In situ observation of the formation, diffusion, and reactions of hydrogenous species in ${\mathrm{F}}_2$-laser-irradiated $\mathrm{Si}{\mathrm{O}}_2$ glass using a pump-and-probe technique

We quantitatively studied the formation, diffusion, and reactions of mobile interstitial hydrogen atoms $\left({\mathrm{H}}^0\right)$ and molecules $\left({\mathrm{H}}_2\right)$ in ${\mathrm{F}}_2$-laser-irradiated silica $\left(\mathrm{Si}{\mathrm{O}}_2\right)$ glass between 10 and $330\mathrm{K}$. Two key techniques were used: single-pulse ${\mathrm{F}}_2$ laser photolysis of silanol (SiOH) groups to selectively create pairs of ${\mathrm{H}}^0$ and oxygen dangling bonds (nonbridging oxygen hole centers, NBOHC), and in situ photoluminescence measurements of NBOHCs to monitor their reactions with ${\mathrm{H}}^0$ and ${\mathrm{H}}_2$ as a function of time and temperature. A smaller quantum yield of the photolysis of the $\mathrm{Si}\mathrm{O}\mathrm{H}$ bond $(0.15\pm 0.05)$ compared with values reported for gas molecules containing $\mathrm{O}\mathrm{H}$ bonds $(\sim 1)$ suggests that the separation of photogenerated ${\mathrm{H}}^0$ from NBOHC is hindered by the cage effect of the $\mathrm{Si}{\mathrm{O}}_2$ glass network. Distribution functions for the diffusion coefficients of ${\mathrm{H}}^0$ and ${\mathrm{H}}_2$ in the structurally disordered $\mathrm{Si}{\mathrm{O}}_2$ glass were evaluated by numerical analysis of the concentration changes of NBOHC based on diffusion-limited reaction theory. The average diffusion coefficient of ${\mathrm{H}}_2$ obtained by integrating the distribution agrees well with the values measured by the permeation of ${\mathrm{H}}_2$ through $\mathrm{Si}{\mathrm{O}}_2$ glass plates. In contrast, the average diffusion coefficient of ${\mathrm{H}}^0$ significantly decreases with time because the distribution of the diffusion coefficient of ${\mathrm{H}}^0$ is broad and ${\mathrm{H}}^0\mathrm{s}$ with greater mobility disappear at a faster rate. We suggest that the efficient conversion of ${\mathrm{H}}^0$ into ${\mathrm{H}}_2$ in $\mathrm{Si}{\mathrm{O}}_2$ glass is due to dissipation of the excess energy of the reaction intermediate via inelastic collisions with the glass network. The fraction of ${\mathrm{H}}^0$ that forms ${\mathrm{H}}_2$ is determined by the ratio of the capture radii of ${\mathrm{H}}^0$ and NBOHC, and it is independent of the diffusion coefficient and the initial concentration of ${\mathrm{H}}^0$.

Figure 1

Temperature-dependent decay curves of the normalized NBOHC concentration in the ${\mathrm{H}}_2$-free and ${\mathrm{H}}_2$-loaded samples measured under a constant heating rate of $3\mathrm{K}{\min }^{-1}$ (thermal decay experiment). The subvertical line near $t=0$ corresponds to data points measured after a delay of $t_{\mathrm{D}}=1\mathrm{ms}$ from the ${\mathrm{F}}_2$ laser pulse that causes the photolysis $(t=0)$. The subsequent sampling interval was $2\mathrm{s}$. The decay can be separated into three temperature ranges: I, $<100\mathrm{K}$; II, $100–160\mathrm{K}$; and III, $>200\mathrm{K}$. The normalized height of the plateau between ranges II and III is denoted by $h$ and used in Eq. (24). The inset shows the NBOHC decay curves plotted with respect to time. The temperature of the sample was held at $10\mathrm{K}$ until $t=500\mathrm{s}$ and then raised by $3\mathrm{K}{\min }^{-1}$.

Figure 2

Time-dependent decay curves of the normalized NBOHC concentration in the ${\mathrm{H}}_2$-free samples measured under constant temperatures (isothermal decay experiment). On the basis of the data shown in Fig. 1, the decay curves are divided into three groups: I, II, and III. The normalized height of the plateau between ranges II and III is denoted by $h$.

Figure 3

Temperature dependence of the measured quantum yield of NBOHC formation, ${\Phi }_{\exp }$, calculated via Eq. (15) using ${\mathrm{H}}_2$-free samples exposed to 100 ${\mathrm{F}}_2$ laser pulses between 10 and $300\mathrm{K}$. The detailed procedure of the calculation is described in the text. The typical delay of the probe pulse from the ${\mathrm{F}}_2$ laser pulse was $t_{\mathrm{D}}=1\mathrm{ms}$ (filled circles). For comparison, an additional data point was measured for $t_{\mathrm{D}}=200\mu \mathrm{s}$ at $300\mathrm{K}$ (open circle).

Figure 4

(Color online) Calculated relation between the normalized concentrations of NBOHC $(\left[\mathrm{NBOHC}\right]∕C_0\equiv x)$ and ${\mathrm{H}}^0$ $(\left[{\mathrm{H}}^0\right]∕C_0\equiv y)$ during the NBOHC decay in ranges I and II below $160\mathrm{K}$, obtained via Eq. (23) (thick colored line). The decay starts at the point $(x_0,y_0)$ and finishes at the point $(h,0)$. Substitutions of parameters $x_0=0.95$, $y_0=0.91$, and $h=0.22$ obtained experimentally from Fig. 1 into Eq. (23) yield the locus of points $(x,y)$ (thick colored line) and the ratio of the capture radii of NBOHC and ${\mathrm{H}}^0$, $\gamma =2r_3∕r_1=0.38$. The initial concentration of NBOHC, $C_0$, and the diffusion coefficient of ${\mathrm{H}}^0$, $D_{{\mathrm{H}}^0}$, do not influence the locus, but determine the movement rate of the point $(x,y)$. The branching ratio (probability that an interstitial ${\mathrm{H}}^0$ reacts with NBOHC rather than with reacting another ${\mathrm{H}}^0$ to form ${\mathrm{H}}_2$) at each point $(x,y)$ is given by $p={(1+\gamma y∕x)}^{-1}$ [Eq. (22)]. The integrated branching ratio $p_{\mathrm{I}}$ is equal to the inverse of the slope of the dashed line connecting the points $(x_0,y_0)$ and $(h,0)$ [Eq. (25)]. Thin line that connects the points $(x_0,y_0)$ and $[h,y_0(1-p_{\mathrm{I}})]$ with slope 1 separates ${\mathrm{H}}^0\mathrm{s}$ used for these two reactions.

Figure 5

Isothermal decay curves of the normalized NBOHC concentration in the ${\mathrm{H}}_2$-free sample at 100 and $260\mathrm{K}$ (solid lines) and simulated curves calculated at several definite values of activation energies for diffusion $\left(E_{\mathrm{a}}\right)$ at $100\mathrm{K}$ for ${\mathrm{H}}^0$ and $260\mathrm{K}$ for ${\mathrm{H}}_2$ (dashed lines).

Figure 6

Simulated isothermal decay curves of normalized NBOHC concentration calculated using the $E_{\mathrm{a}}$ distribution shown in Fig. 9 (open symbols). Experimental decay curves (solid lines) are identical to those shown in Fig. 2.

Figure 7

Thermal decay curves of the normalized NBOHC concentration in the ${\mathrm{H}}_2$-free sample measured under a constant heating rate of $3\mathrm{K}{\min }^{-1}$ (solid line) and simulated curves calculated at several definite values of $E_{\mathrm{a}}$ for the diffusion of ${\mathrm{H}}^0$ and ${\mathrm{H}}_2$ (dashed lines).

Figure 8

Thermal decay curves of the normalized NBOHC concentration in the ${\mathrm{H}}_2$-free and ${\mathrm{H}}_2$-loaded samples measured under a constant heating rate of $3\mathrm{K}{\min }^{-1}$ (solid and dashed lines, respectively) and simulated curves calculated using the $E_{\mathrm{a}}$ distribution shown in Fig. 9 (open symbols). The inset shows the simulated curves of the normalized concentrations of NBOHC, ${\mathrm{H}}^0$, and ${\mathrm{H}}_2$ in the initially ${\mathrm{H}}_2$-free sample.

Figure 9

Calculated distribution of activation energy for the diffusion, $E_{\mathrm{a}}$, of ${\mathrm{H}}^0$ (ranges I and II) and ${\mathrm{H}}_2$ (range III), used to obtain the simulated NBOHC decay curves shown in Figs. 6, 8. Filled symbols denote the discrete $E_{\mathrm{a}}$ values used in the simulation.

Figure 10

(Color online) Arrhenius plots of the diffusion coefficients of (a) ${\mathrm{H}}^0$ and (b) ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$. Thick solid lines denote the diffusion coefficients calculated with activation energy $E_{\mathrm{a}}$ values that correspond to the respective maxima of the distributions $w\left(E_{\mathrm{a}}\right)$ in Fig. 9 $\left(E_{\mathrm{a}}^{\max }\right)$, while thin solid lines denote the diffusion coefficients calculated at $E_{\mathrm{a}}$ values at both half maximum points of $w\left(E_{\mathrm{a}}\right)$ ($E_{\mathrm{a}}^{\mathrm{HM}\text{−}\text{high}}$ and $E_{\mathrm{a}}^{\mathrm{HM}\text{−}\text{low}}$). The dotted lines indicate the average diffusion coefficients $D_{\mathrm{avr}}$ calculated by integrating the diffusion coefficient over the $w\left(E_{\mathrm{a}}\right)$ distribution [Eq. (27)]. This represents the diffusion coefficient for a steady-state flow that maintains a constant concentration of diffusing species. Results taken from Refs. 39, 40, 43 $\left({\mathrm{H}}^0\right)$ and Refs. 13, 19, 27, 30, 33, 35 $\left({\mathrm{H}}_2\right)$ are also shown.