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A DFT-Based Aspherical Ion Model for Sodium Aluminosilicate Glasses and Melts Yoshiki Ishii, Mathieu Salanne, Thibault Charpentier, Koichi Shiraki, Kohei Kasahara, and Norikazu Ohtori J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b08052 • Publication Date (Web): 27 Sep 2016 Downloaded from http://pubs.acs.org on September 30, 2016

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The Journal of Physical Chemistry

A DFT-Based Aspherical Ion Model for Sodium Aluminosilicate Glasses and Melts Yoshiki Ishii,† Mathieu Salanne,‡,¶ Thibault Charpentier,§ Koichi Shiraki, Kohei Kasahara,† and Norikazu Ohtori∗,⊥ †Graduate School of Science and Technology, Niigata University, 8050 Ikarashi 2-no cho, Nishi-ku, Niigata 950-2181, Japan ‡Sorbonne Universités, UPMC Univ Paris 06, CNRS, Laboratoire PHENIX, F-75005 Paris, France ¶Maison de la Simulation, CEA, CNRS, Univ. Paris-Sud, UVSQ, Université Paris Saclay, F-91191 Gif-sur-Yvette, France §NIMBE, CEA, CNRS, Université Paris Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France Nippon Sheet Glass Co., Ltd., 2-13-12, Konoike, Itami, Hyogo 664-8520, Japan ⊥Department of Chemistry, Faculty of Science, Niigata University, 8050 Ikarashi 2-no cho, Nishi-ku, Niigata 950-2181, Japan E-mail: [email protected] Phone: +81 (0)25 262 7752

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ACS Paragon Plus Environment


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Abstract Na+ ions play important roles on the physical and chemical properties of aluminosilicate glasses. It is known that they strongly modify the network of tetahedral SiO4 and AlO4 units, but the microscopic details on how they alter the local structure remain to be fully established. Here we address this issue by performing classical molecular dynamics simulations over a wide range of glasses compositions. The simulations include atomic polarization and deformation effects through the use of a DFT-parameterized aspherical ion model, which is carefully validated against experimental data (bond lengths, neutron and X-ray diffraction, NMR spectroscopy). We show that the structure of the glasses is a subtle interplay between the nature of bridging/non-bridging oxides and the arrangement of Na+ ions around them. This reflects in particular on the oxide instantaneous dipole moments.

Introduction Durability and mechanical properties of oxide glasses at ambient pressure have attracted much attention from the perspective of material chemistry. 1–11 In particular, in the case of aluminosilicates, the mechanical strength can be further improved through the ion-exchanging 12,13 c c procedure on the glass surface, such as in the well-known CorningGorilla glass. Since

aluminosilicates in the form of polycrystalline ceramics also show excellent optical property thanks to structural disorder, they are practically used as transparent materials in electrical devices. 14 The dense packing structure of oxide glasses also enables to seal radioactive ions for a long period. 15–18 A key component of functional glasses are alkali and alkaline-earth ions. Because of the weaker character of the bonds they form with oxide ions, in a pure silicate network, they generally create non-bridging oxygens and modify the tetrahedral network topology; they are acting as network modifiers. However, when coexisting with Al3+ or B3+ , they can also play the role of charge compensators and assist the formation of four-coordinated cations 2


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(tetrahedral AlO4 or BO4 units) and bridging oxygens. 11 As a consequence, they increase the packing fraction of the network structure. Due to the difference of strengths between the Si-O/Al-O/B-O bonds on the one hand and the Na-O bonds on the other hand, these oxide materials are often called iono-covalent glasses, even if most of the interactions are very well captured by purely ionic models. 19 Recently, structural and mechanical properties of several aluminosilicate glasses have been extensively investigated using experimental techniques 4,5,8,20,21 and computer simulations. 7,13,22 One of the main remaining challenges is to fully understand the effect of network modifiers on the glass properties. Thereby, a precise atomistic understanding of the nature of ionic bonding in aluminosilicate glasses is important both for fundamental studies and because of their widespread usage in material design. The most intuitive approaches for the experimental determination of atomic structures are X-ray and neutron diffraction, together with EXAFS measurements. 23–37 They are indeed useful techniques for obtaining first coordination shell bond lengths and numbers, although it remains difficult to extract information on the second coordination shell. For such a task, NMR spectroscopy has proven to be a very powerful tool, that gives access to the shortand intermediate-range information. 38,39 Stebbins et al. reported that the connectivity of bridging oxygen to silicium can be accurately determined using NMR. 40 Furthermore, the multiquantum magic angle spinning (MQMAS) method enables to detect the composition and structure of the first-neighbor shell of bridging and non-bridging oxygens as analytical parameters: 41 the isotropic chemical shift, δiso , (which results from the shielding of the applied external magnetic field by the electronic cloud around the nucleus) strongly depends on the first coordination shell of ions, as well as the quadrupolar interaction (which results from the coupling between nuclear quadrupolar moment and the local electric field gradient via quadrupolar couping constant, CQ ) and symmetry (characterized by the asymmetry parameter, η). They applied the 17 O MQMAS-NMR analysis to sodium aluminosilicate glasses, 42–45 which provided an evidence for the presence of Al-O-Al triplets. It means that the avoid-

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ance rule of Al-O-Al suggested by Loewenstein 46 is practically invalid in aluminosilicate glasses. From

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Na MQMAS-NMR, they also found out that the Na-O distance strongly

depends on the bridging environment of oxygen, and that the Na+ coordination number is not determined randomly. 47 The

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Al MAS-NMR spectroscopy by Yarger et al. proved that

although charge-compensated aluminium atoms adopt a tetrahedral coordination shell (with 4 oxygen atoms) under ambient pressure, five- and six-fold coordinated species become dominant under applied pressures larger than 6 GPa. 48 Further experiments at higher magnetic field by Kelsey et al. proved that aluminum atom exists as five-coordinated by 1-2 % in peralkaline composition even at the ambient pressure. 49 Excess of non-bridging oxygen was also observed near the charge-compensated compositions of calcium aluminosilicate glasses. 50 These results mean that the tetrahedral unit of charge-compensated Al3+ easily breaks down in comparison to that of Si4+ . Recently, calculation methods of NMR spectra were also developed on the basis of first-principles approach. 51–53 The theoretical studies have clearly established relationships between NMR parameters (the chemical shift and the local electric field gradient) with the coordination environment around network formers and oxygens in oxide glasses. 54–58 Molecular dynamics (MD) is a useful tool to deeply understand structural and transport properties of glasses, as it provides a description of the system with a level of details hardly accessible via experiments. However a critical problem is the reliability of the interionic interactions employed. Classical pairwise empirical models 59–61 have been widely used in oxide glasses and melts. Yet, there are critical shortcomings in the structural distribution and dynamic properties obtained. 62,63 An alternative consists in employing first-principles MD (FPMD) based on density functional theory (DFT). It provides a good transferability even for multicomponent systems. Its calculation cost is nevertheless much larger than the one of classical MD, so that it was mostly employed to determine structural as well as vibrational (IR, Raman) properties. 62,64 Therefore, in order to obtain a precise knowledge of both structural and dynamical properties, we should introduce accurate interaction potentials in

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classical MD with the DFT level of accuracy. To this end, Madden et al. proposed to take into account many-body effects such as the polarization and the deformation of the ions, and to fit the parameters to DFT calculations as reference data. 19 An advantage of this approach is to achieve a much lower computation cost with respect to FPMD while keeping a high accuracy. For example, Wilson et al. evaluated the IR spectrum of silica glass with the polarizable ion model (PIM). The dipole polarization remarkably improved the agreement between the experimental IR spectrum with its theoretical counterpart. 65 In the case of aluminosilicates, Jahn and Madden developed an aspherical ion model (AIM), 19,66 which accounts for the ionic-shape deformation effect in repulsive terms. The AIM enables to accurately reproduce the crystalline structures and mechanical properties of various minerals by adjusting the ionic radius and softness in repulsive interaction depending on the coordination environment. Zeidler et al. reported that AIM is also an effective model in borate glasses, 67 since the transformation of coordination environment from BO3 to BO4 unit is reproducible by considering the deformation effect of the oxygen. In this study, we extend the AIM to Na-including aluminosilicates. The whole set of parameters were fitted on DFT data using the generalized gradient approximation PBE functional (instead of the local density approximation in the study of Jahn and Madden 66 ). Transferability of the determined parameters is confirmed from melts to glasses, through the comparison of structure factors and NMR spectra. By using the obtained glass structures, we assess the roles of ionic-shape deformation and dipole polarization in the network structure, as measured by the Si-O-Si, Si-O-Al and Al-O-Al angles. In particular, we focus on the coordination environment with respect to the presence of network modifiers Na+ ions. The relation between the structures around oxygens and the instantaneous dipole moments of oxygens is interpreted by electrostatic interactions. The elastic and mechanical properties of the glasses and their densification mechanism are discussed from the viewpoint of the bridging structures.

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Model and Methods AIM force-field consists of charge-charge, polarization, repulsive and two dispersion terms, as follows, φtot =

qi qj i

j>i

rij

ij C ij ij C 6 + φpol + φrep − f (rij ) + 88 f8ij (rij ) 6 6 r rij ij i j>i

(1)

where qi is the charge of each ion i, and rij the distance between i and j. The polarization energy term φpol includes charge-dipole and dipole-dipole interactions, qi rij · μ j ij μi · rij qj ji φ = f4 (rij ) − f4 (rij ) rij3 rij3 i j>i μi · μj 3(rij · μ i )(rij · μ j ) μ i |2 |μ + − + rij3 rij5 2αi i j>i i pol

(2)

where μ i is the induced dipole moment of particle i. The fnij are damping functions which enable a short-range correction of interactions for the charge-dipole and dispersion interactions, 68 fnij (rij )

=1−

−bij n rij cij ne

n (bij rij )k n

k=0

k!

.

(3)

The induced dipoles are calculated by solving self-consistently the set of equations μj }j=i , μ i = αi Ei {qj }j=i , {μ

(4)

where Ei is the electric field generated at ri by the whole set of charges and induced dipoles from the ions j = i, and αi is the scalar polarizability of ion i. In practice, the instantaneous dipole moments are determined at each time step by minimization of the total energy using the conjugate gradient method. 66 The charge-charge, charge-dipole and dipole-dipole contributions to the potential energy and forces of each ion are evaluated under the periodic boundary condition by using the Ewald summation technique. 69

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For the repulsive term, the AIM potential developed by Madden et al. has been chosen: 70 φrep,AIM =

Aij exp(−aij ρij ) + B ij exp(−bij ρij )

i∈cation j∈O

+

C ij exp(−cij rij ) +

i∈cation j∈O

+

(5)

Aij exp(−aij rij )

i∈O j∈O,i Si-O-Al > Al-O-Al. These agreements indicate that the coordination environment around oxygen species obtained with AIM is precise on a level with NMR experiments. In conclusion, the ionic-shape deformation turns out to be significant on the structural formation of bridging and non-bridging oxygens.

Effects of Na+ ions on the structure around bridging oxygens 3.0 2.5

/D

2.0

O

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1.5 1.0

: Si-BO-Si : Si-BO-Al

0.5

: Al-BO-Al : Si-NBO

0.0

0

1

N

2

3

4

(Na)

O

Figure 8: Dipole moments of bridging and non-bridging oxygens in sodium silicate and aluminosilicate glasses. Solid lines are guides to the eye. We now discuss the coordination environment of oxygens and the effect of Na+ ions as network modifiers. In the present structural models obtained with AIM, the most probable angles discussed later are a little smaller than the predicted values in theoretical and experimental studies. 35,54–56,92,93 However, since the composition dependence of NMR spectra, δiso and CQ agrees well with the experimental

17

O NMR data 42–45,56 as shown in Figure 7, we

can expect that the obtained structure around oxygens are so accurate. 21



5 : Si-BO-Si

NO(Na)

4

: Si-BO-Al : Al-BO-Al : Si-NBO

3 2 1

(a)

0 0.0

0.1

0.2

0.3

xNa O

0.4

0.5

2

2.8

O-Na

/Å

2.6

2.4

l

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2.2

(b) 2.0

0

1

N

2

3

4

(Na)

O

Figure 9: (a) Compositional dependence of the oxygen coordination numbers in terms of Na+ in sodium silicate and aluminosilicate glasses. (b) Dependence of the Na-O bond lengths on the Na+ coordination number. Solid lines are guides to the eye.

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0.05

(a) Si-O-Si in NS

x (Na

2

P(

)

0.04 0.03 0.02

(b) Si-O-Si in NAS

x (Na

O)

2

O)

: 0.50

: 0.50

: 0.43

: 0.42

: 0.33

: 0.34

: 0.25

: 0.25

: 0.20

: 0.17

: 0.12

: 0.13

: 0.06

: 0.00

: 0.00

0.01 0.00 80

120

160

80

120

/ degree

0.05

)

0.04

P(

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


160

/ degree

(c) Si-O-Al in NAS (d) Al-O-Al in NAS

x (Na

x (Na

O)

0.03 0.02

O)

2

2

: 0.42

: 0.42

: 0.34

: 0.34

: 0.25

: 0.25

: 0.17

: 0.17

: 0.13

: 0.13

0.01 0.00 80

120

160

/ degree

80

120

160

/ degree

Figure 10: Bridging angle distributions for (a) Si-O-Si in sodium silicate glasses, and (b) Si-O-Si, (c) Si-O-Al, and (d) Al-O-Al in sodium aluminosilicate glasses. They are normalized as the total intensity of each distribution is unity.

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Figure 8 shows the most probable value in each distribution of the magnitude of dipole moments on BOs or NBO. They are ordered according to Si-O-Na > Si-O-Si > Si-O-Al > Al-O-Al. Since the dipole moment reflects the anisotropic electric field acting on the oxygens, it should correlate with the electric field gradient and CQ . 94 As expected, we can see that the results show good correspondence with the behaviors of CQ shown in Figure 7(b): not only the order but also the dependence on the Na2 O fraction. Relatively large values for Si-O-Al may be due to asymmetry in both charge and size between Si4+ and Al3+ , as well as Si-O-Na. Furthermore, here it is interesting to note that small dependence on the Na2 O fraction for Al-O-Al which corresponds to the similar behavior shown in Figure 7(b). We will discuss these later again, taking the distribution in bridging angle of oxygens into account. Figures 9(a) and (b) show the coordination number and bond length of Na+ to the BOs and NBO in both the sodium silicate and aluminosilicate glasses. It is natural that the coordination number increases with increasing Na2 O fraction, and the order of Si-O-Si > Si-O-Al > Al-O-Al > Si-O-Na in the bond length agrees with the results of

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Na MAS-

NMR experiments. 47 On the other hand, there is room for some consideration on the other behaviors. Usually, as the coordination number increases, the bond length increases owing to steric hindrance. This is true for respective dependence of bond length on the coordination number as shown in Figure 9(b) except for Si-O-Si. However, among all kinds of BOs and NBO, in spite of the order of Si-NBO > Al-O-Al > Si-O-Al > Si-O-Si in the coordination number, the order in the bond length is opposite. We can explain this behavior by taking both cationic sizes and induced dipole moments into consideration, i.e., the cationic radii is ordered as Na+ > Al3+ > Si4+ . Since Si4+ ion has the largest charge and the smallest radius among them, it can coordinate to O2− with the closest distance so that it produces strongest positive electric field around O2− . Although two Si4+ ions coordinating to the same O2− can be stabilized by negative charge of large dipole moment induced on O2− , in contrast, Na+ ion will be repelled by strong positive charge caused by both induced dipole moment and Si4+ ions. Therefore, in the case of Si-O-Si, the coordination number of Na+ is least and the bond

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length is largest. Actually, whereas the bond lengths for Si-O-Al and Al-O-Al are close to the sum of ionic radii between Na+ and O2− , those for Si-O-Si are significantly greater than the sum. As shown in Figure 8, the dipole moments decrease with increasing coordination number of Na+ , which can be brought by some reduction of anisotropy in the electric field on O2− . Thus, we can understand that the anomalous composition dependence of the Na-O bond length in the case of Si-O-Si is mainly caused by the decrease in the dipole moment. Figure 10 shows the bridging angle distribution of oxygens. In the sodium silicate glasses, the increase of the Na2 O fraction tends to reduce both the most probable bridging angle and the peak width. In the sodium aluminosilicate glasses, it can be noticed that the distributions of Si-O-Si angle show totally sharp peaks, in spite of the large decrease of NBO with the addition of Al3+ (shown in Figure 4) which should cause remodeling of the network structure. Nevertheless, as well as the sodium silicate glasses, with the increase of Na+ concentration, the bridging angle distribution becomes slightly sharper. It is also applicable to the Si-O-Al angle. In the case of Al-O-Al, the angle depends strongly on the fraction of Na+ , although the peak becomes sharper with increasing Na2 O fraction. This strong dependence may explain the anomalous composition dependence of the magnitude of dipole moment. That is, the broad angle distribution at low concentrations of Na+ causes relative small dipole moment, that can result in ill-defined coordination structures such as five-coordinated Al and TBO because of the induced instability of bridging angle. However, at higher concentrations, both the effects of the sharp distribution in Al-O-Al angle and the increasing coordination number of Na+ may cancel each other.

Relation of the network structures to mechanical properties Lastly, we discuss the elastic and mechanical properties in the sodium silicate and aluminosilicate glasses. Here, we cite some experimental results for mechanical properties of the glasses, and discussed the correlations of them with our present results. Among many scales to express the durability and strength of glasses, some of the representatives are the Young 25



80 : SiO

2

Eexpt. / GPa

76

: NS

tectosilicate comp.

72

: NAS

p. om ec lin ka ral pe

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68 64 60 56

0

10

20

x

30

40

50

Na O 2

Figure 11: Experimental Young modulus of sodium silicate and aluminosilicate glasses. 95,96 Closed and open symbols mean measured and extrapolated values, respectively. Solid and dotted lines are guides to the eye. modulus E, Vickers hardness HV , and fracture toughness KIC . Actually, some empirical correlations are known between them. 97–101 While the relation between E and HV becomes complicated in mixed-modifier glasses, 102 HV correlates well with E in many kinds of onecomponent modifier glasses of silicates and aluminosilicates as shown in the Supporting Information. 98,100 Furthermore, although KIC depends on variations in some experimental methods such as sample preparation and fracture, 97,99,103 it is known that KIC evaluated by using the bending test of precracked beam correlates well with E and HV in sodium aluminosilicate glasses. 97,103 Therefore, we compare the Young modulus, as a representative of experimental results, 95,96 with the present results. Figure 11 shows the Young modulus for the sodium silicate and aluminosilicate glasses as a function of the Na2 O fraction. It decreases monotonously in the sodium silicate glasses with the increase of Na+ concentration. On the other hand, in the sodium aluminosilicate glasses, after the modulus remains plateau on the tectosilicate composition, then it seems to decrease on the peralkaline composition, with increasing Na2 O fraction. We can find that these behaviors correspond to those of both BOs and NBOs shown in Figures 4(a) and (b). This comparison suggests not only that the NBOs simply degrade the strength of glasses for all compositions in the sodium silicate and aluminosilicate glasses but also that the Si-O-Al mainly contribute to the retention of the

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strength of the sodium aluminosilicate glasses instead of Si-O-Si up to xNa2 O = 0.25, i.e., in the tectosilicate compositions.

Conclusion A new AIM force-field fitted to DFT calculations was constructed for sodium aluminosilicates. MD calculations were performed under the ambient condition and glass structures were generated by the melt-quench method. Comparison with the DFT calculations showed that AIM produces accurate forces and dipole moments in the melt. Bond lengths and coordination numbers in the glasses are in good agreement with the experimental values, with a slight overestimation of bond length which is due to the accuracy of the reference DFT calculations. The experimental speciation of oxygens into bridging and non-bridging species is well predicted regardless of the composition and, moreover, the calculated

17

O MQMAS

NMR spectra show excellent agreement with their experimental couterparts, with significant improvement over previous studies. As a result, AIM successfully reproduces the two roles of Na+ as a network as a network modifier (i.e., a network breaker) and charge compensator. Therefore, we conclude that accounting for deformation effects of the ionic shape in AIM is crucial for obtaining a correct the structure of aluminosilicate glasses. In this study, we evaluated the coordination environment of bridging and non-bridging oxygens in the structures obtained with AIM. As a result, we found out the Na+ coordination number of bridging and non-bridging oxygens clearly depends on the species of connecting network former cations. Additionally, the smaller dipole moments of Al-O-Al than other bridging oxygens results in a broader distribution of its bridging angle. However, the coordination by network modifiers stabilizes this bridging angle. In particular, a much more narrow Al-O-Al angle distribution is obtained when the Na+ coordination number is greater than 2. Therefore, it turns out that atomistic roles of network modifier are to beak down bridging oxygens and the network units, to contract the system volume, to damp the dipole

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moment of bridging oxygens, and to narrow and rigidize the bridging angle of oxygens.

Supporting Information Available Dependence of isotropic chemical shift on isotropic magnetic shielding for

17

O NMR calcu-

lation, Figure S1; Partial radial distribution functions of Si-O, Al-O, Na-O and O-O, Figure S2; Bond angle distribution for O-Si-O and O-Al-O, Figure S3; Orientation of the dipole moments of bridging oxygens, Figure S4; Experimental Vickers hardness of sodium silicate and aluminosilicate glasses, Figure S5.

This material is available free of charge via the

Internet at http://pubs.acs.org/.

Acknowledgement This work was partially supported by Grant-in-Aid for Scientific Research (c) (Grant No. 24540397) from the MEXT-Japan. Y.I. was supported by Grant-in-Aid for JSPS Fellows (Grant No. 15J04359) from the Japan Society for the Promotion of Science. This work was partially granted access to HPC resources of CCRT under the allocation t2015096303 and t2016096303 made by GENCI (Grand Equipement National de Calcul Intensif). T.C was supported by the French Agence Nationale de la Recherche for funding ANR-13-BS08DyStrAS.

References (1) Pedone, A.; Malavasi, G.; Cormack, A. N.; Segre, U.; Menziani, M. C. Insight into Elastic Properties of Binary Alkali Silicate Glasses; Prediction and Interpretation through Atomistic Simulation Techniques. Chem. Mater. 2007, 19, 3144–3154. (2) Pedone, A.; Malavasi, G.; Cristina Menziani, M.; Segre, U.; Cormack, A. N. Molecular

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A DFT-Based Aspherical Ion Model for Sodium ... - ACS Publications

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