First-principles study of the surface of silica and sodium silicate glasses

We use ab initio molecular dynamics simulations to investigate the properties of the dry surface of pure silica and sodium silicate glasses. The surface layers are defined based on the atomic distributions along the direction $\left(z\mathrm{direction}\right)$ perpendicular to the surfaces. We show that these surfaces have a higher concentration of dangling bonds as well as two-membered (2M) rings than the bulk samples. Increasing the concentration of ${\mathrm{Na}}_2\mathrm{O}$ reduces the proportion of structural defects. From the vibrational density of states, one concludes that 2M rings have a unique vibrational signature at a frequency $\approx 850{\mathrm{cm}}^{-1}$, compatible with experimental findings. We also find that, due to the presence of surfaces, the atomic vibration in the $z\mathrm{direction}$ is softer than for the two other directions. The electronic density of states shows clearly the differences between the surface and interior and we can attribute these to specific structural units. Finally, the analysis of the electron localization function allows to get insight on the influence of local structure and the presence of Na on the nature of chemical bonding in the glasses.

Figure 1

Snapshots of the atomic structure of the three glasses at 300 K. Si, O, and Na atoms are represented by spheres in blue, red, and green, respectively. The sticks represent Si-O bonds with bond length smaller than 2 Å.

Figure 2

Atomic distribution along the $z\mathrm{direction}$. (a)–(c) The mass density profiles for silica, NS5, and NS3. (d)–(f) The atomic-number fraction along the $z\mathrm{direction}$ for silica, NS5, and NS3. In all graphs, the solid lines with symbols are for the liquids at temperature $T_0$ (see Table 1). The dashed lines are the corresponding quantities for glasses at 300 K and for clarity are shown only for NS5. The vertical dashed lines indicate the boundary between the surface and interior layers.

Figure 3

Probability distribution function of nearest-neighbor distance for the glasses at 300 K. Upper and lower panels are for Si-O and Si-Si pairs, respectively. From left to right the compositions are silica, NS5, and NS3, the solid lines being for the surface domains, while the dashed lines for the interior ones.

Figure 4

Bond-angle distribution. Upper and lower panels are for O-Si-O and Si-O-Si angles, respectively. From left to right the compositions are silica, NS5, and NS3.

Figure 5

Top view of snapshots showing structural motifs at the surfaces of (a) silica and (b) NS3 glasses. Only the outermost layer of silicon atoms and their nearest-neighbor O and Na atoms are shown (see the text for the construction method). Two-membered rings are highlighted with a circle. Only Si-O bonds are shown and a color code is used taking into account their length, given in Å. The visualization was realized using ovito [77].

Figure 6

Probability distribution functions of the orientation angle for the surface (red line) and interior (blue line) domains in the liquid state (at $T_0$). Panels (a), (b), and (c) are for liquid silica, NS5, and NS3 composition, respectively. The black dashed lines correspond to a random orientation. The inset in (b) illustrates the tetrahedral orientations corresponding to $\theta ={30}^{\circ }$ and ${150}^{\circ }$, respectively.

Figure 7

(a) Total vibrational density of states (VDOS) of the two sandwich glasses at 0 K for the interior and the surface domains. (b)–(d) show the partial VDOS for the Si, O, and Na atoms, respectively. Also included in (a) is the total VDOS for a bulk silica glass from ab initio calculations [60]. The total VDOS in (a) are normalized to unity, which is equal to the sum of the partials as depicted in (b)–(d).

Figure 8

Per-atom VDOS of the surface atoms. Panels (a) and (b) are for corner-sharing and edge-sharing Si atoms, respectively. Panels (c) and (d) are for corner-sharing and edge-sharing BO, respectively. All curves are normalized to unity.

Figure 9

Decomposition of the partial VDOS of NS3 into contributions from different directions. Panels (a)–(c) are for Si, O, and Na, respectively. The arrows indicate the locations at which the spectra depend significantly on the direction. All curves are normalized to unity.

Figure 10

Imaginary part of the dielectric function ${\epsilon }_2\left(\omega \right)$ for bulk silica as well as for the three sandwich systems. (a) Shows the calculated spectra of ${\epsilon }_2\left(\omega \right)$ for bulk (black dotted line) and sandwich sample (black line), and the experimental spectrum (red dashed line) for bulk amorphous silica [81]. (b) Shows the calculated ${\epsilon }_2\left(\omega \right)$ for the silica, NS5, and NS3 sandwich systems, black, blue, and green full line, respectively.

Figure 11

Electronic density of states of the sandwich glasses at 0 K. Panels (a), (b), and (c) are for silica, NS5, and NS3, respectively. The eDOS of the sandwich glasses are decomposed with respect to the surface (surf.) and interior (int.) layers. (a) Shows also the eDOS for bulk silica. All distributions are normalized with respect to the number of atoms. The Fermi level energy $E_f$ is at 0 eV.

Figure 12

Decomposition of the surface eDOS of the silica and NS3 glasses. Left panels: silica. Right panels: NS3. The Fermi level energy $E_f$ is at 0 eV. (a), (d) Decomposition with respect to atomic species, i.e., Si, O, and Na. (b), (e) Decomposition of O into NBO, csO, and esO. (c), (f) Decomposition of Si into csSi and esSi. The eDOS are normalized with respect to the number of atoms.

Figure 13

Analysis of chemical bonding on a ${\mathrm{SiO}}_2$ surface by means of the electron localization function (ELF). (a) The representation of the ELF for a small region on the surface highlighting a ${\mathrm{SiO}}_4$ tetrahedron, centered on an Si atom labeled Si1, bonded to one NBO, O1, and three BO atoms (O2–O4). The isosurface (in yellow) corresponds to the ELF at a value of 0.83. (b), (c) 2D contour plots of the ELF in the planes defined by three atoms: Si1-O2-Si2 (b), and O1-Si1-O4 (c), where the atoms are identified in (a). The increment of isolines is 0.05. (d)–(f) The same representation as in (a)–(c) but for a two-membered ring structure (g), (h): line profiles of the ELF along the bond paths as shown in (a) and (d), respectively. Also included in (g) is the average ELF profile of the BO-Si bonds that belongs to a Si-BO-Si connection in the interior domain (green dashed-dotted line). The O atom is at $r=0$. For each bond path the point corresponding to the maximum ELF is indicated in the parentheses $[r$, $\mathrm{ELF}\left(r\right)]$. The arrows show the location of the average Si-O bond length. The visualization of the ELF was realized by vesta [99].

Figure 14

Analysis of chemical bonding on the surface of NS3 by the electron localization function (ELF). (a) A map of the ELF for the structures on the surface, highlighting a ${\mathrm{SiO}}_4$ tetrahedron which has a Na in its neighborhood. The dashed lines are the O-Na bonds with $r_{\mathrm{O}\text{−}\mathrm{Na}}<2.5$ Å. The isosurface represents the ELF surface at a value of 0.83 and the assignment of different domains are the same as in Fig. 13. (b), (c) 2D contour plots of the ELF in the planes defined by three atoms. The increment of isolines is 0.05. (d)–(f) The same representation as in (a)–(c) but for a two-membered ring structure. (g), (h) Line profiles of the ELF along the bond paths as shown in (a) and (d), respectively. The oxygen atom is at $r=0$. For each bond path the point corresponding to the maximum ELF is indicated in the parentheses. The arrows show the location of the average Si-O or Na-O bond length. ${\mathrm{NBO}}^{2\mathrm{M}}$ denotes the NBO bonded to an esSi. The visualization of the ELF was realized by vesta [99].