Origin of the Fragile-to-Strong Crossover in Liquid Silica as Expressed by its Potential-Energy Landscape

The origin of the fragile-to-strong crossover in liquid silica is characterized in terms of properties of the potential-energy landscape (PEL). Using the standard BKS model [B. W. H. van Beest, G. J. Kramer, and R. A. van Santen, Phys. Rev. Lett. 64, 1955 (1990)] of silica we observe a low-energy cutoff of the PEL. It is shown that this feature of the PEL is responsible for the occurrence of the fragile-to-strong crossover and may also explain the avoidance of the Kauzmann paradox. The number of defects, i.e., deviations from the ideal tetrahedral structure, vanishes for configurations with energies close to this cutoff. This suggests a structural reason for this cutoff.

Figure 1

(a) Temperature dependence of the oxygen diffusion constant for BKS99. In the inset the incoherent scattering function $S(q_{\max }=1.7{\AA }^{-1},t)$ is shown at $T=3300$ and 4000 K for system sizes between 60 and 1000 and after scaling along both axes. (b) Temperature dependence of the average energy of MBs $⟨e(T)⟩$, and the average energy of inherent structures $⟨e_{IS}(T)⟩$. Included are data from Ref. 11, shifted by 0.06 eV. The broken line describes the Gaussian approximation with parameters obtained from Fig. 2.

Figure 2

The energy distribution $G(e)$, obtained from the reweighting of $p(e,T)$ for temperatures between 2800 and 5000 K. The resulting Gaussian-type fits $G_1(e)$ and $G_2(e)$ are included (see text).

Figure 3

The simulated distribution $p(e,T)$ for $T=2800$, 3500, and 4000 K. Furthermore, we include $p_1(e)$ and $p_2(e,T)$ (for the same three temperatures). Note that $p_1(e,T=4000\mathrm{K})\approx p_2(e,T=4000\mathrm{K})$. In the inset the estimation of $p_2(e/n,T=2800\mathrm{K})$ for different systems sizes $n\times 99$ ($n=1,2,3$) is displayed.

Figure 4

Right axis: The fraction of silicon (oxygen) atoms with 3 or 5 oxygen (1 or 3 silicon) atoms in the nearest-neighbor shell for different temperatures per silicon (oxygen) atom. (Silicon: stars; oxygen: squares). Left axis: Width of the partial Si-O structure factor for the nearest-neighbor shell.