Abstract
We conducted molecular dynamics simulations to investigate the diffusion behavior of sodium atoms in sodium silicate glasses, focusing on the analysis of O-polyhedrons containing sodium atoms. The various characteristic parameters for the diffusion process were calculated, including the mean square displacement (MSD) of atoms, the change rate of neighboring oxygen atoms around sodium, the variation in the number of polyhedrons visited by Na, and the forward–backward jump of sodium between O-polyhedrons. Our findings reveal that the Si–O network unchanged while sodium preferentially moves through O-polyhedrons. Diffusion coefficient of sodium atoms exhibits a quadratic dependence on the change rate of the number O coordination. This diffusion law has been observed across different samples with varying temperatures and SiO2 contents. Additionally, we have evaluated the influence of SiO2 content and temperature on the forward–backward jumps of sodium atoms between O-polyhedrons as an important part of this study.
Graphical abstract

The radial distribution function of the model is compared with experiment data







Similar content being viewed by others
Explore related subjects
Discover the latest articles and news from researchers in related subjects, suggested using machine learning.Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is a simulation study with no experimental data. All necessary data are available on reasonable request.]
References
A.O. Davidenko, V.E. Sokol’skii, A.S. Roik, I.A. Goncharov, Structural study of sodium silicate glasses and melts. Inorg. Mater. 50, 1289–1296 (2014). https://doi.org/10.1134/S0020168514120048
H. Jabraoui, E.M. Achhal, A. Hasnaoui, J.L. Garden, Y. Vaills, S. Ouaskit, Molecular dynamics simulation of thermodynamic and structural properties of silicate glass: effect of the alkali oxide modifiers. J. Non-Cryst. SolidsCryst. Solids 448, 16–26 (2016). https://doi.org/10.1016/j.jnoncrysol.2016.06.030
H. Jabraoui, Y. Vaills, A. Hasnaoui, M. Badawi, S. Ouaskit, Effect of sodium oxide modifier on structural and elastic properties of silicate glass. J. Phys. Chem. B 120, 13193–13205 (2016). https://doi.org/10.1021/acs.jpcb.6b09664
Y. Oishi, R. Terai, H. Ueda, A.R. Cooper, A.H. Heuer, Mass transport phenomena in ceramics. J. Mater. Sci. Res. 9, 297–310 (1975). https://link.springer.com/book/10.1007/978-1-4684-3150-6
C. Angell, A., P. Cheeseman, A., S. Tamaddon, Computer simulation studies of migration mechanisms in ionic glasses and liquids. J. Phys. Colloques 43, C9-381–C9-385 (1982). https://doi.org/10.1051/jphyscol:1982972
G.N. Greaves, EXAFS and the structure of glass. J. Non-Cryst. SolidsCryst. Solids 71, 203–217 (1985). https://doi.org/10.1016/0022-3093(85)90289-3
F. Kargl, A. Meyer, M.M. Koza, H. Schober, Formation of channels for fast-ion diffusion in alkali silicate melts: a quasielastic neutron scattering study. Phys. Rev. B 74, 014304 (2006). https://link.aps.org/doi/10.1103/PhysRevB.74.014304
V. Th, J. Horbach, Slow dynamics in ion-conducting sodium silicate melts: simulation and mode-coupling theory. Europhys. Lett. Lett. 74, 459 (2006). https://doi.org/10.1209/epl/i2006-10012-2
Y. Yu, B. Wang, M. Wang, G. Sant, M. Bauchy, Reactive molecular dynamics simulations of sodium silicate glasses—toward an improved understanding of the structure. Int. J. Appl. Glass Sci 8, 276–284 (2017). https://doi.org/10.1111/ijag.12248
J.R. Johnson, R.H. Bristow, H.H. Blau, Diffusion of ions in some simple glasses. J. Am. Ceram. Soc. 34, 165–172 (1951). https://doi.org/10.1111/j.1151-2916.1951.tb11630.x
G.N. Greaves, Structure and ionic transport in disordered silicates. Mineral. Mag. 64, 441–446 (2000). https://www.cambridge.org/core/article/structure-and-ionic-transport-in-disordered-silicates/83FC616A36618C9DCE5F1BDF454B3940
J. Habasaki, K.L. Ngai, The mixed alkali effect in ionically conducting glasses revisited: a study by molecular dynamics simulation. Phys. Chem. Chem. Phys. 9, 4673–4689 (2007). https://doi.org/10.1039/B704014H
C.T. Moynihan, N.S. Saad, D.C. Tran, A.V. Lesikar, Mixed-Alkali effect in the dilute foreign-alkali region. Fail. Strong Electrol. Cation. Interact. Model 63, 458–464 (1980). https://doi.org/10.1111/j.1151-2916.1980.tb10212.x
J. Horbach, W. Kob, K. Binder, Structural and dynamical properties of sodium silicate melts: an investigation by molecular dynamics computer simulation. Chem. Geol. 174, 87–101 (2001). https://doi.org/10.1016/S0009-2541(00)00309-0
W. Smith, G.N. Greaves, M.J. Gillan, Computer simulation of sodium disilicate glass 103, 3091–3097 (1995). https://aip.scitation.org/doi/abs/10.1063/1.470498
A.N. Cormack, J. Du, T.R. Zeitler, Alkali ion migration mechanisms in silicate glasses probed by molecular dynamics simulations. Phys. Chem. Chem. Phys. 4, 3193–3197 (2002). https://doi.org/10.1039/B201721K
A.N. Cormack, J. Du, T.R. Zeitler, Sodium ion migration mechanisms in silicate glasses probed by molecular dynamics simulations. J. Non-Cryst. SolidsCryst. Solids 323, 147–154 (2003). https://doi.org/10.1016/S0022-3093(03)00280-1
F. Noritake, Diffusion mechanism of network-forming elements in silicate liquids. J. Non-Cryst. SolidsCryst. Solids 553, 120512 (2021). https://doi.org/10.1016/j.jnoncrysol.2020.120512
J. Habasaki, Y. Hiwatari, molecular dynamics study of the mechanism of ion transport in lithium silicate glasses: characteristics of the potential energy surface and structures. Phys. Rev. B 69, 144207 (2004). https://link.aps.org/doi/10.1103/PhysRevB.69.144207
J. Horbach, W. Kob, K. Binder, Dynamics of sodium in sodium disilicate: channel relaxation and sodium diffusion. Phys. Rev. Lett. 88, 125502 (2002). https://link.aps.org/doi/10.1103/PhysRevLett.88.125502
A. Meyer, J. Horbach, W. Kob, F. Kargl, H. Schober, Channel formation and intermediate range order in sodium silicate melts and glasses,. Phys. Rev. Lett. 93, 027801 (2004). https://link.aps.org/doi/10.1103/PhysRevLett.93.027801
H.W. Nesbitt, G.S. Henderson, G.M. Bancroft, R. Ho, Experimental evidence for Na coordination to bridging oxygen in Na-silicate glasses: implications for spectroscopic studies and for the modified random network model. J. Non-Cryst. SolidsCryst. Solids 409, 139–148 (2015). https://doi.org/10.1016/j.jnoncrysol.2014.11.024
S.J. Gurman, Bond ordering in silicate glasses: a critique and a re-solution. J. Non-Cryst. SolidsCryst. Solids 125, 151–160 (1990). https://doi.org/10.1016/0022-3093(90)90334-I
H. Maekawa, T. Maekawa, K. Kawamura, T. Yokokawa, The structural groups of alkali silicate glasses determined from 29Si MAS-NMR. J. Non-Cryst. SolidsCryst. Solids 127, 53–64 (1991). https://doi.org/10.1016/0022-3093(91)90400-Z
M. Bauchy, M. Micoulaut, Atomic scale foundation of temperature-dependent bonding constraints in network glasses and liquids. J. Non-Cryst. SolidsCryst. Solids 357, 2530–2537 (2011). https://doi.org/10.1016/j.jnoncrysol.2011.03.017
M. Bauchy, Structural, vibrational, and thermal properties of densified silicates: insights from molecular dynamics. 137, 044510 (2012). https://aip.scitation.org/doi/abs/10.1063/1.4738501
Q. Zhou, T. Du, L. Guo, M.M. Smedskjaer, M. Bauchy, New insights into the structure of sodium silicate glasses by force-enhanced atomic refinement. J. Non-Cryst. SolidsCryst. Solids 536, 120006 (2020). https://doi.org/10.1016/j.jnoncrysol.2020.120006
F. Noritake, Structural transformations in sodium silicate liquids under pressure: new static and dynamic structure analyses. J. Non-Cryst. SolidsCryst. Solids 473, 102–107 (2017). https://doi.org/10.1016/j.jnoncrysol.2017.08.004
M. Fábián, P. Jóvári, E. Sváb, G. Mészáros, T. Proffen, E. Veress, Network structure of 0.7SiO2–0.3Na2O glass from neutron and X-ray diffraction and RMC modelling. J. Phys. Conden. Matter 19, 335209 (2007). https://doi.org/10.1088/0953-8984/19/33/335209
Author information
Authors and Affiliations
Contributions
NTT and NVY analyzed data, provided the main idea of this paper. NTT and NVY, PTL wrote manuscript and edited the manuscript.
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Thao, N.T., Yen, N.V. & Lien, P.T. Diffusion behaviors of sodium atoms within Si–O network in sodium silicate glasses: insights from molecular dynamics simulations. Eur. Phys. J. B 96, 138 (2023). https://doi.org/10.1140/epjb/s10051-023-00610-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjb/s10051-023-00610-2