Real and reciprocal space structural correlations contributing to the first sharp diffraction peak in silica glass

We have applied a “real-reciprocal space analysis,” using the continuous wavelet transform technique, to the experimental neutron and x-ray structure factors of silica glass to elucidate a correlation between the “first sharp diffraction peak (FSDP)” in reciprocal space and the corresponding length scale in real space. The present analysis allows us to obtain compelling evidence that the dominant interatomic distance linked to the FSDP in silica glass is $\sim 5\mathrm{\AA }$, although longer distances are also important, making an exponentially decreasing contribution. Further analysis using molecular-dynamics simulations demonstrates that the interatomic spatial correlations at $r\sim 5\mathrm{\AA }$ are associated with a couple of local “pseudo-Bragg” planes having an interlayer separation of $\sim 4\mathrm{\AA }$, accounting for the origin of structural ordering on the medium-range length scale in silica glass.

Figure 1

(Color) Three-dimensional $r-Q$ diagrams of the instantaneous amplitude $A_d$ of the CWT of the reduced (a) neutron and (b) x-ray experimental structure factors for silica glass. Short-range $\mathrm{Si}\mathrm{O}$, $\mathrm{O}\mathrm{O}$, and $\mathrm{Si}\mathrm{Si}$ correlations, along with the positions of the FDSP, are indicated by arrows. Cross sections of the CWT at $1.5{\mathrm{\AA }}^{-1}$ are also shown on the right-hand side of each wavelet diagram.

Figure 2

(Color online) A schematic representation of the formation of pseudo-Bragg planes as a result of atom-atom correlations at $\sim 5\mathrm{\AA }$. The circles indicate atom-centered spheres of high atomic density resulting from second-nearest-neighbor $\mathrm{Si}\mathrm{Si}$ (or $\mathrm{O}\mathrm{O}$) separations. Centers of the spheres are linked by a dotted line. This dotted line is not straight but winding because of the random nature of the glass network. Even in such a random network, a set of three contiguous near-parallel planes of high atomic density (see the bold lines), whose length scale is comparable to the radius of the spheres $(\sim 5\mathrm{\AA })$, can be well defined. In real silica glass, it is expected that these planes will be decorated by both Si and O atoms. The resulting interplanar distance is less than $\sim 5\mathrm{\AA }$; a probable value is $\sim 4\mathrm{\AA }$ because of geometrical considerations.

Figure 3

(Color) A moiety of a simulated model of silica glass obtained from classical MD calculations showing the identification of several sets of parallel local planes decorated by Si and O atoms. These sets of planes can be found practically everywhere in the simulated silica glass. The interplanar separation is $\sim 4\mathrm{\AA }$, whereas the major $\mathrm{Si}\mathrm{Si}$ and $\mathrm{O}\mathrm{O}$ interatomic separations between the planes are $\sim 5\mathrm{\AA }$, accounting for the peak at $\sim 5\mathrm{\AA }$ seen in the cross sections of the CWT at $Q_{\mathrm{FSDP}}=1.5{\mathrm{\AA }}^{-1}$ $(2\pi ∕Q_{\mathrm{FSDP}}=\sim 4\mathrm{\AA })$ in Fig. 1.