Stochastic atomic acceleration during the X-ray-induced fluidization of a silica glass

Abstract

The X-ray-induced, nonthermal fluidization of the prototypical SiO₂ glass is investigated by X-ray photon correlation spectroscopy in the small-angle scattering range. This process is initiated by the absorption of X-rays and leads to overall atomic displacements which reach at least few nanometers at temperatures well below the glass transition. At absorbed doses of ∼5 GGy typical of many modern X-ray-based experiments, the atomic displacements display a hyperdiffusive behavior and are distributed according to a heavy-tailed, Lévy stable distribution. This is attributed to the stochastic generation of X-ray-induced point defects which give rise to a dynamically fluctuating potential landscape, thus providing a microscopic picture of the fluidization process.

Keywords: XPCS; glasses; out of equilibrium systems.

Fig. 1.

(A) Scattered intensity collected in the LDR run (symbols) together with the best-fitting curve of Eq. 3 (line); the fit parameters are I_s⁰ = (8.6 ± 0.1)⋅10⁻⁴ ph/s/nm^δ, δ = 3.5 ± 0.1 and I_b⁰ = (15.20 ± 0.01)⋅10⁻³ ph/s. Inset, Ratio of the square of the surface-scattered intensity to the total one. The horizontal line shows that for q> 0.34 nm⁻¹, scattering from the bulk dominates. (B) Normalized intensity correlation functions for the LDR series at various q’s from 0.23 to 0.96 nm⁻¹ (blue to red) together with two examples of the best-fitting functions of Eq. 2 (lines). In all panels, the data are averaged over all collected images.

Fig. 2.

(A) q dependence of the relaxation time, τ(q), for the HDR series and at the waiting times indicated in the legend. Inset: Two-times correlation matrix corresponding to the HDR series and q= 0.64 nm⁻¹. (B) q dependence of the shape parameter, β, for the same data as in (A). The range of values observed in wide-angle scattering measurements (1) is also reported (gray stripe).

Fig. 3.

(A) The relaxation times interpolated at a dose of 5 GGy are reported for the LDR (diamonds) and two HDR runs (circles and squares). (B) q dependence of the ratio of the LDR and HDR relaxation times reported in (A). This ratio matches the inverse ratio of the corresponding dose rates (dashed line).

Fig. 4.

Relaxation times as a function of q rescaled to a dose rate of 7.8 MGy/s for the small-angle scattering data (circles) together with three control measurements at high q (squares) and the data from ref. (diamonds and triangles). The data from ref. have been additionally multiplied by a factor 1.1. All data correspond to a dose of 5 GGy. The dashed line is the best-fitting function ${\tau }_5^R(q)=1/(b{q}^{\alpha })$.

Fig. 5.

Main panel: Distribution functions of atomic displacements, w(ΔR), for a SiO₂ glass irradiated with a dose rate of 7.8 MGy/s (HDR) and for a total dose of 5 GGy calculated at times corresponding to the relaxation times, τ(q), at the highest (blue line) and shortest (orange line) q values probed in the present XPCS experiment. The gray-shaded area highlights the reciprocal of the range, where, in q space, our experiment has been carried out. The black dashed vertical line indicates the position of the most probable displacement (the mode of the distribution) for the large-q case. The brown dot-dashed line is the distribution w(ΔR) calculated for a diffusive dynamics, and the value of the diffusion coefficient, D₀, is chosen to match the mode of the distribution to that of the distribution for the induced dynamics for the largest probed q. Inset, Time dependence of the mode, ΔR^*, of the distribution of atomic displacements probed under irradiation at times corresponding to the measured τ(q) (circles). This time dependence is well described by a power law ΔR^* ∝ t^γ with γ= 1.79 (blue line). Very different is the case of the simple diffusion process (red dot-dashed line), where ΔR^* ∝ t^0.5.