Temperature-dependent structural heterogeneity in calcium silicate liquids

X-ray diffraction measurements performed on aerodynamically levitated ${\text{CaSiO}}_3$ droplets have been interpreted using a structurally heterogeneous liquid-state model. When cooled, the high-temperature liquid shows evidence of the polymerization of edge shared Ca octahedra. Diffraction isosbestic points are used to characterize the polymerization process in the pair-distribution function. This behavior is linear in the high-temperature melt but exhibits rapid growth just above the glass transition temperature around $1.2T_{\text{g}}$. The heterogeneous liquid interpretation is supported by molecular-dynamics simulations which show the ${\text{CaSiO}}_3$ glass has more edge-shared polyhedra and fewer corner shared polyhedra than the liquid model.

Figure 1

(Color online) Left: measured x-ray structure factors for ${\text{CaSiO}}_3$ over a temperature range that spans the superheated and supercooled liquid and the glass. Right: comparison of our ${\text{CaSiO}}_3$ data with previously measured x-ray structure factors for glassy and liquid ${\text{CaSiO}}_3$ and ${\text{SiO}}_2$ from the literature. (a) Shows liquid ${\text{SiO}}_2$ (scaled by 0.5) from (Ref. 9) (magenta dotted line). (b) Our measured liquid structure factor for ${\text{CaSiO}}_3$ at $1650°\text{C}$ (black solid line) is compared to that measured by Waseda and Toguri (Ref. 15) at $1600°\text{C}$ (red dashed line). The solid black lines in (c) and (d) are the measured glass structure factors of ${\text{CaSiO}}_3$ at $25°\text{C}$ (this study) compared to Taniguchi et al. (Ref. 16) [(c) blue long dashed-dotted line] and Mead and Mountjoy (Ref. 17) [(d) green short dashed-dotted line]. The curves are offset for clarity.

Figure 2

(Color online) Top: differential distribution functions, $D\left(r\right)$, for liquid ${\text{CaSiO}}_3$ at $1900°\text{C}$ (solid black line) and $1033°\text{C}$ (dashed red line). Middle: molecular-dynamics simulation of ${\text{CaSiO}}_3$ melt at $3700°\text{C}$ (green dotted line) Fourier transformed over the identical $Q$ range to the experiment with same Lorch modification function. Bottom: Faber-Ziman (Ref. 20) x-ray weighted partial distribution functions for the ${\text{CaSiO}}_3$ melt at $3700°\text{C}$ taken directly from the simulation scaled by 0.6 and offset for clarity.

Figure 3

(Color online) Top: differences between the x-ray experimental liquid $D\left(r\right)$’s held at constant temperatures, for $1033°\text{C}$ minus $1900°\text{C}$ (red dashed line), and $1800°\text{C}$ minus $1900°\text{C}$ (thick black solid line). The thin blue lines in between these extremes represent the $D\left(r\right)$ differences in $\sim 100°\text{C}$ increments [see Fig. 1a]. The diffraction isosbestic points are marked with arrows (see text). Inset: shows the $\Delta D\left(r\right)$’s for the liquid at $1033°\text{C}$ minus $1900°\text{C}$ (dashed red line), $800°\text{C}$ minus $1900°\text{C}$ (thin blue solid line), and the room-temperature glass minus $1900°\text{C}$ (thick green solid line). Bottom: differences between the model liquid $D\left(r\right)$’s taken from the MD simulations for 0.5 minus $T_{\text{m}}$ (red dashed line), $0.625T_{\text{m}}$ minus $T_{\text{m}}$, and $0.75T_{\text{m}}$ minus $T_{\text{m}}$ (thin blue lines) $0.875T_{\text{m}}$ minus $T_{\text{m}}$ (thick solid black line).

Figure 4

(Color online) Changes in Ca-polyhedral connectivity of the liquid/glass MD model of ${\text{CaSiO}}_3$ as a function of temperature.

Figure 5

(Color online) The integrals of the differences between the static state differential distribution functions, $\Delta D\left(r\right)$ measurements (see text), shown in Fig. 3 (top) for liquid ${\text{CaSiO}}_3$. The integrals were taken over the region between the isosbestic points for the 2.34 and $3.50\text{Å}$ peaks in $\Delta D\left(r\right)$. The symbols represent different experimental runs. Both curves are fitted with a linear (blue dashed) line which has been extended to lower temperatures by a dashed blue line (see Fig. 6 for more extensive measurements in this region). The glass measured at $25°\text{C}$ was taken as a representative liquid structure at $T_g=781°\text{C}$ for ${\text{CaSiO}}_3$ (Ref. 31) (solid symbols). The $1.2T_g$ line is calculated in Kelvin but shown in degrees Celsius. Inset: viscosity-temperature relation of liquid ${\text{CaSiO}}_3$ (blue squares) (Refs. 10, 11) and ${\text{SiO}}_2$ (circles) (Ref. 32).

Figure 6

(Color online) The integrals of the differences between the differential distribution functions, $\Delta D\left(r\right)$, for liquid ${\text{CaSiO}}_3$. The integrals were taken over the region between the isosbestic points for the $3.50\text{Å}$ Ca-Ca peak in $\Delta D\left(r\right)$. The fast cooling measurements (solid red squares) are compared to isothermal measurements (open symbols from Fig. 5). The dotted line represents $T_g$ (Ref. 31) and the dashed line $1.2T_g$ $\left(992°\text{C}\right)$. The $1.2T_g$ line is calculated in Kelvin but shown in degrees Celsius for consistency.

Figure 7

(Color online) Molecular-dynamics snapshots of the polymerization of CaO polyhedra from the predominantly corner shared ${\text{CaSiO}}_3$ equilibrium melt (a) to more edge-shared ${\text{CaO}}_6$ units in the glass (b) obtained from MD simulations. The Ca ions are shown in green (light) and O in red (dark).