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VNU Journal of Science: Mathematics – Physics, Vol. 35, No. 3 (2019) 107-113 Original Article Distribution of Sodium and Diffusion Mechanism in Sodium Silicate Liquid Nguyen Thi Thanh Ha* Hanoi University of Science and Technology, No. 1, Dai Co Viet, Hanoi, Vietnam Received 19 May 2019 Revised 09 June 2019; Accepted 15 June 2019 Abstracts: Molecular dynamic simulation is employed to study the structural properties and diffusion mechanism in sodium silicate (Na2O.4SiO4). Structural characteristics are clarified through the pair radial distribution function, distribution of SiOx coordination units, network structure. The simulation results reveal that the structure of Na2O.4SiO4 liquid consists of one Si-O network that is mainly formed by SiO4 units. The spatial distribution of sodium is non-uniform; sodium tends to be in the non-bridging oxygen-simplexes and in larger-radius simplex. Moreover, the sodium density for non-bridging oxygen region is significantly higher than the one for others region. Further, we find that Si and O diffuse by bond break-reformation mechanism, while the motion of Na consists of two parallel processes. Firstly, Na atoms hop from one to another O within a disordered network where each bridging oxygen (BO) has one site, while a non-bridging oxygen (NBO) possesses two sites. The average resident time for Na staying near NBO is much longer than that near BO. Keywords: simulation, structure, mechanism diffusion, sodium-silicate 1. Introduction Glass-forming mixtures of SiO2 with an alkali oxide are the important materials group that has been widely applied in many fields such as: microelectronics, medicine (bio-material), high technology materials. Therefore, understanding their structure and dynamical properties is fundamentally necessary [1-3]. By using the neutron, X-ray diffraction (XRD) techniques, magic-angle spinning (MAS) nuclear magnetic resonance (NMR) [4-5] and simulation methods [6-7] observed the change in structure of alkali silicate. Namely, the addition of alkali oxides into pure silica (SiO2) disrupts the basic silica network by breaking part of the Si-O bonds, creating non bridging oxygen (NBO). The percentage of NBOs in the system increases with the alkali oxide concentration [8-9]. In the multicomponent alkali ________ Corresponding author. Email address: ha.nguyenthithanh1@hust.edu.vn https//doi.org/ 10.25073/2588-1124/vnumap.4354 107 N.T.T. Ha / VNU Journal of Science: Mathematics – Physics, Vol. 35, No. 3 (2019) 107-113 108 silicates, the ‘‘mixed alkali effect’’ refers to a drastic change of the relaxation dynamics. The ionic diffusivity of both alkali ions decreases in the mixed alkali composition; compared to the corresponding single-alkali silicate [10]. The effect is caused by mutual interception of jump paths of both kinds of mobile alkali ions. So the cooperative forward-correlated jumps are blocked and the immobilization of faster ions is responsible for the mixed alkali effect [11]. Moreover, alkali atom is found to migrate predominantly within NBO rich region in the system [8] and the diffusion of the alkali atoms mobility that is much higher than that of the silicon and oxygen atoms forming a tetrahedral network structure [12]. According to studies, the alkali atoms can easily move in preferential pathways, also called “channels”. Thus, the fast transport of the alkali ions in silicate melt was explained [13-14]. The partial Na–Na structure factor has a pre-peak at a wave vector q = 0.95 Å−1. These experimental results support a mechanism of ionic transport channel in alkali silicate [15-16]. The preferential pathways have been found via simulation method. The simulation box is divided into cubes and then they calculated the number density of the sodium atoms in each of these small boxes. The research results show that 50% of the cubes have been visited by sodium ions [17] and the most of the Na motion occurs in 6% subsets of the total available space However, the boxes are fixed and placed in the space simulation box. In this paper, we have calculated the statistical and dynamical distribution of sodium through the SiO network of Na2O.4SiO4 (NS4) liquid via simplex method. Furthermore, we focus on two diffusion mechanisms of network former and modifier atoms. 2. Computational method MD simulation is carried out for Na2O.4SiO2 (NS4) melts at pressure of 0.1 MPa and temperature of 1873 K. The model contains 1066 Sodium, 2132 Silicon and 4797 Oxygen atoms. We apply the interatomic potential including two-body and three-body terms. This potential provided the reproduction of structure of silicate crystals and pressure dependence of transport properties of silicate liquid. More details about the applied potential can be found elsewhere [18,19]. The constructed models have been relaxed for long times until reach the equilibrium. Afterward we perform additional runs of 150 ps to produce a series of configurations separated by 10 ps. The dynamical and structural data are collected from these configurations. The simplex is a sphere passing center of four oxygen atoms (NBO or BO) without Si or O atom inside. The simplex has no fixed radius. The radius of simplex depends only on position of four atoms. The simplexes consist of two main types: void-simplex (the sphere passing four atoms without any atom inside) and Na-simplex (the sphere passing four atoms and containing one or many sodium atoms). The Fig.1a, b presents void-simplex. The Fig.1c presents the Na-simplex. The characteristic of simplexes is determined by radius and type (BO, NBO) atom that sphere passing and the number of sodium inside. a b c Fig 1. The schematic illustration of the simplex: void-simplex (a,b); and Na-simplex (c). Here the red, gray and blue spheres represent the NBO, BO and Na atoms, respectively; the circle represents the simplex sphere. N.T.T. Ha / VNU Journal of Science: Mathematics – Physics, Vol. 35, No. 3 (2019) 107-113 109 3. Results and discussion Table 1. the inter-atomic distances ( rAB Å) calculated from PRDF of sodium silicate Reference NS4 [20,21] [2] rOO 2.62 2.62 2.35 rSiO 1.62 1.62 1.65 rONa 2.15 2.29 rSiSi 3.12 3.05 3.12 rSiNa 3.20 3.5 rNaNa 3.32 2.6, 3.05 Firstly, we examine the structural and dynamical characteristics in NS4 liquid. Table 1 lists the interatomic distances calculated from PRDF and these results are compared with experimental data [2, 2021] for comparison. As seen, although rSiNa and rNaNa show some discrepancies, the constructed models are well consistent with experiments. In particular, the simulation reproduces the experimental data for rOO, rSiO, rSiSi and rNaO. The fraction of SiOx and different oxygen types is shown in Table 2. The structure comprises SiO4 tetrahedrons and a small amount of SiO3. Close values of DO and DSi evidence the bond break-reformation mechanism for network atom [22]. Accordingly, the collective movement of network atoms occurs when a Si-O bond is broken and then a new bond is formed. This leads to rearrangement in the Si-O network and that Si moves cooperatively with its coordinated O. From Table 2 follows that fast Na move inside a network of slow atoms. Table 2. Fraction of SiOx units and different oxygen types. Units SiOx Fraction of SiOx Oxygen SiO3 SiO4 SiO5 0.0041 0.9958 0.0001 FO NBO BO Fraction of type Oxygen 0.0007 0.2225 0.7767 Diffusion coefficient, [cm2/s] DO 8.50 x 10-8 DSi 6.50 x 10-8 DNa 4.74 x 10-5 To determine the temporal locations of Na we calculate the distances between every Na and network atoms. Then we determine a network atom which is separated from the given Na at a shortest distance. We assume that this Na is located in a site near the finding network atom. The calculation result is shown in Table 3. We observe that all Na are located in sites near O atoms and no one is present near Si atoms. This is due to both Si and Na is positive charged ions. For the convenience of discussion we refer the phrase 'sites near O atoms' as 'near O atoms' for short. Although the number of BO more than three times excesses that of NBO, about 75% of Na are near NBO. This can be interpreted by the fact that Na is bonded to NBO much stronger than to BO because of NBO is connected only with one Si. From this follows that tNBO is much longer than tBO, where tBO, tNBO is the average resident time for Na being near BO and NBO, respectively. Furthermore, we observe that the number of Na located near an O varies from 0 to 1 when this O is BO and from 0 to 2 if it is NBO. There are some exceptions, for instance, three Na are present near NBO. However such cases occur very rarely. From this follows that each NBO has two sites, while a BO possesses one site. The total number of sites is calculated from the number of NBO and BO. For the configuration at t = 0 it equals to 5870 that is more than five times larger total number of Na. This fact indicates that the simple vacancy mechanism is not appropriate for diffusion of sodium in NS4 liquid. Using simplex method to identify the distribution of sodium in network Si-O, the results present Table 4. The most of NBO4-simplexes (four atoms are NBO) and BONBO3- simplexes (three NBO and one BO) have the existence of Na atoms inside. The fraction of Na decreases with the increasing the number of BO. The result is consistent with the data in Table 3. N.T.T. Ha / VNU Journal of Science: Mathematics – Physics, Vol. 35, No. 3 (2019) 107-113 110 Table 3. Spatial distribution of Na in Si-O network. mNa is the number of Na which are located near NBO or BO; mBO, mNBO is the number of BO and NBO, respectively. mNa t = 0 ps mBO 3485 243 0 0 0 1 2 3 t = 100 ps mNBO 373 570 125 1 mBO 3468 252 1 0 t = 140 ps mNBO 394 555 124 3 mBO 3477 243 1 0 mNBO 391 549 133 2 Table 4. Characteristic of simplex in sodium silicate. Type of simplex NBO4 BONBO3 BO2NBO2 BO3NBO msimplexes 338 1454 4011 6940 Fraction of simplexes 0.0179 0.0770 0.2124 0.3675 Simplexes with Na 327 1339 3396 4768 Fraction of simplexes with Na 0.9675 0.9209 0.8467 0.6870 Moreover, the characteristic of simplex is determined by radius of simplex and the radius distribution of void simplex, 1Na-simplex and 2Na-simplex is illustrated in Fig 2. It reveals that the radius distributions have the Gaussian form and the position of the peak systematically shifts to right (larger radius) as number of sodium inside simplex increases. So, we conclude that Na atoms tend to be in the NBO-simplex and simplex has larger radius. The motion of Na relates strongly to simplex-type (BO or NBO). 0.16 void-simplex 1Na-simplex 2Na-simplex Fraction of simplex 0.12 0.08 0.04 0.00 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Radius, Å Fig 2. The radius distribution of void simplex, 1Na-simplex and 2Na-simplex. N.T.T. Ha / VNU Journal of Science: Mathematics – Physics, Vol. 35, No. 3 (2019) 107-113 111 We also calculate the time dependence of fraction Xn/X, where X is the total number of BO (or NBO); Xn is the number of BO (or NBO) near which n sodium atoms are present. The result is presented in Fig.3. As expected, BO1/BO is significantly smaller than NBO1/NBO and NBO2/NBO. Very small fraction BO1/BO confirms the fact that Na atoms stay near NBO in average for much longer time than that near BO. Thus we can conclude that Na atoms move from sites to sites located near O atoms and the resident time for Na near NBO is much longer than that near BO. 0.6 0.5 Fraction Xn/X 0.4 BO1/BO NBO1/NBO NBO2/NBO 0.3 0.2 0.1 0.0 0 20 40 60 80 100 120 140 Time, ps Fig.3. Fractions Xn/X as a function of time. Next, we examine the status (BO or NBO) and occupancy for O. The occupancy for O is busy if Na is present near this O, otherwise it is free. We consider 15 configurations separated by 10 ps. For every O we count how many times when its status is BO (MBO) and the occupancy for O is busy (MNa). Obviously, MNa and MBO vary from 0 to 15. The plots of number of O versus MNa and MBO are shown in Fig 4. We observe that about 14% of O atoms have MBO from 1 to 14. These O undergo transformations from NBO to BO and vice versa during the time tobs. When the transformations of O status occur, Na atoms will be redistributed between different O atoms. In particular, as NBO transforms to BO, the Na atoms located near this NBO move to other O atoms. In the case when BO transforms to NBO, many Na atoms replace to the transformed BO. Thus, the motions of Na is strongly correlated with the one of network atom. We also mention that 86% of O atoms have MBO equal to 0 or 15. This means that during the time tobs the redistribution of Na happens with a small number of O atoms. As shown in Fig.4, most of O atoms possess MNa varied from 1 to 12 indicating a high rate of Na jumping. However there are 27% of O atoms having MNa = 0, i.e. Na atoms do not enter sites near these O. This indicates the non-uniform spatial distribution of Na. Note that two O atoms connected to a common Si also form a linkage with rlk = 3.6 Å. Further, we observe that Na located near a beforehoping O can jump to one among neighbors of the before-hoping O. From this follows that Na atoms hop from O atom to its neighbors within the O network. The hoping may be blockaded when neighboring atoms are completely occupied by other Na atoms. N.T.T. Ha / VNU Journal of Science: Mathematics – Physics, Vol. 35, No. 3 (2019) 107-113 1500 3750 1200 3000 Number of O atoms Number of O atoms 112 900 600 300 0 2250 1500 750 0 0 2 4 6 8 MNa 10 12 14 16 0 2 4 6 8 10 12 14 16 MBO Fig.4. Plots of number of O versus MNa and MBO. Here MBO, MNa respectively is the number of times when the status is BO and the occupancy is busy. 4. Conclusion The NS4 liquid is systematically analyzed on dynamics and structure by MD simulation. The results show that the structure of liquid consists of a network of SiO4 connected with each other via BO. There is also a large amount of NBO, up to 22 % of total Oxygen atoms. Furthermore, the distribution of sodium is determined via the simplex and the average resident time for Na staying near NBO or BO. It reveals that the density of Na for NBO- region is significantly larger than that for other region and sodium atoms can easily move in NBO regions. Two diffusion mechanisms of network former and modifier are discussed. : the network atoms diffuse by the bond break-reformation, while diffusion of Na consists of two parallel processes. First, Na atoms move from one to another O atom within a disordered O network where the majority of atoms have from 5 to 8 neighbors. The jump of Na is realized between two O atoms forming a linkage with rlk = 3.6 Å. Second, Na atoms are redistributed between O atoms as the transformation of O status happens. Furthermore we found that the O network comprises a number of sites where each BO has one site, while NBO possesses two sites Acknowledgements The authors are grateful for support by the NAFOSTED Vietnam (Grant 103.01-2018.13). References [1] Gergely Molnár, Patrick Ganster, Anne Tanguy, Effect of composition and pressure on the shear strength of sodium silicate glasses: An atomic scale simulation study, Physical Review E 95 (2017) 043001. [2] A.O. Davidenkoa, V.E. Sokol’skiia, A.S. Roika, I.A. Goncharovb, Structural Study of Sodium Silicate Glasses and Melts, Inorganic Materials 50 (12) ( 2014)1289. N.T.T. Ha / VNU Journal of Science: Mathematics – Physics, Vol. 35, No. 3 (2019) 107-113 113 [3] K. Konstantinou, D.M . Duffy, A.L. Shluger, Structure and luminescence of intrinsic localized states in sodium silicate glasses, Physical review B 94 (2016) 174202. [4] S.K. Lee, G.D. Cody, Y. 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