Gaussian lineshape based on the data given in Table 1. We adopt Gaussian lineshapes as these were found to give a good description of the experimental data.14 The Gaussian lineshapes were centered at the respective isotropic chemical shifts resulting from averages over all configurations of a given kind in the two glasses. The comparison with experimental 77 Se NMR spectra14 shows that the agreement is poor for both glasses. The simulated spectrum of GeSe2 appears noticeably shifted toward higher chemical shifts, whereas that of GeSe4 does not reproduce the experimentally observed double-peak feature. Furthermore, the distributions of chemical shifts pertaining to specific bonding configurations are approximately twice as broad compared to typical experimental features, indicating that the atomistic models overestimate the degree of structural disorder. The comparison between simulated and measured spectra in Figure 1 suggests that the atomic fractions of Se sites as found in our models are not representative of the glasses. This is particularly evident in Figure 1(b), where an excessively high percentage of Se Se Ge linkages in the GeSe4 model impedes the appearance of a double peak. Differences between relative atomic fractions in experiment and in simulation should be ascribed to difficulties of the latter in reproducing the atomic processes leading to glass formation. To examine this suggestion, we reconstruct the NMR spectra following a different procedure which involves the most reliable atomic fractions known from experiment. Furthermore, to account for the excessive broadenings, all the standard deviations of the contributions pertaining to the individual Se bonding configurations were reduced by a common factor of 1.7. In our approach, all retained chemical shifts correspond to calculated averages, and the reduction factor for the widths is the sole optimized parameter. For GeSe2, we took atomic fractions of Se coordinations as suggested from neutron diffraction studies.7 These studies
Figure 2. Same as Figure 1, but the simulated spectra are constructed with the atomic fractions and standard deviations given in Table 2.
indicate that 17% of the Se atoms belong to ES arrangements and that 20% are involved in Se homopolar bonds.7 We assume the latter belong to Se Se Ge linkages and assign the remaining 63% to CS arrangements. The adopted set of atomic fractions is given in Table 2, and the corresponding simulated spectrum is shown in Figure 2(a). The simulated spectrum is now displaced toward lower shifts with respect to Figure 1, and the position of the main peak at ∼400 ppm is in good agreement with that in the experimental spectrum.14 However, the simulation and the experiment differ in the detailed lineshape, with weight of the measured one being displaced toward lower shifts. While it is difficult to identify the precise source of this discrepancy, it is interesting to remark that the observed shift of weight is consistent with the effect of homopolar Ge Ge bonds or under-/overcoordination in the second nearest-neighbor shells. We remark that the major source of improvement with respect to atomic fractions resulting from the ab initio molecular dynamics model comes from the high fraction of CS arrangements inferred from the neutron scattering data. As far as the 77Se NMR spectrum is concerned, the use of atomic fractions as obtained in another recently generated GeSe2 model34 would not lead to any sensitive improvement with respect to results obtained with the present GeSe2 model. For GeSe4, partial structure factors obtained by neutron diffraction are not available, and we therefore base our analysis primarily on experimental NMR spectra.14 The peak at 830 ppm in the experimental 77Se NMR spectra can unambiguously be associated to Se Se Se linkages and corresponds to an 7757
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Table 3. Mean and Standard Deviation of Calculated 73Ge Isotropic Chemical Shifts δiso (ppm), of Absolute Quadrupole Coupling Constants CQ (MHz), and of Quadrupole Asymmetry Parameters ηQ for Different Ge Bonding Configurations in Our Glass Models of GeSe2 and GeSe4a config.
f
mean δiso σδiso mean |CQ| σ|CQ| mean ηQ
σηQ
Ge(0)
53%
185
79
28.1
15.8
0.69
0.24
Ge(1) Ge(2)
42% 5%
104 88
88 29
26.7 21.0
16.8 5.2
0.67 0.48
0.24 0.29
Ge Se4
70%
140
86
21.3
11.0
0.67
0.25
Ge others 30%
162
102
41.2
16.8
0.68
0.23
a The atomic fraction f of each considered bonding configuration is also given.
atomic fraction of 33%.14 The second peak in the experimental spectrum lies at 591 ppm and corresponds to an atomic fraction of 24%.14 According to our calculations, this peak should be assigned to the combined contribution of ES and Se Se Ge arrangements. From Raman studies,4,35 the ratio of Ge atoms in ES arrangements between GeSe2 and GeSe4 glasses is found to be 1:5. Therefore, we assumed the Se atoms in ES arrangements amount to ∼3%, leaving 21% of the Se atoms in Se Se Ge linkages. We attribute the remaining 43% to Se atoms in CS arrangements. The adopted set of atomic fractions is summarized in Table 2. Figure 2(b) shows that the simulated spectrum reproduces well the experimental doublet with peaks at ∼800 ppm and at ∼400 ppm. We note that the comparison between the simulated and measured spectra does not show any shift of weight as for GeSe2 [Figure 2(a)], consistent with the lower amount of chemical disorder in GeSe4.10
’ NMR PARAMETERS OF GE While extremely challenging,36 solid state 73Ge NMR spectroscopy is becoming increasingly accessible for the study of GexSe1 x glasses.22 To complete the present study, we thus address 73Ge chemical shifts, quadrupole coupling constants, and quadrupole asymmetry parameters in GeSe2 and GeSe4 glasses. The isotropic chemical shifts calculated for both glasses give narrow distributions with standard deviations of 90 ppm. The mean is at 61 ppm for GeSe2 and at 127 ppm for GeSe4. Global averages over the two glass models yield a mean quadrupole coupling constant of 31 MHz and a mean quadrupole asymmetry parameter of 0.68. For a more detailed analysis, we first partitioned the Ge atoms according to the number of four-membered rings to which they belong.37,38 This results in Ge(0), Ge(1), and Ge(2) configurations corresponding to Ge atoms with no, one, and two rings, respectively. The Ge(0) mostly correspond to CS Ge atoms but also comprise Ge atoms with homopolar bonds, while the Ge(1) and Ge(2) atoms all belong to ES configurations. As can be seen in Table 3, this analysis leads to a meaningful decomposition of the isotropic chemical shifts δiso, in which the widths of the individual subdistributions are of the order of the separation between their mean values. Following an alternative analysis scheme,22 we also distinguished the Ge atoms tetrahedrally bonded to four Se atoms (Ge Se4) from other bonding arrangements (Ge others). While the decomposition of isotropic chemical shifts appears less effective than in the ring analysis, this partition clearly leads to distinct groupings for the quadrupole coupling constant |CQ| (Table 3). The |CQ| of
Ge Se4 configurations are found to be lower by ∼20 MHz than those of Ge other configurations, in qualitative agreement with the simulations that reproduce the available experimental data.22
’ CONCLUSIONS In conclusion, first-principles NMR calculations were carried out on GeSe2 and GeSe4 glass models. Through the use of calculated isotropic chemical shifts, we analyzed the experimental 77 Se NMR spectra and derived a composition of these glasses in terms of local coordinations. Our analysis supports a decomposition in terms of structural motifs which coherently accounts for both NMR and neutron diffraction experiments. For both glasses, about 20% of the Se atoms are found in Se Se Ge linkages. For GeSe4 in particular, this result is not consistent with the phase-separation model13 but rather supports the occurrence of a fully bonded network,14,17 in which Se Se Ge linkages ensure the connection between Se Se Se chains and Ge Se Ge tetrahedral arrangements. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT We thank Jeremy J. Titman (University of Nottingham, UK), John M. Griffin (University of St Andrews, UK), and Philip S. Salmon (University of Bath, UK) for useful interactions as well as Sabyasachi Sen and Erica Gjersing (UC Davis, USA) for useful discussions and for providing experimental data in numerical format. Computing resources were provided by the University of Cambridge High Performance Computing Service HPCS and were funded by the UK EPSRC under Grant No. EP/F032773/1. ’ REFERENCES (1) Zakery, A.; Elliott, S. R. J. Non-Cryst. Solids 2003, 330, 1–12. (2) Shimakawa, K.; Kolobov, A.; Elliott, S. R. Adv. Phys. 1995, 44, 475–588. (3) Ta’eed, V. G.; Baker, N. J.; Fu, L. B.; Finsterbusch, K.; Lamont, M. R. E.; Moss, D. J.; Nguyen, H. C.; Eggleton, B. J.; Choi, D. Y.; Madden, S.; Luther-Davies, B. Opt. Express 2007, 15, 9205–9221. (4) Nemanich, R. J.; Solin, S. A.; Lucovsky, G. Solid State Commun. 1977, 21, 273–276. (5) Susman, S.; Volin, K. J.; Montague, D. G.; Price, D. L. J. NonCryst. Solids 1990, 125, 168–180. (6) Vashishta, P.; Kalia, R. K.; Antonio, G. A.; Ebbsjo, I. Phys. Rev. Lett. 1989, 62, 1651–1654. (7) Petri, I.; Salmon, P. S.; Fischer, H. E. Phys. Rev. Lett. 2000, 84, 2413. (8) Tafen, D. N.; Drabold, D. A. Phys. Rev. B 2005, 71, 054206. (9) Massobrio, C.; Pasquarello, A. Phys. Rev. B 2008, 77, 144207. (10) Massobrio, C.; Celino, M.; Salmon, P. S.; Martin, R. A.; Micoulaut, M.; Pasquarello, A. Phys. Rev. B 2009, 79, 174201. (11) Salmon, P. S.; Petri, I. J. Phys.: Condens. Matter 2003, 15, S1509–S1528. (12) Salmon, P. S. J. Phys.: Condens. Matter 2007, 19. (13) Lucas, P.; King, E. A.; Gulbiten, O.; Yarger, J. L.; Soignard, E.; Bureau, B. Phys. Rev. B 2009, 80, 214114. (14) Gjersing, E. L.; Sen, S.; Aitken, B. G. J. Phys. Chem. C 2010, 114, 8601–8608. (15) Jackson, K.; Briley, A.; Grossman, S.; Porezag, D. V.; Pederson, M. R. Phys. Rev. B 1999, 60, R14985. 7758
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