Temperature-induced structural change through the glass transition of silicate glass by neutron diffraction

Supercooled silicate liquids exhibit several orders of magnitude increase in viscosity at the glass-transition temperature ($T_{\mathrm{g}}$) towards the glassy state. Such a drastic dynamical slowdown leads to an abrupt change in the slope of temperature-dependent thermodynamic properties because the measurements reflect the equilibrium-to-nonequilibrium change from liquid to glass. However, an underlying structural change associated with such a transition remains elusive. For instance, understanding the structural origin of the variation in the coefficient of thermal expansion (CTE) of silicate glasses upon vitrification is critical for glass-manufacturing processes and applications. Here, based on temperature-dependent neutron diffraction, we demonstrate that the temperature dependences of both short- and medium-range order structural parameters show a pronounced change of slope at $T_{\mathrm{g}}$ for a range of silicate glasses of industrial importance. Interestingly, the short- and medium-range order structural parameters are found to be mutually correlated, both below and above $T_{\mathrm{g}}$. Based on these results, we find that the slope change of the area of the first sharp diffraction peak at $T_{\mathrm{g}}$ is correlated with the extent of the CTE jump at $T_{\mathrm{g}}$, which offers a structural origin for the discontinuity in the CTE of glasses at $T_{\mathrm{g}}$. This study can therefore shine light on solving critical industrial problems, such as glass relaxation.

Figure 1

Reciprocal-space I(Q) obtained by Fourier transformation of $G{\left(r\right)}_{\mathrm{Si}-\mathrm{O}}$ for fused silica. (a) Real space: original $G$($r$) (red); $G^{\prime }\left(r\right)$ with first Si-O pair subtracted (blue); $G_{\mathrm{Si}-\mathrm{O}}\left(r\right)$ (black), both blue and black curves are shifted down by 2 for clarity. (b) Reciprocal space: $F$($Q$) of original $G\left(r\right)$ (red); $F^{\prime }\left(Q\right)$ of $G^{\prime }\left(r\right)$ (blue); $I\left(Q\right)$ of first Si-O pairs (black), where $I\left(Q\right)=F\left(Q\right)-F^{\prime }\left(Q\right)$.

Figure 2

Reduced structure factor functions $F$($Q$) of four silicate glasses measured from room temperature up to 150 °C above each specified $T_{\mathrm{g}}$ (except for FS). The RT −$F$($Q$) is plotted in black, then the color changes following the rainbow color spectrum, until the highest temperature $F$($Q$) is plotted in red.

Figure 3

The reduced pair-distribution functions $G$($r$) ($Q_{\max }=50{\AA }^{-1}$) of four silicate glasses from room temperature up to 150 °C above each specified $T_{\mathrm{g}}$ (except for FS). The same color scheme is used as in Fig. 2.

Figure 4

Temperature dependence of $A$-O ($A=\mathrm{Si}$ or Al) (a) and O-O (b) atom-pair distances determined by $I$($Q$) fitting and $A$-O expansions with temperature (c). The fitting-error bar is smaller than the symbol size. The CTE slopes (dotted lines) are determined by a linear fit of the whole temperature-range expansion data for each glass.

Figure 5

Mean-square atom-pair deviation $\langle {\mathit{u}}_{\mathit{ij}}^2\rangle$ changes with temperature. The fitting-error bar is about the same scale as the symbol size.

Figure 6

An analog OLUA plot of scaled atom-pair distance ${{\mathit{r}}_{\mathit{ij}}}_{\mathit{T}}/{{\mathit{r}}_{\mathit{ij}}}_{\mathit{T}\mathbf{g}}$ for $A$-O (a) and O-O (b) atom pairs as a function of scaled temperature, T/$T_{\mathrm{g}}$. Note the significant discontinuous increase of ${{\mathit{r}}_{\mathit{ij}}}_{\mathit{T}}/{{\mathit{r}}_{\mathit{ij}}}_{\mathit{T}\mathbf{g}}$ on passing through $T_{\mathrm{g}}$. The error bars have been propagated from the fitting error.

Figure 7

An analog OLUA plot of scaled mean-square atom-pair deviation ${\langle {\mathit{u}}_{\mathit{ij}}^2\rangle }_T/{\langle {\mathit{u}}_{\mathit{ij}}^2\rangle }_{T_{\mathrm{g}}}$ for $A$-O (a) and O-O (b) atom pairs as a function of scaled temperature, T/$T_{\mathrm{g}}$. Note the significant discontinuous increase of ${\langle {\mathit{u}}_{\mathit{ij}}^2\rangle }_T/{\langle {\mathit{u}}_{\mathit{ij}}^2\rangle }_{T_{\mathrm{g}}}$ on passing through $T_{\mathrm{g}}$. The error bars have been propagated from the fitting error.

Figure 8

Direct T(r) fitting and analog OLUA plot of scaled atom-pair distance ${{\mathit{r}}_{\mathit{ij}}}_{\mathit{T}}/{{\mathit{r}}_{\mathit{ij}}}_{\mathit{T}\mathbf{g}}$ for $A$-O (a) and O-O (b) and mean-square atom-pair deviation ${\langle {\mathit{u}}_{\mathit{ij}}^2\rangle }_T/{\langle {\mathit{u}}_{\mathit{ij}}^2\rangle }_{T_{\mathrm{g}}}$ for $A$-O (c) and O-O (d) atom pairs as a function of scaled temperature, T/$T_{\mathrm{g}}$. Note the sudden slope changes at $T_{\mathrm{g}}$ of both $r_{ij}$ (a)and $\langle {\mathit{u}}_{\mathit{ij}}^2\rangle$ (b) for $A$-O atom pairs, but no slope changes at $T_{\mathrm{g}}$ observed for the (c), (d) O-O atom pairs.

Figure 9

The FSDP region of $F$($Q$) and its corresponding medium-range $G$($r$) of four silicate glasses measured from room temperature up to 150 °C above each specified $T_{\mathrm{g}}$ (except FS). The same color scheme is used as in Fig. 2. Note the FSDP shape change, which skews more to low Q, as shown by the arrow. Also note the abnormal peak change in the region of 4–5 Å in $G$($r$).

Figure 10

$S$($Q$)-FSDP area drop with $T$. (a) $S{\left(Q\right)}_T\text{−}\mathrm{FSDP}$ scaled by the RT value as a function of $T$ for all four glasses. (b) $S{\left(Q\right)}_T\text{−}\mathrm{FSDP}$ scaled with $T_{\mathrm{g}}$ values as a function of scaled $T(T/T_{\mathrm{g}})$ for three glasses except FS. The error bars are calculated from the $S$($Q$)-FSDP area integration error which is propagated from the $S$($Q$) counting statistics error.

Figure 11

Correlation between a structural parameter measured by neutron diffraction and through-$T_{\mathrm{g}}$ bulk CTE changes measured by dilatometry. A positive linear correlation is observed between the $S$($Q$)-FSDP area slope ratio (supercooled liquid vs glass) and the bulk CTE ratio (supercooled liquid vs glass).

Figure 12

Inverse linear correlations between $T_{\mathrm{g}}$-scaled short- and medium-range structural parameters by fitting all three silicate glasses data. (a) Correlation between $T_{\mathrm{g}}$-scaled $r_{A-O}$ and $S$($Q$)-FSDP area; (b) Correlation between $T_{\mathrm{g}}$-scaled $\langle {\mathit{u}}_{\mathit{A}-\mathbf{O}}^2\rangle$ and $S$($Q$)-FSDP area.