Effect of Sodium Oxide Modifier on Structural and Elastic Properties of

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Effect of Sodium Oxide Modifier on Structural and Elastic Properties of Silicate Glass Hicham Jabraoui, Yann Pascal Vaills, Abdellatif Hasnaoui, Michael Badawi, and Said Ouaskit J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b09664 • Publication Date (Web): 30 Nov 2016 Downloaded from http://pubs.acs.org on November 30, 2016

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The Journal of Physical Chemistry

Effect of Sodium Oxide Modifier on Structural and Elastic Properties of Silicate Glass Hicham Jabraoui a,d,*, Yann Vaills b,*, Abdellatif Hasnaoui c,*, Michael Badawi d and Said Ouaskit a a

Laboratoire physique de la matière condensée, Faculté des sciences Ben M’sik, Université Hassan II

de Casablanca, Maroc b

Université d’Orléans, CEMHTI – CNRS UPR 3079, Avenue du Parc Floral, BP 6749, 45067 Orléans

Cedex 2, France c

LS3M, Faculte Poydisciplinaire Khouribga, Univ Hassan 1, B.P. : 145, 25000 Khouribga, Morocco

d

Laboratoire de Chimie et Physique – Approche Multi-Echelle des Milieux Complexes (LCP-A2MC,

EA4632), Institut Jean Barriol FR2843 CNRS, Université de Lorraine, Rue Victor Demange, 57500 Saint-Avold, France.

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ABSTRACT: Molecular dynamics (MD) simulations and Brillouin Light Scattering (BLS) spectroscopy experiments have been carried to study the structure of sodium silicate glasses (SiO2)

(100-X)

(Na2O) X where X ranges from 0 to 45 at room temperature. The MD-obtained

glass structures have been subjected to energy-minimization at zero temperature to extract the elastic constants also found by BLS spectroscopy. The found structures are in good agreement with the structural experimental data realized by different techniques. The simulations show that the values of the elastic constants as function of X Na2O mol% agree well with those measured by (BLS) spectroscopy. The variations of the elastic constants C11 and C44 as a function of the Na2O mol% are discussed and correlated to structural results and potential energies of oxygen atoms.


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Introduction Structural and mechanical properties of amorphous oxide are considered as one of the fundamental complex problems in condensed matter physics, glass science, and materials chemistry. Modifier-silicate glass is a convenient material system to study these fundamental issues. Existing network-modifying cations (e.g., K+, Na+, Ca2+) in silicate glasses leads to the formation of non-bridging oxygen (NOBs). The prediction of these properties according to glass composition is becoming increasingly essential to develop materials with a greater focus on end-user application requirements, reducing product costs by efficient product development and a decrease time to market.

1-2

. Sodium silicate glass, is one of the most

extensively and well-treated materials both theoretically and experimentally. Recently, the binary alkali silicate glasses have taken much attention not only like an archetype of glassy materials, but also because of its anomalous structural and mechanical properties.

2

and its

glass transition behavior.3 For silica glass, the density of Si-O-Si bonds is directly related to the degree of network polymerization; and higher polymerization usually offers the higher elastic constants. The alkali modifiers (such as sodium, lithium and potassium ions) behave like a bond breakers in the silica network.2-3, leading to a decrease of the polymerization degree transforming part of the bridging oxygen atoms (BOs) into NBOs.4 The aim of this paper is the understanding of the involved processes in the sodium silicate glassy state and the study of its physical and chemical properties. In many cases these properties are not always easily accessible from experiments, so theoretical models and simulations have to be developed in order to investigate the influence of alkali elements on physico-chemical properties. Molecular dynamics (MD) simulations is one of the methods that are generally successfully applied in silicate glass study. However, the quality of a simulation strongly depends on the used atom– atom interaction potential.5 BLS spectroscopy is considered as a very useful measurement tool in the laboratory to investigate the dynamic properties of many materials and devices. BLS spectroscopy provides information over the length scale on the order of the relevant acoustic wavelength.6-7 In the present work, we investigate the intriguing role of Na+ modifier ions in modifying the glass structure and its effect on the elastic constants.8 for (SiO2)(100-X) (Na2O)X glass systems containing a %mol of sodium oxide (named X) between X = 0 and 45. We focus our work on 3 ACS Paragon Plus Environment


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the understanding of the structural change of sodium silicate glasses with the increase of the amount of Na2O in order to compare the results with those found by experimental techniques such as EXAFS neutron and X-ray diffractions. To investigate the elastic constants of silicate glasses, the energy minimization using LAMMPS package.9-10 and BLS.11, 7 are employed and the results of the two methods are compared. The local structure is investigated with the help of the visualization tool Ovito.12 This paper is arranged as follows. Firstly, it starts with an introduction followed by a brief description of BLS and its ability to characterize the elastic constants. In section 3, we describe the used simulation technique and the glass making method. Then, we show how the elastic constants can be computed through energy-minimization simulation at zero temperature of the MD-obtained glass structures. The result section is divided in two parts. In the first one we are interested in the elastic constants behaviors found by both simulation and experimental techniques. In the second one we present the sodium oxide Na2O addition effects on the silica glass structures. In the discussion section, we discuss why two different behaviors occur for the variation of elastic constants C11 and C44 of sodium silicate glasses obtained by simulations and experimental method BLS as a function of Na2O mol%. Conclusions of this work are given in section 8.

Experimental protocol Glass preparation. Experiments in the present work have been carried out using the same conditions as in a previous work.11 Indeed, the material had achieved its homogeneity at temperatures of 1600-1650 °C (beyond the melt temperature). The melts were cast onto a cold graphite plate (1x10x15 cm3 optically homogeneous slabs) and annealed in a muffle furnace at the glass temperature transition Tg for 2 h before they were cooled down to room temperature. More details related to experimental techniques are given in Reference 11. Brillouin scattering spectroscopy and elastic constants. Brillouin scattering (or Brillouin-Mandelstam scattering) had been described by Brillouin.13 and Mandelstam.14 The term Brillouin scattering is used in connection with light scattering in solid material considering lattice fluctuations as the origin for the scattering process. In the experimental field, the researchers use BLS spectroscopy to produce an interacting electromagnetic wave with a density wave and photon-phonon scattering. BLS spectroscopy is an optical technique that permits to extract the directional dependence of acoustic velocities in a solid state to a


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wide range of environmental conditions.15 Recently, many experimenters such as Vaills.11, 1617

and Kieffer.18 used BLS spectroscopy to extract the mechanical modulus from the

vibrational modes frequencies at the gigahertz scale (GHz). The two quantities of interest that can be obtained from this spectroscopy are the transverse and longitudinal acoustic velocities (respectively VT and VL of the materials). Both VL and VT velocities are calculated from vL and vT frequencies representing the difference between the frequencies of the Rayleigh line and Brillouin longitudinal and transverse lines, respectively. In the case of right angle scattering for example we write: V T =ν T λ0 / n 2

(1)

V L= ν L λ 0 / n 2

(2)

Where n is the refractive index of the sample at λ 0 . For isotropic symmetry, the relationships between phase velocities of wave propagation and elastic constants are given by: C 11 = ρ V L 2

(3)

C 44 = ρ V T

(4)

2

Where ρ is the measured glass mass density. For this study the Brillion spectra were obtained with scanned triple-passed plane Fabry-Pérot interferometer (effective finesse 70, resolving power 760000) lines, which is frequency-checked by a Michelson interferometer in parallel. The light source is λ 0 = 514 .5nm line of a single frequency Ar-ion laser. The geometry of the experiment corresponds to a right-angle scattering.

Simulations Standard MD simulations are possible to use, where the classical phase space trajectories structure (positions: the material structure, velocities: the motion of material components) are determined by means of a simple forward finite difference process. In this work, the simulation is based on the choice of the Born–Mayer–Huggins potential repulsive term.19, which has been found to accurately reproduce experimental data for silica glasses.20 The potential energy for a given particle is U ij (rij ) =

qi q j 4πε 0 rij

+ f 0 (bi + b j )exp(

(ai + a j ) − rij (bi + b j )

)−


ci c j rij

6

+

Di D j rij

8

(5)


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Where qi is the fictive charge number for each atom. The ionic charges for the constituents are qsi=2.4 for silicon, qNa=0.88 for sodium and that of oxygen qO is determined in such manner that the neutrality of the total system is ensured. The NBO occur not only when modifier atoms are in excess with charge balancing but also in perfect charged-balanced compositions.21 This operation is controlled by a relationship between Na2O mol %. and oxygen charge given in Eq. 6.3 rij denotes the interatomic distance between atoms i and j, and f0 is a normalization constant or standard force equal to f0=0.0434 eV. 22 The parameters a, b, c and D are fitting constants that characterize the material. The last two terms on the righthand side containing rij6 and rij8 represent dipole-dipole and dipole-quadrupole dispersion energies, respectively. For sodium silicate materials, we use the parameters developed by Habasaki et al.23 as shown in Table 1. The simulation uses periodic boundary conditions and an integration time-step of 1 fs. The short-range interaction cutoff was chosen to be 8.0 Å. Even though the choice of the cutoff can be of a critical role, we note that these parameters are often omitted in publications.9, 3 Coulomb interactions were computed using the Ewald summation with a cutoff of 12 Å for the real part with a desired relative error in forces less than 10-6, as described in the LAMMPS package user’s guide.24 The molecular structure of sodium-silicate glasses (SiO2)(100-X) (Na2O)X (with 0 ≤ X ≤ 45) consists of a network of SiO2 tetrahedra in which we modified the system by X Na20 (mol%). Simulations have been performed using different steps in both NPT ensemble (with zero pressure) and NVT ensemble as shown in Figure 1. Firstly, the system was equilibrated during 106 steps at T = 4000K in the NPT ensemble (zero pressure). After this step, another NVT run of 105 steps was performed. These two equilibration steps are needed to reach a steady liquid state independent from the initial guess introduced by the user. Then we perform a quenching stage in NPT ensemble with a cooling rate of 1012 K/s to obtain the glassy state from the high temperature state (liquid) to the glassy state at 300K. Finally, to relax the glassy state structure, we ran 105 steps simulations using NVT ensemble at 300 K. Therefore, the results presented in this work are given at 300 K. In this work, all simulations were performed with the LAMMPS package.10 and the visualization were carried out through Ovito.12 qO =

( 1 − X)q Si + ( 2 × q Na × X) ( 2 − X)


(6)

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Figure 1 MD simulation procedure used to make the glassy-state materials where time step equals 1fs. Table 1. Two-body coefficients for Habasaki’s potential.23

A=f0(bi+bj)(eV)

ρ =(bi+bj)

σ =(ai+aj)( Å )

C=cicj eV/ Å 6

D=DiDj eV/ Å 12

Si-Si

0.0028251

0.0657

1.7376

23.1044332

0.0

Si-O

0.00896593

0.20851

2.9162

69.9590392

0.0

O-O

0.01510679

0.35132

4.0948

212.9332867 0.0

Na-Na 0.00727646

0.16922

2.161

0.0

0.0

Na-Si

0.00505078

0.11746

1.9493

0.0

0.0

Na-O

0.01119161

0.26027

3.1279

0.0

0.0

The calculated densities of the studied glasses for different Na2O mol %. are given in Table 2. The variation of the density as a function of X Na2O mol %. shows an agreement with the experimental behavior.11,

25-27

and a previous MD work.28-29 This variation shows that the

density of sodium silicate glasses increases with the Na2O mol %. as shown in Figure 2. Table 2. Densities of the sodium silicate glasses for various Na2O mol %.

Sample Na2O mol %.

SiO 2

0

Density(g/cm3) 2.200

SN05 SN10 SN15 SN20 SN25 SN30 SN35 SN40 SN45 05

10

15

20

25

30

35

40

45

2.280 2.353 2.395 2.434 2.450 2.470 2.512 2.537 2.58



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Figure 2 Density of the sodium silicate glasses (SiO2) (100-X) (Na2O) X as a function of the Na2O mol %:(a) MD simulation from this study, all densities are obtained after MD relaxation to make the silicate glass as described in the simulation method (i.e. after NPT and NVT runs) (b) experimental (Archimede’s method) from this study, each

sodium silicate glass density has been found it after relaxation at room temperature and at ambient pressure. (c) Du’s MD simulation.28., the final structural data reported to extract the density values here are based on averaging 400 configurations, each separated by 50 steps at the end of the NVE run at 300 K.

Physical property calculations The stiffness Cij tensor elements for a system are defined as the second derivative of the energy U in the local minimum reached (the curvature of the potential energy), with respect to small strain deformations ε i .30 C ij =

1 V

 ∂U     ∂ε ∂ε   i j

(7)

Where V is the volume of the system. Standard mechanical properties such as bulk modulus (K), shear modulus (G), Young’s modulus (E), and Poisson’s ratio (υ ) can be calculated where the stiffness matrix C is known. The calculation of these parameters is performed using the energy minimization method (throughout LAMMPS) at zero temperature with the MDobtained glass structures as an input. At zero temperature, it is easy to evaluate these derivatives by deforming the simulation box in one of the six directions utilizing change of the volume and/or shape and/or boundary conditions for the simulation box in order to measure the change in the stress tensor.20 This allows the box size and form to change during 8 ACS Paragon Plus Environment

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the iterations of the minimizer, in which the final structure will be in a local potential energy minimum, and the system pressure tensor will be near to the specified exterior tensor. The checking of the system isotropy is done through a relationship proposed by ZENER.31 at which the material isotropy is expressed by aT =

2 C 44 C11 − C 12

(8)

The material can be isotropic when the value of aT tends to 1. In general, the amorphous solid came very close to satisfying the ideal isotropy.32 In this work, we found that the system is largely isotropic as shown in the Table 3. Therefore, in an isotropic media there are only two independent elastic constants (e.g. C11, C44). Table 3. Elastic constants for sodium silicate glass obtained in this work at T=300K together with the Zener ratio for checking the system isotropy.

Sample

C11 (GPa)

C44 (GPa)

C12 (GPa)

aT

SiO2

65.96424

28.63000

13.55424

1.09254

SN05

62.55194

24.56730

14.26734

1.01760

SN10

58.01053

23.12665

14.34724

1.05932

SN15

57.11736

22.48840

14.90551

1.06550

SN20

56.77506

21.72820

15.23342

1.04609

SN25

57.96849

21.10676

15.99496

1.00572

SN30

59.90907

20.50149

16.50977

0.94476

SN35

60.69100

20.15703

18.13960

0.94742

SN40

61.18846

19.49978

19.18990

0.92857

SN45

63.55903

18.53534

23.48834

0.92513

Elastic results The density parameter dsi is very important to describe mechanical properties especially deduced from experimental techniques such as Archimedes' method.33 and (BLS) spectroscopy.34 The effect of sodium on silicate glass materials can be highlighted through the computation of the molar density of silicon atoms dsi. This parameter is a combination between the Na2O mol% (also named X), the mass density of (SiO2) the molar weight for both sodium oxide and silicon oxide.

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(1-X)

(Na2O) x glass and


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d Si = ρ /[ M 0 +

X M 1] 100 − X

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(11)

where ρ is the mass density of the (SiO2)(100-X) (Na2O)X glass. M0 and M1 are the molar weight of SiO2 and Na2O, respectively. The results found by MD simulations show that dsi decreases when Na2O mol% increases as shown in Figure 3c. We also observe that the curve of dsi as function of Na2O mol%. is in a good agreement with the experimental results found by buoyancy method.11 Since we aim to assess in detail the simulation ability of MD with energy minimization method to simulate the BLS spectroscopy results, we present hereafter a comparison of the two elastic constants C11 and C44 deduced from both BLS measurements and simulation based on MD-structure. These elastic constants are reported as function of Na2O mol %. fraction, with X=0-45, in Figures 3a and 3b. Despite the quantitative disagreement between the C11 and C44 values found by simulations and by BLS measurements, we notice a good qualitative agreement in both C11 and C44 behaviors. Figure 3 shows the presence of two regimes, the low Na2O mol%. regime for X ≤ 20 and the high Na2Omol % one for 20 ≤ X ≤ 45 . From Figure 3, we observe that for both simulation an experiment as X increases, C11 decreases, passes through a minimum and starts to increases around X = 15 to 20. Whereas C44 shows a continuing decrease over all the X range.

Figure 3 (a) and (b) represent the elastic constants C11 and C44 of sodium silicate glasses (SiO2) (100-X) (Na2O) X obtained at room temperature, computed by energy-minimization using MD (red line) and measured experimentally by BLS (green line); (c) represents the molar density of silicon atoms dSi calculated by MD simulation and Buoyancy method (experimental).


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For all Na2O mol %, the simulated elastic constants are shifted down respectively by 20% and 16% in comparison to the same constants measured by BLS. These results show that although there is a softening observed for the simulation elastic constants, the global qualitative behavior of the experimental result is reproduced and especially the minimum of the C11 that is observed around 20 Na2O mol %. Regarding the size of the simulation box we have used two simulation boxes consisting of 1200 and 3000 atoms to obtain the structural and elastic results for two materials SiO2 and SN30. These box sizes had been used to study the elastic properties in many works using MD simulations20,29 We did not find any difference in C11 and C44 elastic constants for both simulation boxes. Therefore, we have chosen for this investigation a simulation box composed of 1200 atoms, which offers a better ratio accuracy/cost of the calculation. Moreover, Figure 3c shows an excellent agreement between the molar density of silicon atoms calculated by MD simulation and that obtained using Buoyancy method.

Structural properties Former structure. In Figures 4a, 4b and 4c, we plotted the partial pair correlation functions g(r) for the pairs Si-Si, O-O and Si-O. We observe from this figure that the addition of the sodium oxide does not have a strong effect on the positions of the peaks. These peak positions remain almost the same as those found for pure silica with the first peak in the Si–O partial pair correlation function gSiO(r) showing a maximum at r(Å) ~1.62 ± 0.02 Å. This result is in agreement with experimental results using EXAFS spectra.35 and other MD calculation.36 The O-O and Si-Si partial pair correlation functions exhibit maxima at positions of 2.66 Å and 3.15 Å, respectively. This is in agreement with another MD simulation and experimental studies (x-ray and neutron).37-38 In Figure 4f the Si–O coordination number NSiO(r) for all samples indicate that the average coordination of oxygen atoms surrounded by silicon atoms in the first shell is equal to 4, which means that the SiO4 tetrahedron remains the basic unit for all sodium oxide compositions. However, a sodium oxide effect on the basic unit of O-O and Si-Si coordination number Nij(r) is noticeable in Figures 4d and 4e. Indeed, their values decrease as function of X Na2O mol %. from NOO(r) =5.98 to 4.32 and from NSiSi(r) =4.05 to 3.49, respectively. This behavior has been shown experimentally.37, 6



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Figure 4 (a), (b) and (c) represent Si-Si, O-O and Si-O partial pair distribution functions of the (SiO2) (100-X) (Na2O) X glasses obtained from the classical MD simulation, respectively. (d), (e) and (f) represent Si-Si, O-O and Si-O coordination number functions of the (SiO2) (100-X) (Na2O) X glasses obtained from MD simulation, respectively. The results are obtained for X varying from 0 to 45 mol% at 300K.

Modifier structure. The addition of Na+ cation into silica glass network inevitably breaks part of the Si–O bonds and transforms some of the conventional bridging oxygens (BOs) into the so-called non-bridging oxygens (NBOs), which are accompanied by the forming Na-O bonds as a three-dimensional connectivity in sodium-silicate glass network structure. The first peak in the Na–O partial pair correlation function changes slightly from 2.36 Å for 5% sodium oxide composition (SN05 glass) to 2.27Å for 45% sodium oxide composition (SN45 glass), as shown in Figure 5a. These results are in agreement with both neutron diffraction, 12 ACS Paragon Plus Environment

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EXAFS and X-ray studies.37,39-42 This distance shortening can be explained as a result of the transformation of BOs to NBOs where Na-NBO distances are shorter in Na-O-Na bonds than in Na-O-Si bonds due to the strong attractive coulomb Si-O interaction. This phenomenon was already shown by Uchino et al. 43 through DM simulations. The partial radial function of Na-Na computed in the present work is reported in Figure 5b. The first peak varies from ~ 3.617Å for high Na2O mol %. to ~3.88 Å for small Na2O content. The Na-O coordination number NNa-O(r) curves (Figure 5c) show an inflection of about NNa-O(r) ~ 5. This fivefold coordination agrees well with the XAFS data.42,44 In Figure 5d Na-Na coordination number curves NNa-Na(r) show a regular increment of the coordination number as the Na2O mol %. increases. This indication backs the modified random network model proposed by Greaves.45 where Na ions tend to be together leading to a spatial heterogeneous distribution. Therefore, in the case of large amount of Na2O every sodium atom is surrounded by 8 to 9 other sodium atoms.46 However, Na–Na correlation in silicate systems at low sodium oxide composition should be considered carefully because of the small number of Na atoms that may lead to large statistical fluctuations. This behavior about the modifier structure in the sodium silicate glasses, is in good agreement with experimental and theorical results found by Oviedo et al.28 In general, the Na environments in the modeled glass structures are comparable to those in crystalline structure as found by Yuan et al. 47



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Figure 5 (a) and (b) represent Na-O and Na-Na partial pair distribution functions of the sodium silicate glasses (SiO2) (100-X) (Na2O) X obtained from classical MD simulations, respectively. (c) and (d) represent Na-O and NaNa Coordination number functions of the (SiO2) (100-X) (Na2O) X glasses obtained from classical MD simulations, respectively. All curves are obtained for X=0.1-45 mol % at 300K.

The oxygen coordination number. The oxygen environment in the sodium silicate glass contains two different cations (silicon and sodium). We can distinguish between BO and NBO through the nature of cation surrounding each oxygen atom. In which NBOs are defined when the oxygen atom is surrounded by at least one sodium atom in the sodium-silicate glass structure. In the case of NBO we can distinguish two different kinds, the first one NBO1 corresponds to oxygen atoms surrounded by only one sodium atom and the other one NBO2 stands for oxygen atoms surrounded by two sodium atoms. In a general manner, the sodium oxide effect in silicate glass network, shows a compensation at the NO-M(r) coordination number (with M=Si, Na) during the addition sodium oxide. The O-Si coordination number NO-Si(r) curves change slightly from NO-Si(r) =2.07 in the SN05 glass to NO-Si(r) =1.42 in the SN45 glass as shown in Figure 6a. While the NO-Na(r) coordination number curves (Figure 6b) show a regular increment of the coordination number when the sodium oxide content increases. The number of sodium atoms surrounding oxygen atoms change considerably from low values of NO-Na(r) in the SN05 glass to NO-Na(r) =3 in the SN45 glass. The oxygen atoms environment can be energeticlly explained by the atomic potential energy, which is due to the interaction with all other atoms in the simulation.30 Figure 7 presents the potential energy distributions of oxygen atoms for different sodium oxide compositions. We observe from this figure that oxygen atom energies have an unimodal distribution for low Na2O compositon, a bimodal distribution for intermediate compositions and starts to show a trimodal behavior beyond 20% of Na2O. This result corroborates the coordination number results suggesting that for low Na2O mol %. Si-O-Si bonds prevail and as this content increases oxygen atoms transform to less attractive NBOS that have only one Si cation (Si-O-Na) and then to the last type (Na-O-Na) which has the weakest attractive energy confirmed by the larger Na-O bond as discussed before. Figure 8 visualizes clearely this bimodal distribution corresponding to two networks of oxygen atoms uniformly distributed. This analysis indicates that the first peak corresponds to BOs, the second one to NBO1 atoms and the last one that appears for high Na2O mol %., represents the oxygen surrounded by only sodium atoms (NBO2 atoms).


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Where Na2O mol %. is increasing, the number of available bridging oxygens decreases, which can lead to an increase in the total coordination number of sodium ions and to the appearance of the second distribution of oxygen potential energy as shown in Figure 7. In this case, the sodium atoms tend to segregate or to form clusters. For high sodium oxide compositions, the sodium atoms are homogeneously distributed in the network allowing a third distribution of oxygen atom potential energy (Figure 7). The alkali atoms break Si-O bonds and take place between tetrahedra making the Si-O bonds more cohesives with their environment. This result is in agreement with experimental results found by Hauret et al.

48

The addition of sodium

oxide in the silicate glass causes a shift of the NBOs potential energies to lower values, indicating a higher cohesive Na-O bond. This energetic aspect of BOs and NBOs has been also investigated by infrared and Brillouin spectroscopies.

48

and the results showed the same

behavior as we described above. Therefore, the alkali-oxygen bond is less cohesive than the silicon-oxygen one, it is equivalent to supposing that the alkali ions vibrate against the silica network considered as a quasi-rigid heavy entity.48 The percentage of the NBOs in the simulated glasses can also be calculated statistically by checking the environment of each oxygen ions through the potential energy histogram of oxygen. Table 4 shows the NBOs percentage for different Na2O mol %. in silicate glasses found by this method. These results are in agreements with those found by Du et al.27 In the sodium silicate glasses, the percentage of NBOs increases with increasing sodium oxide content.

Figure 6 a) and b) represent O-Si and O-Na coordination number functions of the sodium silicate glasses (SiO2) (100-X) (Na2O) X

obtained from MD simulation, respectively. where X=5 to 45 mol % at T=300K.



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Figure 7 Potential energy distributions of oxygen atoms in the (SiO2) (100-X) (Na2O) X glasses for different X Na2O mol%. at 300K. At low Na2O mol %. only two distribution of oxygen atoms, but at high mol% Na2O the potential energy distribution of oxygen atoms shows a trimodal distribution.

Figure 8 Snapshot showing oxygen atoms in the SN45 glass at 300K. These atoms are colored according to their potential energies mapped from red for -7.43551 eV to blue for -13.3592 eV. Table 4. Non-bridging oxygen distributions in the alkali silicate glasses


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Sample

NBO1 (%) *

NBO2 (%) *

NBO (%) *

NBO (%) **

NB0 (%) ***

SN10

10.232

0

10.232

10.5

10.6

SN20

21.94

0.13

22.07

22.2

22.2

SN30

34.64

0.6

35.24

35.3

35.3

SN40

47.65

2.4

50.05

49.9

50.0

* Our simulation ** The percentage of the NBO was be predicted MD simulation.27 *** The percentage of the NBO was calculated statistically by checking the environment of each oxygen ions.27

Discussion Overall, if we restrict ourselves to the mechanical properties variations of the sodium silicate glass as a function of the sodium oxide content, our simulation results appears to offer a good agreement with experimental behavior measured from BLS. In the present work, the elastic constants calculations have been performed using the energy minimization method (throughout LAMMPS) at zero temperature with the MD-obtained glass structures at 300 K as an input. Therefore, one can wonder about the influence of temperature on the elastic constants values. In the literature, both experimental.7,8,49 and simulation.49 works which address the latter issue have shown that the evolution of C11 and C44 constants with the temperature is quite limited, even for a large temperature range.49 (variation below 5% for interval of 500K). The calculated values of elastic constants obtained in our simulation are in reasonable agreement with the experimental values, though they are shifted down respectively by 20% and 16% in both C11 and C44, respectively. We notice however that the correct qualitative change with Na2O mol %. is reproduced. In fact, the choice of the interaction potential plays a critical role (more important than the temperature effect) on the value of elastic constants. Bauchy.9, Pedone et al.50 and Cagin et al. 51 have found that elastic constants appear to be very sensitive to the choice of the interatomic potential. As a result, we can say that our similations leads to a behavior of the elastic constants C11 and C44 in a good qualitative agreement with experiments and offers a good quantitative comparison for structural results (such as such as EXAFS neutron X-ray diffractions …) and as mentioned above and other simulation results as indicated in Table 5. Thus, we can propose a close relationship between elastic constants behaviors, structure and densities as mentioned by Habasak et al.23 17 ACS Paragon Plus Environment


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Table 5. Parameters of short-range order in sodium silicate glass (Na 2 O)20 (SiO2 )80 estimated from simulated partial pair distribution functions and compared with Zotov’s simulation.52 at T=300K.

In this work structure

i-j pair

ri-j (Å)

Ni-j

(Na 2 O)0.20 (SiO2 )0.80

Si-O

1.62 ± 0.02

4.01 ± 0.1

1.62 ± 0.01 4.00 ± 0.20

O-O

2.68 ± 0.20

5.20 ± 0.01

2.61 ± 0.12

5.50 ± 0.20

Si-Si

3.19 ± 0.23

3.54 ± 0.02

3.06 ± 0.17

3.60 ± 0.60

Na-Na

3.33-3.52

3.60-4.11

3.42 ± 0.25

3.20 ± 1.40

Na-O

2.33 ± 0.29

3.90-4.20

2.45 ± 0.40

3.60 ± 1.10

3.42 ± 0 .11

2.77-3.86

3.42 ± 0.26

2.60 ± 1.40

Si-Na a

(Zotov and Keppler) a

(Zotov and Keppler)’s simulation.

ri-j (Å)

Ni-j

52

Through this work, we assess in detail the quality of the MD simulations, which are used to calculate the elastic constants and try to highlight the effect of the sodium addition on these properties. In the pure silica glass case, MD simulations has shown that the structure of SiO2 glass is based on a three-dimensional continuous random network of SiO4 tetrahedra.3 This structure of glassy state is similar to that found in the crystal state as has been reported by many authors.53-55 When this material is modified by different sodium oxide amounts, these glasses are usually presumed to be mainly made of a network of SiO4 tetrahedra that is disrupted by modifying cations as shown in Figue 9. At the time of the glass making by quenching the material from its equilibrium state at high temperature, the sodium atoms break Si-O bonds to produce NBOs, leading to the formation of interface zones between tetrahedra producing then a depolymerisation of the SiO2 network. We have used the visualization tool OVITO to analyze in more detail the NBO1 and NBO2 pairs based on the atomic potential energy values. We concluded that the Si-O bond involving a NBO is slightly shorter than that involving a BO and that the difference between them is 0.02 Å , which is good agreement previous work.56 This effect is difficult to show up using data of the first peak of Si-O PDF. Therefore, these findings suggest that the structure of silica is built up by SiO4 tetrahedral basic units connected with each other throughout a fourfold network at the medium range order. As the composition of sodium oxide increases these tetrahedral persists at short-range distances but the fourfold symmetry is broken partially where NSiSi(r) passes from 4.05 for silica to 3.49 for sodium silicate glasses as shown above. This result can be explained by the existence of different sub-lattices by effect of NBO1 interfaces and/ or sodium oxide areas Na2(NBO2) created between the SiO4 tetrahedral during the modification of silica, leading to a 18 ACS Paragon Plus Environment

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decrease of the connectivity in the silicate glasses. When decreasing the connectivity throughout this point, such networks undergo a mechanical phase transition from a rigid phase to a floppy phase.57 In this context, Vaills et al.

58

through BLS and modulated Differential

Scanning Calorimetry (MDSC) have allowed the determination of three elastic phases in (Na2O)

X

(SiO2)100−X glasses: stressed-rigid phase for X < 18, intermediate phase for 18 < X

< 23 and a floppy phase where X > 23. At high sodium oxide content, the sodium silicate glass shows several homogeneous areas of sodium oxide in its network. The structure of sodium silicate glass is changed as function of X Na2O content, leading to two different behaviors of elastic constants C11 and C44 observed with both MD simulation and BLS experiments. Below 20% of Na2O mol %. in the silicate network, the elastic constants C11 and C44 decrease, this behavior can be related to :

-

The loss of silicon density and the decrease of the quantity of strong bonds in the system through the presence of clusters at low Na2O content.

-

The existence of the free volume created by the effect of low sodium oxide content due to the decrease in the compacity of the glass.

-

The rigidity loss with the increase of sodium content.58

-

The existence of Na-O bonds between sub-lattices containing sets of SiO4 tetrahedra, these bonds are less cohesive than Si-O bonds of silica glass. Sodium silicate glasses in the composition range between 2% and 20% of Na2O are known to have a propensity for phase separation.59

-

The perturbation role of low amount of sodium oxide in sodium-silicate glass that can mark the existence of the free volume in glass network.

Different works (Lammert et al. 60, Vaills et al. 11, Pedone et al. 61 and Zhao et al. 8) have been interested in the decrease of elastic constants as function of Na2O amount in the silica network. These works suggested that the introduction of alkali atoms leads to the formation of (NBOs) which leads to the apparition of depolymerization in the SiO2 network and consequently to the decrease of the cohesion of the SiO2 network and to the softening the elastic constants. On the other side, at high Na2O mol %. > 20 , each elastic constant marks a special behavior. The shear elastic constant C44 carries on its decrease with a smaller slope until saturation of this values at highest sodium oxide amount. The longitudinal elastic constant C11 shows a 19 ACS Paragon Plus Environment


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completely different behavior where we can distinguish two regimes: below x = 0.20, C11 decreases as function of sodium oxide amount and for x > 0.20 it increase due to layered-like disilicate units. 62 These results can be related to :

-

The increase of Na-O bonds and Si-O cohesion involving modification of elastic behaviour.

-

The change of sodium nature when it does not tend to segregate or to form clusters in silicate network, and it is homogeneously distributed in the silicate glass network.

-

The increase of compacity of the glass which is induced by the increase of its density when the sodium content increases.

Vaills et al. 11, Pedone et al. 61 and Kennedy et al. 63 explained the increase of elastic constants by the creation of new bonds such as the NBO-Na-NBO or NBO-Na-BO bonds would upgrade the cohesion of the glass state, resulting to an increase in the elastic constants as a function of Na2O amount. In the present work, for high amount of Na2O in glasses, oxygen atoms show a more cohesion with its environment than at low amount of sodium oxide. We may relate the increase of elastic constants at high amount of sodium oxide to the decrease of free volume in silicate glasses where sodium anion prefer to distribute homogeneously in silicate glasses as shown in Figure 10 and confirmed previously by Pedone et al. 61 In addition, many structural and opto-mechanical properties of sodium silicate glass such as Pockels coefficients P12 and P44

25

and the fracture toughness.

64

exhibit clearly a marked

nonlinear variation as a function of Na2O mol %. with a minimum at around 20%. This effect was already observed by Jabraoui et al.

3

who measured the glass transition temperature Tg

and had shown a specific effect of sodium addition in silicate glasses as shown in Figure 11a. Moreover, the experimental work of Avramov et al.65 indicates almost the same behavior (Figure 11b) where Tg decreases nolinearly with Na2O content. The inclusion of sodium in the SiO2 network induces a strong reduction of Tg and an increase of the fragility parameter with respect to silica.6 The decrease of Tg destroys the mechanical equilibrium that was dominant in silica.66,67 On the other hand, at high concentrations of Na2O in silicate glassy state (above 20%) the floppy groups start to play a major role. Tg shows a sligh variation above 0.2 of sodium oxide content. Thus, during silicate glasses making the glass transition temperature Tg and the shear elastic constant C44 of the glassy state show the same behavior as a function of sodium oxide content. As shown above in the part concerning the relationship between the velocity of wave propagation and the elastic constants, Heuer and Spiess.68 have shown a correlation between Tg and the sound velocity via Tg = Cg mυ 2 (where C g is estimated 20 ACS Paragon Plus Environment

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to be equal to 0.014, m is the average elementary mass and v is the velocity of sound). Therefore, based on the above remarks, we can conclude that in the case of isotropic glasses, Tg is strongly related to the transversal elastic constant. In the present work, we have also found that the percentage variation of NBOs in silicate network shows a transition like behavior around 20% of Na2O. At low sodium oxide mola fraction, there is a proportionality between the quantity of this modifier and the percentage of NBOs, whereas above 20% the amount of NBOs becomes higher than the Na2O mol %. as shown in Figure 11c and Table 4. Thus, the increase of the sodium amount in silicate goes proportionnely with the sodium-rich regions extending throughout the glass. Nevertheless, Avramov et al. 69 showed that low and high concentrations of modifier such as sodium oxide could lead to opposite effects on many other properties of silicate glasses.

Fig.9. Snapshots showing the structure of the SN25 sodium silicate glass at 300K obtained with a cooling rate of 1012 K/s. Red atoms represent silicon, blue atom stand for oxygen and yellow atoms are sodium ones. The small picture at the right of the figure represents a cut showing local tetrahedral units.



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Fig.10. Snapshot of channels created by Na ions (Yellow) in (SiO2) (100-X) (Na2O) X glasses obtained from MD simulations, for various Na2O mol% content: =5, 15, 25 and 45 at 300K

Fig.11. (a) and (b) represent the glass transition temperature as a function of Na2O mol %. in the silicate matrix, they were carried out by two different methods MD simulation and experimental technique.65 The used cooling rate in MD simulation is equal to 1 K/ps.3 (c) Non-bridging oxygen percentage in silicate glasses as function of sodium oxide content. Through DM, defined glass transition temperature as the temperature which can be determined by the broken lines or intersection between two linear fitting curves according to both high and low range temperatures. The experimental technique defined as the temperature at which viscosity is 1013.5 dPa.s.

Conclusion We have simulated a sodium-silicate glass and studied the effects of sodium composition on both elastic constants and structural properties of silicate binary glasses. Overall, our MD simulation offers a good agreement with experiments for structural results. The structural analysis carried out in the present simulation or in previous works fully supports the intuitive 22 ACS Paragon Plus Environment

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hypothesis initiated by Vaills et al. 11 The combined MD simulations and energy minimization study at zero temperature realized in this work has allowed the quantitative evaluation of the elastic constants C11 and C44. We suggest a quantitative description of the relationship between the structure and the elastic constants, which can deeply help to understand the responsible factors related to the change shown in the silicate glasses with the increasing of Na2O content. These factors are: 1) the loss of silicon density and the decrease of the attractive interactions in the system through the presence of clusters at low Na2O content, may induce a decrease of C11 and C44. 2) The existence of the free volume created by the effect of low Na2O mol %. due to the decrease in the compact structure of the glass, leading to a decrease in the elastic constants C44 and C11 as a function of Na2O content. Consequently, the low amount of Na2O can play the role of structural perturbation in the silicate glasses. 3) The increase of the glass cohesion proportionally with an increase of Na-O bonds and Si-O cohesion as well as the apparition of the homogeneous distribution of sodium oxide in the silicate glass network, lead to the increase of the elastic constant C11 as a function of Na2O sodium for high Na2O concentrations (>20%).

AUTHOR INFORMATION Corresponding Authors * E-mail : [email protected].,[email protected], [email protected] REFERENCES (1) Varshneya, A.K. Fundamentals of Inorganic Glasses; Academic Press. San Diego 1994, 339. (2) 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. (3) Jabraoui, H., Achhal, E.M.; Hasnaoui, A.; Garden, J.-L; Vaills, Y.; Ouaskit, S. Molecular Dynamics

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Effect of Sodium Oxide Modifier on Structural and Elastic Properties of

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